Cynthia Lanius

Algebra - Fun with Calendars

Design Your Own Puzzle


Some Month Some Year
S M T W TH F S
        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  
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.

Which number do you think would be the easiest to call n? I think the one in the middle. Then the first number would be n - 8 and the last number would be n + 8. Add the three numbers:

n + n + 8 + n - 8

Make them equal their sum.

n + n + 8 + n - 8 = 63

Combine like terms.

3n = 63

n = 21

Wow! This one's really easy. You just divide 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 Year
S M T W TH F S
        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  

Design a puzzle of your own.

  1. Describe an interesting pattern on the calendar.
  2. Call one of the days n.
  3. Write the other days in terms of n.
  4. Add up the days (in terms of n) and write it equal to its sum. (The actual number)
  5. 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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