When is Cheryl's birthday?

Albert and

Bernard and Cheryl have just become friends. They want to know when she will be.

The birthday is. Cheryl gave them a list of 10 possible dates.

May 15, May 16, May 19.

June 17, June 18

July 65438, 2004

August 14, August 15, August 17

Cheryl went on to say

Albert and Bernard celebrated her birthday that month and that day respectively.

They are.

Albert: I don't know when Cheryl's birthday is, but I know Bernard doesn't know either.

Bernard: At first I didn't know when Cheryl's birthday was, but now I know.

Albert: Then I also know when Cheryl's birthday is.

When was that

Cheryl's birthday?

Albert and Bernard have just become friends with Cheryl. They wanted to know Cheryl's birthday, and Cheryl finally gave them ten possible dates:

May 15, May 16, May 19.

June 17, June 18

July 65438, 2004

August 14, August 15, August 17.

Cheryl told Albert the month and Bernard the date of her birthday.

Albert: I don't know Cheryl's birthday, but I know Bernard won't know either.

Bernard: I didn't know Cheryl's birthday at first, but now I know.

Albert: Then I also know Cheryl's birthday.

When is Cheryl's birthday?

-Reference ideas

1, in 10 days, only 18 and 19 appeared once. If Cheryl's birthday is 18 or 19, bernal who knows the date can guess the month and definitely know when Cheryl's birthday is. Albert determined that Bernade didn't know Cheryl's birthday, so he inferred that it wouldn't be in 18 or 19, and then decided that it wouldn't be in May or June when 18 or 19 appeared. So her birthday must be July or August.

2. According to bernal, only 14 appeared twice in the remaining five days in July and August. If Cheryl told bernal that her birthday was 14, it would be impossible for bernal to guess her birthday from Albert's words. So 14 is excluded. Now the only possibilities are July 16, August 15 and August 17.

After Bernade's speech, Albert also knew Cheryl's birthday, which indicated that the birthday month could not be in August. Because there are two possible days in August, and there is only one possibility in July.

So the answer is July 16. Have you worked it out?

* * * * The logical analysis of additional reference ideas in the original text is incorrect.

While excluding 18 and 19, exclude May and June! Sufficient necessary conditions are not provided to prove that May 15, May 16 and June 17 are not C's birthday.

Excluding May 19, it can't be C's birthday. The reason is that the date of 19 is only 1 among the dates of 10, which is reasonable. And if you want to exclude May according to 19, logically, 19 and May must be 1. When excluding months and days, excluding 19 must only exclude May and excluding May must only exclude 19. The latter condition is not available. There are three dates in May corresponding to 19. Excluding May means not only excluding 19, but also wrongly excluding May 15 and May 16! This is unreasonable and does not meet the conditions of 1 to 1. So 1 it is wrong to exclude reference ideas!

Even if May and June are wrongly excluded according to 18 and 19, there are five remaining dates, of which only 14 is a duplicate. A can't judge from these five dates, and B can't get the answer. Inconsistent with the original statement.

Furthermore, if B excludes 18, 19 and after May and June, 15, 16 and 17 are unique. If C's birthday is any of these three, B can get the answer at the beginning, unless it is 65438. This is inconsistent with his answer.

-Let's analyze the meaning of the question:

1, excluding 18 and 19 need not be analyzed, and A, B and anyone who has read the questions can be excluded immediately. Therefore, c tells a month and b date. After reading 10 dates, A and B actually face 8 dates. For A, there are 8 dates in 4 months, 2 in May, 2 in June 1, 2 in July and 3 in August; For B, eight dates are distributed in four days, two for each of 14, 15, 16 and 17. Therefore, if the month told to A is not June, A and B can't answer, because for A and B, the remaining answers are 1 or 1, and A and B are staring at each other.

2. So, in the first step, A said he couldn't answer, and B couldn't answer either. Reasoning from the point of view of A, no matter which day B knows (14, 15, 16, 17), there are two months to choose, and B can only choose 1, so B can't get the unique answer. (That is to say, we must add May 15, May 16 and June 17 to the five dates pointed out in this reference train of thought to get eight dates. Where 14 appears in July and August, 15 in May and August, 16 in May and July, and 17 in June and August). A Inference B According to these eight dates, no matter whether the date B knows is 14, 15, 16 or 17, it is impossible to tell which of the two months the answer is. Therefore, A can't get the answer if he knows B. A can say "B can't get the answer."

Step 2, infer from A's answer from B's point of view that C tells A that the month of birth must not be June. Because of the remaining eight dates, there is only 17 in June. If C tells A that her birthday is in June, A will get the answer immediately: June 17. A won't say "I don't know …" A says I don't know, which means that C's birthday month is in May, July and August.

But after B heard A's answer, B had the answer. B said, "I didn't know, but now I have the answer!" " "B how do you know? Inferring and analyzing A's answer from B's point of view, we can exclude the date of June, June 17 (from the perspective of solving problems: there are seven dates left, of which only August 17 is a single choice, and B must know C's birthday in advance). B It is not difficult to infer that the birthday month C told A must be the only month corresponding to 17, August. That is, C's birthday is1August 7. ?

4. In the third step, A sees that B only determines the birthday month mentioned by C through his own answer. Knowing that B must have answered by himself, A deduced that one of the eight dates was 14, 15, 16 and 17, and it could only be 17 June, so 17 only had August left. So through B's answer, A also knows that C's birthday is 17, which means 17 August. A immediately said, "I know!" " "

The results here are completely in line with the original statement.