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?
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:
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.