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Math Magic Archive

Problem of the Month (August 2018)

The problem of packing squares of sides 1, 2, 3, ... n inside the smallest square has been well-studied. The problem of using squares 1, 2, 3, ... n to cover the largest square was studied in the September 2000 Math Magic. We generalize the problem even further. Given n squares of sides 1, 2, 3, ... n, what is the largest square that they can cover k times? In the process, what is the largest area of squares that can be unused and still achieve the covering?


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