Difference between revisions of "2020 AMC 8 Problems/Problem 12"

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Solution 1
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[b]Solution 1[/b]
  
 
Notice that <math>5!</math> = <math>2*3*4*5,</math> and we can combine the numbers to create a larger factorial. To turn <math>9!</math> into <math>10!,</math> we need to multiply <math>9!</math> by <math>2*5,</math> which equals to <math>10!.</math>  
 
Notice that <math>5!</math> = <math>2*3*4*5,</math> and we can combine the numbers to create a larger factorial. To turn <math>9!</math> into <math>10!,</math> we need to multiply <math>9!</math> by <math>2*5,</math> which equals to <math>10!.</math>  

Revision as of 00:56, 18 November 2020

[b]Solution 1[/b]

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