Solving a puzzle-like problem
Source: INAMO 2002 - Problem 5
August 5, 2011
modular arithmeticalgebra unsolvedalgebra
Problem Statement
Nine of the numbers are going to be inputted to the empty cells in the following table:
\begin{array} {|c|c|c|} \cline{1-3}
10 & & \\ \cline{1-3}
& & 9 \\ \cline{1-3}
& 3 & \\ \cline{1-3}
11 & & 17 \\ \cline{1-3}
& 20 & \\ \cline{1-3}
\end{array}
such that each row sums to the same number, and each column sums to the same number. Determine all possible arrangements.