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).