Answer to February 8, 1999 Problem

Magic Square

The following is an example of a magic square, five of whose entries are missing. Determine the missing entries so the sum of each row, column, and diagonal is the same.
37  9  
     
21   13


Solution:

The answer is:

37  9 29
17 25 33
21 41 13
Let x, c, y, w, and m represent the numbers in the five missing cells as follows:

37  9   x
  c   y   w
21   m 13

Then, since the 3 numbers in each row must be the same, equate the top row and the upward diagonal to find y:
21 + y + x = 37 + 9 + x
Therefore y = 25.

Find w in a similar manner:
13 + w + x = 37 + 9 + x
So w = 33.

Since y = 25, the magic sum is 75 (37 + 25 + 13)

Then x = 29, c = 17, and m = 41.

Correctly solved by:

1. Jia Ran Rome, Italy
2. Liz Cotter Centreville, VA
3.Michael Leatherman Norfolk, VA
4. Ginger Anderson Winchester, VA
5. Andrew Crosby Winchester, VA