In 1586, Mary, Queen of Scots, a prisoner in England, secretly corresponded with conspirators plotting to assassinate Elizabeth I. Their letters, encrypted by symbol substitution, were intercepted and decoded by Thomas Phelippes using frequency analysis. The deciphered messages proved she approved the plot. She was executed in 1587: her faith in a weak code cost her life.
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.