2005 Canadian MO Problems/Problem 1
Problem
Consider an equilateral triangle of side length 
, which is divided into unit triangles, as shown. Let 
be the number of paths from the triangle in the top row to the middle triangle in the bottom row, such that adjacent triangles in our path share a common edge and the path never travels up (from a lower row to a higher row) or revisits a triangle. An example of one such path is illustrated below for 
. Determine the value of 
.
