Graham's number, which arose in the 1970s in work on a combinatorics problem, is so colossal that writing it out digit by digit is impossible, even with one digit in every tiniest nook of the observable universe. It entered the Guinness Book of Records as the largest number ever used in a serious proof. The irony: we still know its final digits; it ends in 95387.
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.