The “one-time pad” encrypts a message with a random key as long as the message itself, used only once. In 1949, Claude Shannon proved it perfectly unbreakable: without the key, every possible reading is equally likely. But the slightest slip is fatal. During the Cold War, the Soviets reused key pages, and the Americans were able to decrypt some of their messages: the Venona project.
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.