More Dominoes

As with the earlier problem "Domino Magic Square", this problem also asks for a magic square. From a regular set of dominoes, remove all blanks, leaving 1-1, 1-2, ..., 6-6, 21 dominoes in all. Remove three dominoes of your choice and arrange the remaining 18 dominoes in a 6x6 grid, such that the sum of the dots in each row, column, and major diagonal is the same.

For example, removing the 6-6, 5-6, and either of 4-6, 5-5, will result in each sum being 19. Removing 1-1, 1-2, and either of 1-3, 2-2, the sum must be 23. (Feel free to prove this.)

I usually do not post problems to which I have no solution, but I have made an exception here. I came within 2 dominoes of a solution, so I feel that one must exist. Please send whatever solutions you have. As always, I will post any unique solutions and credit the solver.

Source: Original.

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