Day 2: The Three Wise Men

  • day2_raids.png

    Day 2: The Three Wise Men

    Marcella didn't sleep. Something was stirring in the house, which suddenly felt so alien after the news about her brother's presumed death. When their mother was alive, everything was different. Her mother enjoyed telling stories about her famous grandparents: caravan driver Mark Atilius and Egyptian priestess Nefertari, who met on their way to the Egyptian pyramids, where they looked for a cure for a deadly disease that was about to pull the whole world into darkness. They lived interesting lives, traveled together, and solved puzzles, before settling down and becoming famous healers. She smiled when she remembered how she played "Mark's journey to Egypt" with his brother. They built Egyptian pyramids using pillows. Her brother always chose Mark's role and made his sister portray the mummy in bandages, attacking him from a dark corner, or Mark's friend Lucius, or the old witch.

    Her father didn't approve of those games, but it was her mother's wealth that brought prosperity to the family, so he didn't argue. Everything changed after her mother's death. Her father married again really quickly; then her brother left to serve their father's old commander, while she remained completely alone.

    Father? Her father didn't care much about letting her do whatever she wanted. That was until recently. Her visit to the marketplace with her stepmother yesterday worried her. Her rather greedy stepmother bought her different fabrics and even added a few pearl clasps, similar to those she wore herself.

    Additionally, her father's commander, who had brought the news about her brother's disappearance, still stayed in the house. Her father was usually very cautious about her, but he regularly left them alone in a room. Marcella had to listen to stories about "past glorious battles that no young man could even get close to today" and try to keep her eyes open. That was extremely boring.

    She remembered a funny situation she saw on her way to the marketplace.

    Three old men argued about who was the wisest among them and asked an architect, who had traveled to the lands of Codex Victoria, to resolve their argument. The architect didn't think for long. He looked in his bag and then showed them five hats: three black and two white. He then ordered them to close their eyes, quickly put three black hats on their heads, and hid the two white ones. None of the men could see what color hat was on their own head, but they could see the hats of the other two. Without helping each other, he told them to figure out which hat color they had on their head. They were thinking the whole time while Marcella's stepmother chose the fabrics. Finally, one man jumped in excitement and said he knew the answer!

    Marcella smiled and wondered whether she would have solved it as fast if she had been one of the three. It was a brilliant task and only a very smart person could invent it.


    Give the reasoning for how one of the men could figure out that all three were wearing black hats.

    State your nickname and server played in this thread with your answer to the riddle. All post are disabled.


    Members of the Travian Team works on a voluntary basis and are therefore not available 24 hours a day.

    Post was edited 3 times, last by Ridder Huma ().

  • Mjölnir -


    A = first old man

    B = second old man

    C = third old man

    If A wears a white hat:

    • If B wears a white hat, C can immediately tell that he is wearing a black hat after looking at the two white hats of A and B.
    • If B wears a black hat, C will be unable to tell the color of his hat, because there is a white hat (A) and a black hat (B). So B can quickly deduce from A's white hat and C's lack of response that he is wearing a black hat.

    So if A wears a white hat there will be a fairly quick response from B or C.

    If A wears a black hat:

    • C does not see two white hats, so he is unable to tell his hat color.
    • B sees only a black hat, so he can't tell anything about his hat.

    In this case A, B and C would remain silent for some time, until A finally deduces that he must have a black hat because C and B have remained silent for some time. This is what happened in our story because the old men took some time thinking (solving the puzzle) while Marcella's stepmother chose the fabrics.

    So, all 3 old men were wearing black hats.

  • The Cartels

    TS15 codex Victoria

    The ans is as follows

    Let's say three men as X Y and Z and let's say the man who told the ans was Z

    The Z knew the answer after a while with the following reasoning :

    1. Z thought that had he worn a white hat then X and Y would have seen 1 black and 1 white hat and would have guessed theirs to be black as from the point of view of X or Y:

    A. If X had thought his cap to be white then Y wud have seen two white and guessed his to be black and Y aur have won and vice versa if Y had worn a white

    So as X and Y both were thinking hard ...the only option was that Z was bearing black hat.

    Hence Z was sure he was wearing black hat

  • You see two other men wearing a black hat. If you are wearing white hat, other two men are seeing one white hat and one black hat.

    These two men can figure out the color of their own hat is not white by the fact that the other man not immediately finding out the color of his hat seeing two white hats. This means seeing two black hats and other men not declaring color of their hat for a while only means you are also wearing a black hat.

  • robrob

    7s15 international


    If a man A saw a white hat on man B then he had to have a black hat on or man A would see two whites and know the answer etc

    If he saw two black hats he wouldn't be sure what to call and would pause

    The length of the pause means that no one was sure.. i.e. no one could see a single white hat

    Therefore they all had to be wearing black hats..

    The time delay is crucial

  • There are 3 possible combinations - for 5 hats (W W B B B). i am denoting white hats with "W" and black hats with "B"

    1. W W B

    2. W B B

    3. B B B

    Case 1 - The 3rd person would immediately know that he is wearing B as only 2 W are present

    Case 2 - Any one of the Persons wearing B can know that they are not wearing white. Since that would have been case 1 and the other person would have jumped to answer. Hence If they can see 1 W and 1B, the only possibility for confusion is that they themselves are wearing B.
    Hence, there would not be a stand still.

    Case 3 - The only case where none of them can know what anyone is wearing. So if none of them can find an answer, That means they are each wearing B. B B B.

    jaineelesh from codex victoria -

  • Option 1

    No. 1-white

    No. 2-white

    No. 3-black

    No. 3 must guess right away that it is black (there are only three white hats). But everyone is silent - that means no one sees 2 white hats.

    Option 2

    No. 1-white

    No. 2-black

    No. 3-black

    No. 2 or No. 3 - they see one white hat and should know that they have black, because - everyone is silent, so no one sees 2 white hats.

    The wisest old man understood - everyone is silent - that means there is no option number 1 and there is no option number 2.

    He understands that everyone has black hats.


  • Acc: Climate Change

    each saw two two black hats. you can then deduce that maybe you are wearing white or black, but you know there are not two white hats since you can see 2/3 hats are black.
    if man 1 saw a white and a black hat, and man 2 (wearing a black hat) did not say he had the answer, then man 1 knows he is not wearing white, since then both white hats would be worn and man 2 would know he wore black.

    if they are all wearing black hats, each man could (from his own point of view) be wearing black or white hat, however since no man shouted out the answer, as per the logic with one man wearing white and two wearing black in the paragraph above, then they must be confused due to lack f seeing a white hat, and thus they must all be wearing black.

  • bolangbilogzz

    codex victoria

    to figure how to know the hat color you are wearing. the solution is, wait for the other two to answer first

    - if the 1st person answered white, it would mean that he is seeing 2 black hats because the probability of wearing a white hat 66% and wearing a black is 33%

    - if the 2nd person says black it would mean that he is either seeing white and black or double white. hearing the 1st person chose white means he is seeing thhat both 2nd and 3rd person are wearing black. if the 2nd person says black it would mean his seeing the 1st persons hat is white and what the 3rd person is black. otherwise if he says white then he is seeing both black hat since with the probability of having 2 black hat means you have higher chance to have white hat.

    - for the 3rd person the answer will vary from the 1st answer of the 1st and 2nd person. since he can see both hats. and 1st person choose white he is seeing both black. if 2nd person choose white then he sees two black. if he choose black then he sees white and black. since you can see the hat of the 1st person then you would know that the second person sees thhe 1st person wearing black and you wearing white.

  • oh, my english is very bad. Let's see how the translator handles this.

    The old man reasoned like this:

    those two are sitting in black hats and realizes if he is sitting in a white hat, then the others see such a picture - one is sitting in a white hat and the other is in black and whichever one might think - if I have a white hat, then why doesn't one of us scream that he has black?

    And since everyone is silent, it means there are no white hats and I also have a black hat on.


  • if we name them A,B,C ... then if A saw 2 white hats as u said, it would be black and he may immediately say it. so it must be black or white, if it was white on one of their head, so one of them may say it immediately that the other one must black. so when they all said nothing at first so its all black.

  • 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...


    Now your turn!


    If man can see ⚫ ⚫, he wears ⚫.

    Brokerka, balkans 4

  • If you see two black ones, then he also wears a black hat

    baneks, ts4.balkans

    Q: Da li vam se svidja Bebi Dol?
    A: Odlicno je. Koristim ga i za lice i za telo.
    Q: Koja vam je omiljena zivotinja?
    A: Lav.
    Q: Zasto lav?
    A: Pa car je na sve zivotinje, ima grivu, a i smeker je ovako....:thumbsup:

    Ave Caesar, morituri te salutant

  • Nickname: Fieryfrost


    If there were two white hats the one not wearing a white hat would immediately know he is wearing a black hat. Since no one did this all three now know that there are not two white hats. This concept of additional shared knowledge is very important.

    The winner went through both of the following scenarios in his head:

    1) He is wearing a black hat.

    2) He is wearing a white hat: If this were the case both of his opponents would see one white and one black hat and since they know that there cannot be two white hats(as proven above) at least one of them would quickly have concluded that he is wearing a black hat and would have said so. Neither of them did this so this solution cannot be true and as such scenario 1) is the scenario that corresponds with reality.

    After having concluded this he happily jumped up and down proclaiming that he knew the answer.

    Extended and alternative solution:

    Only three black hats will actually result in a fair competition. As Marcella though the architect was a very smart person it is obvious that he would have to give a fair chance to each of them to prove their wits. Two white hats give and unfair advantage to the person wearing the black hat and two black and one white gives and unfair advantage to the two wearing black hats. This would not have resulted in a battle of wits, but rather the winner being decided by the distribution of the hats.

  • Athelstan playing com 15;

    1 man sees two black hats, in theory that would mean that he could be wearing either black or white, however if he were wearing white those looking at his white hat and a black would never have a solution, which would mean the puzzle is unsolvable, therefore the only solution is that all three are wearing black hats.

  • COM3 server username: kayilioglu

    the man knows that if he were wearing a white hat, there would be no way to find out the solution. Finding out this fact takes time. He looks at his friends and saw their inability to solve the problem. For this puzzle to have a valid solution one guy must wear a white hat. If none of his friends our wearing it, he must.

  • Nickname: LuckyLuke

    Server: ComX


    Let's mark the wise man A, B and C.

    Consider C the guy that announced the answer.

    Scenario if C had a white hat: Each of the other two (A and B) would see one black and one white hat,

    and not know the color of their own. If guy (A) would assume that he has a white hat, he would know

    that the guy (B) sees two white hats, hence B would stand up and say that his hat is black. Since that

    didn't happen, A would know that his color of hat is black, stand up and announce it.

    Since solving this scenario is not that difficult, they are all 'wise' man, and no one has stood up and announce the answer

    for a long time, C knows that they must all be wearing black hats.

  • Name: DeLongest

    Server: COM X


    It cannot be White-White-Black, because one of the men would see 2 white hats and know the answer.

    If someone see White and Black hat on the other men, that means he has Black hat, because it's definitely not White-White-Black situation.

    So because the man saw 2 Black hats on other men, that means he also has Black hat.

  • Name: Mike


    There are three possible outcomes,

    1 - Black Black Black,

    2 - Black Black White

    3 - Black White White

    If it was the 3rd possibility, the men that saw the 2 White hats, would have immediately said he has the Black hat. Didn't happen, so this is not possible

    If it was the 2nd, after a while one of the men that was seeing the other two with a Black hat and the other with a White hat, would eventually say that he has a Black hat, because if he had a White hat another person would have already said it first.

    And if no one is saying anything for a long time the only answer can be that all of them are wearing a Black hat, option 1.

    Because of that, it is only possible to guess your hat after so much time.