Take a four-digit number whose digits aren't all the same, like 3524. Arrange its digits from largest to smallest, then smallest to largest, and subtract: 5432 minus 2345 gives 3087. Repeat with the result: within seven steps at most, you'll land on 6174, which then reproduces itself forever. Indian mathematician D. R. Kaprekar discovered this in 1949.
How many different structures can you build with six classic 2-by-4 Lego bricks of the same colour? The company used to quote just over 102 million. In 2005, Danish mathematician Søren Eilers recounted everything by computer: 915,103,765 combinations. The official estimate had been too low by a factor of about nine.
Fold an A4 sheet in half and you get an A5 with the same proportions. That only works for one ratio between length and width: about 1.414, the square root of 2. The A0 format measures exactly one square metre, and A4 is a sixteenth of it. With standard 80-gram-per-square-metre paper, an A4 sheet therefore weighs exactly 5 grams.