You often read that pi's decimals contain your birthday, your phone number, any sequence imaginable. It may be true, but no one has ever proven it. We don't even know whether each digit from 0 to 9 eventually appears as often as the others. And its apparent randomness has surprises: starting at the 762nd decimal place, six 9s appear in a row.
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.