A $3 \times 3$ arrangement of boxes is filled with one of the numbers one, seven, or nine. Prove that of the eight possible sums along the rows, the columns, and the diagonals, two sums must be equal.
I tried to use the pigeonhole principle, but there are ten possible ways to generate different sets/sums with cardinality three , and I am not able to eliminate enough possibilities. In addition, I tried to find a pattern by placing many possibilities without any luck.