1. The problem statement, all variables and given/known data prove that there are not permutations of order 18 in S_9. 2. Relevant equations 3. The attempt at a solution let t=c_1,...,c_k is cycle decomposition of such permutation. let r_1,...,r_k the orders of c_1,...,c_k. then lcm(r_1,...,r_k) = 18 and r_1+...+r_k = 9. What To Do Next ?