In 1962, David Gale and Lloyd Shapley showed that couples can always be formed “stably”: no two people would both rather leave their current partners to be together. Their method, a series of proposals, is now used to assign young American doctors to hospitals, and pupils to schools in several cities. It earned Shapley and Alvin Roth the 2012 Nobel Prize in economics.
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.