An alphabet consists of letters. What is the maximal length of a word if we know that any two consecutive letters of the word are different and that the word cannot be reduced to a word of the kind with by removing letters.
%V0
An alphabet consists of $n$ letters. What is the maximal length of a word if we know that any two consecutive letters $a,b$ of the word are different and that the word cannot be reduced to a word of the kind $abab$ with $a\neq b$ by removing letters.
Izvor: Međunarodna matematička olimpijada, shortlist 1966
Školjka 
letters. What is the maximal length of a word if we know that any two consecutive letters 
of the word are different and that the word cannot be reduced to a word of the kind 
with 
by removing letters.