MathDB

Consider the set

L

of binary strings of length less than or equal to

9

, and for a string

w

define

w^{+}

to be the set

\{w,w^2,w^3,\ldots\}

where

w^k

represents

w

concatenated to itself

k

times. How many ways are there to pick an ordered pair of (not necessarily distinct) elements

x,y\in L

such that

x^{+}\cap y^{+}\neq \varnothing

Problem Statement