How many paths?
Source: 2022 Nigerian Senior MO Round 2/Problem 5
May 6, 2022
combinatoricsOlympiads
Problem Statement
For how many paths comsisting of a sequence of horizontal and/or vertical line segments, with each segment connecting a pair of adjacent letters in the diagram below, is the word spelled out as the path is traversed from beginning to end?\begin{tabular}{ccccccccccccccccc}& & & & & & & & O & & & & & & & &\\ & & & & & & & O & L & O & & & & & & &\\ & & & & & & O & L & Y & L & O & & & & & &\\ & & & & & O & L & Y & M & Y & L & O & & & & &\\ & & & & O & L & Y & M & P & M & Y & L & O & & & &\\ & & & O & L & Y & M & P & I & P & M & Y & L & O & & &\\ & & O & L & Y & M & P & I & A & I & P & M & Y & L & O & &\\ & O & L & Y & M & P & I & A & D & A & I & P & M & Y & L & O &\\ O & L & Y & M & P & I & A & D & S & D & A & I & P & M & Y & L & O \end{tabular}