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 Square dissection (Posted on 2006-05-16)
Take a square and place two equally spaced points on each side (trisecting the sides.) Starting at one corner label the points and corners around the perimeter A, B, C, D, …, L.
Connect with straight lines the pairs AI, BH, CG, DL, EK, and FJ. The resulting figure has four squares and pieces around the edge that can be rearranged to make 6 more (for a total of 10.)

How could you use a similar method to dissect a square into twenty-nine squares? How about 58? What numbers are possible by this method?

 Submitted by Jer Rating: 3.6667 (3 votes) Solution: (Hide) For 29 squares subdivide the edges into 5 even sections and then connect across with an offset of two. For 58 squares subdivide the edges into 7 even sections and then connect across with an offset of three. Any number that is the sum of two squares is possible, let the larger be the number of subdivisions and the smaller be the offset.

 Subject Author Date What numbers are possible? Leming 2006-05-16 12:34:33 re: (2) Solution - clarification Leming 2006-05-16 10:45:05 re: Solution Charlie 2006-05-16 10:25:22 Solution Leming 2006-05-16 09:48:09

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