Problem - 4218
Let $N = 7\times 8\times 9\times 15\times 16\times 17\times 23\times 24\times 25\times 43$. Compute $N\pmod{11}$.
We have $$\begin{array}{ll} & 7\times 8\times 9\times 15\times 16\times 17\times 23\times 24\times 25\times 43 \\ \equiv & 7\times 8\times 9\times 4\times 5\times 6\times 1\times 2\times 3\times 10 \\ \equiv & 10! \\ \equiv & -1\pmod{11} \end{array}$$
The last step is the result of applying the Wilson's theorem. Therefore the answer is $\boxed{10}$.