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: