2070.51 – Square of Dates

Take a calendar. Draw a square around any nine dates. (It will be a 3 x 3 square, right?) Let $s$ be the smallest number in the square. If you add up all the numbers in the square, the answer will always be a multiple of 9. In particular, the sum will be exactly $9 (s + 8)$.

Why?

Solution

A 3x3 square of dates from a calendar will look like the figure below, where $s$ is the smallest date in the square. Add everything up in the square and you’ll get $9s + 72 = 9 (s + 8).$ Voila!