# A Permutation Teaser

Algebra Level 5

Let $$\{a_1,a_2\ldots a_6\}$$ be a permutation of $$\{1,2,\ldots 6\}$$.

How many permutations satisfy that $\left(\dfrac{a_1+1}{2}\right)\left(\dfrac{a_2+2}{2}\right)\cdots \left(\dfrac{a_6+6}{2}\right) > 6!$

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