MathDB

Decide whether the integers

1,2,\ldots,100

can be arranged in the cells

C(i, j)

of a

10\times10

matrix (where

1\le i,j\le 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, \ldots, 10

the ten entries

C(i, j)

with

i-j\equiv k\bmod{10}

add up to

S

. (Proposed by Gerhard Woeginger, Austria)

Problem Statement