A prime is divisible only by 1 and itself: 1 seems to fit the bill. It's excluded to protect a precious rule: every whole number breaks down into a product of primes in exactly one way. If 1 were prime, you could tack it on at will and that uniqueness would vanish. Yet until the early 20th century, some tables still listed it among the primes.
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.