Domino Magic Square

Consider a small set of dominoes with only one, two, or three dots on each side. A full set then contains only six dominoes: 1-1, 1-2, 1-3, 2-2, 2-3, 3-3. Take one full set plus two duplicate dominoes from a second set. Lay the eight dominoes into a four-by-four grid such that the sum of the dots in any row, column, or major diagonal is the same. You may choose any two dominoes from the second set, as long as they are different.

I know of solutions for at least two different pairs of duplicate dominoes.

Source: Original. Used in "Ken's Puzzle of the Day" March 2, 1995

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