1. The problem statement, all variables and given/known data can cycles a and b create cycle d? let cycle a = 123 cycle b=12345 cycle d = 12 i.e. can some combination of a and b = d 2. Relevant equations only working in S5 3. The attempt at a solution I have tried various different permutations, 23 over all, things like aba, ab(a^-1), bab, (b^2)a(b^2) things like this. I am not sure if a solution exists but I have been trying differnt guesses for hours. I don't want to try 120 times to get it.