2009 AMC 8 Problem 16
Attempt Problem 16 of the 2009 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2009 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
16.
How many -digit positive integers have digits whose product equals
Answer: D
Small hint:
List the unordered triples of digits whose product is
Big hint:
Triplets with three distinct digits have permutations, while has
Solution:
The only triples of integers less than that multiply to are
The triples with distinct numbers can be rearranged to form distinct -digit positive integers. The other triple can be arranged to form distinct -digit positive integers.
This leaves a total of integers.
Thus, D is the correct answer.
Problem 16 in other years
- 1985 AMC 8
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