Problem of the Month (February 2010)

This month we consider another variation. Identify each polyomino with the points at the centers of its component squares. As long as these center points have the shape of the polyomino, the magnification of the polyomino does not matter. For example, the S-tetromino has a tiling of a 5×8 rectangle if we allow such spaced-out polyominoes:

In fact, we also allow polyominoes to be rotated: there is a much smaller tiling possible:

For a given spaced-out polyomino, what is the smallest rectangle it can tile without rotations? What if rotations are allowed? What about tiling other shapes, such as triangles, pyramids, and diamonds, with spaced out polyominoes?

You can see all the best known results here.

Submit your answers here.

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