Enigma 460: Tear me off a strip
10 August 2018
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From New Scientist #1611, 5th May 1988 [link]
I had a rectangular block of stamps four stamps wide. I tore off one stamp. Then I tore off two stamps. Then I tore off three stamps, and so on, and so on. Each time, the stamps which I tore off formed a rectangle of their own, in one piece. And, following this pattern, the last piece I required (which needed no tearing off because it exhausted my supply of stamps) was also a rectangle. And only when I was forced to was any of these rectangles a strip one stamp wide. (So, for example, the four stamps and the subsequent non-primes were not in thin strips).
Each time, after tearing off the stamps, the remaining stamps were in one piece and formed either a rectangle or an L-shaped piece.
How many stamps did I start with?