Three Painters Take Twelve Days; Five Do Not Take Twenty
The rule of three turns 3 → 12 into 5 → 20, and that is right for anything that scales up together. For workers and days it is exactly backwards: the answer is 7.2.
Marco Bianchi · 3 min read
Guides & tutorials
Practical guides, how-tos and comparisons to get the most out of our free online tools.
October 5, 2026
Removing 20 % Is a Division, Not a Subtraction
A price of 120 including 20 % tax has a net of 100, not 96. Subtracting 20 % of the gross is the most common invoicing error there is, and it always errs the same way.
Camille Laurent · 3 min read
Two Points or a Quarter: the Same Fall Reported Twice
500 down to 350 is a fall of 150, or 30 %. When the quantity is itself a percentage, the same fall has two correct descriptions and they differ by more than a factor of ten.
Lena Hoffmann · 3 min read
A 50 % Rise Is Undone by a 33 % Fall
Going from 50 to 75 is +50 %. Coming back from 75 to 50 is −33.3 %. The move is the same 25 units both times; the base is not.
Lena Hoffmann · 3 min read
October 2, 2026
The Expected Value Is a Number That Never Happens
Outcomes of 10, 20 and −5 with probabilities 0.5, 0.3 and 0.2 give an expected value of 10. Shift the probabilities slightly and it becomes 10.5 — a result none of the three outcomes can produce.
Antonio Delgado · 4 min read
A Steeper Roof Does Not Catch More Rain
100 m² of roof under 50 mm of rain yields 4,500 litres. The area to enter is the footprint, not the sloping surface — and the 10 % missing is water the roof never delivers.
Marco Bianchi · 3 min read
Five Points of Learning Rate Turn Fifty Repetitions Into Four Hundred
At an 85 % learning rate, a task that takes 20 minutes first time reaches 8 minutes after 50 attempts. At 90 % it needs 415 — the same task, five points apart.
Aisha Karim · 3 min read
8.25 a Day Is 3,011 a Year, and Only One of Those Numbers Changes Anything
Fifteen cigarettes a day from packs of twenty at 11 costs 8.25 daily and 3,011.25 a year. The same amount saved instead, for twenty years at 5 %, comes to about 99,570.
Sofia Nunes · 3 min read
October 1, 2026
Six Rebounds Can Beat Ten, and the Difference Is the Denominator
Ten rebounds in 32 minutes of a game with 82 boards is 18.3 %. Six rebounds in 18 minutes of the same game is 19.5 % — a better rate from a smaller number.
Aisha Karim · 3 min read
Ten Metres of Copper Pipe Grows Eight Millimetres
A straight run of copper going from 20 to 70 degrees gains 8.5 mm over ten metres. Steel gains 6 mm, and a 100-metre steel span over a 60-degree year moves 72 mm.
Marco Bianchi · 3 min read
Friction Does Not Care How Big the Contact Patch Is
A coefficient of 0.3 against a normal force of 100 N gives 30 N of friction, and the area never enters the formula. What does enter it, and is usually got wrong, is the normal force.
Marco Bianchi · 3 min read
Double the Drop and the Speed Rises 41 %, but the Energy Doubles
A 20-metre fall takes 2.02 seconds and lands at 19.81 m/s. From 40 metres it takes 2.86 seconds and lands at 28.01 m/s — the speed is up by a factor of √2, and the energy by exactly two.
Lena Hoffmann · 4 min read