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Math Magic Archive

Problem of the Month (December 2014)

Given a polyomino, what is the smallest square it can tile, if at most one square is allowed to hang off each edge of the square? The smallest known answers for polyominoes with area 5 or less are shown below. What are the answers for larger polyominoes?

1 2 3 4
5

What are the smallest rectangles that can be tiled, with at most one square hanging off the side of each side? For many small polyominoes, one copy of the polyomino suffices. Here are the smallest known answers for other polyominoes with area 5 or less. What are the answers for larger polyominoes?
5
6

For those polyominoes that can form overlap squares or rectangles, what sizes can they make? For example, here are some larger squares and rectangles that can be made:


You can see all the best known results here.

Submit your answers here.

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