# Day 2: The Three Wise Men

• Nickname: Ion

Server: ts15 Codex Victoria

Answer: it took them so long to guess because they wait for others to response, the man who knew the answer observe the other two men, in the account of first logic, if one of these two saw others with white hat they would have guess immediately, then he observe his friends again according to second logic if they saw he wear white hat, they would have guess immediately, but if they saw he wear black hat they would have hesitated hence it took them a long time to answer and so he know that he wear black hat.

Lets call the 3 wise men as A B and C

Since A sees both black caps he knows he can either have a white cap or a black cap and hence is confused and cannot answer

Noticing that A doesn't answer immediately, B knows that A sees 2 black caps or a Black and white cap. But in either case he could have a black or a white cap and is confused and doesn't answer.

Finally, C, seeing that both A and B don't answer realises that both of them see a black cap on his head and hence concludes that he is wearing a black cap.

• 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.

• Ts15.travian.com

Name: Innapex

You only need to observe, there are only three possible situation, WWB, WBB, BBB. If you see WW, then you immediately know you are wearing black.

However, if you can't judge because it is WB or BB, you only need to observe if the other two men know. If neither of them has stood up and say they know the answer, then you can be sure that all three of you are wearing black.

This is the only situation where no one can figure out immediately,

• Com5 Nickname: Viole

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... there is now way you're wearing white because the only ⚫ would have already get the answer.

Since you know that the other two persons don't see ⚪ ⚪ and ⚪ ⚫, that means both of them also see ⚫ ⚫. That's how you know you also has ⚫ hat.

• Acc: phucloctho

Server: vn1

The smart men asked the 1st men: "Is my hat having the same color with the 2nd men?"

If the 1st men say "yes", it's mean the smart men have a black hat

• he put the colors in this order, white white black black black

they are 3 men.

since he gave the 1st two men black, means the third has to follow the sequence and he's the black hat too.

Sarah z

Codex Victoria

• He saw two Black Hat and wondering his hat is Black or White. If his hat is White, two others man knew the answer, but afer long time, no one has answered. So his hat absolutely is Black, unless the others are fool

My account: OptimusK

Sever: intqualifier

• Because nobody reacts immediately, you know there are no 2 white hats in the game.

So 1 white hat or 0 white hats.

If you have a white hat, you see 2 black hats. The other 2 see both 1 black and 1 white hat, because nobody reacted immediately, somebody else could know he has a black one because there are no 2 white hats in the game.

If you have a black hat, you see 2 black hats. The other 2 also see both 2 black hats. Because nobody reacts you could know you also have a black hat.

Josche1991

ts15 (NL)

• Hi,

server https://ts15.travian.com

player: Georgezz

Let's look at this from the winner's perspective. Option (1) he was wearing a black hat or option (2) he was wearing a white hat.

Let's say he wore a white hat, which is option (2). Then either of his opponents would have seen a man with a white hat and a man with a black hat. Then they would have thought to themselves 'if I'm also wearing a white hat, wouldn't that mean only black hat is left?" then the last man would have declared he had the black hat and won, but this didn't happen. Realising this the second man would have known he had a black hat for sure and declared that he had the black hat! But that didn't happen either.

So option (2) would have been false. If the man had worn a white hat than his opponents would have deducted their own hats. In reality this was the only way to deduct that everyone wore black hats the winner just came to that conclusion first.

• Nickname: Kiwi

Server: Beta

If one of them had been given a black hat and the other white hats, the one with black hat would immediately have known his color (unlike the others). So 1 black and 2 white hats is not a fair distribution.

If there had been one white and two black hats distributed, then the two with black hats would have had advantage. They would have been able to see one black and one white hat and supposing they had been given white hat, then the one with black hat must at once react as in the previous situation. However, if he had remained silent, then the guys with black hats would have known that they wear black hats, whereas the one with white hat would have been forced to eternal thinking with no clear answer. So neither this is a fair situation.

That’s why the only way of giving each old man equal chance is to distribute hats of one color – so 3 black hats.

• Nickname: justinroy

Server: Codex Victoria com

1. Lets assume the #1 got the correct answer.

2. All of them are wise.

3. Lets think that #1 assumes that his wearing white hat.

4. #2 and #3 would see one black and one white

5. If #2 is wearing white, #3 will know that his wearing black because theres only two white hats,(vice versa).

6. But #2 and number #3 didn’t react at all, so the assumption of #1 that his wearing white hat is wrong.

7. Therefore #1 is wearing black hat and his the wisest of them all.

• Since they do not get the answer instantly, it is known that 2 of them do not have white hats on, or else the man wearing black would instantly know his hat.

All of the men see 2 black hats, therefore none of them instantly know the answer, giving the information there is no white hats at all being worn. The man uses this info to deduce that all 3 have black hats on

• If you see ⚪ ⚫, then in theory, you can wear either ⚪ or ⚫, but..if I have a white hat someone would yell I have a black but it didn't happen

If you see ⚫ ⚫, then you can wear either ⚪ or ⚫, but if the other man saw that I had white and the first man have black he would surely say I have black because if he had white as I first man would be said I have black. So I can't have a white hat, just a black.

• If you open yours eyes and see 2 white hats you can be sure that you wear black hat. If you open yours eyes and see black and white and the person who wear black hat doesn't declare that he wear black hat, you can assume that you wear black hat too. So by that logic if you open yours eyes and see 2 black hats and no one declaring that he wear black hat you can assume that you wear black hat too.

• in the first combination (wwb) the black hat would immediately know his colour, in the second combination (wbb) both black hats would immediately know that they are black because if any of then had a white hat it would become the first combination again and the only black hat would react . the third combination (bbb) uses the second combination as proof i.e. if i see 2 black hats and assume that i'm wearing a white one then both of them would see one black and one white hat and using the logic from the second combination deduct the colour of their own hats.

trajle, codex victoria

• Since there were 3 black hats, then one of them certainly had a black hat. First of all, the first man said he doesn't now what hat he is wearing indicating that there is at least one black hat between the 2nd and 3rd man. The reason is that if both of them had white, then the first one would know he had the black one.

When the second man opened his eyes, he wasn't unsure what hat he had but this is why the 3rd man knew he had a black hat. Because if the second man saw a white hat on the 3rd person then he would know he has the black hat because the first man made it clear that either the 2nd or 3rd man has a black hat. So if the first person isn't sure and the 2nd person isn't sure, then the 3rd person would definitely have a black hat.

Account name: Geralt

server: https://tx3.travian.com/

• He see two black

Then he know that his hit is black

Sever tx3. Com

User MISH NORMAL

• If he had seen the three black hats even though they had put them on their heads they would not have known them, why would he have put a different one if he was wise he would not consider one of them for a different answer and he would not ask three of them have different answers,

• Legion from ts5travian.com

If he had seen the three black hats even though they had put them on their heads they would not have known them, why would he have put a different one if he was wise he would not consider one of them for a different answer and he would not ask three of them have different answers,