1978 AMC 12 第 22 题

Question

一张卡片上恰好写着以下四句话：

这张卡片上恰有一句话是假话。
这张卡片上恰有两句话是假话。
这张卡片上恰有三句话是假话。
这张卡片上恰有四句话是假话。

（假设卡片上的每句话非真即假。）其中假话的数量恰为

The following four statements, and only these, are found on a card:

On this card exactly one statement is false.
On this card exactly two statements are false.
On this card exactly three statements are false.
On this card exactly four statements are false.

(Assume each statement on the card is either true or false.) Among them the number of false statements is exactly

0

1

2

3

4

答案：D

知识点：逻辑推理说真话者与说谎者

难度评级：1860

小提示：

设假话的实际数量为

m

Assume the actual number of false statements is

m

大提示：

对每个可能的

m

，数一数上面四句话中有几句会为真

For each possible

m,

count how many of the four displayed statements would then be true

解答：

若假话的实际数量

m

是

1

、

2

、

3

、

4

中的一个，则上面的四句话中恰有一句为真，也就是声称假话数量为

m

的那一句。因此恰有三句话是假话，从而必须有

m=3

。这确实自洽：第三句话为真，其余三句为假。

因此，正确答案是 D。

If the actual number

m

of false statements is one of

1,

2,

3,

4,

exactly one displayed statement—the one naming

m

—is true. Therefore exactly three statements are false, forcing

m=3.

This is consistent: the third statement is true and the other three are false.

Therefore, the correct answer is D.

1978 AMC 12 第 22 题

答案：D

难度评级：1860

小提示：

大提示：

解答：

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