Question 29
If $S$ is a $10^4$-digit binary string consisting of zeroes and ones, and $k \le 10^4$ is a positive integer, a $k$-block of $S$ is any substring consisting of $k$ consecutive digits; two $k$-blocks, $a_1a_2\dots a_k$ and $b_1b_2\dots b_k$, are of the same type if $a_i = b_i$, $i = 1, \dots, k$. Consider all $10^4$-digit binary strings whose 3-blocks are of at most 7 types. Determine the maximum number of types the 10-blocks of such a string may fall in.
Cătălin Gherghe
Cătălin Gherghe