Question

在一个神奇沼泽中，有两种会说话的两栖动物：蟾蜍说的话总是真的，青蛙说的话总是假的。Brian、Chris、LeRoy 和 Mike 四只两栖动物住在这个沼泽里，并作出如下陈述。

Brian：“Mike 和我是不同物种。”

Chris：“LeRoy 是青蛙。”

LeRoy：“Chris 是青蛙。”

Mike：“我们四个中至少有两个是蟾蜍。”

这些两栖动物中有多少只是青蛙？

In a magical swamp there are two species of talking amphibians: toads, whose statements are always true, and frogs, whose statements are always false. Four amphibians, Brian, Chris, LeRoy, and Mike live together in this swamp, and they make the following statements.

Brian: "Mike and I are different species."

Chris: "LeRoy is a frog."

LeRoy: "Chris is a frog."

Mike: "Of the four of us, at least two are toads."

How many of these amphibians are frogs?

$0$

$1$

$2$

$3$

$4$

答案：D

知识点：说真话者与说谎者逻辑推理

难度评级：1540

解答：

如果 Brian 是青蛙，那么他说谎，所以 Mike 必须也是青蛙。

如果 Brian 是蟾蜍，那么他说真话，也得到 Mike 是青蛙。因此 Mike 一定是青蛙，所以 Mike 在说谎。这说明蟾蜍至多有一只。 Chris 和 LeRoy 中至少有一只是青蛙。另一只说的话为真，所以是蟾蜍。因此恰有一只蟾蜍，也就是共有 $3$ 只青蛙。

所以正确答案是 D。

Chris and LeRoy cannot both be frogs, because then both of their statements would be true. They cannot both be toads either, because then both statements would be false. Thus exactly one of them is a toad.

If Brian were a toad, his statement would make Mike a frog. Brian and the one toad among Chris and LeRoy would then make Mike's statement true, which is impossible for a frog. Therefore Brian is a frog. His statement is false, so Mike is also a frog. Along with the one frog among Chris and LeRoy, there are $3$ frogs.

Thus, D is the correct answer.

2010 AMC 10A 第 15 题

答案：D

难度评级：1540

解答：

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