", For what seemed like hours no one spoke. But you may be certain that there are not three white hats. 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. One such puzzle is when you have 3 prisoners, each with a random hat. July 4, 2017

Yesterday, I shared the following puzzle. Oh, and the game master is going to hide the other two hats; at no point will the logicians see which hats are hidden. 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. And again, no hands go up. They must stay in the room until they figure out what colour their own hat is, or until someone else does. * * * 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. But first, let’s set up some combinations. Similarly, seeing WB would have meant that our possible combos are WWB or WBB.

He places one hat on each logician’s head and hides the remaining hats. 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. There are three logicians — that is, people who are really, really, good at logic and reasoning, so much so that it’s their job. How did he figure out what colour his own hat was?

A hat, which they cannot see, is placed on each of their heads. Dan Lewis Three men, who are not wearing glasses, are placed in a room without mirrors. Let’s put ourselves in the shoes — or, I guess, the hat — of one of the logicians. From the look in their eyes he could see their thoughts were the same as his, "What is the color of my hat? He’s going to put one hat on each of logicians’ heads. After about ten minutes, one of the men figures it out and leaves the room.

And, as no one saw two black hats, we can eliminate WBB as one of the potential combinations. Seeing WW doesn’t give our logician enough information — both WWW and WWB are still viable outcomes. He repeats the command. 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.

The game master then says:  “Raise your hand if you know what color hat you have on your head.”, A moment or two passes. Like, in a triangle formation. The solution is available at their subsequent Riddler column, here — you’ll need to scroll a bit. 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 hat is either red or green in color. 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. Want to learn all sorts of interesting things? The hats are given randomly, and there's no maximum amount of hats of any color. We’re left with. And again, she didn’t know what she had on her head, so again, we can eliminate that option. Yesterday, I shared the following puzzle. 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. After passing many tests of cunning and invention, they were pitted against each other in a final battle of the wits. Be warned however, he who guesses wrongly shall be beheaded. Seeing WW could mean there are three white hats or that there are two whites and a black out there. No one responds. Puzzles | Logic puzzles | 3 Hats in a Circle. Their hats are all blue in color. What are the possible hat combinations? The first to correctly announce the color of his hat shall be my advisor. Creative Commons Attribution-ShareAlike License. “Raise your hand if you know what color hat you have on your head.”, Another moment or two passes. 0. 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. He repeats the command again. Maniraj. The hats are either black or white. 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.

“Raise your hand if you know what color hat you have on your head.”. All I will tell you is this- at least one of you is wearing a blue hat. Three are white and two are black.

", "I will shortly remove your blind folds, and the test will begin. So she couldn’t have seen BB. Copyright © 1996-2020 Wx3, All Rights Reserved.

A hat, which they cannot see, is placed on each of their heads. So, everyone saw 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). As it turns out, all the hats are red. They’re standing in such a way that they can see the other two. The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Who spoke, and what color hat is on her head? Puzzles | Logic puzzles | 3 Hats in a Circle Three men, who are not wearing glasses, are placed in a room without mirrors. The answer is below, after the Patreon message. One sage looked around and saw that his competitors each were wearing blue hats. But, had our logician seen WB, she would have immediately known that she had a W on her head. 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. And therefore, everyone is wearing a white hat.

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. None of them could have seen BB for the same reason. 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. The hat is either red or green in color. She had to see either WW or WB. At the second request to raise hands, no one did; therefore, no one could definitively say what they had on their heads. 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. And again, that’s true for all three of our players. Now you are either wearing a blue hat or a white hat. She sees WW.

Therefore, everyone saw WW. 3 hats on stairs puzzle. Seeing WW or WB doesn’t give our logician enough information.

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.

", With that, the king uncovered the sages' eyes and sat in the corner and waited. Want a slightly harder version of this puzzle? you'll learn something new every day. 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. Scroll past the Patreon block for the answer! No one responds. Uncategorized Finally he stood up and said, "The color of the hat I am wearing is...".

Now I Know is a free daily newsletter; The game master then repeats his command — raise your hand if you know what you have on your head. Cowboy hats. If not one of you answers within the hour, you will be sent home and I will seek elsewhere for wisdom. The game master enters the room and informs them that he has with him five hats. If they figure out what colour their own hat is, they are to leave the room immediately without a word to anyone. This page was last edited on 20 December 2017, at 22:15. 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. Each prisoner has to answer at the same time, but can choose to remain silent. Scroll past the Patreon block for the answer! And — here’s the tricky part — that’s true for all three logicians.

He repeats, “Can anyone tell me what color hat is on her own head?” Still no answer. So, that happens, and now we have three logicians wearing hats. A hat salesman comes along and shows the three logicians that he has three white hats and two black hats.



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