The hat is either red or green in color. Puzzles | Logic puzzles | 3 Hats in a Circle Three men, who are not wearing glasses, are placed in a room without mirrors.

* * * The puzzle, in case you missed it: There are three logicians — that is, people who are really, really, good at logic and reasoning, so much so that it’s their job. There are 3 possible hat color combinations: [A] 1 blue, 2 white [B] 2 blue, 1 white [C] 3 blue; The color combination of 3 white hats is not possible since the king has already said that at least one of the wise men has a blue hat.
", For what seemed like hours no one spoke. A hat, which they cannot see, is placed on each of their heads. From Wikibooks, open books for an open world, https://en.wikibooks.org/w/index.php?title=Puzzles/Logic_puzzles/3_Hats_in_a_Circle&oldid=3351350. And, as no one saw two black hats, we can eliminate WBB as one of the potential combinations. Let’s put ourselves in the shoes — or, I guess, the hat — of one of the logicians. This page was last edited on 20 December 2017, at 22:15. So she couldn’t have seen BB. Their hats are all blue in color. One such puzzle is when you have 3 prisoners, each with a random hat. Similarly, seeing WB would have meant that our possible combos are WWB or WBB. He then says to the logicians, “Can anyone tell me what color hat is on her own head?” No one responds. A can see what B and C are wearing, B can see what C is wearing and C can't see any other's hat. Here you go, via FiveThirtyEight’s Riddler (I added the emphasis so you can see the difference): Three smart logicians are standing in a line, so that they can only see the logicians in front of them. Oh, and the game master is going to hide the other two hats; at no point will the logicians see which hats are hidden. There are 3 white hats and 2 black hats in a pack, Three people A, B, C wore those hats randomly and stood on steps facing down. What are the possible hat combinations? Yesterday, I shared the following puzzle. The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. The hat is either red or green in color. Now you are either wearing a blue hat or a white hat. A hat, which they cannot see, is placed on each of their heads. “Raise your hand if you know what color hat you have on your head.”.

0. No one responds. Be warned however, he who guesses wrongly shall be beheaded. At no point will any of the logicians be able to see what they have on their own heads, but they will be able to see what the others are wearing. The hats are either black or white. No one responds. A hat salesman comes along and shows the three logicians that he has three white hats and two black hats. But you may be certain that there are not three white hats. Scroll past the Patreon block for the answer! The three wisest sages in the land were brought before the king to see which of them were worthy to become the king's advisor. Want a slightly harder version of this puzzle? So, that happens, and now we have three logicians wearing hats. From the look in their eyes he could see their thoughts were the same as his, "What is the color of my hat? He places one hat on each logician’s head and hides the remaining hats. After passing many tests of cunning and invention, they were pitted against each other in a final battle of the wits. As it turns out, all the hats are red. Puzzles | Logic puzzles | 3 Hats in a Circle. Seeing WW doesn’t give our logician enough information — both WWW and WWB are still viable outcomes. She had to see either WW or WB. Copyright © 2020 | MH Purity lite WordPress Theme by MH Themes, Click here for more information or to pledge your support, One is wearing a white hat and the other is wearing a black hat (WB). A third time: “Can anyone tell me what color hat is on her own head?” One of the logicians speaks up and gives the correct answer. Like, in a triangle formation.

Yesterday, I shared the following puzzle. We’re left with. Each prisoner has to answer at the same time, but can choose to remain silent. Seeing WW could mean there are three white hats or that there are two whites and a black out there. But, had our logician seen WB, she would have immediately known that she had a W on her head. Cowboy hats. The game master enters the room and informs them that he has with him five hats. Therefore, everyone saw WW. ", With that, the king uncovered the sages' eyes and sat in the corner and waited. So: the third time the game master asks our logicians to raise their hands, all of them do, as they all know they have white hats.

So, everyone saw either WW or WB.

", "I will shortly remove your blind folds, and the test will begin. The first to correctly announce the color of his hat shall be my advisor. Copyright © 1996-2020 Wx3, All Rights Reserved. Who spoke, and what color hat is on her head? There may be only one blue hat and two white hats, there may be two blue hats and one white hat, or there may be three blue hats. They’re standing in such a way that they can see the other two. On the other hand, had our logician seen BB, she would have immediately known that she had a W on her head, as the only combination that allows for that is WBB, and she can see the black hats. He’s going to put one hat on each of logicians’ heads. They must stay in the room until they figure out what colour their own hat is, or until someone else does. Scroll past the Patreon block for the answer! And again, no hands go up. And therefore, everyone is wearing a white hat. The solution is available at their subsequent Riddler column, here — you’ll need to scroll a bit. He repeats, “Can anyone tell me what color hat is on her own head?” Still no answer. He repeats the command again. They are not allowed to inspect their own hats in any way and are forbidden to talk or communicate in any way except as follows: if they see a red hat, they are to raise their right hand. “Raise your hand if you know what color hat you have on your head.”, Another moment or two passes. The hats are given randomly, and there's no maximum amount of hats of any color. Led blind-folded into a small room, the sages were seated around a small wooden table as the king described the test for them. The game master then says:  “Raise your hand if you know what color hat you have on your head.”, A moment or two passes. you'll learn something new every day. Now I Know is a free daily newsletter; How did he figure out what colour his own hat was? One sage looked around and saw that his competitors each were wearing blue hats. He repeats the command.
"Upon each of your heads I have placed a hat. All I will tell you is this- at least one of you is wearing a blue hat. July 4, 2017 If not one of you answers within the hour, you will be sent home and I will seek elsewhere for wisdom. Seeing WW or WB doesn’t give our logician enough information. At the second request to raise hands, no one did; therefore, no one could definitively say what they had on their heads. Uncategorized Creative Commons Attribution-ShareAlike License.

But note that when the game master first asks our logician to raise her hand, she doesn’t — that means she lacks the information to make a pronouncement as to what is on her head.


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