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Quiz

Let Q(n) be the triple mixed hook expression in the Quiz by replacing the number 1001 by n. Then Σ Q(n)x^n is given by the Euler pentagonal theorem. Thus, if n= k(3k+1)/2, then Q(n)=(-1)^k. Now 1001=(-26)(-3*26+1)/2, so that Q(1001)=(-1)^(-26)=1.

The answer is: 1

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