Brainsteem Mathematics Challenges: Rectangles in Squares
Left the hardest one till last, today. I know how cumbersome it is to type mathematical notation into websites (would be great if one of the Steem platforms would implement MathJax!) so I try to select problems that will not require excessive notation. Pen and paper remains the fastest way of writing maths, so will accept scans of handwritten solutions - assuming they are vaguely legible!
Question
Determine all positive integers M for which the MxM square can be dissected into five rectangles, the side lengths of which are the integers 1, 2, 3, ... 10 in some order.
Show at least one such solution for each possible value of M.
An interesting question from EGMO 2013. As in many such problems, finding the limits of M will save a lot of time compared to mere trial-and-error.
One possible extension, not in the original question, is to find how many solutions there are for each valid value of M.
The first correct answer and further interesting comments will be rewarded with an upvote.
Enjoy!
More Brainsteems coming soon...
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@rycharde manages the AAKOM project and the MAP forum.
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