Question 92
Given a positive integer $n$. Let us call a *word* any sequence of $n$ letters of an alphabet. Define the distance $\rho(A, B)$ between the words $A = a_1a_2...a_n$ and $B = b_1b_2...b_n$ as the number of positions in which they differ (i.e. the number of indices $i$ for which $a_i \ne b_i$). We say that the word $C$ lies between the words $A$ and $B$ if $\rho(A, B) = \rho(A, C) + \rho(C, B)$. What is the largest number of words that can be chosen so that among every three of them there is a word that lies between the other two?