A devilish puzzle by Lee Sallows:

In the diagram above, nine numbered counters occupy the cells of a 3×3 checkerboard so as to form a magic square. Any 3 counters lying in a straight line add up to 15. There are 8 of these collinear triads.

Reposition the counters (again, one to each cell) to yield 8 new collinear triads, but now showing a common sum of 16 rather than 15.