2013 Mock AIME I Problems/Problem 4
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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