Answer to June 2, 2003 Problem

Magic Square

The following is an example of a magic square, five of whose entries are missing. Determine the missing entries A, B, C, D, and E so the sum of each row, column, and diagonal is the same.
  A     B   10.5
6.75 C D
8 E 5.5


Solution:

The answer is:

A = 13
B = 4.25
C = 9.25
D = 11.75
E = 14.25

13 4.25 10.5
6.75 9.25 11.75
8 14.25 5.5

Since the 3 numbers in each row must be the same, equate the middle row and the last column to find C:
6.75 + C + D = 10.5 + D + 5.5
Therefore C = 16 - 6.75 = 9.25

Then the magic sum must be 8 + 9.25 + 10.5 = 27.75.
Therefore, A = 13
B = 4.25
E = 14.25 and
D = 11.75

Correctly solved by:

1. Rick Jones Kennett Square, Pennsylvania
2. Walt Arrison Philadelphia, Pennsylvania
3. Richard Johnson La Jolla, California
4. William Funk San Antonio, Texas
5. Misty Carlisle Winchester, Virginia
6. John Funk Ventura, California
7. John Beasley Winchester, Virginia
8. James Alarie University of Michigan -- Flint,
Flint, Michigan
9. Bob Hearn Winchester, Virginia
10. Dash Waughquasebarth Winchester, Virginia
11. Jeffrey Gaither Winchester, Virginia
12. George Gaither Winchester, Virginia
13. Josh Feingold Winchester, Virginia
14. Kirstine Wynn Bellingham, Washington
15. David and Judy Dixon Bennettsville, South Carolina