## Spring 2017, problem 35

Let $m_1,m_2,m_3,\dots,m_n$ be a rearrangement of the numbers $1,2,\dots,n$. If $n$ is odd, show that the product $$\left(m_1-1\right)\left(m_2-2\right)\cdots \left(m_n-n\right)$$ is an even integer.