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Solution found:
{4,5,6,7}
{16,3,8,9}
{2,15,10,11}
{1,14,13,12}

{15,7,8,9}
{16,14,6,10}
{2,5,13,11}
{1,3,4,12}

{15,7,8,9}
{16,14,6,10}
{1,5,13,11}
{2,3,4,12}

{6,7,8,9}
{16,5,3,10}
{15,2,4,11}
{1,14,13,12}

{8,7,6,4}
{16,9,3,5}
{15,2,10,11}
{1,14,13,12}
Number of solutions: 5+




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