In the 16th century, a code appeared that changed its shift with every letter according to a keyword: frequency analysis was suddenly blind. It's credited to Blaise de Vigenère, though the Italian Giovan Battista Bellaso described it first. Dubbed “the indecipherable cipher”, it fell only in the 19th century, cracked by Charles Babbage and then, publicly, by Friedrich Kasiski in 1863.
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.