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 9*s* + 72 = 9 · (*s* + 8). Viola.