You want to design a set of yes/no questions for quickly searching the symmetric group. The questions have to be of the form "Does your permutation move $a_1$ to $b_1$ or $a_2$ to $b_2$ or ... or $a_k$ to $b_k$?" Given a random permutation, you will ask all of your questions about that permutation, and your goal is to know what the permutation is once you know the answers to your questions.