Enigma 1336: Rectangles
29 March 2014
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From New Scientist #2495, 16th April 2005
George has a rectangular piece of paper, 3 inches by 4 inches, marked with a 1-inch grid. He is wondering in how many ways he can mark a rectangle (which may be a square) on it, following the grid lines.
He has identified eight [*] different possible sizes and shapes, and various different places in which each can be marked, ranging from 1 to 17 different positions per shape. The total is 60.
He now has a larger rectangular piece of paper of integer dimensions (more than 100 square inches) and he has tackled the same problem. Instead of 60, he has calculated a much larger number which is the product of four consecutive primes.
What are the dimensions of this piece of paper?
[*] I think there is a mistake in this puzzle, in that it should read “He has identified nine different possible sizes and shapes…”. It all seems to make sense if you make that change.