Water lilies double their area every day and will cover the whole pond in 30 days, so the pond is only half covered on day 29. Five days before the end, they occupy just about 3%, and all seems calm. The 1972 report “The Limits to Growth” popularised this French riddle to show how exponential growth catches us off guard.
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.