The number 6 is “perfect”: it equals the sum of its other divisors, 1, 2 and 3, just like 28, 496 and 8,128. The Greeks already knew them, and only about fifty have been found since, all even. Does an odd perfect number exist? After more than two millennia of searching, it remains one of the oldest open problems in mathematics.
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.