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From any letter in the diagram, a move can only be made to a letter diagonally adjacent and below. In how many different ways can a path that spells MATHCOUNTS be taken?

 

\(\begin{array}{ccccccccc} & & & &M& & & & \\ & & &A& &A& & & \\ & &T& &T& &T& & \\ &H& &H& &H& &H& \\ C& &C& &C& &C& &C\\ &O& &O& &O& &O& \\ & &U& &U& &U& & \\ & & &N& &N& & & \\ & & & &T& & & & \\ & & & & &S& & & \\ \end{array}\)
 

 Apr 21, 2023
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There are 2^4 ways to get to the Cs, and thinking backwards, we see that there are 2^4 ways to get from the Cs to the S.  So there are 2^4*2^4 = 256 ways.

 Apr 21, 2023

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