Two accomplices are questioned separately. If neither talks, both get a light sentence; if one betrays, he walks free and the other gets the maximum; if both betray, each gets a heavy sentence. Whatever the other does, betraying pays more individually… yet together they end up worse off. Devised in 1950 at the RAND Corporation, this trap sheds light on arms races and price wars.
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.