A Rubik's Cube can take more than 43 quintillion different configurations. Yet in 2010, a team proved every one can be solved in 20 moves or fewer, counting each turn of a face as one move. It took the equivalent of 35 years of computing on a single processor, donated by Google. The number 20 has been dubbed “God's number”.
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.