Brain-twister. The answer.

Looks like no-one has managed to crack the puzzle, so I got down to work. It took me quite some time,  mainly because I approached the task as if it were Riemannian geometry, but it turned out to be much simpler.
The first step is to rearrange the numbers to make 34 in each row, column and diagonal. You’ll see that numbers 1, 8 and 13, 7, 9, 2 stay put, while numbers 15, 5, 12, 10, 4, swapped places with numbers 11, 6, 16, 14, 3. So all you have to do is cut the square 1 along the red lines and switch pink and blue figures to form the square 2.

     

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

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

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