Math Magic is a web site devoted to
original mathematical recreations. If you
have a math puzzle, discovery, or observation,
please e-mail me about it. You can also send
answers to the problem of the month.

Problem of the Month (May 2012)

How can a integer-sided square be packed with smaller distinct integer-sided squares with the smallest waste? For small n, the best packing of square with side n is by squares of sides n-1 and 1, with waste 2n. But for larger n, we can do better. What are the best packings for larger n?

waste=21

waste=29

waste=20

waste=25

waste=30

What if squares are replaced with almost squares, rectangles of the form n×(n+1)?

You can see all the best known results here.

Submit your answers here.

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