Give the following instructions to a friend:
1. Choose a 3 x 3 square on a calendar.
2. Add the nine numbers together.
3. Tell me the sum, and I will tell you the middle number of your square.Divide by 9 to get the middle number.
Subtract 8 from that result to get the top left number in the square.
Why does this work? Use some algebra to prove it.
Let n = the number in the upper left corner of the 3 x 3 square.
Then the other eight numbers in the square are represented as follows:
| n | n + 1 | n + 2 |
| n + 7 | n + 8 | n + 9 |
| n + 14 | n + 15 | n + 16 |
The sum of the nine numbers is 9n + 72 = 9(n + 8).
So, when you divide by 9, you get the middle number (n + 8),
and when you subtract 8, you get n (the upper left number).