1976 AMC 12 Problem 28
Attempt Problem 28 of the 1976 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 1976 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
28.
Lines are distinct. All lines a positive integer, are parallel to each other. All lines a positive integer, pass through a given point The maximum number of points of intersection of pairs of lines from the complete set is
Answer: B
Small hint:
Start with intersections in general position
Big hint:
Remove the pairs among the parallel lines and collapse the pairs among the concurrent lines to one point
Solution:
There are indices divisible by and congruent to Starting from the parallel group contributes no intersections, removing The concurrent group’s pairs all give one point rather than distinct points, removing another All remaining intersections can be chosen distinct, so the maximum is
Therefore, the correct answer is B.
Problem 28 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
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- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
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