A rectangle is divided into a finite number of subrectangles. The sides of the subrectangles are all parallell to sides of the large rectangle.
Each subrectangle has at least one side with integer length.
Prove that the large rectangle also has at least one side with integer length.
Do you need advanced mathematics for this?
A nice puzzle.
I can see why it fails although I don't find a mathematically sound proof yet that covers all weird cases.
The only proof I know of uses advanced mathematics. But if you have an elementary proof, it would be interesting to see it :).
I should add the the "advanced" proof is very short, simple and surprising, if one masters this particular advanced topic.
I keep running into cases that are completely irrelevant (situations that won't lead to solutions anyway), but keep ruining an elementary approach.
mfb solved the problem, and should be given the credit!
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