The three numbers in every row, column, and diagonal have the same sum. This is called a magic square. Three numbers are given. Can you find the other six?
| 25 | 30 | |
| 21 |
Solution to the Problem:
| 25 | 47 | 30 |
| 39 | 34 | 29 |
| 38 | 21 | 43 |
To solve this, I assigned the letters A, B, C, D, E, and F to the six missing numbers:
| 25 | A | 30 |
| B | C | D |
| E | 21 | F |
Then, since I knew that each row, column, and diagonal add up to the same number,
I wrote the following:
A + 25 + 30 = B + C + D = E + F + 21 =
25 + B + C = A + C + 21 = 30 + D + F =
25 + C + F = E + C + 30
Since these eight expressions are all equal, I can set any two of them equal to each other.
So, A + 25 + 30 = A + C + 21
So, C = 34.
Then set E + F + 21 = E + C + 30 and replace C by 34 to obtain F = 43.
Now, we know the Magic Sum is 25 + C + F = 102.
So, E = 102 - 21 - 43 = 38.
Then B = 102 - 25 - 38 = 39.
Then D = 102 - 39 - 34 = 29.
Finally, A = 102 - 25 - 30.
Correctly solved by:
| 1. K. Sengupta | Calcutta, INDIA |
| 2. John Funk | Ventura, California |
| 3. Richard K. Johnson | La Jolla, California |
| 4. Les Walker | Ventura, California |