How can two strangers agree on a secret key while only communicating in public? Picture it: each mixes a shared colour with their own secret colour, they swap the mixtures, then each adds their own secret colour again. Both end up with the same final shade, which an eavesdropper can't reconstruct. That's the idea of Whitfield Diffie and Martin Hellman (1976), who won the Turing Award in 2015.
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.