Question 30
a_1, a_2, ..., a_{49} is a permutation of the set $\{2, 3, ..., 50\}$. Denote $S_1 = a_1$, $S_2 = a_1 + a_2$, ..., $S_{49} = a_1 + a_2 + ... + a_{49}$. Find the number of different sequences $S_1, S_2, ..., S_{49}$ in which no one of $S_i$ is divisible by $3$.