Problem: For how many paths consisting 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 CONTEST spelled out as the path is traversed from beginning to end?
Answer Choices:
A.
B.
C.
D.
E. none of these answers
Solution:
All admissible paths must end at the bottom " " of the diagram. Proceeding backwards from this point and considering only those paths which include the central column and that are to the left of the central column, there are two possible paths which lead to the bottom " " in each row (excluding the first row at the top from which there is one admissible path which was already counted). Thus there are possible paths. Similarly, there are possible paths including the central column to the right of the central column. Therefore, since the central column was counted twice there are or possible paths.