Difference between revisions of "2013 Mock AIME I Problems/Problem 4"
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* [[2013 Mock AIME I Problems/Problem 11|Preceded by Problem 3]] | * [[2013 Mock AIME I Problems/Problem 11|Preceded by Problem 3]] | ||
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Revision as of 07:08, 30 July 2024
Problem
Compute the number of ways to fill in the following magic square such that:
1. the product of all rows, columns, and diagonals are equal (the sum condition is waived),
2. all entries are nonnegative integers less than or equal to ten, and
3. entries CAN repeat in a column, row, or diagonal.
![[asy] size(100); defaultpen(linewidth(0.7)); int i; for(i=0; i<4; i=i+1) { draw((0,2*i)--(6,2*i)^^(2*i,0)--(2*i,6)); } label("$1$", (1,5)); label("$9$", (3,5)); label("$3$", (1,1)); [/asy]](http://latex.artofproblemsolving.com/1/5/f/15fdbd63c43e4345cf06b18956239b7aa40ec839.png)
Solution
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