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。”

这四只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 four 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

小提示：

Chris 和 LeRoy 不可能是同一物种。

Chris and LeRoy cannot have the same species

大提示：

如果 Brian 是蟾蜍，Mike 的陈述会导致矛盾。

If Brian were a toad, Mike’s statement would create a contradiction

解答：

Chris 和 LeRoy 不可能都是青蛙，否则他们的陈述都会是真的；也不可能都是蟾蜍，否则他们的陈述都会是假的。因此两者中恰有一只是蟾蜍。

如果 Brian 是蟾蜍，他的陈述会说明 Mike 是青蛙。这样 Brian 与 Chris、LeRoy 中的那只蟾蜍就使 Mike 的陈述为真，这与青蛙总说假话矛盾。因此 Brian 是青蛙。他的陈述为假，所以 Mike 也是青蛙。再加上 Chris、LeRoy 中的那只青蛙，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

小提示：

大提示：

解答：

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