Difference between revisions of "2020 AMC 8 Problems/Problem 12"
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− | For positive | + | For a positive integer <math>n</math>, the factorial notation <math>n!</math> represents the product of the integers from <math>n</math> to <math>1</math>. What value of <math>N</math> satisfies the following equation? <cmath>5!\cdot 9!=12\cdot N!</cmath> |
==Solution 1== | ==Solution 1== |
Revision as of 01:01, 18 November 2020
For a positive integer , the factorial notation
represents the product of the integers from
to
. What value of
satisfies the following equation?
Solution 1
Notice that =
and we can combine the numbers to create a larger factorial. To turn
into
we need to multiply
by
which equals to
Therefore, we have
We can cancel the
's, since we are multiplying them on both sides of the equation.
We have
From here, it is obvious that
-iiRishabii