What's so special about the 4 numbers forming a square? Think of creating a different pattern, say 3 in a row diagonally. Have your friend add up any three numbers diagonally left-to-right. But this time we wouldn't divide by 4 and subtract 4 to find the numbers. So we have to figure out how the trick would be played.

Some Month Some YearS M T W TH F S 1 2 3456789101112131415161718192021222324252627282930Which number do you think would be the easiest to call

I think the one in the middle. Then the first number would ben?and the last number would ben - 8. Add the three numbers:n + 8n + n + 8 + n - 8Make them equal their sum.

n + n + 8 + n - 8 = 63Combine like terms.

3n = 63n = 21Wow! This one's

reallyeasy. You justdivide by 3.So how do you solve this puzzle? Your friend adds the 3 numbers and tells you the sum. You divide by three and that gives you the middle number. You subtract 8 to get one number and add 8 to get the other.

## Now you try one.

Some Month Some YearS M T W TH F S 1 2 3456789101112131415161718192021222324252627282930Design a puzzle of your own.

- Describe an interesting pattern on the calendar.
- Call one of the days
.n- Write the other days in terms of
.n- Add up the days (in terms of
) and write it equal to its sum. (The actual number)n- Figure out the puzzle's solution by actually solving the equation.
Let me hear what you come up with. lanius@math.rice.edu

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