361 distinct sources across 365 days and 52 start-here pages. Each day also shows its own sources on the last slide of its Learn tab. Where a figure is a physical constant or plain arithmetic, that is said rather than dressed up as a study.
Week 1 · Seven tricks that feel like magic
Times 11, times 5 and 25, squares ending in 5, times 9, near 100, doubling and halving, and a speed round.
Start here · How to read this year's numbers- Benjamin, A. & Shermer, M. (2006), Secrets of Mental Math, Three Rivers Press: left-to-right method and the decomposition strategies. Dowker, A. (2005), Individual Differences in Arithmetic, Psychology Press: strategy use, not fact drill, predicts fluency. Pesenti, M. et al. (2001), 'Mental calculation in a prodigy is sustained by right prefrontal and medial temporal areas', Nature Neuroscience 4: expert calculators use strategies and trained memory. https://doi.org/10.1038/82831
Day 1 · Times eleven- Benjamin & Shermer (2006), Secrets of Mental Math, ch. 1, the 11 rule; distributive law a × 11 = a × 10 + a. https://en.wikipedia.org/wiki/Multiplication_algorithm
Day 2 · Times 5, 50 and 25- Benjamin & Shermer (2006), Secrets of Mental Math, ch. 2; commutativity and associativity of multiplication (a × 5 = a × 10 ÷ 2). https://en.wikipedia.org/wiki/Mental_calculation
Day 3 · Squares that end in 5- (10n + 5)² = 100n(n + 1) + 25; Benjamin & Shermer (2006), Secrets of Mental Math, ch. 3. https://en.wikipedia.org/wiki/Mental_calculation#Squaring_numbers_ending_in_5
Day 4 · Times nine- a × 9 = a × 10 − a; divisibility by 9 and the digit sum (casting out nines); the finger method for 9× (elementary arithmetic folklore, documented in Benjamin & Shermer 2006). https://en.wikipedia.org/wiki/Casting_out_nines
Day 5 · Numbers near 100- (100 − a)(100 − b) = 100(100 − a − b) + ab; the 'Nikhilam' method of Bharati Krishna Tirtha's Vedic Mathematics (1965) — a 20th-century book, not ancient (Dani, S.G. 1993, 'Myths and reality: on Vedic mathematics'). https://en.wikipedia.org/wiki/Vedic_Mathematics
Day 6 · Doubling and halving- Associativity: a × b = (a ÷ 2) × (2b); the Egyptian/Russian peasant multiplication uses repeated doubling and halving (Rhind Mathematical Papyrus, c. 1550 BCE). https://en.wikipedia.org/wiki/Ancient_Egyptian_multiplication
Day 7 · The speed round- The week's six days and their sources; on timed practice with feedback: Ericsson, K.A. et al. (1993), 'The role of deliberate practice in the acquisition of expert performance', Psychological Review 100. https://doi.org/10.1037/0033-295X.100.3.363
Week 2 · Adding fast
Left to right, round and fix, pairs that make ten, and long columns without a pen.
Start here · How adding works in the head- Benjamin, A. & Shermer, M. (2006), Secrets of Mental Math, ch. 1: left-to-right addition; Dowker, A. (2005), Individual Differences in Arithmetic: decomposition strategies and fluency. https://en.wikipedia.org/wiki/Mental_calculation
Day 8 · Three digits, left to right- Benjamin & Shermer (2006), Secrets of Mental Math, ch. 1; the associative law lets the second number be added in parts. https://en.wikipedia.org/wiki/Mental_calculation
Day 9 · Round and fix- Compensation strategy in mental arithmetic (Benjamin & Shermer 2006, ch. 1; Dowker 2005); psychological pricing at 99-endings (Schindler & Kibarian, Journal of Retailing 1996). https://doi.org/10.1016/S0022-4359(96)90005-8
Day 11 · Adding money- South African Reserve Bank: 1c and 2c coins withdrawn 2002, cash totals rounded to 5c; Consumer Protection Act price display rules. Left-to-right addition per Benjamin & Shermer (2006). https://www.resbank.co.za/
Day 12 · A column of numbers- Column addition strategies and the tens-then-units method (bookkeeping practice); Benjamin & Shermer (2006), Secrets of Mental Math, ch. 1. https://en.wikipedia.org/wiki/Addition#Performing_addition
Day 13 · The running total at the till- Rounding-up running totals as a shopper's estimation strategy; 99-ending prices (Schindler & Kibarian 1996). https://doi.org/10.1016/S0022-4359(96)90005-8
Day 14 · The adding speed round- The week's six days and their sources; deliberate practice with immediate feedback (Ericsson et al. 1993, Psychological Review 100). https://doi.org/10.1037/0033-295X.100.3.363
Week 3 · Subtracting fast
Count up instead of down, the change at the till, and why 1,000 minus anything is easy.
Start here · Subtracting is counting up- Counting-up (complementary addition) as the cashier's method; Benjamin & Shermer (2006), Secrets of Mental Math, ch. 1: subtraction left to right and by complements. https://en.wikipedia.org/wiki/Subtraction#Methods
Day 18 · Same difference- Equal additions / constant-difference method for subtraction (Benjamin & Shermer 2006; Dowker 2005). https://en.wikipedia.org/wiki/Subtraction#Methods
Day 19 · Change at the till- Counting-up change-making (retail practice); SARB cash rounding to 5c since 2002. https://www.resbank.co.za/
Day 20 · Years and minutes between- Elapsed-time computation by counting up through round marks (elementary arithmetic practice); complement to 60. https://en.wikipedia.org/wiki/Mental_calculation
Week 4 · Multiplying fast
Break a number apart, the times tables to 20, and the moves that turn hard products into easy ones.
Day 22 · Split the big number- Distributive law a(b + c) = ab + ac; Benjamin & Shermer (2006), ch. 2. https://en.wikipedia.org/wiki/Distributive_property
Day 23 · The tables to twenty- (10 + a)(10 + b) = 10(10 + a + b) + ab; Benjamin & Shermer (2006), ch. 3. https://en.wikipedia.org/wiki/Multiplication_algorithm
Day 24 · Two two-digit numbers- Benjamin & Shermer (2006), Secrets of Mental Math, ch. 3: two-by-two multiplication by the addition method. https://en.wikipedia.org/wiki/Mental_calculation
Day 25 · Moving the factors- Associativity and factoring the multiplier; Benjamin & Shermer (2006), ch. 2: the factoring method. https://en.wikipedia.org/wiki/Mental_calculation
Day 26 · The difference of squares- (n − d)(n + d) = n² − d²; Benjamin & Shermer (2006), ch. 3: the 'close together' method. https://en.wikipedia.org/wiki/Difference_of_two_squares
Day 27 · Price times quantity- Compensation with a multiplier: n(P − ε) = nP − nε; 99-ending prices (Schindler & Kibarian 1996). https://doi.org/10.1016/S0022-4359(96)90005-8
Week 5 · Dividing fast
Divisibility rules for 2 to 12, sharing a bill, and halving your way to a quarter.
Day 29 · Halving down- Repeated halving as division by powers of two; Benjamin & Shermer (2006), ch. 4. https://en.wikipedia.org/wiki/Division_by_two
Day 31 · What divides by what- Divisibility rules and casting out nines: 10 ≡ 1 (mod 9), 100 ≡ 0 (mod 4). https://en.wikipedia.org/wiki/Divisibility_rule
Day 32 · Splitting the bill- Distributive law for division: (a + b) ÷ n = a ÷ n + b ÷ n; Benjamin & Shermer (2006), ch. 4. https://en.wikipedia.org/wiki/Mental_calculation
Day 33 · Long division in the head- Division as repeated subtraction of multiples (the 'chunking' method); Benjamin & Shermer (2006), ch. 4. https://en.wikipedia.org/wiki/Chunking_(division)
Day 34 · Dividing by 12, 15 and 24- Division by a composite divisor as successive division by its factors; Benjamin & Shermer (2006), ch. 4. https://en.wikipedia.org/wiki/Mental_calculation
Day 35 · The dividing speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 6 · Squares and roots
Squares to 30, the difference of two squares, and square roots close enough for the shop.
Day 38 · Near 50 and near 100- (50 + d)² = 2500 + 100d + d²; (100 − d)² = 100(100 − 2d) + d²; Benjamin & Shermer (2006), ch. 3. https://en.wikipedia.org/wiki/Mental_calculation#Squaring
Day 40 · Roots you can see- Last-digit patterns of perfect squares (quadratic residues mod 10); Benjamin & Shermer (2006), ch. 3. https://en.wikipedia.org/wiki/Square_root#Computation
Day 41 · Roots close enough- Linear approximation √(s² + e) ≈ s + e/(2s) (first-order Taylor / Newton step). https://en.wikipedia.org/wiki/Methods_of_computing_square_roots
Day 42 · The squares speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 7 · Percentages in your head
Ten percent first, the swap trick, VAT and tips without a calculator.
Start here · Ten percent first- Benjamin & Shermer (2006), Secrets of Mental Math, ch. 5: percentages; commutativity of multiplication for the swap (a × b/100 = b × a/100). https://en.wikipedia.org/wiki/Percentage
Day 45 · The swap- Commutativity: (a/100)·b = (b/100)·a; Benjamin & Shermer (2006), ch. 5. https://en.wikipedia.org/wiki/Percentage
Day 46 · VAT on and off- South African VAT 15% (VAT Act 89 of 1991, rate since April 2018); VAT fraction 15/115 = 3/23. https://www.sars.gov.za/types-of-tax/value-added-tax/
Day 48 · Discounts, and what percent is that- Benjamin & Shermer (2006), ch. 5; Consumer Protection Act price display (discounts as a percentage of the displayed price). https://www.gov.za/documents/consumer-protection-act
Day 49 · The percent speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 8 · Fractions you know by heart
The fractions everyone should recognise as decimals and percentages, and how to compare two.
Day 51 · Thirds and sixths- Divisibility by 3 and the digit sum; repeating decimals of thirds and sixths. https://en.wikipedia.org/wiki/Repeating_decimal
Day 53 · Which fraction is bigger- Comparing fractions by cross-multiplication: a/b > c/d ⇔ ad > bc for positive b, d. https://en.wikipedia.org/wiki/Fraction#Comparing_fractions
Day 55 · Adding fractions- Addition of fractions with a common denominator; least common multiple. https://en.wikipedia.org/wiki/Fraction#Addition
Day 56 · The fractions speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 9 · Place value and rounding
What each digit is worth, rounding well, and how many digits a number deserves.
Day 58 · Rounding money- SARB: 1c and 2c coins withdrawn 2002; cash rounding to 5c (Consumer Protection Act price guidance). https://www.resbank.co.za/
Day 59 · Significant figures- Significant figures and measurement precision (NIST Guide to the SI, §7); the Home & Life edition's estimation week. https://www.nist.gov/pml/special-publication-811
Day 60 · Moving the point- Positional notation and multiplication by powers of ten; SI prefixes. https://www.bipm.org/en/measurement-units/si-prefixes
Day 61 · Estimate by rounding first- Order-of-magnitude estimation by rounding to one significant figure; the Home & Life edition's estimation week (Fermi). https://en.wikipedia.org/wiki/Order_of_magnitude
Day 62 · Reading big numbers- Short scale (billion = 10⁹) now standard in South African and British usage; SI decimal comma in SA official documents (SANS 10001). https://en.wikipedia.org/wiki/Long_and_short_scales
Week 10 · Estimating
Ballpark first, then refine: the habits that catch a wrong answer before it costs you.
Start here · Ballpark first- Fermi estimation; Weinstein & Adam (2008), Guesstimation, Princeton: one figure per factor and the geometric mean of bounds. https://press.princeton.edu/books/paperback/9780691129495/guesstimation
Day 64 · The trolley total- Running-total estimation as a shopper's check; rounding to the nearest unit before summing (the adding week). https://en.wikipedia.org/wiki/Estimation
Day 65 · Dividing roughly- Estimation of quotients by compatible numbers (elementary arithmetic practice); the dividing week. https://en.wikipedia.org/wiki/Estimation
Day 66 · A rate times a count- Order-of-magnitude products; Weinstein & Adam (2008), Guesstimation. https://press.princeton.edu/books/paperback/9780691129495/guesstimation
Day 67 · Bounds and the geometric middle- Geometric mean as the estimator for log-uniform uncertainty; Weinstein & Adam (2008), Guesstimation; the Home & Life edition's estimation week. https://en.wikipedia.org/wiki/Geometric_mean
Day 68 · Three numbers at once- Fermi estimation with several factors; error cancellation in products of rounded factors. https://en.wikipedia.org/wiki/Fermi_problem
Day 69 · Per person- Per-capita estimation; the Home & Life edition's per capita day. https://en.wikipedia.org/wiki/Per_capita
Day 70 · The estimating speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 11 · Checking your answer
Last digits, casting out nines, size checks, and why a wrong answer is usually wrong in a way you can see.
Day 71 · The last digit- Arithmetic mod 10; last-digit rules for products and sums. https://en.wikipedia.org/wiki/Modular_arithmetic
Day 72 · Digital roots- Digital root and casting out nines: dr(n) = 1 + (n − 1) mod 9. https://en.wikipedia.org/wiki/Digital_root
Day 73 · How many digits- Digit count of a product: ⌊log₁₀ a⌋ + ⌊log₁₀ b⌋ + 1 or + 2. https://en.wikipedia.org/wiki/Order_of_magnitude
Day 74 · Odd or even- Parity rules for sums and products. https://en.wikipedia.org/wiki/Parity_(mathematics)
Day 76 · The second route- Independent verification by recomputation; Benjamin & Shermer (2006), Secrets of Mental Math. https://en.wikipedia.org/wiki/Mental_calculation
Day 77 · The checking speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 12 · Number sense on the street
Prices, portions, distances and crowds: sizing things up at a glance.
Start here · Anchors- Typical reference sizes: passenger car length ~4.5 m (SANS 10400 parking bay 2.5 × 5 m); rugby field 100 m goal line to goal line (World Rugby Law 1); standard brick 222 × 106 × 73 mm (SANS 227); walking speed ~5 km/h. https://www.world.rugby/the-game/laws
Day 78 · Distances by strides and cars- Pacing as a surveying method (pace count calibrated over a known distance); car length and rugby field references as in the primer. https://en.wikipedia.org/wiki/Pacing_(surveying)
Day 79 · Heights and walls- Standard brick 222 × 106 × 73 mm with 10 mm joints (SANS 227; ~50 bricks/m² single skin); typical storey height 3 m (SANS 10400-C). https://www.sabs.co.za/
Day 80 · Weights at a glance- Densities: water 1.0, petrol ~0.75, dry sand ~1.5, concrete ~2.4 kg/L; cement 50 kg bags (SANS 50197); brick ~3 kg. https://www.engineeringtoolbox.com/density-materials-d_1652.html
Day 81 · Crowds and queues- Crowd density guidance: ~2 persons/m² comfortable standing, 4 packed, >5 hazardous (Fruin, Pedestrian Planning and Design, 1971; UK Green Guide). https://en.wikipedia.org/wiki/Crowd_density
Day 82 · The price per unit- Unit pricing as a consumer comparison tool (Consumer Protection Act price display); the Home & Life edition's price-per-kilogram day. https://www.gov.za/documents/consumer-protection-act
Day 83 · Time and speed on the street- Average walking speed ~5 km/h (Bohannon & Williams Andrews 2011, Physiotherapy 97); minutes per kilometre = 60 / (km/h). https://doi.org/10.1016/j.physio.2010.12.004
Day 84 · The street speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 13 · Ratios and scaling
Recipes for eight, maps, mixing ratios, and why doubling a photo quadruples the ink.
Start here · A ratio is a recipe- Proportional reasoning and scale factors; the Home & Life edition's kitchen week (doubling a recipe) and shapes week (the square–cube law). https://en.wikipedia.org/wiki/Ratio
Day 85 · Scaling a recipe- Scale factors in recipes (McGee, On Food and Cooking, 2004, on why cooking time does not scale linearly); the Home & Life edition's kitchen week. https://en.wikipedia.org/wiki/Ratio
Day 86 · Mixing ratios- Part-to-part and part-to-whole ratios; two-stroke fuel mixes 50:1 = 20 mL/L; concrete mix 1:3:6 by volume for general use (Cement & Concrete SA guidance). https://cemcon-sa.org.za/
Day 87 · Map scales- Representative fraction map scales; South African 1:50 000 topographic series (Chief Directorate: National Geo-spatial Information). https://ngi.dalrrd.gov.za/
Day 90 · Unit rates- Unit rates and proportional reasoning; the Home & Life edition's car week (litres per hundred). https://en.wikipedia.org/wiki/Rate_(mathematics)
Day 91 · The ratios speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 14 · Averages in your head
Mean, median and mode without a spreadsheet, and the average that hides the truth.
Start here · Three middles- Mean, median, mode; the assumed-mean method for computing a mean. Huff, D. (1954), How to Lie with Statistics, ch. 2 (the well-chosen average). https://en.wikipedia.org/wiki/Average
Day 92 · The mean by balancing- Assumed-mean (provisional mean) method; the mean as the balance point of a distribution. https://en.wikipedia.org/wiki/Assumed_mean
Day 93 · Updating a mean- Incremental (running) mean: μₙ₊₁ = μₙ + (xₙ₊₁ − μₙ)/(n+1). https://en.wikipedia.org/wiki/Moving_average
Day 96 · The average speed- Harmonic mean of speeds over equal distances: v = 2v₁v₂/(v₁ + v₂). https://en.wikipedia.org/wiki/Harmonic_mean
Day 97 · The average that misleads- Huff (1954), How to Lie with Statistics, ch. 2; skewed distributions and the mean–median gap; the Home & Life edition's news week. https://en.wikipedia.org/wiki/Skewness
Day 98 · The averages speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 15 · Money in your head
Change, splitting the bill, per-unit prices, and the interest sum you can do standing in the bank.
Day 99 · Totals and change- The adding, subtracting and dividing weeks of this edition; SARB cash rounding. https://www.resbank.co.za/
Day 100 · Tips and service- Restaurant tipping conventions in South Africa (10–15%); percentages week of this edition. https://en.wikipedia.org/wiki/Gratuity
Day 101 · Interest in your head- Simple interest I = P·r·t; monthly interest as a twelfth of the annual; the Home & Life edition's interest week. https://en.wikipedia.org/wiki/Interest
Day 102 · Instalments- National Credit Act 34 of 2005: disclosure of total cost of credit; the Home & Life edition's interest week. https://www.ncr.org.za/
Day 103 · Exchange rates- Exchange-rate arithmetic; SARB daily rates. Rates used are illustrative, not the day's. https://www.resbank.co.za/en/home/what-we-do/statistics/key-statistics/selected-historical-rates
Day 104 · The price of an hour- Standard monthly hours 160–173 (40–45 h week, BCEA); opportunity cost of time; the Home & Life edition's Day 358. https://www.gov.za/documents/basic-conditions-employment-act
Day 105 · The money speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 16 · Time in your head
Hours to decimals, time zones, how long until, and the twelve-hour clock as a circle.
Start here · Sixty, twenty-four, seven- Sexagesimal time; decimal hours in timesheets; South African Standard Time UTC+2 with no daylight saving. https://en.wikipedia.org/wiki/South_African_Standard_Time
Day 106 · Hours as decimals and back- Decimal-hour timekeeping conventions in payroll (BCEA overtime calculated in hours and fractions). https://www.gov.za/documents/basic-conditions-employment-act
Day 107 · How long until- Elapsed time by counting up (complementary addition); 24-hour clock arithmetic. https://en.wikipedia.org/wiki/24-hour_clock
Day 108 · Adding times- Mixed-radix addition (hours and minutes); carrying at 60. https://en.wikipedia.org/wiki/Mixed_radix
Day 109 · Time zones- UTC offsets; SAST = UTC+2 with no daylight saving; the Home & Life edition's time zones day. https://en.wikipedia.org/wiki/List_of_UTC_offsets
Day 110 · Paces and speeds- Pace–speed reciprocity: km/h = 60 / (min/km); the Home & Life edition's sport week. https://en.wikipedia.org/wiki/Pace_(speed)
Day 111 · Time and money- BCEA overtime at 1.5× the hourly rate; billing in fractions of an hour. https://www.gov.za/documents/basic-conditions-employment-act
Day 112 · The time speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 17 · The calendar in your head
The day of the week for any date, leap years, and the days between two dates.
Start here · The calendar's round numbers- Gregorian calendar rules (leap years: divisible by 4, except centuries not divisible by 400); Conway's Doomsday rule (1973). https://en.wikipedia.org/wiki/Doomsday_rule
Day 113 · Days between dates- Day counting and the fencepost (off-by-one) distinction; the Home & Life edition's days-between-dates day. https://en.wikipedia.org/wiki/Off-by-one_error
Day 115 · Leap years- Gregorian leap-year rule (1582); tropical year 365.2422 days. https://en.wikipedia.org/wiki/Leap_year
Day 116 · The day of the week- Conway's Doomsday rule (1973); Zeller's congruence (1882) for the drill's scoring. https://en.wikipedia.org/wiki/Doomsday_rule
Day 117 · Ages and anniversaries- Age computation by year difference with the birthday adjustment; the subtracting week's years-between day. https://en.wikipedia.org/wiki/Age
Day 119 · The calendar speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 18 · Conversions in your head
Kilometres and miles, Celsius and Fahrenheit, kilograms and pounds, cups and millilitres.
Start here · The few factors- 1 mile = 1.609344 km; °F = °C × 9/5 + 32; 1 lb = 0.45359237 kg; 1 inch = 2.54 cm (exact, 1959); SA metric cup 250 mL (SANS 10012). https://www.bipm.org/en/measurement-units
Day 124 · Cups, spoons and litres- SA metric cup 250 mL, tablespoon 15 mL, teaspoon 5 mL (SANS 10012); UK gallon 4.546 L, US gallon 3.785 L. https://en.wikipedia.org/wiki/Cup_(unit)
Day 125 · Fuel figures- L/100 km = 100 / (km/L); mpg (US) to L/100 km = 235.2 / mpg; the Home & Life edition's car week. https://en.wikipedia.org/wiki/Fuel_economy_in_automobiles
Week 19 · Speed, distance and time
Arrival times, pace, and the sums a driver and a runner do on the move.
Start here · The triangle- Kinematics: d = vt; km/h ÷ 3.6 = m/s; the two-second rule (Arrive Alive, SA road safety guidance). https://www.arrivealive.co.za/
Day 128 · Average speed- Average speed = total distance / total time; the averages week's harmonic-mean day. https://en.wikipedia.org/wiki/Speed#Average_speed
Day 130 · Stopping distances- Reaction time ~1.5 s (AASHTO uses 2.5 s for design); braking distance ∝ v² (kinetic energy); the Home & Life edition's braking day. https://en.wikipedia.org/wiki/Braking_distance
Day 131 · Fuel for the trip- Fuel consumption in L/100 km; the Home & Life edition's car week. https://en.wikipedia.org/wiki/Fuel_economy_in_automobiles
Day 133 · The road speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 20 · Rates at a glance
Per hour, per kilometre, per hundred grams: comparing anything sold by a rate.
Start here · Per what- Rates as ratios to a unit; unit conversion of rates; harmonic combination of rates. https://en.wikipedia.org/wiki/Rate_(mathematics)
Day 135 · Per kilometre- Cost per kilometre as a unit rate; the Home & Life edition's car week; AA of SA operating-cost tables. https://aa.co.za/
Day 136 · Per hundred grams to per pack- Unit pricing per 100 g on South African shelf labels (Consumer Protection Act price display); food labels per 100 g (R146 regulations). https://www.gov.za/documents/consumer-protection-act
Day 137 · Per person per day- Compound unit rates (per person per day); the Home & Life edition's water week (150 L per person per day). https://en.wikipedia.org/wiki/Rate_(mathematics)
Day 138 · Rates that add- Combined work rates: 1/t = 1/a + 1/b; harmonic relation. https://en.wikipedia.org/wiki/Harmonic_mean
Day 139 · Minutes to years- Time unit conversions: 1,440 min/day, 86,400 s/day, 8,760 h/year, 525,600 min/year. https://en.wikipedia.org/wiki/Unit_of_time
Day 140 · The rates speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 21 · Big numbers
Million, billion, trillion, what a national budget is per person, and how to say a big number so it means something.
Day 142 · Per person- Per-capita arithmetic; National Treasury Budget Review 2025 (consolidated spending ~R2.4 trillion); Stats SA population ~62 million. https://www.treasury.gov.za/
Day 143 · Doublings- Powers of two; 2¹⁰ = 1,024 ≈ 10³; the rule of 72 (the Home & Life edition's interest week). https://en.wikipedia.org/wiki/Power_of_two
Day 145 · Comparing big numbers- Ratio comparison across scale names; the Home & Life edition's news week ('compared with what'). https://en.wikipedia.org/wiki/Order_of_magnitude
Week 22 · Small numbers
Thousandths, millionths and billionths, micrograms and nanometres, and the small chance that is not zero.
Day 148 · Milli and micro- SI: 1 mg = 1,000 µg; medication error literature on µg/mg confusion (ISMP); the Home & Life edition's medicine week. https://www.ismp.org/
Day 152 · Small chances- Small-probability arithmetic; additivity for rare independent events; the Home & Life edition's risk week. https://en.wikipedia.org/wiki/Probability
Day 153 · Thin things- Human hair diameter ~50–100 µm; office paper ~0.1 mm; paint dry film ~50 µm per coat; red blood cell ~8 µm. https://en.wikipedia.org/wiki/Hair#Description
Week 23 · Powers of ten
Scientific notation, orders of magnitude, and the prefixes from kilo to tera.
Start here · Tens- Scientific notation; SI prefixes (BIPM); logarithmic scales (Richter, pH, decibel). https://www.bipm.org/en/measurement-units/si-prefixes
Day 157 · The prefixes- SI prefixes (BIPM); decimal prefixes in data storage (1 GB = 1,000 MB by the SI convention). https://www.bipm.org/en/measurement-units/si-prefixes
Day 159 · The log scales- Richter/moment magnitude (10× amplitude per unit); pH = −log₁₀[H⁺]; decibel (10 dB = 10× power). The Home & Life edition's earthquake, chemistry and sound weeks. https://en.wikipedia.org/wiki/Logarithmic_scale
Day 161 · The powers speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 24 · Powers of two
Doublings, the chessboard, folding paper to the moon, and why computers count in twos.
Start here · Twos- Powers of two; the wheat-and-chessboard problem; paper-folding to the moon (42 folds). https://en.wikipedia.org/wiki/Power_of_two
Day 163 · The chessboard- Wheat and chessboard problem: 2^64 − 1 ≈ 1.8 × 10¹⁹ grains. https://en.wikipedia.org/wiki/Wheat_and_chessboard_problem
Day 164 · Folding paper- Paper folding: 42 folds of 0.1 mm exceed the Earth–Moon distance; Britney Gallivan's 12-fold record (2002). https://en.wikipedia.org/wiki/Mathematics_of_paper_folding
Day 165 · Halving- Half-life; caffeine half-life ~5 h (adults); the Home & Life edition's radiation week. https://en.wikipedia.org/wiki/Half-life
Day 166 · Bits and bytes- Binary prefixes (kibi, mebi, gibi; IEC 80000-13); a 1 TB drive ≈ 931 GiB. https://en.wikipedia.org/wiki/Binary_prefix
Day 167 · Twenty questions- Binary search: ⌈log₂ n⌉ comparisons; the game of twenty questions. https://en.wikipedia.org/wiki/Binary_search_algorithm
Day 168 · The twos speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 25 · Prime numbers
What a prime is, how to spot one, why they matter for your bank card, and the largest ones known.
Start here · The building blocks- Prime numbers; Euclid's theorem; largest known prime 2^136,279,841 − 1 (GIMPS, October 2024, 41,024,320 digits). https://www.mersenne.org/primes/
Day 169 · What a prime is- Prime number; primes of the form 6k ± 1; 25 primes below 100. https://en.wikipedia.org/wiki/Prime_number
Day 172 · Primes and your bank card- RSA (Rivest, Shamir, Adleman 1977); RSA-250 factored February 2020 (~2,700 core-years); 2048-bit keys ≈ 617 digits. https://en.wikipedia.org/wiki/RSA_cryptosystem
Day 173 · Famous primes- Mersenne primes; M136279841 (GIMPS, Luke Durant, October 2024); Goldbach's conjecture verified to 4 × 10¹⁸. https://www.mersenne.org/primes/
Day 174 · Primes in the wild- Periodical cicadas (Magicicada, 13- and 17-year broods); hunting-tooth gear design; least common multiple. https://en.wikipedia.org/wiki/Periodical_cicadas
Day 175 · The primes speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 26 · Pi
The one number every circle shares: where it comes from, how to remember it, and what it is good for.
Start here · The circle's number- Pi: irrational (Lambert 1768); 100 trillion digits (Google, 2022); 39 digits suffice for the observable universe to atomic precision (NASA/JPL). https://en.wikipedia.org/wiki/Pi
Day 176 · Where pi comes from- Archimedes' bounds 223/71 < π < 22/7 (c. 250 BC); William Jones introduced π (1706). https://en.wikipedia.org/wiki/Approximations_of_%CF%80
Day 177 · Remembering pi- Piphilology (mnemonic sentences); 355/113 (Zu Chongzhi, 5th c.); recitation record 70,000 digits (Rajveer Meena, 2015). https://en.wikipedia.org/wiki/Piphilology
Day 180 · Tins and tables- Cylinder volume πr²h; 1 cm³ = 1 ml; the Home & Life edition's water week. https://en.wikipedia.org/wiki/Cylinder
Day 181 · The odd facts- Pi irrational (Lambert 1768), transcendental (Lindemann 1882); Pi Day 14 March; π² ≈ 9.87 and the seconds pendulum. https://en.wikipedia.org/wiki/Pi_Day
Day 182 · The pi speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 27 · The golden ratio, e and root two
Three famous numbers, where they hide, and what is true and untrue about them.
Start here · Three famous numbers- √2 (Pythagoras; irrationality, c. 5th c. BC); golden ratio (Euclid, 'extreme and mean ratio'); e (Bernoulli 1683, Euler); Markowsky, 'Misconceptions about the golden ratio' (1992). https://en.wikipedia.org/wiki/Golden_ratio
Day 183 · Root two- ISO 216 paper (√2 aspect ratio); Pythagorean theorem; Plato's Meno (doubling the square). https://en.wikipedia.org/wiki/ISO_216
Day 184 · The golden ratio- Golden ratio φ = (1+√5)/2; Fibonacci sequence; phyllotaxis and the golden angle (Vogel 1979). https://en.wikipedia.org/wiki/Golden_ratio
Day 185 · e and growth- e as lim (1+1/n)ⁿ (Bernoulli 1683); natural logarithm; rule of 70 from ln 2 = 0.693. https://en.wikipedia.org/wiki/E_(mathematical_constant)
Day 186 · Where they hide, and where they do not- Markowsky, 'Misconceptions about the golden ratio', College Mathematics Journal 23(1), 1992; f-number sequence (√2 steps); nautilus spiral ratio ≈ 1.33. https://doi.org/10.1080/07468342.1992.11973428
Day 187 · What irrational means- Irrationality of √2 (Euclid, Elements X); repeating decimals; transcendence of e (Hermite 1873) and π (Lindemann 1882). https://en.wikipedia.org/wiki/Square_root_of_2
Day 188 · Using them- Rule of thirds vs golden section; f-stops; diagonal = side × √2. https://en.wikipedia.org/wiki/Rule_of_thirds
Week 28 · Zero and negative numbers
The number that took a thousand years, temperatures below zero, debts, and why minus times minus is plus.
Day 191 · Below zero- Kelvin scale: 0 K = −273.15°C; the Home & Life edition's weather week. https://en.wikipedia.org/wiki/Kelvin
Week 29 · Number patterns
Triangular numbers, square numbers, Fibonacci, and Gauss adding 1 to 100 as a boy.
Start here · Patterns- Figurate numbers; Gauss and 1 to 100 (Hayes, 'Gauss's Day of Reckoning', American Scientist 2006); Moser's circle problem. https://en.wikipedia.org/wiki/Triangular_number
Day 201 · Cubes and pyramids- Sum of cubes = (n(n+1)/2)²; square pyramidal numbers; 204 squares on a chessboard. https://en.wikipedia.org/wiki/Square_pyramidal_number
Day 202 · Patterns that break- Moser's circle problem (regions = C(n,4) + C(n,2) + 1); Euler's prime-generating polynomial n² + n + 41; 333333331 = 17 × 19607843. https://en.wikipedia.org/wiki/Dividing_a_circle_into_areas
Day 203 · The patterns speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 30 · Sequences and sums
Adding a run of numbers fast, the sum of the odds, and the series that never ends but adds to two.
Start here · Runs and ratios- Arithmetic and geometric progressions; the fence-post (off-by-one) error; Zeno's dichotomy. https://en.wikipedia.org/wiki/Arithmetic_progression
Day 204 · Runs with a step- Arithmetic progression: aₙ = a + (n−1)d; Sₙ = n(a + aₙ)/2. https://en.wikipedia.org/wiki/Arithmetic_progression
Day 207 · Savings that grow- 52-week money challenge (Σ 1..52 = 1,378); arithmetic series; the Home & Life edition's saving week. https://en.wikipedia.org/wiki/Arithmetic_progression
Day 208 · Series that never end- Repeating decimals as geometric series; 0.999… = 1; bouncing-ball total distance h(1+r)/(1−r); harmonic series divergence. https://en.wikipedia.org/wiki/0.999...
Day 209 · Counting the terms- Off-by-one (fence-post) error; counting terms of an arithmetic progression. https://en.wikipedia.org/wiki/Off-by-one_error
Day 210 · The sequences speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 31 · Digits and divisibility
Why the digit sum tells you about nine, the tricks for 7, 11 and 13, and what a digital root is.
Day 214 · Casting out nines- Casting out nines; limits (errors that are multiples of 9 pass). https://en.wikipedia.org/wiki/Casting_out_nines
Day 216 · Odd and even- Parity arguments; the mutilated chessboard (Gamow & Stern 1958); the handshaking lemma. https://en.wikipedia.org/wiki/Parity_(mathematics)
Day 217 · The digits speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 32 · Check digits
The last digit of your ID number, your bank card, a barcode and a book's ISBN, and how it catches a typo.
Day 218 · Why a check digit- Check digit schemes and error classes (single-digit, transposition). https://en.wikipedia.org/wiki/Check_digit
Day 219 · Barcodes- EAN-8 and EAN-13 check digit (GS1); GS1 prefix 600–601 South Africa. https://www.gs1.org/services/how-calculate-check-digit-manually
Day 221 · Your ID number- South African ID number structure (Department of Home Affairs); Luhn check digit. https://en.wikipedia.org/wiki/South_African_identity_card
Day 222 · ISBN and mod 11- ISBN-10 check digit (mod 11) and the 2007 move to ISBN-13. https://en.wikipedia.org/wiki/ISBN#Check_digits
Day 223 · What a check digit cannot catch- Error detection of Luhn (misses 09↔90), EAN (misses transpositions differing by 5), ISBN-10 (catches all adjacent transpositions). https://en.wikipedia.org/wiki/Luhn_algorithm#Weaknesses
Week 33 · Number bases
Binary, hexadecimal, why 60 minutes, and how to count to 1,023 on your fingers.
Day 225 · Binary- Binary numeral system; conversion by repeated halving. https://en.wikipedia.org/wiki/Binary_number
Day 227 · Hexadecimal- Hexadecimal; web colours as three hex bytes. https://en.wikipedia.org/wiki/Hexadecimal
Day 228 · Why sixty- Sexagesimal (Babylonian origin); French Republican decimal time (1793–1795). https://en.wikipedia.org/wiki/Sexagesimal
Day 229 · Any base- Radix; numeral systems in world languages (vigesimal, body-count systems). https://en.wikipedia.org/wiki/Radix
Day 231 · The bases speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 34 · Old ways of counting
Roman numerals, dozens and scores, tallies and the abacus, and the words we still use.
Start here · Before the digits- Ishango bone (c. 20,000 BP); Roman numerals; tally marks; South African decimalisation 14 Feb 1961 (R2 = £1). https://en.wikipedia.org/wiki/Roman_numerals
Day 232 · Tallies and scores- Tally marks and tally sticks; vigesimal counting (French, Danish, Maya). https://en.wikipedia.org/wiki/Tally_marks
Day 234 · Dozens and grosses- Dozen, gross, great gross; baker's dozen (Assize of Bread and Ale, 13th c.). https://en.wikipedia.org/wiki/Dozen
Day 235 · The abacus- Soroban (1:4 beads) and suanpan (2:5); the 1946 Tokyo contest (Kiyoshi Matsuzaki vs Thomas Wood). https://en.wikipedia.org/wiki/Soroban
Day 237 · The old money- £sd; South African decimalisation, 14 February 1961 (R2 = £1; 1 shilling = 10 cents). https://en.wikipedia.org/wiki/South_African_rand
Week 35 · Classic number puzzles
Magic squares, the 6174 trick, the missing-rand puzzle, and the ones to try on the family.
Start here · Puzzles- Lo Shu square; Dürer, Melencolia I (1514); Kaprekar's routine (1949); the missing dollar riddle. https://en.wikipedia.org/wiki/Magic_square
Day 239 · Magic squares- Lo Shu square; Dürer's magic square (1514); magic constant M = n(n² + 1)/2. https://en.wikipedia.org/wiki/Magic_square
Day 240 · Kaprekar's 6174- D. R. Kaprekar (1949); 6174 reached in at most 7 iterations; 495 for three digits. https://en.wikipedia.org/wiki/6174
Day 241 · The missing rand- The missing dollar riddle (R. M. Abraham, Diversions and Pastimes, 1933). https://en.wikipedia.org/wiki/Missing_dollar_riddle
Day 242 · The snail and the bat- Frederick (2005), Cognitive Reflection Test (bat and ball); the snail-in-the-well puzzle. https://doi.org/10.1257/089533005775196732
Day 243 · Cuts and cubes- Lazy caterer's sequence n(n+1)/2 + 1; painted cube problem. https://en.wikipedia.org/wiki/Lazy_caterer%27s_sequence
Day 245 · The puzzles speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 36 · Mental-maths games
Games that build speed: 24, countdown, the doubling ladder, and rounds for the car.
Start here · Games that build speed- The 24 Game (Robert Sun, 1988); Countdown numbers round; Ericsson et al. (1993) on deliberate practice. https://en.wikipedia.org/wiki/24_(puzzle)
Day 247 · Countdown- Countdown (Channel 4, 1982–) numbers round; Des Chiffres et des Lettres (1965–). https://en.wikipedia.org/wiki/Countdown_(game_show)#Numbers_round
Day 250 · Beat the calculator- Benjamin & Shermer, Secrets of Mental Math (2006); the tricks week of this edition. https://en.wikipedia.org/wiki/Mental_calculation
Day 252 · The games speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 37 · Chance in your head
Dice, coins and cards: the odds you can work out at the table.
Day 253 · Dice- Dice probabilities; the Chevalier de Méré's bet (at least one six in four rolls, 51.8%). https://en.wikipedia.org/wiki/Problem_of_points
Day 254 · Coins- Binomial counts and Pascal's triangle; the gambler's fallacy. https://en.wikipedia.org/wiki/Gambler%27s_fallacy
Day 255 · Cards- Card probabilities; poker hand frequencies. https://en.wikipedia.org/wiki/Poker_probability
Day 256 · At least one- Complement rule; the birthday problem (23 people, 50.7%). https://en.wikipedia.org/wiki/Birthday_problem
Day 257 · Odds and the lottery- Odds vs probability; SA Lotto 6/52 (C(52,6) = 20,358,520); PowerBall 1 in 42,375,200. https://en.wikipedia.org/wiki/Lottery_mathematics
Day 258 · Independence and its mistakes- Independence; the Sally Clark case (1 in 73 million by squaring, Royal Statistical Society statement 2001); Gilovich, Vallone & Tversky (1985) on the hot hand. https://en.wikipedia.org/wiki/Sally_Clark
Day 259 · The chance speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 38 · Counting the ways
How many orders, how many teams, how many PINs: combinations without a formula sheet.
Day 261 · Orders- Permutations and factorials; 52! ≈ 8 × 10⁶⁷. https://en.wikipedia.org/wiki/Factorial
Day 262 · Teams- Combinations C(n,k) = n!/(k!(n−k)!); C(52,6) = 20,358,520. https://en.wikipedia.org/wiki/Combination
Day 265 · Counting shortcuts- Complementary counting; treating adjacent items as a block; subsets 2ⁿ. https://en.wikipedia.org/wiki/Combinatorial_principles
Day 266 · The counting speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 39 · Paradoxes
The birthday paradox, Monty Hall, the two envelopes, and why intuition fails on chance.
Start here · Where intuition fails- Monty Hall problem (vos Savant 1990); birthday problem; base-rate neglect (Kahneman & Tversky); Simpson's paradox (Berkeley 1973, Bickel et al. 1975); inspection paradox. https://en.wikipedia.org/wiki/Monty_Hall_problem
Day 267 · Monty Hall- Monty Hall problem; vos Savant, Parade (1990); Selvin (1975). https://en.wikipedia.org/wiki/Monty_Hall_problem
Day 269 · The false positive- Base-rate neglect; Gigerenzer & Hoffrage (1995), natural frequencies; Casscells et al. (1978). https://doi.org/10.1037/0033-295X.102.4.684
Day 270 · Simpson's paradox- Simpson's paradox; Charig et al. (1986) kidney stones; Bickel, Hammel & O'Connell (1975), Berkeley admissions. https://en.wikipedia.org/wiki/Simpson%27s_paradox
Day 272 · Averages that lie- Inspection paradox; the friendship paradox (Feld 1991); waiting-time paradox. https://en.wikipedia.org/wiki/Friendship_paradox
Day 273 · The paradoxes speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 40 · Expected value
What a bet, a warranty, a raffle and a queue are worth, in one sum.
Start here · Chance times value- Expected value (Huygens 1657; Pascal–Fermat); house edge; coupon collector's problem. https://en.wikipedia.org/wiki/Expected_value
Day 274 · What a bet is worth- House edge (roulette single-zero 2.7%, double-zero 5.3%); expected value of bets. https://en.wikipedia.org/wiki/House_edge
Day 276 · The warranty- Extended warranties: Consumer Reports and Which? on expected value; loss aversion. https://en.wikipedia.org/wiki/Extended_warranty
Day 277 · Insurance- Insurance loading; expected utility (Bernoulli 1738); the Home & Life edition's insurance week. https://en.wikipedia.org/wiki/Expected_utility_hypothesis
Day 278 · Tries and queues- Geometric distribution mean 1/p; coupon collector's problem n·Hₙ. https://en.wikipedia.org/wiki/Coupon_collector%27s_problem
Week 41 · Growth and doubling
The rule of 72, compound growth, and why a small percent for a long time beats a big one for a short time.
Start here · The rule of 72- Rule of 72 (Pacioli 1494; ln 2 = 0.693); compound interest; logistic growth. https://en.wikipedia.org/wiki/Rule_of_72
Day 284 · Inflation- SARB inflation target 3–6%; Fisher equation (real ≈ nominal − inflation). https://www.resbank.co.za/en/home/what-we-do/monetary-policy
Day 285 · Epidemics and populations- Doubling time in epidemiology; basic reproduction number R₀; world population growth ~2% (1960s). https://en.wikipedia.org/wiki/Basic_reproduction_number
Day 286 · The limits of growth- Logistic growth (Verhulst 1838); the lily-pad riddle; Meadows et al., The Limits to Growth (1972). https://en.wikipedia.org/wiki/Logistic_function
Day 287 · The growth speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 42 · Infinity
Hilbert's hotel, a googol, why some infinities are bigger, and why you can never reach it.
Start here · Bigger than any number- Googol (Kasner & Sirotta, 1920/1940); Hilbert's hotel (1924); Cantor's diagonal argument (1891). https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel
Day 288 · Big but finite- Googol and googolplex; ~10⁸⁰ atoms in the observable universe; Graham's number. https://en.wikipedia.org/wiki/Googol
Day 289 · Hilbert's hotel- Hilbert's paradox of the Grand Hotel (1924); Gamow, One Two Three… Infinity (1947). https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel
Day 290 · Counting the infinite- Galileo's paradox (1638); Cantor, countable sets; the zigzag enumeration of the rationals. https://en.wikipedia.org/wiki/Countable_set
Day 291 · Bigger infinities- Cantor's diagonal argument (1891); Cantor's theorem |P(S)| > |S|. https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument
Day 292 · Never reaching it- Zeno's dichotomy; harmonic series divergence (Oresme, c. 1350); 0.999… = 1. https://en.wikipedia.org/wiki/Harmonic_series_(mathematics)
Day 294 · The infinity speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 43 · Geometry in your head
Areas, the 3-4-5 triangle, angles from the clock face, and the sums a builder does without paper.
Day 296 · The 3-4-5 triangle- Pythagorean triples; the 3-4-5 rule in construction; Plimpton 322 (c. 1800 BC). https://en.wikipedia.org/wiki/Pythagorean_triple
Day 298 · Angles in shapes- Angle sum of polygons; exterior angles sum to 360°. https://en.wikipedia.org/wiki/Internal_and_external_angles
Day 299 · Volumes- Volume of a cuboid; 1 L = 1,000 cm³; 1 m³ = 1 kL; the square–cube law. https://en.wikipedia.org/wiki/Square%E2%80%93cube_law
Day 300 · The builder's sums- Construction estimating: perimeter, tile counts, paint coverage; the 3-4-5 rule; roof pitch as rise over run. https://en.wikipedia.org/wiki/Roof_pitch
Day 301 · The geometry speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 44 · Logarithms without tears
Why decibels, earthquakes and pH climb by tens, and the log scale you already read.
Start here · The exponent, named- Logarithms (Napier 1614; Briggs 1617); decibel; moment magnitude; pH; apparent magnitude. https://en.wikipedia.org/wiki/Logarithm
Day 302 · What a log is- Common logarithm; log 2 ≈ 0.301, log 3 ≈ 0.477, log 5 ≈ 0.699. https://en.wikipedia.org/wiki/Common_logarithm
Day 304 · Decibels- Decibel; 3 dB ≈ ×2 power; NIOSH 85 dBA exposure limit with 3-dB exchange rate. https://en.wikipedia.org/wiki/Decibel
Day 305 · Earthquakes- Moment magnitude scale; energy ∝ 10^(1.5 M) (≈31.6 per unit); Valdivia 1960 M 9.5. https://en.wikipedia.org/wiki/Moment_magnitude_scale
Day 306 · pH and other tens- pH (Sørensen 1909); apparent magnitude (Pogson 1856, 5 magnitudes = 100×); Weber–Fechner law. https://en.wikipedia.org/wiki/Apparent_magnitude
Week 45 · Numbers in sport
Run rates, strike rates, handicaps, seedings and league tables done in your head.
Start here · The scoreboard- Cricket statistics (run rate, strike rate, average, economy); league points systems (football 3-1-0; rugby 4-2-0 plus bonus points); Stableford scoring; single-elimination tournaments. https://en.wikipedia.org/wiki/Cricket_statistics
Day 310 · League tables- Three points for a win (FIFA); rugby union bonus point system; goal difference as tiebreaker. https://en.wikipedia.org/wiki/Bonus_points_(rugby_union)
Day 311 · Golf- Stableford scoring (1932); World Handicap System (2020): best 8 of 20. https://en.wikipedia.org/wiki/Stableford
Day 313 · Draws and seedings- Single-elimination tournaments (n − 1 matches); byes; seeding. https://en.wikipedia.org/wiki/Single-elimination_tournament
Day 314 · Percentages in sport- Winning percentage (draws as half); points percentage; field goal percentage. https://en.wikipedia.org/wiki/Winning_percentage
Day 315 · The sport speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 46 · Numbers in the kitchen
Halving a recipe, oven temperatures, portions, and the baker's percentage.
Start here · The recipe as arithmetic- Baker's percentage; oven temperature equivalents (gas marks, fan −20 °C); portion sizes (rice 75–100 g dry, meat 150–250 g). https://en.wikipedia.org/wiki/Baker_percentage
Day 316 · Scaling a recipe- Recipe scaling; conversion factor = desired yield / original yield (Culinary Institute of America). https://en.wikipedia.org/wiki/Recipe
Day 317 · Portions and yield- Portion sizes (British Nutrition Foundation); cooking yield and shrinkage (~25% for roasts). https://en.wikipedia.org/wiki/Serving_size
Day 318 · Oven temperatures- Oven temperature equivalents (gas mark, °C, °F, fan); roasting times; safe internal temperatures (USDA). https://en.wikipedia.org/wiki/Gas_mark
Day 321 · Kitchen equivalents- Cooking weights and measures; egg sizes (large ≈ 50 g); flour ≈ 125 g per cup. https://en.wikipedia.org/wiki/Cooking_weights_and_measures
Day 322 · The kitchen speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 47 · Numbers on the road
Fuel, distances, speed limits, tolls and the sums in the driver's seat.
Start here · The driver's seat- Fuel consumption in L/100 km; AA South Africa running-cost guidance; SANRAL toll tariffs; tyre pressure units (bar, kPa, psi). https://en.wikipedia.org/wiki/Fuel_economy_in_automobiles
Day 327 · Tyres and loads- Tyre pressure units (1 bar = 100 kPa = 14.5 psi); under-inflation and fuel use (~0.2% per psi); vehicle payload. https://en.wikipedia.org/wiki/Tire-pressure_gauge
Day 329 · The road speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 48 · Numbers in music
Beats, tempo, time signatures, octaves and the ratios that sound good.
Start here · Counting in music- Tempo and time signatures; A440 (ISO 16); just intonation ratios; equal temperament 2^(1/12); polyrhythms. https://en.wikipedia.org/wiki/Equal_temperament
Day 330 · Tempo and time- Tempo markings and BPM; Maelzel's metronome (1815); running cadence ~180 spm. https://en.wikipedia.org/wiki/Tempo
Day 336 · The music speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 49 · Numbers in nature
Spirals, hexagons, symmetry, and the counts that keep turning up in living things.
Start here · The counts that keep turning up- Phyllotaxis and the golden angle (Vogel 1979); honeycomb conjecture (Hales 2001); Kleiber's law (1932); ~1 billion heartbeats per mammalian lifetime. https://en.wikipedia.org/wiki/Kleiber%27s_law
Day 338 · Hexagons and honeycomb- Honeycomb conjecture (Hales 1999); centred hexagonal numbers; hexagon area (3√3/2) s². https://en.wikipedia.org/wiki/Honeycomb_conjecture
Day 339 · Symmetry- Symmetry in biology (bilateral vs radial); snowflake six-fold symmetry; dihedral groups. https://en.wikipedia.org/wiki/Symmetry_in_biology
Day 340 · The rules of scale- Square–cube law (Galileo 1638); Kleiber's law (1932), metabolic rate ∝ M^0.75; West, Brown & Enquist (1997). https://en.wikipedia.org/wiki/Kleiber%27s_law
Day 342 · Counting in the wild- Lincoln–Petersen mark-recapture; dendrochronology; similar triangles for height. https://en.wikipedia.org/wiki/Mark_and_recapture
Day 343 · The nature speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 50 · A short history of numbers
From tally sticks to the zero, the Hindu-Arabic numerals, and the calculator in your pocket.
Start here · Where the numbers came from- Ifrah, The Universal History of Numbers (1998); Brahmagupta 628; al-Khwarizmi c. 825; Fibonacci 1202; Stevin 1585; HP-35 1972. https://en.wikipedia.org/wiki/History_of_the_Hindu%E2%80%93Arabic_numeral_system
Day 344 · Tallies and tokens- Ishango bone (c. 20,000 BP); Schmandt-Besserat, Before Writing (1992) on clay tokens; Sumerian sexagesimal. https://en.wikipedia.org/wiki/Ishango_bone
Day 345 · Egypt and the doubling- Rhind Mathematical Papyrus (c. 1550 BC); Egyptian fractions; ancient Egyptian multiplication. https://en.wikipedia.org/wiki/Ancient_Egyptian_multiplication
Day 346 · India and the zero- Brahmagupta, Brāhmasphuṭasiddhānta (628); al-Khwarizmi, On the Calculation with Hindu Numerals (c. 825); Fibonacci, Liber Abaci (1202); Florence ban 1299. https://en.wikipedia.org/wiki/Al-Khwarizmi
Day 347 · Fractions and the point- Stevin, De Thiende (1585); the decimal point (Clavius 1593, Napier 1614); metric system (1795). https://en.wikipedia.org/wiki/Simon_Stevin
Day 348 · The machines- Pascaline (1642); Leibniz stepped reckoner (1673); Analytical Engine (1837); ENIAC (1945); HP-35 (1972); Moore (1965). https://en.wikipedia.org/wiki/HP-35
Day 349 · The names of numbers- Long and short scales; lakh and crore (Indian numbering); 'zero' and 'cipher' from sifr. https://en.wikipedia.org/wiki/Long_and_short_scales
Day 350 · The history speed round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 51 · The speed rounds
The year's tricks combined: seven mixed timed rounds to find your personal bests.
Start here · The whole year, timed- Deliberate practice with feedback (Ericsson, Krampe & Tesch-Römer 1993); the year's weeks and their sources. https://doi.org/10.1037/0033-295X.100.3.363
Day 357 · The grand round- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363
Week 52 · The year in numbers
Your best rounds, the tricks you use, the ones you will teach, and what to keep.
Start here · The year in numbers- The year's own 51 weeks and their sources; deliberate practice with feedback (Ericsson, Krampe & Tesch-Römer 1993). https://doi.org/10.1037/0033-295X.100.3.363
Day 358 · Your best rounds- The year's own 51 weeks and their sources; deliberate practice with feedback (Ericsson, Krampe & Tesch-Römer 1993). https://doi.org/10.1037/0033-295X.100.3.363
Day 359 · The tricks you use- The year's own 51 weeks and their sources; deliberate practice with feedback (Ericsson, Krampe & Tesch-Römer 1993). https://doi.org/10.1037/0033-295X.100.3.363
Day 360 · Your error rate- The year's own 51 weeks and their sources; deliberate practice with feedback (Ericsson, Krampe & Tesch-Römer 1993). https://doi.org/10.1037/0033-295X.100.3.363
Day 361 · The trick that pays- The year's own 51 weeks and their sources; deliberate practice with feedback (Ericsson, Krampe & Tesch-Römer 1993). https://doi.org/10.1037/0033-295X.100.3.363
Day 362 · Teaching it- The year's own 51 weeks and their sources; deliberate practice with feedback (Ericsson, Krampe & Tesch-Römer 1993). https://doi.org/10.1037/0033-295X.100.3.363
Day 363 · Your numbers card- The year's own 51 weeks and their sources; deliberate practice with feedback (Ericsson, Krampe & Tesch-Römer 1993). https://doi.org/10.1037/0033-295X.100.3.363
Day 364 · The year's count- The year's own 51 weeks and their sources; deliberate practice with feedback (Ericsson, Krampe & Tesch-Römer 1993). https://doi.org/10.1037/0033-295X.100.3.363
Day 365 · What to keep- The year's own 51 weeks and their sources; deliberate practice with feedback (Ericsson, Krampe & Tesch-Römer 1993). https://doi.org/10.1037/0033-295X.100.3.363
Alphabetical. Click a day to open it.
- (10 + a)(10 + b) = 10(10 + a + b) + ab; Benjamin & Shermer (2006), ch. 3. https://en.wikipedia.org/wiki/Multiplication_algorithmCited by: Day 23
- (100 − a)(100 − b) = 100(100 − a − b) + ab; the 'Nikhilam' method of Bharati Krishna Tirtha's Vedic Mathematics (1965) — a 20th-century book, not ancient (Dani, S.G. 1993, 'Myths and reality: on Vedic mathematics'). https://en.wikipedia.org/wiki/Vedic_MathematicsCited by: Day 5
- (10n + 5)² = 100n(n + 1) + 25; Benjamin & Shermer (2006), Secrets of Mental Math, ch. 3. https://en.wikipedia.org/wiki/Mental_calculation#Squaring_numbers_ending_in_5Cited by: Day 3
- (50 + d)² = 2500 + 100d + d²; (100 − d)² = 100(100 − 2d) + d²; Benjamin & Shermer (2006), ch. 3. https://en.wikipedia.org/wiki/Mental_calculation#SquaringCited by: Day 38
- (n − d)(n + d) = n² − d²; Benjamin & Shermer (2006), ch. 3: the 'close together' method. https://en.wikipedia.org/wiki/Difference_of_two_squaresCited by: Day 26
- 1 inch = 25.4 mm exactly (1959); 1 foot = 0.3048 m. https://en.wikipedia.org/wiki/InchCited by: Day 123
- 1 lb = 0.45359237 kg (International Yard and Pound Agreement, 1959). https://en.wikipedia.org/wiki/Pound_(mass)Cited by: Day 122
- 1 m/s = 3.6 km/h. https://en.wikipedia.org/wiki/Metre_per_secondCited by: Day 129
- 1 mile = 1.609344 km; Fibonacci ratio → φ ≈ 1.618 as a mile–km approximation. https://en.wikipedia.org/wiki/MileCited by: Day 120
- 1 mile = 1.609344 km; °F = °C × 9/5 + 32; 1 lb = 0.45359237 kg; 1 inch = 2.54 cm (exact, 1959); SA metric cup 250 mL (SANS 10012). https://www.bipm.org/en/measurement-unitsCited by: Week 18 start here
- 24 Game (Suntex, 1988). https://en.wikipedia.org/wiki/24_(puzzle)Cited by: Day 246
- 365 days, 8,760 hours, 31.5 million seconds in a year. https://en.wikipedia.org/wiki/YearCited by: Day 144
- 52-week money challenge (Σ 1..52 = 1,378); arithmetic series; the Home & Life edition's saving week. https://en.wikipedia.org/wiki/Arithmetic_progressionCited by: Day 207
- a × 9 = a × 10 − a; divisibility by 9 and the digit sum (casting out nines); the finger method for 9× (elementary arithmetic folklore, documented in Benjamin & Shermer 2006). https://en.wikipedia.org/wiki/Casting_out_ninesCited by: Day 4
- a ÷ 5 = 2a ÷ 10; a ÷ 25 = 4a ÷ 100; Benjamin & Shermer (2006), ch. 4. https://en.wikipedia.org/wiki/Mental_calculationCited by: Day 30
- AA South Africa vehicle rates; fuel cost per km = price × L/100 km ÷ 100. https://aa.co.za/Cited by: Day 323
- Addition of fractions with a common denominator; least common multiple. https://en.wikipedia.org/wiki/Fraction#AdditionCited by: Day 55
- Age computation by year difference with the birthday adjustment; the subtracting week's years-between day. https://en.wikipedia.org/wiki/AgeCited by: Day 117
- Algebraic number tricks; the 1089 trick. https://en.wikipedia.org/wiki/1089_(number)Cited by: Day 244
- Angle sum of polygons; exterior angles sum to 360°. https://en.wikipedia.org/wiki/Internal_and_external_anglesCited by: Day 298
- Archimedes' bounds 223/71 < π < 22/7 (c. 250 BC); William Jones introduced π (1706). https://en.wikipedia.org/wiki/Approximations_of_%CF%80Cited by: Day 176
- Area formulas; Pythagorean triples (3-4-5, 5-12-13, 8-15-17); clock angle problems. https://en.wikipedia.org/wiki/Pythagorean_tripleCited by: Week 43 start here
- Area of a disk πr²; the rearrangement argument (Archimedes). https://en.wikipedia.org/wiki/Area_of_a_circleCited by: Day 178
- Area of a trapezoid, parallelogram; dissection arguments. https://en.wikipedia.org/wiki/TrapezoidCited by: Day 295
- Arithmetic and geometric progressions; the fence-post (off-by-one) error; Zeno's dichotomy. https://en.wikipedia.org/wiki/Arithmetic_progressionCited by: Week 30 start here
- Arithmetic mod 10; last-digit rules for products and sums. https://en.wikipedia.org/wiki/Modular_arithmeticCited by: Day 71
- Arithmetic progression: aₙ = a + (n−1)d; Sₙ = n(a + aₙ)/2. https://en.wikipedia.org/wiki/Arithmetic_progressionCited by: Day 204
- Associativity and factoring the multiplier; Benjamin & Shermer (2006), ch. 2: the factoring method. https://en.wikipedia.org/wiki/Mental_calculationCited by: Day 25
- Associativity: a × b = (a ÷ 2) × (2b); the Egyptian/Russian peasant multiplication uses repeated doubling and halving (Rhind Mathematical Papyrus, c. 1550 BCE). https://en.wikipedia.org/wiki/Ancient_Egyptian_multiplicationCited by: Day 6
- Assumed-mean (provisional mean) method; the mean as the balance point of a distribution. https://en.wikipedia.org/wiki/Assumed_meanCited by: Day 92
- Average speed = total distance / total time; the averages week's harmonic-mean day. https://en.wikipedia.org/wiki/Speed#Average_speedCited by: Day 128
- Average walking speed ~5 km/h (Bohannon & Williams Andrews 2011, Physiotherapy 97); minutes per kilometre = 60 / (km/h). https://doi.org/10.1016/j.physio.2010.12.004Cited by: Day 83
- a² = (a + d)(a − d) + d²; Benjamin & Shermer (2006), Secrets of Mental Math, ch. 3. https://en.wikipedia.org/wiki/Mental_calculation#SquaringCited by: Day 37
- a² − b² = (a − b)(a + b). https://en.wikipedia.org/wiki/Difference_of_two_squaresCited by: Day 39
- Baker's percentage; oven temperature equivalents (gas marks, fan −20 °C); portion sizes (rice 75–100 g dry, meat 150–250 g). https://en.wikipedia.org/wiki/Baker_percentageCited by: Week 46 start here
- Baker's percentage; typical hydrations (sandwich 60–65%, ciabatta 75–80%). https://en.wikipedia.org/wiki/Baker_percentageCited by: Day 319
- Base-rate neglect; Gigerenzer & Hoffrage (1995), natural frequencies; Casscells et al. (1978). https://doi.org/10.1037/0033-295X.102.4.684Cited by: Day 269
- Basis point = 0.01%; the percentages week of this edition. https://en.wikipedia.org/wiki/Basis_pointCited by: Day 150
- BCEA overtime at 1.5× the hourly rate; billing in fractions of an hour. https://www.gov.za/documents/basic-conditions-employment-actCited by: Day 111
- Benjamin & Shermer (2006), ch. 5. https://en.wikipedia.org/wiki/PercentageCited by: Day 43
- Benjamin & Shermer (2006), ch. 5; Consumer Protection Act price display (discounts as a percentage of the displayed price). https://www.gov.za/documents/consumer-protection-actCited by: Day 48
- Benjamin & Shermer (2006), ch. 5; fraction–percent equivalents. https://en.wikipedia.org/wiki/PercentageCited by: Day 44
- Benjamin & Shermer (2006), Secrets of Mental Math, ch. 1, the 11 rule; distributive law a × 11 = a × 10 + a. https://en.wikipedia.org/wiki/Multiplication_algorithmCited by: Day 1
- Benjamin & Shermer (2006), Secrets of Mental Math, ch. 1: left-to-right subtraction. https://en.wikipedia.org/wiki/Subtraction#MethodsCited by: Day 17
- Benjamin & Shermer (2006), Secrets of Mental Math, ch. 1; the associative law lets the second number be added in parts. https://en.wikipedia.org/wiki/Mental_calculationCited by: Day 8
- Benjamin & Shermer (2006), Secrets of Mental Math, ch. 2; commutativity and associativity of multiplication (a × 5 = a × 10 ÷ 2). https://en.wikipedia.org/wiki/Mental_calculationCited by: Day 2
- Benjamin & Shermer (2006), Secrets of Mental Math, ch. 2–3: the distributive method, factoring, and the squares method. https://en.wikipedia.org/wiki/Mental_calculationCited by: Week 4 start here
- Benjamin & Shermer (2006), Secrets of Mental Math, ch. 3: squaring by (a + d)(a − d) + d²; the last-digit test for squares. https://en.wikipedia.org/wiki/Square_numberCited by: Week 6 start here
- Benjamin & Shermer (2006), Secrets of Mental Math, ch. 3: two-by-two multiplication by the addition method. https://en.wikipedia.org/wiki/Mental_calculationCited by: Day 24
- Benjamin & Shermer (2006), Secrets of Mental Math, ch. 4: division; divisibility rules. https://en.wikipedia.org/wiki/Divisibility_ruleCited by: Week 5 start here
- Benjamin & Shermer (2006), Secrets of Mental Math, ch. 5: percentages; commutativity of multiplication for the swap (a × b/100 = b × a/100). https://en.wikipedia.org/wiki/PercentageCited by: Week 7 start here
- Benjamin & Shermer, Secrets of Mental Math (2006); the tricks week of this edition. https://en.wikipedia.org/wiki/Mental_calculationCited by: Day 250
- Benjamin, A. & Shermer, M. (2006), Secrets of Mental Math, ch. 1: left-to-right addition; Dowker, A. (2005), Individual Differences in Arithmetic: decomposition strategies and fluency. https://en.wikipedia.org/wiki/Mental_calculationCited by: Week 2 start here
- Benjamin, A. & Shermer, M. (2006), Secrets of Mental Math, Three Rivers Press: left-to-right method and the decomposition strategies. Dowker, A. (2005), Individual Differences in Arithmetic, Psychology Press: strategy use, not fact drill, predicts fluency. Pesenti, M. et al. (2001), 'Mental calculation in a prodigy is sustained by right prefrontal and medial temporal areas', Nature Neuroscience 4: expert calculators use strategies and trained memory. https://doi.org/10.1038/82831Cited by: Week 1 start here
- Binary numeral system; conversion by repeated halving. https://en.wikipedia.org/wiki/Binary_numberCited by: Day 225
- Binary prefixes (kibi, mebi, gibi; IEC 80000-13); a 1 TB drive ≈ 931 GiB. https://en.wikipedia.org/wiki/Binary_prefixCited by: Day 166
- Binary search: ⌈log₂ n⌉ comparisons; the game of twenty questions. https://en.wikipedia.org/wiki/Binary_search_algorithmCited by: Day 167
- Binomial counts and Pascal's triangle; the gambler's fallacy. https://en.wikipedia.org/wiki/Gambler%27s_fallacyCited by: Day 254
- Birthday problem: P(23) = 50.7%, P(57) = 99.0%. https://en.wikipedia.org/wiki/Birthday_problemCited by: Day 268
- Brahmagupta, Brāhmasphuṭasiddhānta (628); al-Khwarizmi, On the Calculation with Hindu Numerals (c. 825); Fibonacci, Liber Abaci (1202); Florence ban 1299. https://en.wikipedia.org/wiki/Al-KhwarizmiCited by: Day 346
- Brahmagupta, Brāhmasphuṭasiddhānta (628); Fibonacci, Liber Abaci (1202); Kaplan, The Nothing That Is (1999). https://en.wikipedia.org/wiki/0Cited by: Week 28 start here
- Buzz and fizz-buzz; skip counting; arithmetic progressions. https://en.wikipedia.org/wiki/Fizz_buzzCited by: Day 251
- Cantor's diagonal argument (1891); Cantor's theorem |P(S)| > |S|. https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argumentCited by: Day 291
- Card probabilities; poker hand frequencies. https://en.wikipedia.org/wiki/Poker_probabilityCited by: Day 255
- Casting out nines (digital roots); parity; modular arithmetic mod 10. https://en.wikipedia.org/wiki/Casting_out_ninesCited by: Week 11 start here
- Casting out nines; limits (errors that are multiples of 9 pass). https://en.wikipedia.org/wiki/Casting_out_ninesCited by: Day 214
- Check digit schemes and error classes (single-digit, transposition). https://en.wikipedia.org/wiki/Check_digitCited by: Day 218
- Check digits; Luhn algorithm (US patent 2,950,048, 1960); EAN-13; ISBN-10 mod 11. https://en.wikipedia.org/wiki/Check_digitCited by: Week 32 start here
- Classical probability (Laplace); SA Lotto 6/52 odds 1 in 20,358,520; the birthday problem. https://en.wikipedia.org/wiki/ProbabilityCited by: Week 37 start here
- Clock angle problem; degrees per hour and minute. https://en.wikipedia.org/wiki/Clock_angle_problemCited by: Day 297
- Column addition strategies and the tens-then-units method (bookkeeping practice); Benjamin & Shermer (2006), Secrets of Mental Math, ch. 1. https://en.wikipedia.org/wiki/Addition#Performing_additionCited by: Day 12
- Combinations C(n,k) = n!/(k!(n−k)!); C(52,6) = 20,358,520. https://en.wikipedia.org/wiki/CombinationCited by: Day 262
- Combined work rates: 1/t = 1/a + 1/b; harmonic relation. https://en.wikipedia.org/wiki/Harmonic_meanCited by: Day 138
- Common logarithm; log 2 ≈ 0.301, log 3 ≈ 0.477, log 5 ≈ 0.699. https://en.wikipedia.org/wiki/Common_logarithmCited by: Day 302
- Commutativity: (a/100)·b = (b/100)·a; Benjamin & Shermer (2006), ch. 5. https://en.wikipedia.org/wiki/PercentageCited by: Day 45
- Comparing fractions by cross-multiplication: a/b > c/d ⇔ ad > bc for positive b, d. https://en.wikipedia.org/wiki/Fraction#Comparing_fractionsCited by: Day 53
- Compensation in subtraction (Benjamin & Shermer 2006; Dowker 2005). https://en.wikipedia.org/wiki/Mental_calculationCited by: Day 16
- Compensation strategy in mental arithmetic (Benjamin & Shermer 2006, ch. 1; Dowker 2005); psychological pricing at 99-endings (Schindler & Kibarian, Journal of Retailing 1996). https://doi.org/10.1016/S0022-4359(96)90005-8Cited by: Day 9
- Compensation with a multiplier: n(P − ε) = nP − nε; 99-ending prices (Schindler & Kibarian 1996). https://doi.org/10.1016/S0022-4359(96)90005-8Cited by: Day 27
- Complement rule; the birthday problem (23 people, 50.7%). https://en.wikipedia.org/wiki/Birthday_problemCited by: Day 256
- Complementary counting; treating adjacent items as a block; subsets 2ⁿ. https://en.wikipedia.org/wiki/Combinatorial_principlesCited by: Day 265
- Complements and compensation; Benjamin & Shermer (2006), Secrets of Mental Math. https://en.wikipedia.org/wiki/Method_of_complementsCited by: Day 10
- Compound interest; (1+r)ⁿ. https://en.wikipedia.org/wiki/Compound_interestCited by: Day 281
- Compound unit rates (per person per day); the Home & Life edition's water week (150 L per person per day). https://en.wikipedia.org/wiki/Rate_(mathematics)Cited by: Day 137
- Construction estimating: perimeter, tile counts, paint coverage; the 3-4-5 rule; roof pitch as rise over run. https://en.wikipedia.org/wiki/Roof_pitchCited by: Day 300
- Conway's Doomsday rule (1973); Zeller's congruence (1882) for the drill's scoring. https://en.wikipedia.org/wiki/Doomsday_ruleCited by: Day 116
- Cooking weights and measures; egg sizes (large ≈ 50 g); flour ≈ 125 g per cup. https://en.wikipedia.org/wiki/Cooking_weights_and_measuresCited by: Day 321
- Cost per kilometre as a unit rate; the Home & Life edition's car week; AA of SA operating-cost tables. https://aa.co.za/Cited by: Day 135
- Countdown (Channel 4, 1982–) numbers round; Des Chiffres et des Lettres (1965–). https://en.wikipedia.org/wiki/Countdown_(game_show)#Numbers_roundCited by: Day 247
- Counting-up (complementary addition) as the cashier's method; Benjamin & Shermer (2006), Secrets of Mental Math, ch. 1: subtraction left to right and by complements. https://en.wikipedia.org/wiki/Subtraction#MethodsCited by: Week 3 start here
- Counting-up change-making (retail practice); SARB cash rounding to 5c since 2002. https://www.resbank.co.za/Cited by: Day 19
- Cricket statistics (run rate, strike rate, average, economy); league points systems (football 3-1-0; rugby 4-2-0 plus bonus points); Stableford scoring; single-elimination tournaments. https://en.wikipedia.org/wiki/Cricket_statisticsCited by: Week 45 start here
- Cricket statistics; net run rate. https://en.wikipedia.org/wiki/Cricket_statisticsCited by: Day 309
- Crowd density guidance: ~2 persons/m² comfortable standing, 4 packed, >5 hazardous (Fruin, Pedestrian Planning and Design, 1971; UK Green Guide). https://en.wikipedia.org/wiki/Crowd_densityCited by: Day 81
- Cyclicity of last digits of powers; possible last digits of squares (quadratic residues mod 10). https://en.wikipedia.org/wiki/Modular_arithmeticCited by: Day 215
- Cylinder volume πr²h; 1 cm³ = 1 ml; the Home & Life edition's water week. https://en.wikipedia.org/wiki/CylinderCited by: Day 180
- D. R. Kaprekar (1949); 6174 reached in at most 7 iterations; 495 for three digits. https://en.wikipedia.org/wiki/6174Cited by: Day 240
- Day counting and the fencepost (off-by-one) distinction; the Home & Life edition's days-between-dates day. https://en.wikipedia.org/wiki/Off-by-one_errorCited by: Day 113
- Decibel; 3 dB ≈ ×2 power; NIOSH 85 dBA exposure limit with 3-dB exchange rate. https://en.wikipedia.org/wiki/DecibelCited by: Day 304
- Decimal place value (Hindu–Arabic numeral system); rounding half up; significant figures. https://en.wikipedia.org/wiki/Positional_notationCited by: Week 9 start here
- Decimal place value; the place-value week of this edition. https://en.wikipedia.org/wiki/DecimalCited by: Day 149
- Decimal-hour timekeeping conventions in payroll (BCEA overtime calculated in hours and fractions). https://www.gov.za/documents/basic-conditions-employment-actCited by: Day 106
- Deliberate practice with feedback (Ericsson, Krampe & Tesch-Römer 1993); the year's weeks and their sources. https://doi.org/10.1037/0033-295X.100.3.363Cited by: Week 51 start here
- Densities: water 1.0, petrol ~0.75, dry sand ~1.5, concrete ~2.4 kg/L; cement 50 kg bags (SANS 50197); brick ~3 kg. https://www.engineeringtoolbox.com/density-materials-d_1652.htmlCited by: Day 80
- Dice probabilities; the Chevalier de Méré's bet (at least one six in four rolls, 51.8%). https://en.wikipedia.org/wiki/Problem_of_pointsCited by: Day 253
- Digit count of a product: ⌊log₁₀ a⌋ + ⌊log₁₀ b⌋ + 1 or + 2. https://en.wikipedia.org/wiki/Order_of_magnitudeCited by: Day 73
- Digital root and casting out nines: dr(n) = 1 + (n − 1) mod 9. https://en.wikipedia.org/wiki/Digital_rootCited by: Day 72
- Distributive law a(b + c) = ab + ac; Benjamin & Shermer (2006), ch. 2. https://en.wikipedia.org/wiki/Distributive_propertyCited by: Day 22
- Distributive law for division: (a + b) ÷ n = a ÷ n + b ÷ n; Benjamin & Shermer (2006), ch. 4. https://en.wikipedia.org/wiki/Mental_calculationCited by: Day 32
- Divisibility by 3 and 9 via digit sums (10 ≡ 1 mod 9). https://en.wikipedia.org/wiki/Divisibility_ruleCited by: Day 212
- Divisibility by 3 and the digit sum; repeating decimals of thirds and sixths. https://en.wikipedia.org/wiki/Repeating_decimalCited by: Day 51
- Divisibility by 4, 8, 25 via trailing digits; Gregorian leap-year rule. https://en.wikipedia.org/wiki/Divisibility_ruleCited by: Day 211
- Divisibility rules and casting out nines: 10 ≡ 1 (mod 9), 100 ≡ 0 (mod 4). https://en.wikipedia.org/wiki/Divisibility_ruleCited by: Day 31
- Divisibility rules; casting out nines; digital root. https://en.wikipedia.org/wiki/Divisibility_ruleCited by: Week 31 start here
- Divisibility rules; trial division up to √n. https://en.wikipedia.org/wiki/Divisibility_ruleCited by: Day 170
- Divisibility tests for 7, 11, 13; 1001 = 7 × 11 × 13. https://en.wikipedia.org/wiki/Divisibility_rule#Divisibility_by_7Cited by: Day 213
- Division as repeated subtraction of multiples (the 'chunking' method); Benjamin & Shermer (2006), ch. 4. https://en.wikipedia.org/wiki/Chunking_(division)Cited by: Day 33
- Division by a composite divisor as successive division by its factors; Benjamin & Shermer (2006), ch. 4. https://en.wikipedia.org/wiki/Mental_calculationCited by: Day 34
- Division by zero undefined; x⁰ = 1; parity of zero. https://en.wikipedia.org/wiki/Parity_of_zeroCited by: Day 195
- Doubling as a mental-arithmetic game; powers of two. https://en.wikipedia.org/wiki/Power_of_twoCited by: Day 248
- Doubling time in epidemiology; basic reproduction number R₀; world population growth ~2% (1960s). https://en.wikipedia.org/wiki/Basic_reproduction_numberCited by: Day 285
- Dozen, gross, great gross; baker's dozen (Assize of Bread and Ale, 13th c.). https://en.wikipedia.org/wiki/DozenCited by: Day 234
- e as lim (1+1/n)ⁿ (Bernoulli 1683); natural logarithm; rule of 70 from ln 2 = 0.693. https://en.wikipedia.org/wiki/E_(mathematical_constant)Cited by: Day 185
- EAN-8 and EAN-13 check digit (GS1); GS1 prefix 600–601 South Africa. https://www.gs1.org/services/how-calculate-check-digit-manuallyCited by: Day 219
- Elapsed time by counting up (complementary addition); 24-hour clock arithmetic. https://en.wikipedia.org/wiki/24-hour_clockCited by: Day 107
- Elapsed-time computation by counting up through round marks (elementary arithmetic practice); complement to 60. https://en.wikipedia.org/wiki/Mental_calculationCited by: Day 20
- Equal additions / constant-difference method for subtraction (Benjamin & Shermer 2006; Dowker 2005). https://en.wikipedia.org/wiki/Subtraction#MethodsCited by: Day 18
- Error detection of Luhn (misses 09↔90), EAN (misses transpositions differing by 5), ISBN-10 (catches all adjacent transpositions). https://en.wikipedia.org/wiki/Luhn_algorithm#WeaknessesCited by: Day 223
- Estimation of quotients by compatible numbers (elementary arithmetic practice); the dividing week. https://en.wikipedia.org/wiki/EstimationCited by: Day 65
- Exchange-rate arithmetic; SARB daily rates. Rates used are illustrative, not the day's. https://www.resbank.co.za/en/home/what-we-do/statistics/key-statistics/selected-historical-ratesCited by: Day 103
- Expected value (Huygens 1657; Pascal–Fermat); house edge; coupon collector's problem. https://en.wikipedia.org/wiki/Expected_valueCited by: Week 40 start here
- Exponential growth; 1.01³⁶⁵ ≈ 37.8; rule of 240 for tenfold (ln 10 / ln 2 × 72). https://en.wikipedia.org/wiki/Exponential_growthCited by: Day 283
- Extended warranties: Consumer Reports and Which? on expected value; loss aversion. https://en.wikipedia.org/wiki/Extended_warrantyCited by: Day 276
- Fermi estimation in powers of ten; the Home & Life edition's estimation week. https://en.wikipedia.org/wiki/Fermi_problemCited by: Day 160
- Fermi estimation with several factors; error cancellation in products of rounded factors. https://en.wikipedia.org/wiki/Fermi_problemCited by: Day 68
- Fermi estimation; Weinstein & Adam (2008), Guesstimation, Princeton: one figure per factor and the geometric mean of bounds. https://press.princeton.edu/books/paperback/9780691129495/guesstimationCited by: Week 10 start here
- Fibonacci, Liber Abaci (1202); sum identity ΣF = F(n+2) − 1; phyllotaxis counts. https://en.wikipedia.org/wiki/Fibonacci_sequenceCited by: Day 200
- Figurate numbers; Gauss and 1 to 100 (Hayes, 'Gauss's Day of Reckoning', American Scientist 2006); Moser's circle problem. https://en.wikipedia.org/wiki/Triangular_numberCited by: Week 29 start here
- Finger binary; 2¹⁰ − 1 = 1,023. https://en.wikipedia.org/wiki/Finger_binaryCited by: Day 226
- Fortnight; stone (14 lb); ream (500 sheets); hand (4 in); brace. https://en.wikipedia.org/wiki/Stone_(unit)Cited by: Day 236
- Fractions with power-of-two denominators by repeated halving. https://en.wikipedia.org/wiki/FractionCited by: Day 50
- Fraction–decimal–percent equivalents; Benjamin & Shermer (2006), Secrets of Mental Math, ch. 5. https://en.wikipedia.org/wiki/FractionCited by: Week 8 start here
- Fraction–percent equivalents; the Home & Life edition's percent-of-what day. https://en.wikipedia.org/wiki/PercentageCited by: Day 75
- Frederick (2005), Cognitive Reflection Test (bat and ball); the snail-in-the-well puzzle. https://doi.org/10.1257/089533005775196732Cited by: Day 242
- Fuel consumption in L/100 km; AA South Africa running-cost guidance; SANRAL toll tariffs; tyre pressure units (bar, kPa, psi). https://en.wikipedia.org/wiki/Fuel_economy_in_automobilesCited by: Week 47 start here
- Fuel consumption in L/100 km; the Home & Life edition's car week. https://en.wikipedia.org/wiki/Fuel_economy_in_automobilesCited by: Day 131
- Fuel range calculation; typical reserve 5–10 L. https://en.wikipedia.org/wiki/Fuel_gaugeCited by: Day 324
- Fundamental theorem of arithmetic; divisor function d(n) = ∏(aᵢ + 1). https://en.wikipedia.org/wiki/Divisor_functionCited by: Day 171
- Galileo's paradox (1638); Cantor, countable sets; the zigzag enumeration of the rationals. https://en.wikipedia.org/wiki/Countable_setCited by: Day 290
- Geometric distribution mean 1/p; coupon collector's problem n·Hₙ. https://en.wikipedia.org/wiki/Coupon_collector%27s_problemCited by: Day 278
- Geometric mean as the estimator for log-uniform uncertainty; Weinstein & Adam (2008), Guesstimation; the Home & Life edition's estimation week. https://en.wikipedia.org/wiki/Geometric_meanCited by: Day 67
- Geometric series: a/(1−r) for |r|<1; 2ⁿ − 1 for doublings. https://en.wikipedia.org/wiki/Geometric_seriesCited by: Day 206
- Golden ratio φ = (1+√5)/2; Fibonacci sequence; phyllotaxis and the golden angle (Vogel 1979). https://en.wikipedia.org/wiki/Golden_ratioCited by: Day 184
- Googol (Kasner & Sirotta, 1920/1940); Hilbert's hotel (1924); Cantor's diagonal argument (1891). https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_HotelCited by: Week 42 start here
- Googol and googolplex; ~10⁸⁰ atoms in the observable universe; Graham's number. https://en.wikipedia.org/wiki/GoogolCited by: Day 288
- Gregorian calendar rules (leap years: divisible by 4, except centuries not divisible by 400); Conway's Doomsday rule (1973). https://en.wikipedia.org/wiki/Doomsday_ruleCited by: Week 17 start here
- Gregorian leap-year rule (1582); tropical year 365.2422 days. https://en.wikipedia.org/wiki/Leap_yearCited by: Day 115
- Half-life; caffeine half-life ~5 h (adults); the Home & Life edition's radiation week. https://en.wikipedia.org/wiki/Half-lifeCited by: Day 165
- Harmonic mean of speeds over equal distances: v = 2v₁v₂/(v₁ + v₂). https://en.wikipedia.org/wiki/Harmonic_meanCited by: Day 96
- Hayes, 'Gauss's Day of Reckoning', American Scientist 94(3), 2006; arithmetic series. https://doi.org/10.1511/2006.59.200Cited by: Day 199
- Heart rate and lifespan scaling (~1–1.5 billion beats per mammal lifetime; Levine 1997). https://doi.org/10.1016/S0735-1097(97)00246-5Cited by: Day 341
- Hexadecimal; web colours as three hex bytes. https://en.wikipedia.org/wiki/HexadecimalCited by: Day 227
- Hilbert's paradox of the Grand Hotel (1924); Gamow, One Two Three… Infinity (1947). https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_HotelCited by: Day 289
- History of negative numbers (Brahmagupta 628; Maseres 1758 'absurd'); Seife, Zero: The Biography of a Dangerous Idea (2000). https://en.wikipedia.org/wiki/Negative_number#HistoryCited by: Day 190
- Honeycomb conjecture (Hales 1999); centred hexagonal numbers; hexagon area (3√3/2) s². https://en.wikipedia.org/wiki/Honeycomb_conjectureCited by: Day 338
- House edge (roulette single-zero 2.7%, double-zero 5.3%); expected value of bets. https://en.wikipedia.org/wiki/House_edgeCited by: Day 274
- Huff (1954), How to Lie with Statistics, ch. 2; skewed distributions and the mean–median gap; the Home & Life edition's news week. https://en.wikipedia.org/wiki/SkewnessCited by: Day 97
- Human hair diameter ~50–100 µm; office paper ~0.1 mm; paint dry film ~50 µm per coat; red blood cell ~8 µm. https://en.wikipedia.org/wiki/Hair#DescriptionCited by: Day 153
- Ifrah, The Universal History of Numbers (1998); Brahmagupta 628; al-Khwarizmi c. 825; Fibonacci 1202; Stevin 1585; HP-35 1972. https://en.wikipedia.org/wiki/History_of_the_Hindu%E2%80%93Arabic_numeral_systemCited by: Week 50 start here
- Incremental (running) mean: μₙ₊₁ = μₙ + (xₙ₊₁ − μₙ)/(n+1). https://en.wikipedia.org/wiki/Moving_averageCited by: Day 93
- Independence; the Sally Clark case (1 in 73 million by squaring, Royal Statistical Society statement 2001); Gilovich, Vallone & Tversky (1985) on the hot hand. https://en.wikipedia.org/wiki/Sally_ClarkCited by: Day 258
- Independent verification by recomputation; Benjamin & Shermer (2006), Secrets of Mental Math. https://en.wikipedia.org/wiki/Mental_calculationCited by: Day 76
- Inspection paradox; the friendship paradox (Feld 1991); waiting-time paradox. https://en.wikipedia.org/wiki/Friendship_paradoxCited by: Day 272
- Insurance loading; expected utility (Bernoulli 1738); the Home & Life edition's insurance week. https://en.wikipedia.org/wiki/Expected_utility_hypothesisCited by: Day 277
- IPv4 (32-bit) exhaustion; the year 2038 problem; binary addition. https://en.wikipedia.org/wiki/Year_2038_problemCited by: Day 230
- Irrationality of √2 (Euclid, Elements X); repeating decimals; transcendence of e (Hermite 1873) and π (Lindemann 1882). https://en.wikipedia.org/wiki/Square_root_of_2Cited by: Day 187
- ISBN-10 check digit (mod 11) and the 2007 move to ISBN-13. https://en.wikipedia.org/wiki/ISBN#Check_digitsCited by: Day 222
- Ishango bone (c. 20,000 BP); Roman numerals; tally marks; South African decimalisation 14 Feb 1961 (R2 = £1). https://en.wikipedia.org/wiki/Roman_numeralsCited by: Week 34 start here
- Ishango bone (c. 20,000 BP); Schmandt-Besserat, Before Writing (1992) on clay tokens; Sumerian sexagesimal. https://en.wikipedia.org/wiki/Ishango_boneCited by: Day 344
- ISO 216 paper (√2 aspect ratio); Pythagorean theorem; Plato's Meno (doubling the square). https://en.wikipedia.org/wiki/ISO_216Cited by: Day 183
- Just intonation; Pythagorean comma (1.0136); equal temperament. https://en.wikipedia.org/wiki/Pythagorean_commaCited by: Day 333
- Kelvin scale: 0 K = −273.15°C; the Home & Life edition's weather week. https://en.wikipedia.org/wiki/KelvinCited by: Day 191
- Kinematics: d = vt; km/h ÷ 3.6 = m/s; the two-second rule (Arrive Alive, SA road safety guidance). https://www.arrivealive.co.za/Cited by: Week 19 start here
- L/100 km = 100 / (km/L); mpg (US) to L/100 km = 235.2 / mpg; the Home & Life edition's car week. https://en.wikipedia.org/wiki/Fuel_economy_in_automobilesCited by: Day 125
- Last-digit patterns of perfect squares (quadratic residues mod 10); Benjamin & Shermer (2006), ch. 3. https://en.wikipedia.org/wiki/Square_root#ComputationCited by: Day 40
- Laws of exponents: 10ᵃ × 10ᵇ = 10ᵃ⁺ᵇ. https://en.wikipedia.org/wiki/ExponentiationCited by: Day 155
- Lazy caterer's sequence n(n+1)/2 + 1; painted cube problem. https://en.wikipedia.org/wiki/Lazy_caterer%27s_sequenceCited by: Day 243
- Limits; e as lim (1+1/n)ⁿ; the lemniscate (Wallis 1655); hyperfocal distance in photography. https://en.wikipedia.org/wiki/Limit_of_a_sequenceCited by: Day 293
- Lincoln–Petersen mark-recapture; dendrochronology; similar triangles for height. https://en.wikipedia.org/wiki/Mark_and_recaptureCited by: Day 342
- Linear approximation √(s² + e) ≈ s + e/(2s) (first-order Taylor / Newton step). https://en.wikipedia.org/wiki/Methods_of_computing_square_rootsCited by: Day 41
- Lo Shu square; Dürer's magic square (1514); magic constant M = n(n² + 1)/2. https://en.wikipedia.org/wiki/Magic_squareCited by: Day 239
- Lo Shu square; Dürer, Melencolia I (1514); Kaprekar's routine (1949); the missing dollar riddle. https://en.wikipedia.org/wiki/Magic_squareCited by: Week 35 start here
- Logarithmic scale charts; semi-log plots for exponential growth. https://en.wikipedia.org/wiki/Semi-log_plotCited by: Day 307
- Logarithms (Napier 1614; Briggs 1617); decibel; moment magnitude; pH; apparent magnitude. https://en.wikipedia.org/wiki/LogarithmCited by: Week 44 start here
- Logistic growth (Verhulst 1838); the lily-pad riddle; Meadows et al., The Limits to Growth (1972). https://en.wikipedia.org/wiki/Logistic_functionCited by: Day 286
- Long and short scales; digit counts of powers of ten. https://en.wikipedia.org/wiki/Long_and_short_scalesCited by: Day 141
- Long and short scales; lakh and crore (Indian numbering); 'zero' and 'cipher' from sifr. https://en.wikipedia.org/wiki/Long_and_short_scalesCited by: Day 349
- Luhn algorithm (Hans Peter Luhn, IBM, patent filed 1954). https://en.wikipedia.org/wiki/Luhn_algorithmCited by: Day 220
- Markowsky, 'Misconceptions about the golden ratio', College Mathematics Journal 23(1), 1992; f-number sequence (√2 steps); nautilus spiral ratio ≈ 1.33. https://doi.org/10.1080/07468342.1992.11973428Cited by: Day 186
- Mean Gregorian month 30.436875 days = 4.348 weeks; 52.18 weeks a year. https://en.wikipedia.org/wiki/MonthCited by: Day 118
- Mean, median, mode; the assumed-mean method for computing a mean. Huff, D. (1954), How to Lie with Statistics, ch. 2 (the well-chosen average). https://en.wikipedia.org/wiki/AverageCited by: Week 14 start here
- Median and mode; robustness to outliers. Huff (1954), How to Lie with Statistics. https://en.wikipedia.org/wiki/MedianCited by: Day 94
- Mersenne primes; M136279841 (GIMPS, Luke Durant, October 2024); Goldbach's conjecture verified to 4 × 10¹⁸. https://www.mersenne.org/primes/Cited by: Day 173
- Method of complements (nines' complement + 1); Benjamin & Shermer (2006), ch. 1. https://en.wikipedia.org/wiki/Method_of_complementsCited by: Day 15
- Mixed-radix addition (hours and minutes); carrying at 60. https://en.wikipedia.org/wiki/Mixed_radixCited by: Day 108
- Modular arithmetic mod 7 for weekdays. https://en.wikipedia.org/wiki/Modular_arithmeticCited by: Day 114
- Moment magnitude scale; energy ∝ 10^(1.5 M) (≈31.6 per unit); Valdivia 1960 M 9.5. https://en.wikipedia.org/wiki/Moment_magnitude_scaleCited by: Day 305
- Monty Hall problem (vos Savant 1990); birthday problem; base-rate neglect (Kahneman & Tversky); Simpson's paradox (Berkeley 1973, Bickel et al. 1975); inspection paradox. https://en.wikipedia.org/wiki/Monty_Hall_problemCited by: Week 39 start here
- Monty Hall problem; vos Savant, Parade (1990); Selvin (1975). https://en.wikipedia.org/wiki/Monty_Hall_problemCited by: Day 267
- Moser's circle problem (regions = C(n,4) + C(n,2) + 1); Euler's prime-generating polynomial n² + n + 41; 333333331 = 17 × 19607843. https://en.wikipedia.org/wiki/Dividing_a_circle_into_areasCited by: Day 202
- Napier, Mirifici Logarithmorum Canonis Descriptio (1614); the slide rule (Oughtred 1622). https://en.wikipedia.org/wiki/Slide_ruleCited by: Day 303
- National Credit Act 34 of 2005: disclosure of total cost of credit; the Home & Life edition's interest week. https://www.ncr.org.za/Cited by: Day 102
- National Lottery (SA) prize payout ≈ 50% of sales (Ithuba annual reports); raffle arithmetic. https://en.wikipedia.org/wiki/LotteryCited by: Day 275
- Net worth = assets − liabilities; Brahmagupta's fortunes and debts. https://en.wikipedia.org/wiki/Net_worthCited by: Day 192
- Number-plate games; digit ordering; Kaprekar's routine. https://en.wikipedia.org/wiki/6174Cited by: Day 249
- Octave = 2:1; A440 standard (ISO 16, 1975); range of hearing 20 Hz–20 kHz. https://en.wikipedia.org/wiki/OctaveCited by: Day 332
- Odds vs probability; SA Lotto 6/52 (C(52,6) = 20,358,520); PowerBall 1 in 42,375,200. https://en.wikipedia.org/wiki/Lottery_mathematicsCited by: Day 257
- Off-by-one (fence-post) error; counting terms of an arithmetic progression. https://en.wikipedia.org/wiki/Off-by-one_errorCited by: Day 209
- Order of magnitude as a factor of ten. https://en.wikipedia.org/wiki/Order_of_magnitudeCited by: Day 158
- Order-of-magnitude estimation by rounding to one significant figure; the Home & Life edition's estimation week (Fermi). https://en.wikipedia.org/wiki/Order_of_magnitudeCited by: Day 61
- Order-of-magnitude products; Weinstein & Adam (2008), Guesstimation. https://press.princeton.edu/books/paperback/9780691129495/guesstimationCited by: Day 66
- Oven temperature equivalents (gas mark, °C, °F, fan); roasting times; safe internal temperatures (USDA). https://en.wikipedia.org/wiki/Gas_markCited by: Day 318
- Pace and speed; marathon 42.195 km; Comrades Marathon ~89 km. https://en.wikipedia.org/wiki/MarathonCited by: Day 312
- Pace–speed reciprocity: km/h = 60 / (min/km); the Home & Life edition's sport week. https://en.wikipedia.org/wiki/Pace_(speed)Cited by: Day 110
- Pacing as a surveying method (pace count calibrated over a known distance); car length and rugby field references as in the primer. https://en.wikipedia.org/wiki/Pacing_(surveying)Cited by: Day 78
- Paper folding: 42 folds of 0.1 mm exceed the Earth–Moon distance; Britney Gallivan's 12-fold record (2002). https://en.wikipedia.org/wiki/Mathematics_of_paper_foldingCited by: Day 164
- Parity arguments; the mutilated chessboard (Gamow & Stern 1958); the handshaking lemma. https://en.wikipedia.org/wiki/Parity_(mathematics)Cited by: Day 216
- Parity rules for sums and products. https://en.wikipedia.org/wiki/Parity_(mathematics)Cited by: Day 74
- Part-to-part and part-to-whole ratios; two-stroke fuel mixes 50:1 = 20 mL/L; concrete mix 1:3:6 by volume for general use (Cement & Concrete SA guidance). https://cemcon-sa.org.za/Cited by: Day 86
- Pascaline (1642); Leibniz stepped reckoner (1673); Analytical Engine (1837); ENIAC (1945); HP-35 (1972); Moore (1965). https://en.wikipedia.org/wiki/HP-35Cited by: Day 348
- Password entropy; NIST SP 800-63B on length over complexity. https://en.wikipedia.org/wiki/Password_strengthCited by: Day 264
- Per-capita arithmetic; National Treasury Budget Review 2025 (consolidated spending ~R2.4 trillion); Stats SA population ~62 million. https://www.treasury.gov.za/Cited by: Day 142
- Per-capita estimation; the Home & Life edition's per capita day. https://en.wikipedia.org/wiki/Per_capitaCited by: Day 69
- Percent change = (new − old)/old; successive percentage changes compound: (1 + p)(1 − p) = 1 − p². https://en.wikipedia.org/wiki/Relative_changeCited by: Day 47
- Percent equivalents of unit fractions. https://en.wikipedia.org/wiki/PercentageCited by: Day 52
- Periodical cicadas (Magicicada, 13- and 17-year broods); hunting-tooth gear design; least common multiple. https://en.wikipedia.org/wiki/Periodical_cicadasCited by: Day 174
- Permutations and factorials; 52! ≈ 8 × 10⁶⁷. https://en.wikipedia.org/wiki/FactorialCited by: Day 261
- Permutations vs combinations; P(n,k) = k!·C(n,k). https://en.wikipedia.org/wiki/PermutationCited by: Day 263
- pH (Sørensen 1909); apparent magnitude (Pogson 1856, 5 magnitudes = 100×); Weber–Fechner law. https://en.wikipedia.org/wiki/Apparent_magnitudeCited by: Day 306
- Phyllotaxis and the golden angle (Vogel 1979); honeycomb conjecture (Hales 2001); Kleiber's law (1932); ~1 billion heartbeats per mammalian lifetime. https://en.wikipedia.org/wiki/Kleiber%27s_lawCited by: Week 49 start here
- Pi irrational (Lambert 1768), transcendental (Lindemann 1882); Pi Day 14 March; π² ≈ 9.87 and the seconds pendulum. https://en.wikipedia.org/wiki/Pi_DayCited by: Day 181
- Pi: irrational (Lambert 1768); 100 trillion digits (Google, 2022); 39 digits suffice for the observable universe to atomic precision (NASA/JPL). https://en.wikipedia.org/wiki/PiCited by: Week 26 start here
- Piano range (A0–C8, 88 keys); harmonic series; cents (Ellis 1885). https://en.wikipedia.org/wiki/Cent_(music)Cited by: Day 335
- Piphilology (mnemonic sentences); 355/113 (Zu Chongzhi, 5th c.); recitation record 70,000 digits (Rajveer Meena, 2015). https://en.wikipedia.org/wiki/PiphilologyCited by: Day 177
- Polyrhythm and least common multiples; tuplets; swing ratio. https://en.wikipedia.org/wiki/PolyrhythmCited by: Day 334
- Portion sizes (British Nutrition Foundation); cooking yield and shrinkage (~25% for roasts). https://en.wikipedia.org/wiki/Serving_sizeCited by: Day 317
- Positional notation and multiplication by powers of ten; SI prefixes. https://www.bipm.org/en/measurement-units/si-prefixesCited by: Day 60
- Positional notation; binary and hexadecimal; Babylonian sexagesimal. https://en.wikipedia.org/wiki/Positional_notationCited by: Week 33 start here
- Powers of two; 2^10 = 1,024 (2.4% over a thousand). https://en.wikipedia.org/wiki/Power_of_twoCited by: Day 162
- Powers of two; 2¹⁰ = 1,024 ≈ 10³; the rule of 72 (the Home & Life edition's interest week). https://en.wikipedia.org/wiki/Power_of_twoCited by: Day 143
- Powers of two; the wheat-and-chessboard problem; paper-folding to the moon (42 folds). https://en.wikipedia.org/wiki/Power_of_twoCited by: Week 24 start here
- ppm as mg/kg, and mg/L for water; atmospheric CO₂ ~420 ppm (NOAA). https://gml.noaa.gov/ccgg/trends/Cited by: Day 151
- Prime number; primes of the form 6k ± 1; 25 primes below 100. https://en.wikipedia.org/wiki/Prime_numberCited by: Day 169
- Prime numbers; Euclid's theorem; largest known prime 2^136,279,841 − 1 (GIMPS, October 2024, 41,024,320 digits). https://www.mersenne.org/primes/Cited by: Week 25 start here
- Proportional reasoning and scale factors; the Home & Life edition's kitchen week (doubling a recipe) and shapes week (the square–cube law). https://en.wikipedia.org/wiki/RatioCited by: Week 13 start here
- Prospect theory (Kahneman & Tversky 1979); expected utility; ruin and the Kelly criterion. https://doi.org/10.2307/1914185Cited by: Day 279
- Pythagorean triples; the 3-4-5 rule in construction; Plimpton 322 (c. 1800 BC). https://en.wikipedia.org/wiki/Pythagorean_tripleCited by: Day 296
- Radix; numeral systems in world languages (vigesimal, body-count systems). https://en.wikipedia.org/wiki/RadixCited by: Day 229
- Rates as ratios to a unit; unit conversion of rates; harmonic combination of rates. https://en.wikipedia.org/wiki/Rate_(mathematics)Cited by: Week 20 start here
- Ratio comparison across scale names; the Home & Life edition's news week ('compared with what'). https://en.wikipedia.org/wiki/Order_of_magnitudeCited by: Day 145
- Ratios as parts of a whole; sharing in a given ratio. https://en.wikipedia.org/wiki/RatioCited by: Day 88
- Reaction time ~1.5 s (AASHTO uses 2.5 s for design); braking distance ∝ v² (kinetic energy); the Home & Life edition's braking day. https://en.wikipedia.org/wiki/Braking_distanceCited by: Day 130
- Recipe scaling; conversion factor = desired yield / original yield (Culinary Institute of America). https://en.wikipedia.org/wiki/RecipeCited by: Day 316
- Repeated halving as division by powers of two; Benjamin & Shermer (2006), ch. 4. https://en.wikipedia.org/wiki/Division_by_twoCited by: Day 29
- Repeating decimals as geometric series; 0.999… = 1; bouncing-ball total distance h(1+r)/(1−r); harmonic series divergence. https://en.wikipedia.org/wiki/0.999...Cited by: Day 208
- Representative fraction map scales; South African 1:50 000 topographic series (Chief Directorate: National Geo-spatial Information). https://ngi.dalrrd.gov.za/Cited by: Day 87
- Restaurant tipping conventions in South Africa (10–15%); percentages week of this edition. https://en.wikipedia.org/wiki/GratuityCited by: Day 100
- Rhind Mathematical Papyrus (c. 1550 BC); Egyptian fractions; ancient Egyptian multiplication. https://en.wikipedia.org/wiki/Ancient_Egyptian_multiplicationCited by: Day 345
- Richter/moment magnitude (10× amplitude per unit); pH = −log₁₀[H⁺]; decibel (10 dB = 10× power). The Home & Life edition's earthquake, chemistry and sound weeks. https://en.wikipedia.org/wiki/Logarithmic_scaleCited by: Day 159
- Roman numerals; Roman abacus and counting boards. https://en.wikipedia.org/wiki/Roman_numeralsCited by: Day 233
- Rounding half up; the error of successive rounding (double rounding). https://en.wikipedia.org/wiki/Rounding#Double_roundingCited by: Day 57
- Rounding-up running totals as a shopper's estimation strategy; 99-ending prices (Schindler & Kibarian 1996). https://doi.org/10.1016/S0022-4359(96)90005-8Cited by: Day 13
- RSA (Rivest, Shamir, Adleman 1977); RSA-250 factored February 2020 (~2,700 core-years); 2048-bit keys ≈ 617 digits. https://en.wikipedia.org/wiki/RSA_cryptosystemCited by: Day 172
- Ruhlman, Ratio (2009); rice absorption method 1:2; vinaigrette 3:1. https://en.wikipedia.org/wiki/VinaigretteCited by: Day 320
- Rule of 72 (Pacioli 1494; ln 2 = 0.693); compound interest; logistic growth. https://en.wikipedia.org/wiki/Rule_of_72Cited by: Week 41 start here
- Rule of 72 and its accuracy; rule of 70/69.3. https://en.wikipedia.org/wiki/Rule_of_72Cited by: Day 282
- Rule of product; permutations and combinations; password entropy. https://en.wikipedia.org/wiki/Rule_of_productCited by: Week 38 start here
- Rule of product; permutations without repetition 10!/(10−n)!. https://en.wikipedia.org/wiki/Rule_of_productCited by: Day 260
- Rule of thirds vs golden section; f-stops; diagonal = side × √2. https://en.wikipedia.org/wiki/Rule_of_thirdsCited by: Day 188
- Rules of signs; the number-line model (walking and facing). https://en.wikipedia.org/wiki/Negative_number#Arithmetic_involving_negative_numbersCited by: Day 193
- Running-total estimation as a shopper's check; rounding to the nearest unit before summing (the adding week). https://en.wikipedia.org/wiki/EstimationCited by: Day 64
- SA metric cup 250 mL, tablespoon 15 mL, teaspoon 5 mL (SANS 10012); UK gallon 4.546 L, US gallon 3.785 L. https://en.wikipedia.org/wiki/Cup_(unit)Cited by: Day 124
- SANRAL toll tariffs (N1, N3); trip cost = distance × rate + tolls. https://www.sanral.co.za/Cited by: Day 325
- SARB inflation target 3–6%; Fisher equation (real ≈ nominal − inflation). https://www.resbank.co.za/en/home/what-we-do/monetary-policyCited by: Day 284
- SARB: 1c and 2c coins withdrawn 2002; cash rounding to 5c (Consumer Protection Act price guidance). https://www.resbank.co.za/Cited by: Day 58
- Scale factors in recipes (McGee, On Food and Cooking, 2004, on why cooking time does not scale linearly); the Home & Life edition's kitchen week. https://en.wikipedia.org/wiki/RatioCited by: Day 85
- Scientific notation (normalised form). https://en.wikipedia.org/wiki/Scientific_notationCited by: Day 156
- Scientific notation; SI prefixes (BIPM); logarithmic scales (Richter, pH, decibel). https://www.bipm.org/en/measurement-units/si-prefixesCited by: Week 23 start here
- Service intervals; tyre life (typically 40,000–60,000 km); depreciation (15–20% in year one). https://en.wikipedia.org/wiki/Car_costsCited by: Day 328
- Sexagesimal (Babylonian origin); French Republican decimal time (1793–1795). https://en.wikipedia.org/wiki/SexagesimalCited by: Day 228
- Sexagesimal division of the hour (Babylonian origin); 60 as a highly composite number. https://en.wikipedia.org/wiki/SexagesimalCited by: Day 54
- Sexagesimal time; decimal hours in timesheets; South African Standard Time UTC+2 with no daylight saving. https://en.wikipedia.org/wiki/South_African_Standard_TimeCited by: Week 16 start here
- Short scale (billion = 10⁹) in South African and British usage; Stats SA mid-year population estimate ~62 million (2022–2024). https://www.statssa.gov.za/Cited by: Week 21 start here
- Short scale (billion = 10⁹) now standard in South African and British usage; SI decimal comma in SA official documents (SANS 10001). https://en.wikipedia.org/wiki/Long_and_short_scalesCited by: Day 62
- SI prefixes (BIPM); decimal prefixes in data storage (1 GB = 1,000 MB by the SI convention). https://www.bipm.org/en/measurement-units/si-prefixesCited by: Day 157
- SI prefixes milli (10⁻³), micro (10⁻⁶), nano (10⁻⁹); ppm = mg/kg; basis point = 0.01%. https://www.bipm.org/en/measurement-units/si-prefixesCited by: Week 22 start here
- SI: 1 mg = 1,000 µg; medication error literature on µg/mg confusion (ISMP); the Home & Life edition's medicine week. https://www.ismp.org/Cited by: Day 148
- Sign rules by the distributive pattern; Brahmagupta's rules for debts and fortunes (628). https://en.wikipedia.org/wiki/Negative_number#MultiplicationCited by: Day 194
- Significant figures and measurement precision (NIST Guide to the SI, §7); the Home & Life edition's estimation week. https://www.nist.gov/pml/special-publication-811Cited by: Day 59
- Simple interest I = P·r·t; monthly interest as a twelfth of the annual; the Home & Life edition's interest week. https://en.wikipedia.org/wiki/InterestCited by: Day 101
- Simpson's paradox; Charig et al. (1986) kidney stones; Bickel, Hammel & O'Connell (1975), Berkeley admissions. https://en.wikipedia.org/wiki/Simpson%27s_paradoxCited by: Day 270
- Single-elimination tournaments (n − 1 matches); byes; seeding. https://en.wikipedia.org/wiki/Single-elimination_tournamentCited by: Day 313
- Small-probability arithmetic; additivity for rare independent events; the Home & Life edition's risk week. https://en.wikipedia.org/wiki/ProbabilityCited by: Day 152
- Soroban (1:4 beads) and suanpan (2:5); the 1946 Tokyo contest (Kiyoshi Matsuzaki vs Thomas Wood). https://en.wikipedia.org/wiki/SorobanCited by: Day 235
- South African ID number structure (Department of Home Affairs); Luhn check digit. https://en.wikipedia.org/wiki/South_African_identity_cardCited by: Day 221
- South African Reserve Bank: 1c and 2c coins withdrawn 2002, cash totals rounded to 5c; Consumer Protection Act price display rules. Left-to-right addition per Benjamin & Shermer (2006). https://www.resbank.co.za/Cited by: Day 11
- South African VAT 15% (VAT Act 89 of 1991, rate since April 2018); VAT fraction 15/115 = 3/23. https://www.sars.gov.za/types-of-tax/value-added-tax/Cited by: Day 46
- Speed of light 299,792 km/s; Earth–Moon mean distance 384,400 km; Earth–Sun 149.6 million km. https://en.wikipedia.org/wiki/Speed_of_lightCited by: Day 146
- Square–cube law (Galileo 1638); Kleiber's law (1932), metabolic rate ∝ M^0.75; West, Brown & Enquist (1997). https://en.wikipedia.org/wiki/Kleiber%27s_lawCited by: Day 340
- Square–cube law (Galileo 1638); the Home & Life edition's shapes week. https://en.wikipedia.org/wiki/Square%E2%80%93cube_lawCited by: Day 89
- Stableford scoring (1932); World Handicap System (2020): best 8 of 20. https://en.wikipedia.org/wiki/StablefordCited by: Day 311
- Standard 160-hour working month; the money week's price of an hour. https://www.gov.za/documents/basic-conditions-employment-actCited by: Day 134
- Standard brick 222 × 106 × 73 mm with 10 mm joints (SANS 227; ~50 bricks/m² single skin); typical storey height 3 m (SANS 10400-C). https://www.sabs.co.za/Cited by: Day 79
- Standard monthly hours 160–173 (40–45 h week, BCEA); opportunity cost of time; the Home & Life edition's Day 358. https://www.gov.za/documents/basic-conditions-employment-actCited by: Day 104
- Stevin, De Thiende (1585); the decimal point (Clavius 1593, Napier 1614); metric system (1795). https://en.wikipedia.org/wiki/Simon_StevinCited by: Day 347
- Sum of cubes = (n(n+1)/2)²; square pyramidal numbers; 204 squares on a chessboard. https://en.wikipedia.org/wiki/Square_pyramidal_numberCited by: Day 201
- Sum of odd numbers = n²; (n+1)² = n² + 2n + 1. https://en.wikipedia.org/wiki/Square_numberCited by: Day 198
- Sum of the first n odd numbers is n²; Benjamin & Shermer (2006), ch. 3. https://en.wikipedia.org/wiki/Square_numberCited by: Day 36
- Sums of multiples via the triangular numbers; sum of first n odd numbers = n². https://en.wikipedia.org/wiki/Triangular_numberCited by: Day 205
- Symmetry in biology (bilateral vs radial); snowflake six-fold symmetry; dihedral groups. https://en.wikipedia.org/wiki/Symmetry_in_biologyCited by: Day 339
- t = d/v; minutes per km = 60/v. https://en.wikipedia.org/wiki/SpeedCited by: Day 127
- Tally marks and tally sticks; vigesimal counting (French, Danish, Maya). https://en.wikipedia.org/wiki/Tally_marksCited by: Day 232
- Tempo and time signatures; A440 (ISO 16); just intonation ratios; equal temperament 2^(1/12); polyrhythms. https://en.wikipedia.org/wiki/Equal_temperamentCited by: Week 48 start here
- Tempo markings and BPM; Maelzel's metronome (1815); running cadence ~180 spm. https://en.wikipedia.org/wiki/TempoCited by: Day 330
- The 24 Game (Robert Sun, 1988); Countdown numbers round; Ericsson et al. (1993) on deliberate practice. https://en.wikipedia.org/wiki/24_(puzzle)Cited by: Week 36 start here
- The adding, subtracting and dividing weeks of this edition; SARB cash rounding. https://www.resbank.co.za/Cited by: Day 99
- The adding, subtracting, multiplying and percentages weeks of this edition; SARB cash rounding to 5c. https://www.resbank.co.za/Cited by: Week 15 start here
- The missing dollar riddle (R. M. Abraham, Diversions and Pastimes, 1933). https://en.wikipedia.org/wiki/Missing_dollar_riddleCited by: Day 241
- The week's six days and their sources; deliberate practice with feedback (Ericsson et al. 1993). https://doi.org/10.1037/0033-295X.100.3.363Cited by: Day 21, Day 28, Day 35, Day 42, Day 49, Day 56, Day 63, Day 70, Day 77, Day 84, Day 91, Day 98, Day 105, Day 112, Day 119, Day 126, Day 133, Day 140, Day 147, Day 154, Day 161, Day 168, Day 175, Day 182, Day 189, Day 196, Day 203, Day 210, Day 217, Day 224, Day 231, Day 238, Day 245, Day 252, Day 259, Day 266, Day 273, Day 280, Day 287, Day 294, Day 301, Day 308, Day 315, Day 322, Day 329, Day 336, Day 343, Day 350, Day 357
- The week's six days and their sources; deliberate practice with immediate feedback (Ericsson et al. 1993, Psychological Review 100). https://doi.org/10.1037/0033-295X.100.3.363Cited by: Day 14
- The week's six days and their sources; on timed practice with feedback: Ericsson, K.A. et al. (1993), 'The role of deliberate practice in the acquisition of expert performance', Psychological Review 100. https://doi.org/10.1037/0033-295X.100.3.363Cited by: Day 7
- The year's own 51 weeks and their sources; deliberate practice with feedback (Ericsson, Krampe & Tesch-Römer 1993). https://doi.org/10.1037/0033-295X.100.3.363Cited by: Week 52 start here, Day 358, Day 359, Day 360, Day 361, Day 362, Day 363, Day 364, Day 365
- Three points for a win (FIFA); rugby union bonus point system; goal difference as tiebreaker. https://en.wikipedia.org/wiki/Bonus_points_(rugby_union)Cited by: Day 310
- Time saved vs speed (the time-saving bias, Svenson 2008); fuel consumption vs speed (drag ∝ v²). https://doi.org/10.1016/j.aap.2008.03.018Cited by: Day 326
- Time signature; note values; dotted notes and ties. https://en.wikipedia.org/wiki/Time_signatureCited by: Day 331
- Time unit conversions: 1,440 min/day, 86,400 s/day, 8,760 h/year, 525,600 min/year. https://en.wikipedia.org/wiki/Unit_of_timeCited by: Day 139
- Triangular numbers; handshake problem = C(n,2). https://en.wikipedia.org/wiki/Triangular_numberCited by: Day 197
- Two envelopes problem; St Petersburg paradox (D. Bernoulli 1738). https://en.wikipedia.org/wiki/St._Petersburg_paradoxCited by: Day 271
- Two-second rule (Arrive Alive; UK Highway Code rule 126). https://www.arrivealive.co.za/Cited by: Day 132
- Typical reference sizes: passenger car length ~4.5 m (SANS 10400 parking bay 2.5 × 5 m); rugby field 100 m goal line to goal line (World Rugby Law 1); standard brick 222 × 106 × 73 mm (SANS 227); walking speed ~5 km/h. https://www.world.rugby/the-game/lawsCited by: Week 12 start here
- Tyre pressure units (1 bar = 100 kPa = 14.5 psi); under-inflation and fuel use (~0.2% per psi); vehicle payload. https://en.wikipedia.org/wiki/Tire-pressure_gaugeCited by: Day 327
- Unit pricing as a consumer comparison tool (Consumer Protection Act price display); the Home & Life edition's price-per-kilogram day. https://www.gov.za/documents/consumer-protection-actCited by: Day 82
- Unit pricing per 100 g on South African shelf labels (Consumer Protection Act price display); food labels per 100 g (R146 regulations). https://www.gov.za/documents/consumer-protection-actCited by: Day 136
- Unit rates and proportional reasoning; the Home & Life edition's car week (litres per hundred). https://en.wikipedia.org/wiki/Rate_(mathematics)Cited by: Day 90
- UTC offsets; SAST = UTC+2 with no daylight saving; the Home & Life edition's time zones day. https://en.wikipedia.org/wiki/List_of_UTC_offsetsCited by: Day 109
- Vogel (1979), 'A better way to construct the sunflower head'; phyllotaxis. https://en.wikipedia.org/wiki/PhyllotaxisCited by: Day 337
- Volume of a cuboid; 1 L = 1,000 cm³; 1 m³ = 1 kL; the square–cube law. https://en.wikipedia.org/wiki/Square%E2%80%93cube_lawCited by: Day 299
- Weeks 13–20 of this edition. https://en.wikipedia.org/wiki/Conversion_of_unitsCited by: Day 353
- Weeks 1–6 of this edition; Benjamin & Shermer (2006). https://en.wikipedia.org/wiki/Mental_calculationCited by: Day 351
- Weeks 21–24 and 33 of this edition. https://en.wikipedia.org/wiki/Scientific_notationCited by: Day 354
- Weeks 25, 29–32 and 34 of this edition. https://en.wikipedia.org/wiki/Divisibility_ruleCited by: Day 355
- Weeks 37–41 of this edition. https://en.wikipedia.org/wiki/ProbabilityCited by: Day 356
- Weeks 7–12 of this edition. https://en.wikipedia.org/wiki/PercentageCited by: Day 352
- Weighted arithmetic mean. https://en.wikipedia.org/wiki/Weighted_arithmetic_meanCited by: Day 95
- Wheat and chessboard problem: 2^64 − 1 ≈ 1.8 × 10¹⁹ grains. https://en.wikipedia.org/wiki/Wheat_and_chessboard_problemCited by: Day 163
- Wheel circumference and odometers; 700c bicycle wheel ≈ 70 cm overall. https://en.wikipedia.org/wiki/OdometerCited by: Day 179
- Winning percentage (draws as half); points percentage; field goal percentage. https://en.wikipedia.org/wiki/Winning_percentageCited by: Day 314
- Zeno's dichotomy; harmonic series divergence (Oresme, c. 1350); 0.999… = 1. https://en.wikipedia.org/wiki/Harmonic_series_(mathematics)Cited by: Day 292
- £sd; South African decimalisation, 14 February 1961 (R2 = £1; 1 shilling = 10 cents). https://en.wikipedia.org/wiki/South_African_randCited by: Day 237
- °F = °C × 9/5 + 32; the scales coincide at −40. https://en.wikipedia.org/wiki/FahrenheitCited by: Day 121
- √2 (Pythagoras; irrationality, c. 5th c. BC); golden ratio (Euclid, 'extreme and mean ratio'); e (Bernoulli 1683, Euler); Markowsky, 'Misconceptions about the golden ratio' (1992). https://en.wikipedia.org/wiki/Golden_ratioCited by: Week 27 start here