Fold a Strip of Eight Stamps Into One Stack
Take a strip of eight postage stamps in a row, each joined to the next by a perforation. Using only the existing creases, fold the strip into a single stack the size of one stamp. There are many possible folding sequences — but only some end with stamp number 1 sitting face-up on top. How many ways can it be done?
Reveal the answer
There are exactly 40 ways to fold the strip of eight stamps so that stamp 1 ends up face-up on top of the stack. Henry Dudeney posed this as puzzle No. 214, 'Folding Postage Stamps,' in his 1926 book Modern Puzzles and How to Solve Them; Martin Gardner revived it in his Scientific American column in 1959, launching the field of 'map folding' combinatorics.
— Henry Dudeney, Modern Puzzles and How to Solve Them — Puzzle No. 214, 'Folding Postage Stamps' (1926); revisited by Martin Gardner, Scientific American, 1959
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