The Four Postage Stamps

+---+----+----+----+ | 1 | 2 | 3 | 4 | +---+----+----+----+ | 5 | 6 | 7 | 8 | +---+----+----+----+ | 9 | 10 | 11 | 12 | +---+----+----+----+

"It is as easy as counting," is an expression one sometimes hears. But mere counting may be puzzling at times. Take the following simple example. Suppose you have just bought twelve postage stamps, in this form--three by four--and a friend asks you to oblige him with four stamps, all joined together--no stamp hanging on by a mere corner. In how many different ways is it possible for you to tear off those four stamps? You see, you can give him 1, 2, 3, 4, or 2, 3, 6, 7, or 1, 2, 3, 6, or 1, 2, 3, 7, or 2, 3, 4, 8, and so on. Can you count the number of different ways in which those four stamps might be delivered? There are not many more than fifty ways, so it is not a big count. Can you get the exact number?

H. E. Dudeney, Amusements in Mathematics (1917) · No. 285