Take a calendar, and 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?
Try it with a real calendar to see some examples that work.
| 1 | 2 | 3 | ||||
| 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 11 | 12 | 13 | 14 | 15 | 16 | 17 |
| 18 | 19 | 20 | 21 | 22 | 23 | 24 |
| 25 | 26 | 27 | 28 | 29 | 30 |
Then draw a 3×3 square using s:
| s | s + 1 | s + 2 |
| s + 7 | s + 8 | s + 9 |
| s + 14 | s + 15 | s + 16 |
Add everything up and you’ll get 9s + 72 = 9 · (s + 8). Viola.