Can you fill a 4x4 grid with every number from 1 to 16, such that every row, every column and every 2x2 sub-grid of numbers sum to the same value?
1 15 2 16 14 4 13 3 7 9 8 10 12 6 11 5
A B C D E F G H I J K L M N O P
A+B = G+H = I+J = O+P
C+D = E+F = K+L = M+N
A+E = J+N = C+G = L+P
I+M = B+F = K+O = D+H
B+C = J+K = E+H = M+P
F+G = N+O = A+D = I+L
E+I = G+K = B+N = D+P
F+J = H+L = A+M = C+O
which are enough constraints to make it manageable by trial and error.