Find three distinct integers, X, Y and Z, such that X + Y, X + Z, Y + Z, X - Y, X - Z, and Y - Z are all squares of integers.
Apparently, there are many solutions.

Find the set [X, Y, Z] with the smallest X + Y + Z.

Well it's easy if one assumes Y=-Z, but I've suggested a new puzzle that investigates some other cases where this sort of question could be considered.