A car hides behind one door, goats behind the other two. You pick one; the host, who knows everything, always opens another door with a goat and offers you a switch. Switching wins 2 times out of 3; staying, only 1 in 3. When Marilyn vos Savant explained this in a magazine in 1990, hundreds of PhDs wrote in to tell her she was wrong.
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.