Difference between revisions of "2023 AMC 12B Problems/Problem 23"
(→Solution) |
(→Solution) |
||
Line 54: | Line 54: | ||
~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com) | ~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com) | ||
+ | |||
+ | ==See Also== | ||
+ | {{AMC12 box|year=2023|ab=B|num-b=23|num-a=25}} | ||
+ | {{MAA Notice}} |
Revision as of 20:35, 15 November 2023
Solution
The product can be written as
Therefore, we need to find the number of ordered tuples where
,
,
,
,
are non-negative integers satisfying
.
We denote this number as
.
Denote by the number of ordered tuples
where
with
.
Thus,
Next, we compute .
Denote . Thus, for each given
, the range of
is from 0 to
.
Thus, the number of
is
Therefore,
By solving , we get
.
~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)
See Also
2023 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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.