2018 AIME II Problems/Problem 8
Problem
A frog is positioned at the origin of the coordinate plane. From the point 
, the frog can jump to any of the points 
, 
, 
, or 
. Find the number of distinct sequences of jumps in which the frog begins at 
and ends at 
.
Solution
We solve this problem by working backwards. Notice, the only points the frog can be on to jump to 
in one move are 
and 
. This applies to any other point, thus we can work our way from 
to , recording down the number of ways to get to each point.
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