Difference between revisions of "2020 AMC 8 Problems/Problem 12"
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Line 8: | Line 8: | ||
<cmath>10!*12=12*N!.</cmath> | <cmath>10!*12=12*N!.</cmath> | ||
− | We can cancel the <math> | + | We can cancel the <math>12</math>'s, since we are multiplying them on both sides of the equation. |
We have | We have | ||
<cmath>10!=N!.</cmath> | <cmath>10!=N!.</cmath> | ||
− | From here, it is obvious that <math>N=10(A).</math> | + | From here, it is obvious that <math>N=\boxed{10\textbf{(A)}}.</math> |
-iiRishabii | -iiRishabii |
Revision as of 00:59, 18 November 2020
For positive integers , the notation
denotes 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