1977 AMC 12 Problem 20
Attempt Problem 20 of the 1977 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 1977 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
20.
For how many paths consisting of a sequence of horizontal and/or vertical line segments, with each segment connecting a pair of adjacent letters in the diagram below, is the word CONTEST spelled out as the path is traversed from beginning to end?
none of these
Answer: E
Small hint:
Reverse each path, starting from the central in the bottom row
Big hint:
Count the left-going and right-going families separately, then correct for their common path
Solution:
Reverse the paths and spell TSETNOC from the central bottom In the family whose horizontal moves go left, each of the six steps has two choices: up or left. This gives paths. By symmetry, paths have horizontal moves going right. The all-vertical central path belongs to both families, so the total is This number is not among the first four choices.
Therefore, the correct answer is E.
Problem 20 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
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- 1954 AMC 12
- 1955 AMC 12
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