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Revision as of 02:23, 8 February 2020
Let denote the number of ways of writing the positive integer
as a product
where
, the
are integers strictly greater than
, and the order in which the factors are listed matters (that is, two representations that differ only in the order of the factors are counted as distinct). For example, the number
can be written as
,
, and
, so
. What is
?
Solution
Bash.
Since , for the number of
, we have the following cases:
Case 1: , we have
, only 1 case.
Case 2: , we have
, totally
cases.
Case 3: , we have
, totally
cases.
Case 4: , we have
, totally
cases.
Case 5: , we have
, totally
cases.
Case 6: , we have
, totally
cases.
Thus, add all of them together, we have cases. Put
.
~FANYUCHEN20020715
See Also
2020 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 23 |
Followed by Problem 25 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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