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
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 |