Each player picks a number from 0 to 100; whoever comes closest to two-thirds of the average wins. If everyone reasons perfectly, the only stable choice is 0. But in reality, you must guess how far others will take the reasoning. In a 1997 Financial Times contest, the winning number was 13, and Keynes had long compared the stock market to this kind of “beauty contest”.
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.