2020 AMC 8 Problems/Problem 12

Revision as of 00:56, 18 November 2020 by Iirishabii (talk | contribs)

Solution 1

Notice that $5!$ = $2*3*4*5,$ and we can combine the numbers to create a larger factorial. To turn $9!$ into $10!,$ we need to multiply $9!$ by $2*5,$ which equals to $10!.$

Therefore, we have

\[10!*12=12*N!.\] We can cancel the $12s,$ since we are multiplying them on both sides of the equation.

We have

\[10!=N!.\] From here, it is obvious that $N=10(A).$

-iiRishabii