A2. Find all permutations a_{1}, a_{2}, ... , a_{9} of 1, 2, ... , 9 such that a_{1} + a_{2} + a_{3} + a_{4} = a_{4} + a_{5} + a_{6} + a_{7} = a_{7} + a_{8} + a_{9} + a_{1} and a_{1}^{2} + a_{2}^{2} + a_{3}^{2} + a_{4}^{2} = a_{4}^{2} + a_{5}^{2} + a_{6}^{2} + a_{7}^{2} = a_{7}^{2} + a_{8}^{2} + a_{9}^{2} + a_{1}^{2}.


A5. Given a permutation s_{0}, s_{2}, ... , s_{n} of 0, 1, 2, .... , n, we may transform it if we can find i, j such that s_{i} = 0 and s_{j} = s_{i1} + 1. The new permutation is obtained by transposing s_{i} and s_{j}. For which n can we obtain (1, 2, ... , n, 0) by repeated transformations starting with (1, n, n1, .. , 3, 2, 0)?

