Calendar Trick #1

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).

Send any comments or questions to: David Pleacher