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Let {a1,a2…a6}\{a_1,a_2\ldots a_6\}{a1,a2…a6} be a permutation of {1,2,…6}\{1,2,\ldots 6\}{1,2,…6}.
How many permutations satisfy that (a1+12)(a2+22)⋯(a6+62)>6!\left(\dfrac{a_1+1}{2}\right)\left(\dfrac{a_2+2}{2}\right)\cdots \left(\dfrac{a_6+6}{2}\right) > 6!(2a1+1)(2a2+2)⋯(2a6+6)>6!
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