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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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