Browse · MATH
Printjmc
algebra intermediate
Problem
In a magic square, the sum of the three entries in any row, column, or diagonal is the same value. The figure below shows four of the entries of a magic square. Find . 
Solution
Denote the remaining entries by as shown: One possible solution proceeds in three steps, as follows:
The leftmost column and up-right diagonal have the same sum, so which gives The down-right diagonal and the rightmost column have the same sum, so which gives Finally, the first row and second sum have the same sum, so which gives
The leftmost column and up-right diagonal have the same sum, so which gives The down-right diagonal and the rightmost column have the same sum, so which gives Finally, the first row and second sum have the same sum, so which gives
Final answer
200