# Day 2: The Three Wise Men

• The three settlers always wear black hats.

• Sorry, forgot to include server/nickname details earlier, but I don't think I can edit the earlier post

Server: com5

nickname: sebysebyseby

If two men had white hats, the man with the black hat would have seen 2 white hats, and known immediately he has a black hat.

But that didn't happen.

If only 1 man had a white hat, then one of the the men with a black hat would have seen one white hat and one black hat. Since the situation above (two white hats) didn't immediately happen, he would know he was not wearing a white hat, and would have confidently said he was wearing a black hat

But that didn't happen.

The only possible case left is that everyone was wearing black hats (and no white hats), so the men know they must be wearing a black hat.

• Because none of them can talk about other's color.

if anyone of them saw two white hats, that would means that his hat was black. this is the first probability.

And since the case of the other two men, who didn't spoken, or none of them have spoken or know the color of their hat, it's two possibilities.

First, they saw two black hats or a white hat and a black one, and that possibility is shared by both of them, meaning that they both have to see only one white hat....

It's something they have in common.... That is, the two of them have a view of one white hat or two black hats, and the possibility is that the white hat will be his hat, not the third man's hat.

And because the third man, who's smart man, who didn't see any white hat in front of him.

That means the possibility that the three were silent was that they were all wearing black hats because none of them spoke because they didn't see any white hat and about to have his hat white, and the third smart guy didn't see any white hat.

and below is the solution with probability equation :

morsy

https://ts15.travian.com

Serial number first man, second man, third man.

1 probability ratio 3/3 black black black

2 Probability ratio 1/3 black black white

3 Probability ratio 1/3 black black black

4 Probability ratio 1/3 White black black

5 Probability Ratio 3/0 White White White

6 Probability ratio 3/0 white white black

According to the previous schedule, the only possibility is the real one is the first one

• Server ts15
Nickname: Gemini1976

Answer: If Both of the other men had white hats then the hat on his own head was guaranteed to be black since there were more black hats than white
If Both of the other men wore Black hats there is a chance that the hat on his own head was white but there was also a chance that this own hat would be black.
Therefore his own hat would be black regardless and the same goes for the other two

• If he can see the two other hats, and they are black there are 2 possibilities:

1. He had a Black hat

2. He had a White hat

But if he had a white hat this means that the other immediately announce that he has a black one by the logic:

if he has an white one and the other a black one there are two possibilities:

1. He was wearing a white hat and the other announce immediately that he wearing a black

2. He was wearing a black hat.

Nickname: Bacescu

Server: https://ts15.travian.com

• (1) If you see ⚪ ⚪, then you will know immediately that you wear ⚫. Solution found!

(2) If you see ⚪ ⚫, then in theory, you can wear either ⚪ or ⚫, but..

.. but if you wear a ⚪, the one who wears ⚫ would have found the solution (1) immediately. So solution found! (Albeit it wasnt -and couldnt have been- you who solved first.)

If the one who wears the ⚫ dont say a thing (dont find the solution 'immediately'), you know you wear ⚫. (And apparently the other one, who wears ⚫ should reach the same conclusion at the very same time.) Solution found 'almost immediately'!

(3) If you see ⚫⚫, then in theory you still can wear either ⚪ or ⚫, but

if you wear a ⚪, the other 2 ⚫s should reach the (2) solution. If neither solves this 'almost immediately', you know that your hat is ⚫ (and again, the other 2 should reach the same conclusion at the same time). So solution found 'a bit later than almost immediately'.

• nickname : Matt

Server: ts15.travian.com

Hi there! I really enjoyed this riddle and my guess would be:

All three of the wisemen were aware of the 3 hats atleast 2 were black thus they all only needed to find confirmation on their hat color.

I believe one of the wisemen caught a glance of his hat color in the pearls from the daughter and mothers pearlclasps since they are reflective white and with the correct angle you may see a black hats reflection.

And thus one of the men knew for sure that all 3 hats worn were black.

• Nickname: Obelix

Server : ts15.travian.com

The 3rd man could see that the other 2 men were wearing black hats, So 2 white hats is not possible. That means his own hat is either black or white. The third man also realized that had his own hat been white then at least one of the other 2 men would have easily guessed the color of their hat to be black. Since the other two men have not been able to answer yet, that means the combination of ⚪ ⚫ is not possible. Therefore, his own hat cannot be White. So he quickly answers Black.

• Step one:

If anybody sees two white hats, gives answer immediately.

All 3 of them are not giving the answer, they are all aware that in the game are 1 white and 3 black hats.

And they are all aware of that (being wise).

Step two:

As in the game are 1 white and 3 black hats (they know it after some time)

if anybody sees white hat, knows that he wears black hat and gives answer.

No one sees white hat, at first no one gives immediate answer being aware that he could have either third black or white hat.

Step three:

The time is passing...

The one who is fastest reasoning this described way, becomes aware that no one is giving the answer because not seeing the white hat and he concludes that everyone is wearing black hats.

• cam1258

Codex Victoria COM

If two hats were white, the man who could see them (man 1) would have called out the color of his hat as black because that is the only option left.

If this man (man 1) saw that one hat was white, and he did not call out any color, the man 2 could deduce that his hat was black because he did not see a white hat on man 3.

Since neither man called out a color, the third man would know that his hat is black, which is the only color that does not allow either the second or third man to guess the color of their own hat.

• Nickname: Narcos

Server: Codex Victoria COM

1) You are one of the man. You look to another guys and see that both of them are wearing white hats. There are only two white hats and it means that your are wearing black hat.

2) You look to another guys and see that one of them is wearing white hat and another man black hat. If your hat is white, than guy who is wearing black hat is himself and he could see two white hats. If it is he will that his hat is black (because he see two white hats). If he didn't tell nothing it means, that your hat is black.

3) If you see two black hats you can't do with this information nothing. But if your hat is white, other two guys see white and black hat, and one of them would tell his hat according to mentioned above. Nobody of them didn't do this and it means that they see two black hats and your hat is black.

Because of that rules one of the guy knew correct answer

• He can figure out on two ways, first by luck because it can be two answer and one is right one. One is for example that if man see 2 black heat he can guess that third is also black, or if he is wrong and he had bad luck in guessing, next one will have right answer 2 heats are black and 3th is white, but he can also read body gesture of two others and guess right answer :).

• Sorry i didnt write all nessesary, nickname is Jehudijel and server played Codex Victoria COM.

He can figure out on two ways, first by luck because it can be two answer and one is right one. One is for example that if man see 2 black heat he can guess that third is also black, or if he is wrong and he had bad luck in guessing, next one will have right answer 2 heats are black and 3th is white, but he can also read body gesture of two others and guess right answer :).

• Account: maxwell

Server: ts1.travian.com.vn

Situation 1: If I see 2 white hats, then I will immediately answer that my hat is black.

Situation 2: If I see one black hat and one white hat, my hat might be black or white. If my hat is white then the other will already answer. If the black hat guys hesitated to answer right away, that mean he isn't entirely sure whether his hat is black or white, so he must see one black (my hat) and one white (the white hat guy I see). Therefore, my hat is black.

Situation 3: If I see 2 black hats, then I cannot tell whether my hat is black or white. If my hat is white then after a while, one of two black hat guys will notice the situation 2 and will definitely answer before me.

But, because all of the men are waiting for each other to answer for so long, there might be a chance that all of us are black hats. The longer the time we waiting, the higher the chance that we are all black hat. So eventually, one of us will answer that we are all black hat.

• Hi,

1. If 2 men have white hats then that one who sees 2 white hats will know that they have 2 white and one black hat (his).
2. If 1 man (lets call him Atius) would see white hat and black hat and that man with black hat doesnt say he knows the answer it means that Atius doesnt have white hat. And then Atius would say the answer.
3. But if none of them sees white hat they all stay silent trying to figure out if they have white or black hat. And therefore they all must have black hats.

Tiirp
ts15.travian.com
Codex Victoria

• Man number 1 sees 2 black hats, that means that he could have black or white hat.

After that you need to start thinking from other man (number 2) perspective.

option A : man number 2 sees a white cap on you. That means that he could have only black hat, otherwise man number 3 sees 2 white hats and its easy answer for him. Because man number 3 is quite, that means, that man number 2 doesn't have a white hat. But man number 2 is quite as well, so that means he doesn't know what color his hat- This is possible only if man 1 number has a black hat. After man number 3 and 2 are quite for a long time, man number 1 realizes that he has a black hat.

• Nickname: TheGoldOne

Server: Codex Vicyoria, .com

A tough one....

So, assuming each of those 3 is designated by A, B and C.

A would know the hat he's wearing if both B and C were wearing white hats. But since they are both black, his hat might be white or black.

Now B, would also think this way naturally, but... If C was wearing a white hat, A would have guessed his hat if B is wearing also a white hat, which is not the case. Leaving him confused whether he has a white or black hat.

Which leaves us with C, looking at both A and B, and seeing them confused with their black hats, it would only mean that he also is wearing a black hat.

A really tough one, I don't even know if I was able to describe it as it should be...

Or or or, he just looked into the reflection of the polished helmet in the armory nearby or the pearl clasps and found it out haha

• По реакции других.

Если бы я только видел черные шапки. Я могу предположить, что я одет в белое.

Второй мудрец также посоветовал бы ... чтобы на нем были белые, а третий немедленно ответил бы, увидев 2 белых шапки .....

Но оба молчат

Так что я ношу черное

Newproblema https://ts15.travian.com

• If A sees B (Black) and C (Black) he does not know which he is wearing until he realises,

B (Black) must be seeing C (Black) and A

C (Black) must be seeing B (Black) and A

If A's Hat is white then both B & C will be stuck in an insolvable problem as they cannot know for a fact if they are wearing Black or White (both being possible).

As B & C stay silent so long and A realises the puzzle must have an answer he concludes he must be wearing a Black Hat.