You drive one way at 60 km/h and back at 40 km/h. Your average speed isn't 50 but 48 km/h, because you spend more time driving slowly. Even more mind-bending: if the outward leg is 1 km and you cover it at 30 km/h, no return speed, even an infinite one, will give you a 60 km/h average for the round trip.
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.