This is applid combinatorics.  1a) Suppose a dictionary in a computer has a “start” from which one can branch to any of the 26 letters: at any letter one can go to the preceding and succeeding letters. Model this data structure with a graph. (b) Suppose additionally that one can return to “start” from letters c or k or t. Now what is the longest directed path between any two letters?

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This is applid combinatorics. 

1a) Suppose a dictionary in a computer has a “start” from which one can branch to
any of the 26 letters: at any letter one can go to the preceding and succeeding
letters. Model this data structure with a graph.
(b) Suppose additionally that one can return to “start” from letters c or k or t.
Now what is the longest directed path between any two letters?

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