1977 AHSME Problems/Problem 20

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Problem

$\begin{tabular}{ccccccccccccc}& & & & & & C & & & & & &\\  & & & & & C & O & C & & & & &\\  & & & & C & O & N & O & C & & & &\\  & & & C & O & N & T & N & O & C & & &\\  & & C & O & N & T & E & T & N & O & C & &\\  & C & O & N & T & E & S & E & T & N & O & C &\\  C & O & N & T & E & S & T & S & E & T & N & O & C \end{tabular}$


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 above, is the word CONTEST spelled out as the path is traversed from beginning to end?

$\textbf{(A) }63\qquad \textbf{(B) }128\qquad \textbf{(C) }129\qquad \textbf{(D) }255\qquad  \textbf{(E) }\text{none of these}$

Solution

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