MathDB

On Babba Island they use a two-letter alphabet,

a

and

b

, and every (finite) sequence of letters is a word. For each set

P

of six words of

4

letters each, we denote

N_P

to the set of all words that do not contain any of the words of

P

as a syllable (subword). Prove that if

N_P

is finite, then all its words are of length less than or equal to

10

, and find a set

P

such that

N_P

is finite and contains at least one word of length

10

2