Question

哪位亲帮忙解答一道英文奥数题！急急急！！！

9、Five children, Amelia, Bongani, Charles, Devine and Edwina, were in the
classroom when one of them broke a window. The teacher asked each of them to make a statement about the event, knowing that three of them always lie and two always tell the truth. Their statements were as follows:
Amelia: “Charles did not break it, nor did Devine.”
Bongani: “I didn’t break it, nor did Devine.”
Charles: “I didn’t break it, but Edwina did.”
Devine: “Amelia or Edwina broke it.”
Edwina: “Charles broke it.”
Who broke the window?

Answer 1

1. Since there was only one person that broke the window, the third sentence: Charles: “I didn’t break it, but Edwina did.” is equal to: Charles: “Edwina did.”

2. Rewrite it as follows:
Amelia: “Charles did not break it, nor did Devine.”
Bongani: “I didn’t break it, nor did Devine.”
Charles: “Edwina did.”
Devine: “Amelia or Edwina broke it.”
Edwina: “Charles broke it.”

3. The 4th and the 5th statement above cannot be both right, for it is a paradox.

4. Suppose the 3rd statement was true, so that the 1st and 2nd statement were both right.
Thus the statement 1, 2 and 3 were all right. There were 3 true statements, so that it is a paradox. Therefore the 3rd statement is wrong.

5. Suppose the 4th statement was true, so that Amelia was the one,
Thus the 1st and the 2nd statement were true. It is a paradox.
Therefore the 4th statement is wrong.

6. Suppose the 1st statement was true, so that the 5th statement was wrong.
Thus the statement 2, 3, 4 and 5 were wrong, so it is a paradox.
Therefore the 1st statement is wrong.

7. Given consequence from above, thus the statement 1, 3, and 4 are wrong. So that the statement 2, and 5 are true. Therefore from the statement 5, "Charles broke it.”, we conclude that Charles broke the window.

基本思路：
思路1. 先假设是谁，然后看有几个句子对，是否符合题设条件。
思路2. 根据句子之间的矛盾关系，假设哪个句子是对的，最后推出那几个对。

推理过程：
第3句等价于Charles: “Edwina did.”
假设3正确，则1,2 都对。那么加上3，共有三句对。与题设矛盾。所以3错误。
假设4对，则1,2 都对，那么加上假设的3，共有三句对。与题设矛盾。所以4错误。
假设1对，则5错。那么3,4,5都错。由3,4,5推知2错。2,3,4,5都错，与题设矛盾。所以1错误。
因此2,5都对。由5知Charles broke the window.

另一个简单的方法是：假设5正确，则1,3,4错，2,5对。正好符合。

仔细看看，看过程想清楚了没有。

Answer 2

假设C说真话，则B和D也是真话，不成立，
假设D说真话，A和B都为真，不成立，
此时可知A和E均没打碎。
假设A说真话，则E为假，B为真，则BCD也没有打碎，不成立，
所以A也说假话，只有B和E说真话……C打碎了窗户

Answer 3

9、五个孩子，阿米莉亚，邦哈尼，查尔斯，迪和埃德温娜，都在教室里当他们打破了一扇窗户。老师要求每个人作出声明的事件，知道三人总是撒谎和两个总是告诉真相。他们的声明如下：1、她说：“查尔斯并没有违背，也没有发现。”
2、 邦哈尼：“我没有打破它，也没有发现。”
3、查尔斯：“我没有打破它，但是埃德温娜做到了。”
4、 迪瓦恩说：“爱米丽亚或埃德温娜打破了它。”
5、埃德温娜：“查尔斯把它弄坏了。”谁打破了窗户？
一个简单的方法是：假设5（或1,2,3,4,）正确，最后得出 5正确（1,3,4错，2,5对。）正好符合。

Answer 4

Charles broke the window
若A 则三个说实话ABD
若B则只有一个说实话A
若C则两个说实话BE
若D则没有人说实话
若E则只有E说假话

追问

原因 详细点啊 亲

Answer 5

Edwina broke the window，Charles and Devine tell the truth