Here are the answers for the practice problems. Note that, in the actual quiz, you should show all your work and reasoning, not just the answers. First 4 problems: 1. n 3^{n-1}. 2. 0. 3. 1 if n>= 8; and 0 if n < 8. (A self-conjugate partition is a partition whose Young diagram is symmetric with respect to reflection around the diagonal.) 4. Stirling number of 2nd kind S(n-1,2) = 2^{n-2}-1 if n >= 2 (0 if n <= 2). Next 5 problems: 1. 3^n. 2. 2^{n+1}/(n+1). 3. 0 if n < 6. Otherwise, k(k+1)(2k+1)/6 if n is even and k = (n-4)/2; and m(m+1)(m+2)/3 if n is odd and m = (n-5)/2. 4. Stirling number of 2nd kind S(n,3) = (1+3^{n-1}-2^n)/2. 5. (n+1 choose 2)! (factorial of (n+1 choose 2)). Note that problems 3 and 4 (especially problem 3) are too hard for an actual quiz.