MathDB
Squares in Factorial Product

Source:

February 20, 2008
factorial

Problem Statement

How many perfect squares are divisors of the product 1!⋅2!⋅3!⋯9! 1!\cdot 2!\cdot 3!\cdots 9!? <spanclass=′latex−bold′>(A)</span> 504<spanclass=′latex−bold′>(B)</span> 672<spanclass=′latex−bold′>(C)</span> 864<spanclass=′latex−bold′>(D)</span> 936<spanclass=′latex−bold′>(E)</span> 1008 <span class='latex-bold'>(A)</span>\ 504 \qquad <span class='latex-bold'>(B)</span>\ 672 \qquad <span class='latex-bold'>(C)</span>\ 864 \qquad <span class='latex-bold'>(D)</span>\ 936 \qquad <span class='latex-bold'>(E)</span>\ 1008
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