1995 AMC 12 Problem 29
Attempt Problem 29 of the 1995 AMC 12 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 1995 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
29.
For how many three-element sets of positive integers is it true that
Answer: C
Small Hint:
Factor into distinct primes and assign each prime to one of the factors
Big Hint:
Count separately the cases in which one factor is and in which all three factors exceed
Solution:
Since each prime belongs to exactly one of the three factors. If all factors exceed their unordered prime groups form a partition of five objects into three nonempty blocks, counted by If one factor is the primes are partitioned into two nonempty blocks, giving The factors are distinct because their disjoint prime sets differ. Thus the total is and the correct answer is C.
Problem 29 in Other Years
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