Question 60
The people of an ancient tribe used a language in which the words were formed with two letters only: $A$ and $B$. Researchers discovered that any two words of equal length differ in at least three positions. For instance, the words $ABBAA$ and $AAAAB$ differ in positions $2$, $3$ and $5$, that is, in three positions.
Let $n \in \mathbb{N}$, $n \ge 3$. Prove that this language cannot contain more than $\left\lfloor \frac{2^n}{n+1} \right\rfloor$ words of length $n$.
Let $n \in \mathbb{N}$, $n \ge 3$. Prove that this language cannot contain more than $\left\lfloor \frac{2^n}{n+1} \right\rfloor$ words of length $n$.