## 3 hats puzzle

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. A hat, which they cannot see, is placed on each of their heads. No one responds.

But first, let’s set up some combinations. Seeing WW could mean there are three white hats or that there are two whites and a black out there. “Raise your hand if you know what color hat you have on your head.”, Another moment or two passes. How did he figure out what colour his own hat was? No one responds. So, everyone saw either WW or WB. The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. They’re standing in such a way that they can see the other two. He then says to the logicians, “Can anyone tell me what color hat is on her own head?” No one responds. "Upon each of your heads I have placed a hat. 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. She had to see either WW or WB. Want a slightly harder version of this puzzle? 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. Scroll past the Patreon block for the answer! ", "I will shortly remove your blind folds, and the test will begin. The game master then says: “Raise your hand if you know what color hat you have on your head.”, A moment or two passes. So, that happens, and now we have three logicians wearing hats. Similarly, seeing WB would have meant that our possible combos are WWB or WBB. Finally he stood up and said, "The color of the hat I am wearing is...". 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. Dan Lewis The hats are either black or white. At the second request to raise hands, no one did; therefore, no one could definitively say what they had on their heads.

July 4, 2017 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. And — here’s the tricky part — that’s true for all three logicians. 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.

Each prisoner has to answer at the same time, but can choose to remain silent. Be warned however, he who guesses wrongly shall be beheaded.

He’s going to put one hat on each of logicians’ heads. We’re left with. The solution is available at their subsequent Riddler column, here — you’ll need to scroll a bit. Oh, and the game master is going to hide the other two hats; at no point will the logicians see which hats are hidden. 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. 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. One sage looked around and saw that his competitors each were wearing blue hats. Uncategorized Their hats are all blue in color. ", For what seemed like hours no one spoke. Scroll past the Patreon block for the answer! Therefore, everyone saw WW. Maniraj. The answer is below, after the Patreon message. Now you are either wearing a blue hat or a white hat. One such puzzle is when you have 3 prisoners, each with a random hat.

* * * 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. 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.

He places one hat on each logician’s head and hides the remaining hats. He repeats, “Can anyone tell me what color hat is on her own head?” Still no answer. From the look in their eyes he could see their thoughts were the same as his, "What is the color of my hat?

Cowboy hats. Seeing WW doesn’t give our logician enough information — both WWW and WWB are still viable outcomes. If they figure out what colour their own hat is, they are to leave the room immediately without a word to anyone. 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. Yesterday, I shared the following puzzle. Let’s put ourselves in the shoes — or, I guess, the hat — of one of the logicians. There are three logicians — that is, people who are really, really, good at logic and reasoning, so much so that it’s their job. The game master then repeats his command — raise your hand if you know what you have on your head. This page was last edited on 20 December 2017, at 22:15. The game master enters the room and informs them that he has with him five hats. But, had our logician seen WB, she would have immediately known that she had a W on her head. They must stay in the room until they figure out what colour their own hat is, or until someone else does. And again, she didn’t know what she had on her head, so again, we can eliminate that option. 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. There are only two black hats, so here are only three possible combos: Similarly, our logician and see three possible combinations on the heads of others: Now, to the game. She sees WW. What are the possible hat combinations? He repeats the command again. A hat, which they cannot see, is placed on each of their heads. Creative Commons Attribution-ShareAlike License.

Want to learn all sorts of interesting things? Three are white and two are black. Like, in a triangle formation. And again, that’s true for all three of our players.

As it turns out, all the hats are red. 0. A hat salesman comes along and shows the three logicians that he has three white hats and two black hats. you'll learn something new every day. All I will tell you is this- at least one of you is wearing a blue hat. And again, no hands go up. The hat is either red or green in color. None of them could have seen BB for the same reason. If not one of you answers within the hour, you will be sent home and I will seek elsewhere for wisdom. 3 hats on stairs puzzle. “Raise your hand if you know what color hat you have on your head.”. Copyright © 1996-2020 Wx3, All Rights Reserved. The hat is either red or green in color. And therefore, everyone is wearing a white hat. Puzzles | Logic puzzles | 3 Hats in a Circle Three men, who are not wearing glasses, are placed in a room without mirrors. But you may be certain that there are not three white hats. He repeats the command. After about ten minutes, one of the men figures it out and leaves the room. 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. The first to correctly announce the color of his hat shall be my advisor. Three men, who are not wearing glasses, are placed in a room without mirrors. Led blind-folded into a small room, the sages were seated around a small wooden table as the king described the test for them. After passing many tests of cunning and invention, they were pitted against each other in a final battle of the wits. 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. So she couldn’t have seen BB. ", With that, the king uncovered the sages' eyes and sat in the corner and waited. Puzzles | Logic puzzles | 3 Hats in a Circle. And, as no one saw two black hats, we can eliminate WBB as one of the potential combinations. The hats are given randomly, and there's no maximum amount of hats of any color. Yesterday, I shared the following puzzle. Who spoke, and what color hat is on her head? 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). Now I Know is a free daily newsletter; Seeing WW or WB doesn’t give our logician enough information.

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