2020 AMC 8 Problems/Problem 12
Contents
[hide]Problem
For a positive integer , the factorial notation
represents the product of the integers from
to
. What value of
satisfies the following equation?
Solution 1
We have , and
. Therefore the equation becomes
, and so
. Cancelling the
s, it is clear that
.
Solution 2 (variant of Solution 1)
Since , we obtain
, which becomes
and thus
. We therefore deduce
.
Solution 3 (using answer choices)
We can see that the answers to
contain a factor of
, but there is no such factor of
in
. Therefore, the answer must be
.
Video Solution
See also
2020 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
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All AJHSME/AMC 8 Problems and Solutions |
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