Question 193
In a language, an alphabet with 25 letters is used; *words* are exactly all sequences of (not necessarily different) letters of length $17$. Two ends of a paper strip are glued so that the strip forms a ring; the strip bears a sequence of $5^{18}$ letters. Say that a word is *singular* if one can cut out a piece bearing exactly that word from the strip, but one cannot cut out two such non-overlapping pieces. It is known that one can cut out $5^{16}$ non-overlapping pieces each containing the same word. Determine the largest possible number of singular words. (Bogdanov I.)