Decide whether the integers 1,2,…,100 can be arranged in the cells C(i,j) of a 10×10 matrix (where 1≤i,j≤10), such that the following conditions are fullfiled:
i) In every row, the entries add up to the same sum S.
ii) In every column, the entries also add up to this sum S.
iii) For every k=1,2,…,10 the ten entries C(i,j) with i−j≡kmod10 add up to S.
(Proposed by Gerhard Woeginger, Austria) linear algebramatrixcombinatorics unsolvedcombinatorics