# Difference between revisions of "2003 AMC 8 Problems/Problem 23"

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## Solution

Break this problem into two parts: where the cat will be after the $247^{th}$ move, and where the mouse will be.

The cat has four possible configurations which are repeated every four moves. $247$ has a remainder of $3$ when divided by $4$. This corresponds to the position the cat has after the 3rd move, which is the bottom right corner.

Similarly, the mouse has eight possible configurations that repeat every eight moves. $247$ has a remainder of $7$ when divided by $8$. This corresponds to the position the rat has after the 7th move, which can easily be found by writing two more steps to be the bottom edge on the left side of the grid.

The only configuration with the mouse in that position and the cat in the bottom right square is $\boxed{\textbf{(A)}}$.

## Video Solution

https://youtu.be/RCUzhVOi7XI ~DSA_Catachu

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