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Problem of the Month (September 2014)

Consider the sided-polyominoes below representing the digits 0-8:

We say two sets of polyominoes X and Y are equal if they both tile the same shape. For example, 3+3 = 1+1+1+7 because of the following tilings:

We say two sets of polyominoes X and Y are equivalent if there is another set of polyominoes Z so that X and Z tile the same shape as Y and Z. For example, 3 ≈ 5 because of the following tilings:

What sets of digits are equal? What sets of digits are equivalent? If X ≈ Y, what is the smallest area Z with X + Z = Y + Z? Are every set of polyominoes with equal area equivalent?


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