A repeating word is defined by one that has a string of characters repeated, back to back, anywhere inside it. Using the English alphabet, "banana" is a repeating word, as are "inn" and "tartar", of repeating substring lengths 2, 1, and 3 respectively.

Mathematically speaking, it means you can't write word 'W' such that W=abbc, a, b, and c being substrings, if b is the non-null string.

As can be expected, there are a whole lot of non-repeating "words" in the English language (word, now, is defined as any set of characters in the alphabet)... it's easy to form one, because there are 26 unique characters in the alphabet. This brings us to our problem...

(1) How many non-repeating words are there, total, in an alphabet with two characters?

(2) How many non-repeating words are there of length 6 using the English alphabet?

(3) How many non-repeating words are there of length 10 in an alphabet with three characters?

(4) How many non-repeating words are there of length L in an alphabet with three characters?

Parts 1, 2, and 3 are relatively easy, part 4 is unsolved.
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