In the 9th century, the scholar al-Kindi described a formidable method: in any language, some letters appear far more often than others. Count the symbols in a message encrypted by simple substitution, match the most frequent to the most common letters, and the text reveals itself. His treatise, rediscovered in 1987 in Istanbul archives, is the oldest known account of this “frequency analysis”.
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.