AMC 8 1993 Problem 23
AMC8 1993 年第 23 题
逻辑推理（跨域）★★★☆☆
Five runners, , , , , , have a race, and beats , beats , beats , and finishes after and before . Who could NOT have finished third in the race?
五名跑步者 、、、、 参加比赛。 击败 ， 击败 ， 击败 ， 在 之后、 之前完赛。谁不可能获得第三名？
- A.
- B.
- C.
- D.
- E.
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
First, note that must beat , , , and by transitivity, . Thus is in first, and not in 3rd. Similarly, is beaten by , , and by transitivity, , so is in fourth or fifth, and not in third. All of the others can be in third, as all of the following sequences show. Each follows all of the assumptions of the problem, and they are in order from first to last: PTQRS, PTRQS, PRTQS. Thus the answer is .
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