Intuitively, this problem seems isomorphic to the famous NP-complete problem, 3SAT[1]. Instead of picking binary states, you have to pick symbols to insert, and

Intuitively, this problem seems isomorphic to the famous NP-complete problem, 3SAT[1]. Instead of picking binary states, you have to pick symbols to insert, and where, that yield the desired outcome. If this intuition is true, then if you can write a program to generate these expressions (in polynomial time) then you'd have also proven P=NP. You could probably brute force it though as the difficulty scales with the length of your target number. 1. https://en.wikipedia.org/wiki/Boolean_satisfiability_problem https://en.wikipedia.org/wiki/Boolean_satisfiability_problem