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Cans in a Box

© Copyright 2002, Jim Loy

How can you pack cylindrical cans into a the smallest possible square box (one deep in the third dimension)? This puzzle is normally described as packing circles into squares. On the left, we have my solutions (some are not optimal). Note that I use unit cans (their diameter is 1). Alternatively, we can use unit squares and then pack the largest possible cans into them. It is the same puzzle, but with different numbers. Can you improve upon my solutions?

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