# Day 2: The Three Wise Men

After the holiday break, we are opening again the suggestion channel on Public Suggestions Board that gets updated on weekly basis.

The process is the following:
🔸 First, discuss your suggestion with the community in the #💬│suggestions-discussions channel
🔸 Once the suggestion is final and contains all the details post it in the #🎮│suggestions channel
🔸 A team member will review the suggestion and either give feedback or add the suggestion to the #📋│suggestions-vote channel
🔸 Around once per week the voted suggestions are evaluated by Game Design, a note is added on the Trello Board and they are moved to the most suitable list within the board.

🔹 Suggestions may take up to 4 days to be processed (depending on the team availability)
🔹 Do NOT place more than one suggestion per message in the #🎮│suggestions channel
• I assume that the first man is the one who found out the answer.

the first man has understood that if he wore a white hat the second man would see one white and one black then the second man would think that if he wore white too then the third man would see two white hats and would find out that he wore black hat and would shout out the answer but the third man didn’t, so the second man would find out he wore black and would shout out the answer. but the second man didn’t, so the second man hasn’t seen any white hat and he sees two blacks. then the first man realizes that he is wearing a black hat.

• Lets call them A B and C.

C was the one that knew the solution could see that the others had 2 black ones. So assuming that he had a white hat he thought:

If I have a white hat it means that A and B can see that there is one white in game. And A can also see that B isnt jumping to say that he has a black one as if A had a white one B would immediately say that I have a black one as there were only 2 whites. So while B wasn't saying anything it means that A wouldn't be having a white one and would easily say he has a black one.

But while neither A nor B is saying they have a black hat it means that C cant have a white hat.

So C knows that he has a black hat.

Eglis

ts4.com

(hopefully less people this time ahhahah)

• The architect was the one that watched the others wear black hat's

Alexisgr codex Victoria ts15.travian.com

• Anglosphere 1, LordLinux (lordlinux)

OK, so the first man sees 2 black hats, so he replies "I don't know what color I have on!"

The second man says the same thing, as he sees 2 black hats as well.

The third man ponders, and then realizes that the first man MUST see two black hats or a black and a white hat, for if he saw two white hats, he'd know that he had on a black hat. If he saw two black hats, or a black and a white hat, he still would not know what hat he was wearing. The second man, from his statement that he does not know what color hat he has on, indicates that IF he saw a white hat, he would have known that he was wearing black, from the first man's statement.

Detailed:

There are only 7 possible combinations here: (first man, second man, third man order)

1) BWW This is eliminated, for if the first man saw two white hats, he know he had on a black hat!

2) WBW eliminated as below

3) BBW eliminated as below

4) BWB

5) WBB

6) WWB

7) BBB

The second man sees two black hats. Since the first man couldn't answer, he thereby deduces that since one of the three men (In this case both) has a black hat on, then either WBW (eliminated as in (1) or BBW (ie: he has on a black hat) is correct. Since he cannot answer, then both combinations 2 and 3 are eliminated.

This leaves the last 4 combinations. Since all remaining combinations have he third man wearing black, this is the only color the third man can be wearing!

Simplified:

The third man realized he was wearing a black hat because he knew the first man did not see two white hats, and if the second man did not see one white hat because if he saw a white hat, the second man would have known that his hat was black from hearing the first man's statement.

• So if his hat and one of the other's were both white one would have said that he knows his is back since all whites are there. So if one of the others tought that way and saw that him had a white hat they knew they had to have a black one, but no one said nothing so he assumed they tought like he did so he must have a black one since no one said anything.

nick: GypsyKing

Server:Codex Victoria

• They were thinking the wholetime while Marcella's stepmother chose the fabrics.

Hi

the man get helped by the color of fabric chosen by the stepmother.

e11even

ts15.travian.com (codex victoria COM)

• I assume that the first man is the one who found out the answer.

the first man has understood that if he wore a white hat the second man would see one white and one black then the second man would think that if he wore white too then the third man would see two white hats and would find out that he wore black hat and would shout out the answer but the third man didn’t, so the second man would find out he wore black and would shout out the answer. but the second man didn’t, so the second man hasn’t seen any white hat and he sees two blacks. then the first man realizes that he is wearing a black hat.

Codex Victoria COM

• Anyone of the other 2 would have called out if they saw 2 white hats on other's head and since no one of them said anything he sure had a black hat

• Server : ts15.travian.com - Codex Victoria

IGN - RealRonin

Anyone of the other 2 would have called out if they saw 2 white hats on other's head and since no one of them said anything he sure had a black hat

• 1) If there are no black hats, then no man knows his hat color, each man sees that the others do not say their hat color and thus concludes that his hat must be white, so he knows what color his hat is. This did not happen, so there is at least one black hat.

2) If there is exactly one black hat, then the man wearing the black hat does not know his hat color, but the other two men do. The man wearing the black hat sees no black hats but does see that the others know the color, so he concludes that his hat must be black.

3) If there are exactly two black hats, then all hands are raised. Each black hat-wearing man sees a black and a white hat and deduces that his hat must be black because the other black hat-wearing man would say he knows his color. Thus the two black hat-wearing men know their hat color.

4) If there are three black hats, then everyone knows and says their color, so cases 1 and 2 are eliminated. Each man sees that the other two men do not know their color immediately. Since this must be the logical conclusion of case 3, there must be at least three black hats. Thus someone deduces their hat is black, knowing everyone is wearing a black hat.

• When the first old man said that he did not know what he had on his head, the third concluded that he certainly did not see two white hats, because if he had seen them he would have known that he was black on his head (because of the total of 5 hats, 2 are white). The third old man concluded that the first could see either 2 black or black and white.

The second the old man heard the answer from the first, so he knew what the first old man saw. The third old man was led by the logic that the second old man could only answer what he had on his head if he saw a white hat on him, because if one is black, then the other he sees must surely be white (considering that the first sees 2 black or black and white). If the second the old man saw a black hat on him, then both black and white could be on his head because the first old man in both cases could not know which hat was on his head.

Driven by this logic, the third old man concludes that there is a black hat on his head!

• An architect will always follow symmetry. So he option are

1. Black Black Black

2. White Black White

3. Black White Black

It would be difficult for the old man sitting in between to guess the colour of his hat if other two are black (as his hat csn either be black or white), but for the old men in the corners, it won't be difficult to guess.

abhi1102 - Codex Victoria

• user: milota

server: ts15

let's call the wise men A, B and C.

A thinks: let's suppose I have a white hat. Than, B would think: "If I had a white hat, C would know, that he has a black hat. But C is quiet, that means I have a black hat." But B is not saying, that he has a black hat, that means that I also have a black hat.

And A wins.

• Классическое решение. Если мудрец видит, что у его соперников белый колпаки (Ситуация 1), то он может смело утверждать, что у него - черный колпак, поскольку оба белые уже заняты.

Если мудрец видит на головах соперников белый и черный колпаки (ситуация 2), то он может рассудить так: «Если у меня на голове колпак белый , то мудрец в черном колпаке видит перед собой два белых колпака (находится в ситуации 1), и должен сообразить, что на нем колпак черный. Но он молчит, значит на мне черный колпак».

Наконец, увидев перед собой обоих соперников в черных колпаках (ситуация 3), мудрец мог рассудить: «если у меня белый колпак, то любой из моих соперников видит перед собой белый и черный колпаки (ситуация 2), и должен понять, что на нем колпак черный. Но он молчит, значит на мне черный колпак».
biorobots https://ts15.travian.com

Вы зря раскатали свою губу,

Пытаясь меня отправить на плаху.

Я, даже лёжа в дешёвом гробу,

Сумею послать вас на х…!

• The man who knows (first guy) knows that he is wearing black because,

if he wore white, two other guys would see one white and one black hat;

and one of them (second guy) would say, I can't be wearing white, because the third guy would see two white hats and know he is wearing black, the third guy does not know the answer so I'm wearing black.

Since the second guy does not think like this and still doesn't know the answer, the first guy must be wearing black.

Codex Victoria COM- Scarface

• Source Code
1. The classic solution. If a wise man sees that his rivals have white caps (Situation 1), then he can safely say that he has a black cap, since both white ones are already occupied.
2. If a sage sees white and black caps on the heads of his rivals (situation 2), then he can reason like this: “If I have a white cap on my head, then a sage in a black cap sees two white caps in front of him (he is in situation 1), and he should realize that it is black cap. But he is silent, that means a black cap is on me. ”
3. Finally, when he saw both rivals in black caps (situation 3), the sage could reason: "if I have a white cap, then any of my opponents sees white and black caps in front of me (situation 2), and I must understand what is on it the cap is black. But he is silent, that means a black cap is on me. "
4. biorobots https://ts15.travian.com

Вы зря раскатали свою губу,

Пытаясь меня отправить на плаху.

Я, даже лёжа в дешёвом гробу,

Сумею послать вас на х…!

• Nickname:Leonidas

Server:Codex Victoria COM

The man who knows knows that he is wearing a black hat because, if he wore a white hat, the other guys would see one white and one black hat; and one of them would say, I can't be wearing a white hat, because the last guy would see two white hats and know he is wearing a black hat, the last guy does not know the answer so I'm wearing black. Since the second man does not think like this and still doesn't know the answer, the first man must be wearing a black hat.

• Если мудрец видит, что у его соперников белые колпаки (Ситуация 1), то он может смело утверждать, что у него - черный колпак, поскольку оба белых уже заняты.

Если мудрец видит на головах соперников черный и белый колпаки (ситуация 2), то он может рассудить так: «Если у меня на голове колпак белый, то мудрец в черном колпаке видит перед собой два белых колпака (находится в ситуации 1), и должен сообразить, что на нем колпак черный. Но он молчит, значит на мне черный колпак».

Наконец, увидев перед собой обоих соперников в черных колпаках (ситуация 3), мудрец мог рассудить: «если у меня белый колпак, то любой из моих соперников видит перед собой черный и белый колпаки (ситуация 2), и должен понять, что на нем колпак черный. Но он молчит, значит на мне черный колпак».

Jazz1 ts15.travian.com

• Point of Logic #1: Two white hats is not a possibility or seeing this, someone would answer right away that their own is black.

Point of Logic #2: Supposing one of them saw 1 white and 1 black hat, there are two possibilities, you could be wearing black or white on your own head. But if you were wearing white, then the only one wearing black would anounce their own hat color by point of logic #1. This did not happen, so you would have to be wearing black in this case.

Point of Logic #3: supposing you see two black hats, and the other two men understand points of logic 1 and 2, if you were wearing a white hate then they should announce their own hat as black, but they don't, so your own hat can not be white!

Thus your hat must be black.

INCONCEIVABLE!!

It is a lot of supposition of the other two mens logical abilities, but that is the only way this can work, I believe.

Name: Locomotion

Server: COM3

• There are three wise men...w1...w2...w3. Say w1 got the answer. Let's look at it from his perspective. He saw both the other two men wearing black hats. So he knew his hat was either black or white.

Let's test for white. If w1 was wearing a white hat, then both w2 and w3 would see one man wearing a white hat and one man wearing a black hat. Therefore...from either w2 or w3 perspective...if either have a white hat on the other would immediately know they have a black hat on and announce it. But none did. Therefore the only option left is that his hat is also black.