Hat Trick (riddle)

***Ace Mercury*** · 07-04-2009, 08:48 PM

A cute little logic riddle with coloured hats.

Quote:

Originally Posted by http://www.futilitycloset.com/2009/06/25/hat-trick/

A group of men, all versed in logic, sits around a table. Fifteen of them are wearing red hats, the rest blue. Each can see the others' hats but not his own. On the table is a clock which strikes once each hour. The men are given the following instructions: 'You are not allowed to discuss the color of your hats. However, should any of you find that he is wearing a red hat, he should leave the table on the clock-strike immediately following his discovery.' Now it is assumed that no one is initially aware of the color of his own hat. Furthermore, since the men cannot see the color of their own hats, nor discuss it with their colleagues, nothing happens for a while. Then a guest arrives. She looks at the hats around the table, and says, clearly: 'At least one man here is wearing a red hat!' What happened and why?

Luigiman7 · 07-04-2009, 11:08 PM

well duh at least 1 of them is wearing a red hat

there are 15 red hats

***Ace Mercury*** · 07-04-2009, 11:12 PM

Yeah, but the guys with hats don't know that. If they already knew that, it would've made it too easy for them.

I don't see why you're angry. Calm down, it's only a riddle.

Panfan · 07-04-2009, 11:21 PM

they can't see their own but they can see the other hats, so they can see 14 red hats, so the guest pointed out the obvious.

***CaptHayfever*** · 07-05-2009, 12:40 AM

I'm not sure what the riddle is asking. I can't see the particular significance of an outsider to the experiment walking in & restating part of the instructions.

And remember, "I'm-a Luigi, number one!"

**Deku Trii** · 07-05-2009, 01:12 AM

Hmm.

Spoiler Below

If there were one man wearing a red hat, learning that there was at least one man wearing a red hat would let him know that he had a red hat, and he could leave at the next strike of the clock.

If there were two men wearing red hats, upon learning that there was one or more men wearing red hats, both could know that they had red hats and leave on the second strike. They can each see at least one red hat, and they should have expected the owner of that hat to leave on the first strike if he was the sole wearer of a red hat.

If there were three men wearing red hats, all three should leave on the third strike. They can each see two red hats, and should have expected both owners of those red hats to leave on the second strike if they were the only wearers of red hats.

This can be extended to 15 people, who would all leave on the 15th strike having seen that the 14 people they each see with red hats have not figured out that they can leave yet.

***Saria Dragon of the Rain Wilds*** · 07-05-2009, 02:56 AM

^ That makes sense. Cool.

***Ace Mercury*** · 07-05-2009, 01:31 PM

Quote:

Originally Posted by CaptHayfever

I'm not sure what the riddle is asking. I can't see the particular significance of an outsider to the experiment walking in & restating part of the instructions.

The number of red hats isn't told to the guys with hats; it's part of the instructions to us to figure out what happens afterwards.

Spoiler Below

I think we agree that if the outsider didn't say anything, and there was one red hat, the red hat couldn't be sure he had a red hat (maybe no one had a red hat and the host was just ****ing with them).

I'm trying to imagine if there were only two red hats; would they be able to leave at the second stroke if the outsider didn't say anything?

**Deku Trii** · 07-05-2009, 03:16 PM

Spoiler Below

I don't think they could. If there were two red hats, both wearers would know there was at least one hat, but neither would know that the other knew there was at least one red hat. You're able to leave on the second strike only if you know that the other wearer of the other red cap could deduce he had a red cap if all the other hats were blue.

If there were three or more red hats, then the contribution the outsider makes is a little less intuitive. Everyone knows that there's at least one red hat, and everyone knows everyone else knows there's at least one red hat.

CuccoLady · 07-08-2009, 02:51 AM

I think I get it.

Spoiler Below

There are only sixteen people in the room. The guy wearing the red hat saw only blue around him, but when the guest announced that there was a red hat in the room, that guy realized it had to be him.

--reads DT's post---

That's actually pretty neato. I didn't think of that.

***Ace Mercury*** · 07-08-2009, 02:29 PM

Yeah, I live for those sort of moments; the dopamine rush when you grok the pivotal aspect of a riddle.

chibimod3 · 07-13-2009, 04:55 PM

Given by the instructions stated the man who interprets them correctly takes off his hat to check the color. Then the men who are left will determine if that was cheating or not and go accordingly to their own judgment. Or they find a way to see their own hat as in the reflection of metal or a mirror or in another person's eyes. This is one of the correct answers to that riddle.

Where did you get it? I've heard it before at school.

***Ace Mercury*** · 07-13-2009, 05:18 PM

^ "Each can see the others' hats but not his own." -- take this literally. The hats are magic, and only people other than the owner can see them. So, even if someone had a cup of mercury instead of tea, they can't see it. They are extremely afraid of their host due to his other-worldly warlock powers, hence they follow the instructions to the letter. Skilled logicians are familiar with how wizards like setting up traps for people who like to dismantle puzzles and bum-rush the guy behind the curtain.

Also, the source URL was in the OP post. It was cleverly hidden, I guess =\

chibimod3 · 07-14-2009, 12:28 PM

Why would they have magic hats and why would they be participating if they could die?

No in the riddle it only states they cannot discuss or see the color of there own hats and if the magic card is played. I trade my hat which is invisible to me with the man on my left therefore learning the color of my own hat and he learning his. Of the new hat of course.

***Ace Mercury*** · 07-14-2009, 01:03 PM

The riddle states they're all versed in logic. Logically, no one would want to sit at a table for hours on end. Therefore, there must be a powerful compelling force (warlock, wizard, predator drones, Rosie O' Donnell). This compelling force would not look kindly on cheating. From lemma one*, they will not cheat.

*Lemma one: logical people prefer to remain living, as living is better than the alternative (not living). Therefore they prefer not to cheat.

chibimod3 · 07-15-2009, 10:43 AM

None of the things I have stated are cheating given the parameters of the riddle and the rules given. Your trying to add to a riddle written by a guy who probably expected the answers I just gave. On the off chance maybe one like DT's answer. Secondly then in the riddle with the lemma one theory have you looked up when this riddle was written? Because that may be true to us in the modern days but way back when people did do that and they just sat there and talked or read.

**Deku Trii** · 07-15-2009, 04:31 PM

I'm bored, so I'm going to humor this for a moment. If your approach to the riddle were valid, why did none of them leave before a guest announced that at least one of them had a red hat?

CuccoLady · 07-16-2009, 04:22 AM

^ Because if there was only one dude with the red hat, the dude wearing the red hat would just see blue around him and without knowledge that there IS a red hat there, he wouldn't know if he was wearing a red hat or if everyone was wearing blue.

**Deku Trii** · 07-16-2009, 09:09 AM

I was talking about chibimod3's answer, CL. He suggests people simply switch hats or look at their own hats, which is something they would have done immediately if it were a valid approach.

chibimod3 · 07-16-2009, 10:45 AM

How many of us spent time thinking of a long complicated answer before realizing that the simplest answer works? This is true for a lot of riddles. Now DT I'm 100% sure your answer would be thought of by maybe one or two of the men there but that said those two men might not have a red hat. And in logic one of the first and foremost rules you have to learn is that the answer doesn't have to be long and complicated but it can be short and sweet.

07-04-2009, 11:08 PM	#2
Luigiman7 ~)´◡｀(~ Join Date: Jul 2006 Location: representin da bronx yo Gender: Posts: 17,303 Thanks: 1,099 Thanked 992 Times in 698 Posts Blog Entries: 8	well duh at least 1 of them is wearing a red hat there are 15 red hats __________________ ／人◕ ‿‿ ◕人＼ＷＯＮ’Ｔ　ＹＯＵ　ＢＥＣＯＭＥ　Ａ　ＭＡＧＩＣＡＬ　ＧＩＲＬ？

07-04-2009, 11:12 PM	#3
*Ace Mercury* Marshmallow Knight ☆ Supermod Join Date: Jun 2000 Location: Southern Ontario Gender: Posts: 22,962 Thanks: 558 Thanked 3,205 Times in 1,531 Posts Blog Entries: 1	Yeah, but the guys with hats don't know that. If they already knew that, it would've made it too easy for them. I don't see why you're angry. Calm down, it's only a riddle.

07-04-2009, 11:21 PM	#4
Panfan Analrapist Join Date: Jun 2005 Location: I'm awesome, and I **** dolphins Gender: Posts: 18,540 Thanks: 1,384 Thanked 2,201 Times in 1,311 Posts Blog Entries: 15	they can't see their own but they can see the other hats, so they can see 14 red hats, so the guest pointed out the obvious.

07-05-2009, 12:40 AM	#5
*CaptHayfever* Smash SuperMod Join Date: Jul 2002 Location: (n) - the place where I am Gender: Posts: 27,011 Thanks: 1,785 Thanked 2,371 Times in 1,423 Posts	I'm not sure what the riddle is asking. I can't see the particular significance of an outsider to the experiment walking in & restating part of the instructions. And remember, "I'm-a Luigi, number one!"

07-05-2009, 01:12 AM	#6
Deku Trii PP&R Mod Current Events Mod Join Date: Jun 2000 Location: Texas Gender: Posts: 8,930 Thanks: 490 Thanked 1,063 Times in 559 Posts	Hmm. Spoiler Below If there were one man wearing a red hat, learning that there was at least one man wearing a red hat would let him know that he had a red hat, and he could leave at the next strike of the clock. If there were two men wearing red hats, upon learning that there was one or more men wearing red hats, both could know that they had red hats and leave on the second strike. They can each see at least one red hat, and they should have expected the owner of that hat to leave on the first strike if he was the sole wearer of a red hat. If there were three men wearing red hats, all three should leave on the third strike. They can each see two red hats, and should have expected both owners of those red hats to leave on the second strike if they were the only wearers of red hats. This can be extended to 15 people, who would all leave on the 15th strike having seen that the 14 people they each see with red hats have not figured out that they can leave yet.

07-05-2009, 02:56 AM	#7
*Saria Dragon of the Rain Wilds* Admin "mine.. not yours. NO. MINE." Epic Ladynerd Join Date: Jul 2000 Location: Forteresse de Valois Gender: Posts: 28,199 Thanks: 1,510 Thanked 1,719 Times in 993 Posts	^ That makes sense. Cool.

07-05-2009, 03:16 PM	#9
Deku Trii PP&R Mod Current Events Mod Join Date: Jun 2000 Location: Texas Gender: Posts: 8,930 Thanks: 490 Thanked 1,063 Times in 559 Posts	Spoiler Below I don't think they could. If there were two red hats, both wearers would know there was at least one hat, but neither would know that the other knew there was at least one red hat. You're able to leave on the second strike only if you know that the other wearer of the other red cap could deduce he had a red cap if all the other hats were blue. If there were three or more red hats, then the contribution the outsider makes is a little less intuitive. Everyone knows that there's at least one red hat, and everyone knows everyone else knows there's at least one red hat.

07-08-2009, 02:51 AM	#10
CuccoLady Anime and Cartoons Mod Join Date: Jun 2006 Location: THIS LOCATION REMINDS ME OF A PUZZLE, LUKE Gender: Posts: 8,457 Thanks: 2,666 Thanked 1,075 Times in 724 Posts	I think I get it. Spoiler Below There are only sixteen people in the room. The guy wearing the red hat saw only blue around him, but when the guest announced that there was a red hat in the room, that guy realized it had to be him. --reads DT's post--- That's actually pretty neato. I didn't think of that.

07-08-2009, 02:29 PM	#11
*Ace Mercury* Marshmallow Knight ☆ Supermod Join Date: Jun 2000 Location: Southern Ontario Gender: Posts: 22,962 Thanks: 558 Thanked 3,205 Times in 1,531 Posts Blog Entries: 1	Yeah, I live for those sort of moments; the dopamine rush when you grok the pivotal aspect of a riddle.

07-13-2009, 04:55 PM	#12
chibimod3 Junior Member Join Date: Jan 2007 Location: The bottom of a Dr. Pepper bottle Gender: Posts: 497 Thanks: 52 Thanked 18 Times in 16 Posts	Given by the instructions stated the man who interprets them correctly takes off his hat to check the color. Then the men who are left will determine if that was cheating or not and go accordingly to their own judgment. Or they find a way to see their own hat as in the reflection of metal or a mirror or in another person's eyes. This is one of the correct answers to that riddle. Where did you get it? I've heard it before at school.

07-13-2009, 05:18 PM	#13
*Ace Mercury* Marshmallow Knight ☆ Supermod Join Date: Jun 2000 Location: Southern Ontario Gender: Posts: 22,962 Thanks: 558 Thanked 3,205 Times in 1,531 Posts Blog Entries: 1	^ "Each can see the others' hats but not his own." -- take this literally. The hats are magic, and only people other than the owner can see them. So, even if someone had a cup of mercury instead of tea, they can't see it. They are extremely afraid of their host due to his other-worldly warlock powers, hence they follow the instructions to the letter. Skilled logicians are familiar with how wizards like setting up traps for people who like to dismantle puzzles and bum-rush the guy behind the curtain. Also, the source URL was in the OP post. It was cleverly hidden, I guess =\

07-14-2009, 12:28 PM	#14
chibimod3 Junior Member Join Date: Jan 2007 Location: The bottom of a Dr. Pepper bottle Gender: Posts: 497 Thanks: 52 Thanked 18 Times in 16 Posts	Why would they have magic hats and why would they be participating if they could die? No in the riddle it only states they cannot discuss or see the color of there own hats and if the magic card is played. I trade my hat which is invisible to me with the man on my left therefore learning the color of my own hat and he learning his. Of the new hat of course.

07-14-2009, 01:03 PM	#15
*Ace Mercury* Marshmallow Knight ☆ Supermod Join Date: Jun 2000 Location: Southern Ontario Gender: Posts: 22,962 Thanks: 558 Thanked 3,205 Times in 1,531 Posts Blog Entries: 1	The riddle states they're all versed in logic. Logically, no one would want to sit at a table for hours on end. Therefore, there must be a powerful compelling force (warlock, wizard, predator drones, Rosie O' Donnell). This compelling force would not look kindly on cheating. From lemma one, they will not cheat. Lemma one: logical people prefer to remain living, as living is better than the alternative (not living). Therefore they prefer not to cheat.

07-15-2009, 10:43 AM	#16
chibimod3 Junior Member Join Date: Jan 2007 Location: The bottom of a Dr. Pepper bottle Gender: Posts: 497 Thanks: 52 Thanked 18 Times in 16 Posts	None of the things I have stated are cheating given the parameters of the riddle and the rules given. Your trying to add to a riddle written by a guy who probably expected the answers I just gave. On the off chance maybe one like DT's answer. Secondly then in the riddle with the lemma one theory have you looked up when this riddle was written? Because that may be true to us in the modern days but way back when people did do that and they just sat there and talked or read.

07-15-2009, 04:31 PM	#17
Deku Trii PP&R Mod Current Events Mod Join Date: Jun 2000 Location: Texas Gender: Posts: 8,930 Thanks: 490 Thanked 1,063 Times in 559 Posts	I'm bored, so I'm going to humor this for a moment. If your approach to the riddle were valid, why did none of them leave before a guest announced that at least one of them had a red hat?

07-16-2009, 04:22 AM	#18
CuccoLady Anime and Cartoons Mod Join Date: Jun 2006 Location: THIS LOCATION REMINDS ME OF A PUZZLE, LUKE Gender: Posts: 8,457 Thanks: 2,666 Thanked 1,075 Times in 724 Posts	^ Because if there was only one dude with the red hat, the dude wearing the red hat would just see blue around him and without knowledge that there IS a red hat there, he wouldn't know if he was wearing a red hat or if everyone was wearing blue.

07-16-2009, 09:09 AM	#19
Deku Trii PP&R Mod Current Events Mod Join Date: Jun 2000 Location: Texas Gender: Posts: 8,930 Thanks: 490 Thanked 1,063 Times in 559 Posts	I was talking about chibimod3's answer, CL. He suggests people simply switch hats or look at their own hats, which is something they would have done immediately if it were a valid approach.

07-16-2009, 10:45 AM	#20
chibimod3 Junior Member Join Date: Jan 2007 Location: The bottom of a Dr. Pepper bottle Gender: Posts: 497 Thanks: 52 Thanked 18 Times in 16 Posts	How many of us spent time thinking of a long complicated answer before realizing that the simplest answer works? This is true for a lot of riddles. Now DT I'm 100% sure your answer would be thought of by maybe one or two of the men there but that said those two men might not have a red hat. And in logic one of the first and foremost rules you have to learn is that the answer doesn't have to be long and complicated but it can be short and sweet.