MathDB

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 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.)

Problem Statement