Take city populations, river lengths or accounting figures: about 30% of those numbers start with a 1, and fewer than 5% start with a 9. This is Benford's law, and it shows up in data spanning several orders of magnitude. People who fabricate numbers tend to spread first digits too evenly, which is why auditors use it to sniff out fraud.
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.