![]() ![]() This means that either our hat or A's is multicolored. This means we have Scenario 3, and C's hat is Black. Since B's hat is Green in both scenarios, let's look at D's hat. In Scenarios 1 and 3: C knows that the hats are MGBB, and thus Scenario 2 does not apply because it would require a different hat distribution. Sadly, this leaves C stuck with no information. (If it's multicolored, B could think the opposite as pointed out after my first attempt, if it's Black, B knows his hat without A's input.īlack knows his hat, because between B, C, and D, there is one of each type of hat. (If it's Black, he could believe the inverse is true.)ģ: A's hat is Black, and B's hat is Green. Since there is only one solution to this puzzle and these arrangements of hats lead to no contractions with the premises given then A is Black, B is Green, C is Black and D is Multicoloured must be the solution.įor B to positively identify his hat, any of the following must be true:ġ: A's hat is multicolored, and B's is Green. He was wondering if he was g, m or b from a's statement, b or m from Bs and so he knows that he can only be M. If C can know what his hat is with all the statements so far D knows that he must only be m. Prior to this As statement would have made him unsure if he was b or g too. If A is m and B is g then D is b and from this C would not know whether it is m or b so D must be m. Let us see whether this leads to a contradiction later on or not. If B and A were B then B would know he was b before A has spoken. If B was b and A was m then again B cannot know whether he is b or m. But then B cannot know whether he is m or b from A's statement. Well if they know that there are 2b, 1g and 1m and A sees only two black hats, then he cannot be g. Let Green be g, Black be b and Multicoloured be m. The conclusion is the same as Braegh but the reasons are different. ![]() Reminder: In order to "know their hat", they must know exactly which of the three types of hat they have, i.e., they must be sure if they're wearing the multicolor hat or a simple one. EDIT: However, all do know the exact amount there is of each type! You know there is one multicolor hat, but you don’t know how many green and black hats there are of each color (all of them must be wearing one). He can only figure it out after listening to C, not before. Pay attention to the order, they give tips one by one:ġ- A sees 2 prisoners wearing black (1 of them could be the multicolor hat)Ģ- Only after listening to A can B figure out which hat he is wearing (remember it could be black, green or multicolor)ģ- Only after listening to B can C figure out what hat he is wearing.Ĥ- And finally, D can figure out which hat he is wearing. The rest of the hats are simple black or green.ĭESCRIPTION: Each one can see the hats that are in front of them, and not their own. There is one multicolored hat, which is both green and black. SPECIAL RULE: There are three types of hats now. And today's puzzle, a freshly made one that I am thinking of adding to my collection, I hope it's challenging enough!ĬHALLENGE: Guess the hats of the prisoners. ![]()
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