Decide whether the integers $1,2,...,100$ can be arranged in cell $C(i,j)$ of $10×10$ $matrix$ (where $1 \le i,j \le 10$), such that following conditions are satisfied :
- In every row, the entries add up to the same sum $S$
- In every column, the entries also add up to this sum of $S$
- For every $k = 1,2,...,10$ the ten entries $C(i,j)$ with $i-j \equiv k(mod10)$ add up to $S$.
I have tried guessing numbers in the table. But I have given up on guessing. Am stuck so I need help from you guys, please help.