China DOS Union

There are 50 people going to take a bath... There are two places: a men's bath and a women's bath.
Rules: 1. There must be women among them...
　　　2. Everyone can tell whether other people are male or female, but cannot determine whether they themselves are male or female. (Dizzying, who doesn't know their own sex?? But the problem is defined this way. Hehe...)
　　　3. They must not go to the wrong bath. Once they determine which bath they should go to, they go take a bath.
Conditions: On the first day, no one heard the sound of anyone jumping into the bath...
　　　　On the second day, no one heard the sound of anyone jumping into the bath...
　　　　On the third day, someone was heard jumping into the bath!!!
Question: How many women are there among these 50 people???

Everyone is welcome to write out the answer and the reasoning process...

All of them are women?

The following is quoted from what 西西 posted at 2003-6-12 16:29:03:
All of them are women?

If it's like you said, then why did no one go take a bath on the first or second day? Why did someone only go on the third day???

Because on the first day, everyone saw that all the people going to bathe were women, so they didn't know whether they themselves were male or female, so they didn't go.
On the second day, what they saw was the same as on the first day, so they still didn't go.
By the third day, they could be sure that they were women too, so they went.


The first two times they saw that the others were all women, and in the end they decided that they were women too, so they went to bathe......

Sheesh, who would not know their own sex but know other people's sex??
This kind of question is really, well, that, that~~

The following is quoted from what 西西 posted at 2003-6-12 16:41:29:
By the third day, they could be sure that they were women too, so they went.

The first two times they saw that the others were all women, and in the end they decided that they were women too, so they went to bathe......

Why is it that by the third day, they suddenly "can be sure they're women too"? That doesn't make sense...

Either they are or they aren't, it's not something that can be solved just by "deciding," hehe...

The following is quoted from what 西西 posted at 2003-6-12 16:41:29:
Because on the first day, everyone saw that all the people going to bathe were women, so they didn't know whether they themselves were male or female, so they didn't go.

Please note: on the first day no one went to take a bath!!! Only on the third day was the sound of someone jumping into the bath heard, which means only then did people start going to bathe!!!

Could it be that they only found out on the third day that they were female??
Then they must have lived for nothing before that~~ who could live that long and still not know their own sex??

The following is quoted from what Dark-Destroy posted at 2003-6-12 16:53:33:
Could it be that they only found out on the third day that they were female??
Then they must have lived for nothing before that~~ who could live that long and still not know their own sex??

Sheesh... DD, can you stop derailing, okay?
The problem is defined this way, it's not talking about real life...
In real life of course you know your own sex clearly.

The following is quoted from what ko20010214 posted at 2003-6-12 16:51:39:

The following is quoted from what 西西 posted at 2003-6-12 16:41:29:
Because on the first day, everyone saw that all the people going to bathe were women, so they didn't know whether they themselves were male or female, so they didn't go.

Please note: on the first day no one went to take a bath!!! Only on the third day was the sound of someone jumping into the bath heard, which means only then did people start going to bathe!!!

Because on the first day, everyone saw that the others were all women, so they couldn't confirm their own sex. So no one dared go take a bath.
On the second day, everyone still saw women, and still didn't know their own sex, so they still didn't dare rashly go take a bath.
As for the third day, there are two possibilities. First, no one took a bath in the first two days, so today someone decided to be the first to try. Second, since for two days they saw only women and those women didn't bathe, that means those women also were afraid of being a different sex and so didn't bathe, and then....


Hehe, tell us your answer, I really can't guess it....

Sheesh, there is no possibility of "today someone decided to be the first to try," because you have to follow the rules of the game!!!

Second, since for two days they saw only women and those women didn't bathe, that means

Just what exactly does that mean???

It should be three women. KO, right?

1. If there were one woman, then everything that woman saw would be men. Since the condition says there must be women, then she could immediately determine that she is a woman, so she should have gone to take a bath on the first day. But she didn't, so there was more than one woman.
2. If there were two women, the first woman would see 48 men and one woman. She would think, if I were a man, then that other woman could immediately determine that she is a woman, and she would go take a bath right away. But she didn't on the first day, so on the second day this first woman could determine that she is not a man, therefore she would go bathe. But she didn't bathe on the second day either, which shows there were not just two women either.
3. By the same reasoning, when there are three women, after the first two days, this first woman can confirm that she is a woman. So on the third day she can go take a bath.
Therefore, it can be concluded that there are three women.

The following is quoted from what yiyesong posted at 2003-6-12 23:41:34:
1. If there were one woman, then everything that woman saw would be men. Since the condition says there must be women, then she could immediately determine that she is a woman, so she should have gone to take a bath on the first day. But she didn't, so there was more than one woman.
2. If there were two women, the first woman would see 48 men and one woman. She would think, if I were a man, then that other woman could immediately determine that she is a woman, and she would go take a bath right away. But she didn't on the first day, so on the second day this first woman could determine that she is not a man, therefore she would go bathe. But she didn't bathe on the second day either, which shows there were not just two women either.
3. By the same reasoning, when there are three women, after the first two days, this first woman can confirm that she is a woman. So on the third day she can go take a bath.
Therefore, it can be concluded that there are three women.

Really impressive! But I only went by my sixth sense, while you could actually put it into words. Ah, my head is spinning just reading it. You're really too smart. I believe you'll get a good result on the final exam~!