Multiplying two large primes is easy; recovering them from the result is extraordinarily hard. This asymmetry lies at the heart of RSA, published in 1977 by Rivest, Shamir and Adleman, which still protects much of our online traffic. Yet as early as 1973, Clifford Cocks had found an equivalent method inside GCHQ, Britain's intelligence agency. It remained classified until 1997.
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.