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Math puzzle, square pieces

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Jun 25, 2012 3:05pm
avatar for Ace_Blue Ace_Blue 1082 posts
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My turn! I have a puzzle made of 24 perfectly square pieces. The smallest is 1 × 1 in, the next one 2 × 2 in, and so on to the last one which is 24 × 24 inches in size. Once assembled, the puzzle is a perfect square 70 × 70 in. How should I assemble the pieces?

Please provide your solution in the form of a picture.
 
Jun 25, 2012 3:35pm
avatar for Draco18s Draco18s 6860 posts
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No solution.

Perfect square dissections correspond to square numbers which are the sum of square numbers. The simplest place to look for such a square might therefore be thought to be square pyramidal numbers. However, there are only two such numbers: 1 and 4900, and even though

It turns out not to be possible to arrange the 24 squares to form a 70×70 square.
 
Jun 25, 2012 4:03pm
avatar for Ace_Blue Ace_Blue 1082 posts
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Sooo, you’re just going to take their word for it? :p
 
Jun 25, 2012 4:07pm
avatar for qwerber qwerber 4717 posts
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maybe with 24 squares, but not ones with incremental side lengths from 1 to 24 i think.
 
Jun 25, 2012 5:29pm
avatar for Draco18s Draco18s 6860 posts
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Originally posted by qwerber:

maybe with 24 squares, but not ones with incremental side lengths from 1 to 24 i think.

That would be this one. Squares are numbered by side length:

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