A sheet of paper is about a tenth of a millimeter thick, and each fold doubles that. After 10 folds it's over 10 cm thick; after 30, more than 100 km. By the 42nd fold, the stack would exceed 400,000 km, farther than the Moon. In practice, even with paper rolls kilometers long, nobody has managed much more than a dozen folds.
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.