1996 AIME Problems/Problem 1
Problem
In a magic square, the sum of the three entries in any row, column, or diagonal is the same value. The figure shows four of the entries of a magic square. Find .
Solution
Let's make a table.
Solution 2
Use the table from above. Obviously . Hence . Similarly, .
Substitute that into the first to get , so , and so the value of is just
Solution 3
The formula can be used. Therefore, . Similarly, So .
Now we have this table: By property of magic squares, observe that The 's cancel! We now have Thus
See also
1996 AIME (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
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