MathDB

1

Part of 2005 South africa National Olympiad

Problems(1)

Prove that the sum is always the same

Source: South African MO 2005 Q1

5/27/2012
Five numbers are chosen from the diagram below, such that no two numbers are chosen from the same row or from the same column. Prove that their sum is always the same.
14710131619222528313437404346495255586164677073\begin{array}{|c|c|c|c|c|}\hline 1&4&7&10&13\\ \hline 16&19&22&25&28\\ \hline 31&34&37&40&43\\ \hline 46&49&52&55&58\\ \hline 61&64&67&70&73\\ \hline \end{array}
number theory unsolvednumber theory