The most prestigious law school admissions discussion board in the world.
|
 |
 
|
ITT: We do fun INDUCTION brain teasers (hat puzzles etc.)
Poast new message in this thread
Date: April 26th, 2026 11:27 PM Author: oomox Here is a common variation of the HAT PUZZLE. Unlike the TTT blue/red button thought experiment, this is a LOGIC problem (not a feeling problem) that has a correct answer.
----
Three poasters are competing for a girl's attention. She's mildly receptive to their jestermaxxing and decides to give them a few minutes of attention. She has them all face each other and tells them: "I'm going to place a hat on each of your heads so that you can only see each other's, not your own. Each hat is either red, blue, or yellow (but there may be multiple or none of a given color). You will all guess at the same time. If any of you gets your hat color right, I'll make out with each of you for like 5 seconds. You may agree on a strategy beforehand and let me know when you're ready."
What strategy can they use to ensure that at least one of them guesses their own color correctly? |
Date: April 26th, 2026 11:30 PM Author: ,.,.,:,,:,..,:::,...,:,.,..:.,:.::,. everyone says 'red' at the same time (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845612) |
 |
Date: April 26th, 2026 11:32 PM Author: oomox There isn't necessarily one of each color. Those are just the three possible colors. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845618) |
|
Date: April 26th, 2026 11:31 PM Author: scholarship (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845614) |
|
Date: April 26th, 2026 11:32 PM Author: ,.,.,:,,:,..,:::,...,:,.,..:.,:.::,. wait I didn't read it (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845617) |
|
Date: April 26th, 2026 11:33 PM Author: peeface i'd look at the other guys hats and tell them what color they are so they can answer correctly
|
|
Date: April 26th, 2026 11:33 PM Author: oomox You all guess at the same time. You don't have the hats yet when you're working out your stratgy. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845622) |
|
Date: April 26th, 2026 11:34 PM Author: ,.,.,:,,:,..,:::,...,:,.,..:.,:.::,. so what does the 'strategizing' consist in? why isn't telling him his hat color a strategy?
edit: oh, I see. |
|
Date: April 26th, 2026 11:37 PM Author: oomox Sorry I stealth edited that poast to clarify that you don't have the hats yet when you're agreeing on the strategy. Your task is to figure out how to guarantee that one of you gets it right when you all guess your colors simultaneously.
We're assuming they all want to win the kisses despite being POASTERS. |
|
Date: April 26th, 2026 11:36 PM Author: peeface yeah i'd blurt it out as soon as she put them on their heads before we all guess
|
|
Date: April 26th, 2026 11:37 PM Author: Juan Eighty the poasters would decide to make out with each other (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845632) |
|
Date: April 26th, 2026 11:38 PM Author: oomox Cr and 180 you posted this at the same time as I posted "We're assuming they all want to win the kisses despite being POASTERS." (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845633) |
|
Date: April 26th, 2026 11:38 PM Author: peeface to make sure you don't fight the hypo, the other poasters are benzo and nyuug (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845634) |
|
Date: April 26th, 2026 11:40 PM Author: oomox (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845641) |
|
Date: April 27th, 2026 12:34 AM Author: futtbucker (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845721) |
|
Date: April 26th, 2026 11:49 PM Author: ,.,.,:,,:,..,:::,...,:,.,..:.,:.::,. i'm stumped. if you can't share the other 2 men's hat colors as part of a strategy, i don't see how it works.
just seeing the other two men's hat colors gives you no information about your own hat color since there are no rules governing color distribution (your hat color could still be Y, R, B regardless of the other men's colors). |
|
Date: April 26th, 2026 11:51 PM Author: oomox Well the idea is to come up with a way to guarantee one of you is correct. That's a slightly different question from "how does anyone know their own color?" (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845662) |
|
Date: April 27th, 2026 12:05 AM Author: ,.,.,:,,:,..,:::,...,:,.,..:.,:.::,. but it's the same question, because you are looking for a strategy in which everyone gives Y/R/B as their own answer such that at least one is correct.
if the rule is "All or none of your hats could be Y/R/B in ANY combination regardless of the color of any other man's hat" then there can be no strategy because there is no rule. seeing the other hats provides no information as to the distribution of colors (no rule), other than the information about what the other 2 men's hat colors are, but this cannot be signaled as part of the strategy.
there is nothing we can all agree to say that guarantees one of us is right. |
|
Date: April 27th, 2026 12:10 AM Author: oomox Well you're thinking in the right direction of like, aren't there too many possibilities to cover with the three guesses? But the problem space is smaller than it seems. It helps to assign numbers to the colors and start looking at the possibilities that way.
edit: "other than the information about what the other 2 men's hat colors are, but this cannot be signaled as part of the strategy." – They can't "signal" that information bc they're guessing simultaneously, but they can still incorporate it into their guesses |
|
Date: April 27th, 2026 12:14 AM Author: niggerstomper59 (✅🍑) The blue/red button thought experiment is a clean logic problem. You don't understand the logic and incorrectly think it is about feels and therefore you choose incorrectly, resulting in your death. Life is one big IQ test that you failed. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845692) |
|
Date: April 27th, 2026 12:16 AM Author: oomox It could be made a clean logic problem if you specified that everyone on Earth can be assumed to be a rational actor. Then there's a correct answer, red. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845695) |
|
Date: April 27th, 2026 12:18 AM Author: niggerstomper59 (✅🍑) No. The logic exists independently of whether any specific individual is a rational actor. With red, you always live. With blue, you only possibly live contingent on others' acts. You either understand this and live, thereby passing the IQ test, or you don't understand this and perhaps die, thereby failing the IQ test. You failed. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845696) |
|
Date: April 27th, 2026 12:22 AM Author: oomox I might be unusually principled but I would rather be wrong about people and die trying to save us all than take the self-interested route and survive with blood on my hands. I think a lot of other people have that same intuition of "I would do the thing that can save everyone and assume half of people have similar morals to mine." (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845701) |
|
Date: April 27th, 2026 12:27 AM Author: niggerstomper59 (✅🍑) I think this might be one of those irregular verbs with an irregular conjugation: I am principled, you don't understand the logic, he/she is a flaming retard. As for the hysterical "self-interested route" and "blood on my hands", if everyone picks red, everyone survives, and so the only people with "blood on their hands" (lol) are dumbs with their own blood on their hands. |
|
Date: April 27th, 2026 12:28 AM Author: oomox We understand the logic. And if you're so great, try to solve the hat puzzle! (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845712) |
|
Date: April 27th, 2026 12:29 AM Author: niggerstomper59 (✅🍑) No, I don't think you do. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845714) |
|
Date: April 27th, 2026 12:34 AM Author: Is it not the case (Is it not the case) Your risk is way too high. Your projected outcome is skewed towards your own demise based on values when most people are going to push red to save themselves and not have to worry about whether they'll be killed. You'll never get to 50% of people who are willing to risk dying for other people. Therefore 100% of red pushers live, 100% of blue pushers die, 100% of the time. It would be stupid to die for your beliefs. Save yourself! (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845720) |
|
Date: April 27th, 2026 12:41 AM Author: oomox I'm sure there are forums where everyone is like, "Obviously blue! Most people would just choose blue right? Since it's the right thing to do so we all survive?" but you guys are like the most cynical people on the internet and don't understand why anyone would risk their dEmIsE for the collective good (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845731) |
|
Date: April 27th, 2026 12:45 AM Author: Is it not the case (Is it not the case) All anyone has to do to not die is push red. It's safe, it's secure. Blue is giga idealistic. In the end blue is foolish. If you pushed blue and were about to die you'd be thinking damn I should have pushed red. Boy that was stupid. You'll never get all the world to agree. Most people are unwilling to go down with the ship. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845742) |
|
Date: April 27th, 2026 12:25 AM Author: Cletus Van Damme just spit dip on the floor and call her a dumb whore and be done with it. millennials are such fags. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845705) |
|
Date: April 27th, 2026 12:27 AM Author: niggerstomper59 (✅🍑) This would seem to solve the problem. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845707) |
|
Date: April 27th, 2026 12:33 AM Author: Cletus Van Damme why does the op say "make out with you for five seconds" like thats relevant (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845718) |
|
Date: April 27th, 2026 12:29 AM Author: Is it not the case (Is it not the case) I'm a Liberal Artist imo. I'm a failure at STEM. I can't compute logic problems. I guess I would just write a short story about the experience and double down on jestermaxxing. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845713) |
|
Date: April 27th, 2026 12:31 AM Author: oomox 180. A computer science background does help with this problem. Like it uses a specific... operation you only really encounter in CS or advanced formal logic classes. But I'm sure non-STEM people can figure it out too. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845715) |
|
Date: April 27th, 2026 12:35 AM Author: Is it not the case (Is it not the case) I eagerly await the Big Reveal whereupon my mind will be blown. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845722) |
|
Date: April 27th, 2026 12:46 AM Author: peeface this is one of those old puzzle book things where you sum up the hats mod 3 to reach a target number that makes no intuitive sense at all but seems to work despite that if you brute force it out
|
|
Date: April 27th, 2026 12:46 AM Author: Is it not the case (Is it not the case) I have no clue what you're saying, peeface tp (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845746) |
|
Date: April 27th, 2026 12:49 AM Author: peeface im gay (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845748) |
|
Date: April 27th, 2026 12:55 AM Author: oomox Crrrrr SOLUTION: (Before you go on - if you have a CS background and haven't figured it out, try again with the hint that it involves modular division.)
You assign each color a number 0, 1, or 2.
You reason that when the numbers are added up, the total either: - is divisible by 3 - has a remainder of 1 when divided by 3, or - has a remainder of 2 when divided by 3
In CS terms, that's modular division: https://en.wikipedia.org/wiki/Modulo
You assign each person as remainder 0, remainder 1, and remainder 2. They add up the other people's hats and guess their hat such that the remainder when divided by 3 would be their assigned number. |
|
Date: April 27th, 2026 12:33 AM Author: ,.,.,:,,:,..,:::,...,:,.,..:.,:.::,. ok, I see it now, but I don't like it. this is worse than the Monty Hall problem. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845719) |
|
Date: April 27th, 2026 12:43 AM Author: futtbucker thread title promised teasers (plural) but there's only 1 followed by a subthread wasteland about another thread (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845737) |
|
Date: April 27th, 2026 12:44 AM Author: oomox The problem in the OP is difficult enough that I figured I'd let this one simmer for a while. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845740) |
|
Date: April 27th, 2026 12:50 AM Author: futtbucker It's not that hard, you assign each color a number and each poaster a target of 0, 1, 2 and then they add up the color they see and guess their own color based on that target. Two will be wrong and one will be right. Next? (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id.#49845749) |