Counting

 

Starting with the A moving one letter at a time vertically, horizontally, or diagonally, how many different paths spell ARCH?   

 

        A   

     RRR   

  CCCCC   

HHHHHHHH   

 

From the A, there are three ways to get to an R.  

From the R, there are three ways to get to a C.    

From the C, there are three ways to get to an H.   

 

3 x 3 x 3  =  27 paths   

 

There are 8 H's in the bottom row.  That 8th one is superfluous.   

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