# Day 2: The Three Wise Men

• Clarissa - COM3

The man (let’s call him A) who gets it, is thinking it through. He knows that if he has a white hat, one of the others (B) is looking at a white and a black hat. That person will then think of themselves and think “I can’t have a white hat because if I did, then (C) would have shouted already because they’d see two white hats” so by the fact that C is still thinking it through, it means A doesn’t have a white hat.

I hope that makes sense

• The wisest man had thinking like that:

1. There are no two white hats, because will be too easy to guess for one of them;

2. There are no two black / one white hats - it will be impossible to solve, the architect will not asking for a unsolvable case;

So the only correct answer will be three black hats (because 1&2).

• 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.

• Hey,

if one of them seen one white and one black hat, he would be wondering if he is white hat, but if he was white hat, the last old man (black hat) would know the answer, that's how first old man knows he is not a white hat. That's why one old man realized if he was a white hat, one of other old men would've realized the answer by then.

Nick: Dinulja

Server: comx

• the man understood he wore black hat because there was no reaction from the other men;

w=white hate,b=black hat

situation 1.

w-w-b(2white hats and 1 black hat, since there are 2 white hats in total, the man wearing the black hat would've known immediately hes wearing black)

situation 2.

w-b-b(one of the men in the black hat sees a white hat and a black one,the other man with the black hate sees the same,each one of them has couple of seconds to realize that theyre wearing a black hat since none of them yet called the color)

situation 3.

b-b-b(they all see 2 black hats,so the possibility of 2 white hats is eliminated.but they all stay silents. so they all have equally couple of seconds to realize that theyre all wearing black)

{COM 3 stbanana}

• The first man must not have seen two white hats on the second or third man, or he would have known his own hat must be black since there are only two white hats. So the first man's answer establishes that at least one of other 2 men's hat is black.

Based on the first man's answer, the second man knows that he and the third man are either both wearing black, or one is wearing black and one is wearing a white hat. If the second man sees that the third man is wearing a white hat, then he would know his own hat had to be black. But the second man does not know what color hat he is wearing, which means the third man's hat is not white and must be black.

Since both the first and second man cannot deduce the color of their own hats, the third man will know that he is wearing a black hat.

Anaethema on COM3

• If any of the men had seen 2 white hats then they would have known their hat was black. Because each man could see two black hats,there was a chance theirs could be white. When the last man realised no one else guessed a colour and he could see the black hats on the other two, he had to guess his must be black? Only thing that makes sense to me

Name - suzystar

Server - Codex Victoria

• The old man who supplied the answer, knew that all three of them were wearing black hats (and not white) because neither of his companions had observed that he himself was wearing a white hat. Obviously, he was able to observe that they were wearing black and so concluded that they all were.

I am playing in https://ts15.travian.com/dorf1.php and my nickname is Fingolfin.

• The first man knows that the other 2 people are wearing black hats. If the second or third guy would've seen that I had a white hat. They would know that the other person would've said something about them having a white hat also if they did, because that would mean that the 2 white hats are used which would result into him knowing he had a black hat. If the other person didn't say anything, this meant that they (not the other guy) would have known that their hats are black, because the other person didn't know the color of his hat (which he would've if 2 other guy's hats where white). But since neither of them said anything about their hats being either black or white. the first person couldn't had worn a white hat, since nobody else had an answer.

I play on International Qualification.

Have played on International com2 and com3.

My ign on my current server (International Qualifications) is PYROZ and I'm a beast.

• Asume we are the first of the three men. If we see two white hats, we know we must be wearing black, and could immediately proclaim so.

But we don't, so we must either wear black or white

so far as stated in the the puzzle.

but, if we were wearing a white hat, then the others would see a black and white, and THEY could reasonably deduce themselves to be wearing black, because if they were also wearing white then THE OTHER OF THE TWO would be seeing two white and would proclaim black immediately and because they don't do so, we know we must be wearing black!

nic: Nice

server: Codex TS15.travian.com

• Nickname: Theza

Server: https://ts15.travian.com.vn

There are only 5 hats (⚪ ⚪ ⚫ ⚫ ⚫), so the men had to choose out of 3 possible combinations:

1) ⚪ ⚪ ⚫

2) ⚪ ⚫ ⚫

3) ⚫ ⚫ ⚫

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

If you see ⚪ ⚫, then in theory, you can wear either ⚪ or ⚫.

But if you wear ⚪, old men wears ⚫ will know immediately that him wears ⚫

Inferred you wear ⚫

If you see ⚫ ⚫, then in theory, you can wear either ⚪ or ⚫.

But if you wear ⚪, two others old men will Inferred them wear ⚫ because them seen ⚪ ⚫

So no one see ⚪ ⚫ or ⚪ ⚪ inferred all old men wear ⚫

• First of all they each have the same perspective so the reasoning applies to any of them.

Each can see that between them there isn't two white hats hence none of them can know for sure what is on their own head - it could be a black one or it could be a white one.

From here they can reason that IF they could see one white hat then their hat would be black because they know there isn't two white hats to be seen. From this they can reason that if either of the others could see a white hat they also would come to the same conclusion and also know their hat is black.

However, since none of them speak out to say they know their hat is black then they also can not see one white hat and so the final conclusion is there are no white hats being worn and they must be wearing a black hat!

https://ts15.travian.com

IGN: Ghost Rider

• Since they were all wise if any of them would see two whites , he would instantly say he was the black one. None of them said nothing for quite a while, that would mean that none of them is seeing two whites and that case 1) is out. All of them now are seeing two black hats , it could be either case 2) or case 3). Since all of them know instantly that those are the only cases left , if any of them is seeing a white and a black, he could assume the second case ( relying on the wiseness of the other two ). Therefore none of them said anything again and that could only mean that they are not sure of the response. One of them realised this uncertainty and isolated case 3) because everyone would have thought for so long. That's how one of them guessed right. ( If he didn't simply see the reflection in his wise men friends / or some mirror if they had any back then ).

• Let's say 3 men are Men1, Men 2, Men 3

As there are only 2 white hats, if any 2 men had white the other would have found it.

Since nice one can guess that option, 2 white hats is rules => So there is either 1 white or no white

Men 1 sees 2 black hats which means his hat could be white or black.

If his hat is white, then for sure,

Men 2 would see 1 white and 1 black ;

Men 3 would see 1 white and 1 black

As per above logic they both would have guessed their hat is black;

but since they were not sure only other option left was his hat is black ; so all 3 black

• Let's say 3 men are Men1, Men 2, Men 3

As there are only 2 white hats, if any 2 men had white the other would have found it.

Since nice one can guess that option, 2 white hats is rules => So there is either 1 white or no white

Men 1 sees 2 black hats which means his hat could be white or black.

If his hat is white, then for sure,

Men 2 would see 1 white and 1 black ;

Men 3 would see 1 white and 1 black

As per above logic they both would have guessed their hat is black;

but since they were not sure only other option left was his hat is black ; so all 3 black

Name = Salvus

Server = ts1.travian.com

• Situation 1: Assuming that the architect had placed 2 white hats and one black hat on the three men, the man wearing the black hat would have been able to solve the riddle instantly.

Situation 2: Assuming the architect had placed 2 black hats and one white hat on the three men. One of the black hatted man would see one black hat and one white hat. Now, since no one could instantly figure out the answer, he will understand that he's not wearing a white hat. Else, the other black hatted man would be able to solve it instantly. Hence, he will be able to decipher that he's wearing a black hat.

Solution: With three black hatted men, each one will only be able to see 2 black hats. One would wonder whether the hat he's wearing is black or white. However, if it were white, this would be situation 2 and someone black hatted would have figured out the answer. But with no response, the wisest man will eventually figure out that everyone was black hatted as all other combinations are eliminated.

• Nick: Tomekku

World: ts15 - codex Victoria

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 if there I would were ⚪ than the other one that wears ⚫ would tell what is he wearing. (solution 1), if no one would shout that than it means that I could be wearing ⚫

3. If the other two were wearing black ⚫ ⚫, than the other 2 could follow the logic in case 2, and if they did not than it would mean that option is that I am also wearing ⚫

Hard to explain but this is how it works.