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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.
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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) |
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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) |
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Date: April 26th, 2026 11:31 PM Author: scholarship (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49845614) |
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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) |
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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
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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 strategy. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49845622) |
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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. |
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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. |
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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
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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) |
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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) |
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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) |
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Date: April 26th, 2026 11:40 PM Author: oomox (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49845641) |
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Date: April 27th, 2026 10:37 AM Author: Mideast "Peace" "Agreement" (No Future) (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846359) |
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Date: April 27th, 2026 12:34 AM Author: Paying a Japanese girl to spit in my drink (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49845721) |
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Date: April 27th, 2026 3:44 AM Author: The Penis (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49845879) |
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Date: April 27th, 2026 10:36 AM Author: Mideast "Peace" "Agreement" (No Future) (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846358) |
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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). |
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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) |
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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. |
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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 |
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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) |
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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) |
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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) |
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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) |
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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. |
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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) |
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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) |
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Date: April 27th, 2026 10:37 AM Author: Mideast "Peace" "Agreement" (No Future) (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846362) |
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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) |
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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) |
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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) |
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Date: April 27th, 2026 1:01 AM Author: peeface don't discourage them. after the holocaust of the blues we will finally be free of women, immigrants, and libs.
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Date: April 27th, 2026 1:09 AM Author: Is it not the case (Is it not the case) OP is a good egg worth saving (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49845769) |
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Date: April 27th, 2026 1:11 AM Author: peeface we'll put him last in the button line.
once we show him the running tally and it is clear hitting the blue button won't save the blues from their well deserved genocide i assume he will press red.
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Date: April 27th, 2026 1:18 AM Author: Is it not the case (Is it not the case) 🤞🏻 (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49845775) |
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Date: April 27th, 2026 10:42 AM Author: Mideast "Peace" "Agreement" (No Future) I was team blue for a moment until I realized that red is better
I do think it matters if you stipulate whether kids are involved or if you limit it to people who are generally competent to consider the issue. If there’s lots of kids etc involved then you may figure that there’s enough blameless non rational actors we want to save that the ethical choice is to switch to blue and try to save them. If you’re assuming a game theory sterile abstraction where “everyone” is just rational actors then it’s absolutely red. |
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Date: April 27th, 2026 10:59 AM Author: non stop prop op from israel (gunneratttt) if we assume everyone is a rational actor the hypo is solved with red. but we know that's not true.
empirically we can see many people choose blue and cannot be dissuaded. so we know in reality many people will choose blue.
the hypo requires universal participation, so "opting out" by choosing red is bullshit. you're still participating, team red interprets it as a moral choice. but we know from observation that many people will choose blue and that humans are perfect rational actors. |
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Date: April 27th, 2026 12:14 PM Author: niggerstomper59 (✅🍑) It doesn't matter whether or not everyone is rational, it just matters what you do contingent on what everyone else is doing. You either definitely live, or you possibly die, irrespective of everyone else's rationality. (Although if you want to express it in game theoretic terms, "red" is a strictly dominant strategy for everyone, therefore you should absolutely pick "red" in all circumstances, and "all pick red" is a dominant strategy equilibrium) Life is a big IQ test. Those that pick "blue" fail. |
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Date: April 27th, 2026 10:46 AM Author: Mideast "Peace" "Agreement" (No Future) I think the key issue is whether or not anyone is constrained from making the logical decision. If there are people who are going to push blue because of disability or they’re too young etc then I think there’s a moral argument that everyone has to choose blue (and you individually have to) because it will stop harm. That’s what the blue people are assuming—they start off with an assumption of “well some people will always choose blue” so we need to do the option that saves them. But if we are in pure sterile abstraction thought land, anyone whose initial impulse is blue is an idiot.
The funny thing is that these people are probably thinking along Kantian lines when they hit blue but 1) red is fully consistent with categorical imperative and 2) Kant’s political writings are explicit that you have to go with the world you want to see. If you’re a lib sitting and thinking “well maybe nobody should pick blue in the first instance but somebody will so I’ll save them and pick blue,” then it’s a self fulfilling prophecy. |
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Date: April 27th, 2026 10:50 AM Author: Is it not the case (Is it not the case) The universe doesn't care about your feelings. Blue is a death sentence. You subliminally want to die. You only have one option to survive, to push red. Women, children, the indigent. Their best hope is for someone to convince them to preserve themselves. All blue pushers are going to die 100% of the time. It's very tragic but we cannot risk our own lives to save everyone. It's black and white here. You either live or you kill yourself. The blue pill is that most people will choose life. Can't save everybody, unfortunately. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846415) |
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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) |
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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) |
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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) |
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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) |
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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) |
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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) |
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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
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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) |
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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) |
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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 three hats' numbers are added up, the total 0-6 falls into one of these categories: - { 0, 3, 6 }: have a remainder of 0 when divided by 3 - { 1, 4 }: have a remainder of 1 when divided by 3 - { 2, 5 }: have a remainder of 2 when divided by 3
So if you each cover one of those 3 possibilities, it's guaranteed that exactly one of you will be correct.
You assign one person to remainder 0, one to remainder 1, and one to remainder 2. Everyone adds up the other people's hats and guesses their hat such that the remainder of total/3 is their assigned number. |
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Date: April 27th, 2026 12:57 AM Author: Is it not the case (Is it not the case) As a 660 math SATmo this is way above my skill level (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49845754) |
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Date: April 27th, 2026 5:32 PM Author: oomox For example: Red = 0, Yellow = 1, Blue = 2
I am assigned remainder 0. - If I see a red hat and a yellow hat, the total is 1, so I need to guess Blue for a total of 3 in order to get a number in my assigned category. - If I see two red hats, the total is 0, so I need to guess Red for a total of 0 to get a number in my assigned category. |
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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) |
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Date: April 27th, 2026 12:43 AM Author: Paying a Japanese girl to spit in my drink 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) |
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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) |
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Date: April 27th, 2026 12:50 AM Author: Paying a Japanese girl to spit in my drink 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) |
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Date: April 27th, 2026 1:02 AM Author: oomox Yes but explain how exactly they guess their color based on the sum of the other ones? (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49845759) |
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Date: April 27th, 2026 1:02 AM Author: Paying a Japanese girl to spit in my drink you explained up thread already but the riddle was that only one of them needs to do that, not all 3 (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49845760) |
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Date: April 27th, 2026 1:20 AM Author: oomox [removed second hat question to use later in thread] (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49845779) |
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Date: April 27th, 2026 1:25 AM Author: Paying a Japanese girl to spit in my drink any riddles that don't involve modulo division? (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49845780) |
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Date: April 27th, 2026 1:42 AM Author: oomox NEXT (not "inductive," just a logic puzzle): This one involves some real-world assumptions you can ask about if you have questions. It's not quite as abstract as the hat ones.
I capture you and lock you in my dungeon as my slave. I treat you well and feed you and stuff and you enjoy spending time with me BUT you'd much rather be free to go back to your life. After a couple weeks I tell you that I'm going to give you a chance to escape. There are three switches in your cell that have always been a mystery to you. They're each marked "on" and "off" and you've kept them off after some initial experimentation.
I tell you that each switch connects to a lightbulb in my room directly above the dungeon. Each lightbulb is controlled by one switch. I tell you to do whatever you want with the switches until tomorrow morning, at which point I will take you upstairs to where the lightbulbs are. If you can figure out which switch corresponds to each lightbulb, I'll set you free.
What is your strategy to escape? |
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Date: April 27th, 2026 1:50 AM Author: peeface i'd turn one on, one off, and flick one off and on rapidly all night until the bulb burns out.
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Date: April 27th, 2026 1:55 AM Author: oomox The solution is actually really close to that. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49845823) |
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Date: April 27th, 2026 1:57 AM Author: ,.,.,:,,:,..,:::,...,:,.,..:.,:.::,. can you touch the bulbs when examining them? (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49845827) |
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Date: April 27th, 2026 1:57 AM Author: oomox Yes you can examine them however you want (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49845828) |
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Date: April 27th, 2026 1:58 AM Author: ,.,.,:,,:,..,:::,...,:,.,..:.,:.::,. so leave the switch on all night then flip it off at the last minute then examine the bulb for heat, is what I would do. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49845829) |
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Date: April 27th, 2026 2:16 AM Author: oomox Crrrr! That's my favorite brainteaser. Next INDUCTION puzzle here: https://xoxohth.com/thread.php?thread_id=5860893&forum_id=2#49845889 (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49845842) |
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Date: April 27th, 2026 4:55 AM Author: ,.,.,:,,:,..,:::,...,:,.,..:.,:.::,. 1800000 look at me! i'm like Sherlock Holmes! |
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Date: April 27th, 2026 10:47 AM Author: non stop prop op from israel (gunneratttt) HYPO DID NOT SPECIFY THAT THEY ARE INCANDESCENT BULBS >:(
sat here for 10 min trying to figure out if it could he solved in one night. this is BULLSHIT |
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Date: April 27th, 2026 4:40 PM Author: oomox Lol that's why I said there are real-world things you can ask about. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49847288) |
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Date: April 27th, 2026 1:47 AM Author: Juan Eighty (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49845809) |
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Date: April 27th, 2026 1:33 AM Author: peeface again, i'm just going to tell the guys next to me what hats they have on
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Date: April 27th, 2026 1:34 AM Author: Paying a Japanese girl to spit in my drink turns out you hate em all. reminds me of this old joke:
"A bus full of ugly people unexpectedly crashes and kills everyone on board
Everyone shows up at the Gates of Heaven where God comes to meet them all Himself.
"Gee guys, I didn't intend for that to happen, I'm really sorry. I can't just resurrect you all, but to make up for it I'll grant you all one wish before I let you in."
The first person steps up and thinks for a moment. He says "You know God, I've been ugly all my life. For once I would like to know what it is like to be beautiful. Make me beautiful." So God snaps his fingers and it is so.
Everyone else starts chattering amongst themselves at such a brilliant idea. They all start wishing for the same thing.
God steps up to the last guy in line who is laying on his side laughing so hard he is crying. After several minutes of patiently waiting, God finally says "Now what in Heaven could be so funny boy?" The man stands up, wipes a tear from his eye and says "Make them all ugly again."" |
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Date: April 27th, 2026 1:37 AM Author: peeface that guy sounds like a real jerk! (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49845793) |
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Date: April 27th, 2026 1:43 AM Author: oomox 180 (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49845803) |
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Date: April 27th, 2026 3:43 AM Author: The Penis Each poaster bets on a different total sum for the hats (0, 1, or 2). Since those are the only three mathematical possibilities, one of them is legally obligated to be right. First time in bort history (maybe human history) that discrete maths gets used as a viable flirting strategy. Its a lot of mental labor for 5 seconds of glory but for a poaster thats a high return on investment (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49845878) |
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Date: April 27th, 2026 3:47 AM Author: oomox Correct except that technically the possibilities are 0-6 so you have to reduce that to 0, 1, 2 by doing modular division. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49845880) |
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Date: April 27th, 2026 3:53 AM Author: VoteRepublican (A true Chad!! where's your gf/wifew?) best explanation (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49845884) |
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Date: April 27th, 2026 4:55 PM Author: Diamond Dallas Chad I don't get it at all. By giving the total sum of all hats, the poasters are not answering in the format required. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49847323) |
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Date: April 27th, 2026 5:14 PM Author: oomox Yeah, his answer works for slightly different formulations of the problem. In this case there are 7 possible sums, 0-6. You need to break down those possibilities into three categories, one of which must be true.
We can break it down into: - { 0, 3, 6 }: have a remainder of 0 when divided by 3 - { 1, 4 }: have a remainder of 1 when divided by 3 - { 2, 5 }: have a remainder of 2 when divided by 3
Since we have 3 guesses, we have each person construct his guess so that the total meets his assigned condition (remainder 0, 1, or 2). One of them will be right and the other two will be wrong.
For example: Red = 0, Yellow = 1, Blue = 2
I am assigned remainder 0. - If I see a red hat and a yellow hat, the total is 1, so I need to guess Blue for a total of 3 in order to get a number in my assigned category. - If I see two red hats, the total is 0, so I need to guess Red for a total of 0 to get a number in my assigned category. |
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Date: April 27th, 2026 3:51 AM Author: lfo Who's the FOB trying to draft OP? (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49845883) |
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Date: April 27th, 2026 4:27 AM Author: oomox NEXT QUESTION: We live in a strict matriarchy where every woman has to pass a logic exam before she is allowed to marry and therefore all married women are perfect reasoners. Every woman knows (from observation) whether each man in the kingdom is faithful to his wife, EXCEPT for her own husband. It is taboo to tell a woman whether her husband is faithful, and no one has done it or would ever. Also, all of the women have great hearing and would definitely hear a gunshot from anywhere in the kingdom.
One day, the Queen tells everyone that she is observing male infidelity in the kingdom and wants to eradicate it. She says that women with cheating husbands are now legally required to shoot and kill their husbands at midnight after discovering the infidelity, starting that night.
How does each married woman know when/if to kill her husband? |
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Date: April 27th, 2026 10:29 AM Author: non stop prop op from israel (gunneratttt) every woman tallies up how many cheating men are in the kingdom and writes down the numner. only two sums are possible: women with faithful husbands will write down N, the true total, and women with unfaithful husbands will write down N-1. thus, if you wrote down N-1 you can deduce your husband is unfaithful and shoot him at midnight. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846346) |
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Date: April 27th, 2026 11:48 AM Author: The Penis I don’t think that works. For instance if I see 5 cheating husbands, I don't know if N = 5 (my husband is faithful) or if N = 6 my husband is the 6th cheater). There has to be something that gives the first wife a reason to kill then the inductive chain starts but I’m having trouble intuiting it.
Wait it might be simpler than I was thinking. They might just count down the nights, and since they are all perfect reasoners they literally shoot at the same time on the last night. |
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Date: April 27th, 2026 11:58 AM Author: non stop prop op from israel (gunneratttt) if every woman shares what they believe is the total number lf cheating husbands, everyone with the lower number can deduce that their husband is unfaithful. they know there is at least one cheater because the queen announced it. and the two different sums confirm it.
let's use your numbers and say that there are 10 women total and 6 have unfaithful husbands. the 4 with faithful husbands will say there are 6 cheaters. the 6 with unfaithful husbands will say that there are 5 because they only can't see their own. this doesnt break the taboo because none of the wives are telling the other ones their husband is cheating. the numbers could all just be written anonymously too. the women with unfaithful husbands know the number the wrote down and can deduce their husband is the cheater. |
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Date: April 27th, 2026 12:02 PM Author: rear naked choke (guy who thinks like a lawyer) (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846607) |
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Date: April 27th, 2026 12:06 PM Author: The Penis I feel like thats fighting the hypo (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846618) |
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Date: April 27th, 2026 12:17 PM Author: non stop prop op from israel (gunneratttt) i think you're "right" and the answer rear naked choke came up with is the answer the question anticipates since it requires the perfect hearing component. but thats using meta-reasoning to figure out what the answer the drafter wanted is. i don't think my answer breaks the taboo, and chokes answer requires the women to track the number of nigjts passed, for no one to die for other reasons, and for shots to only occur for the specific purpose. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846651) |
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Date: April 27th, 2026 12:22 PM Author: The Penis I think that's fair if we are treating the story as a realistic social process. But these logic puzzles are always idealizing the environment. "Perfect reasoners" "Great Hearing" etc. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846657) |
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Date: April 27th, 2026 12:38 PM Author: non stop prop op from israel (gunneratttt) cr. however those premises are explictly established by the hypo. if you accept that this is a logic puzzle and make additional assumptions that weren't explicit (another is mine uses deductive reasoning and the thread says inductive), then that meta-reasoning gets you to the answer the question is searching for. but i still think mine works as drafted and better in a realistic scenario.
if this was on the LSAT and both mine and chokes answers were available, id select his because it's "best", i.e. what the drafter would think is best. |
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Date: April 27th, 2026 11:11 AM Author: UN peacekeeper by induction, hth (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846473) |
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Date: April 27th, 2026 5:25 PM Author: oomox Mfcr this is the most pure INDUCTION problem so far. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49847390) |
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Date: April 27th, 2026 11:58 AM Author: rear naked choke Assume 3 wives in the kingdom, exactly one of whom is cucked (but ofc doesn't know it). On day one, there are no murders because no wives know they are cucked. On day two, same. On day three, there has to be at least one murder bc queen said there is infidelity. Cuckwife observes that other two wives are not cucks. Cuckwife therefore deduces that she is the cuck and murders her husband on day three.
Solution is generalizable to greater populations and numbers of cucks.
Edit: nm I fucked up and am retarded. On day one, cuckwife would deduce that she is cuckwife and murder her husband on day one. Oomox explains below. |
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Date: April 27th, 2026 12:11 PM Author: non stop prop op from israel (gunneratttt) this works too and is probably the answer the hypo is seeking. women are not compelled to root out the infidelity, so they wouldn't have to share the total number of cheaters like in my solution. but they would arive at the same conclusion after a certain number of nights (if we assume they're tracking them and have perfect memory).
in my solution with 10 women with 6 unfaithful husbands, the women who could see 5 cheaters would realize on the 6th night when the queen announces infidelity still remains that their husbands are cheaters and will shoot them after midnight. i was wondering where the perfect hearing component worked here. it's necessary for all the women to know whether murders occurred. |
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Date: April 27th, 2026 12:12 PM Author: The Penis yeah I think thats it. they wait the number of nights and all shoot at the same time on night N given the number of cucks (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846638) |
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Date: April 27th, 2026 1:51 PM Author: oomox That's really close. More precise SOLUTION: If there's only one cuckwife, she shoots her husband on the first night because the Queen announced that *someone* was cheating and she doesn't see anyone else's husband cheating. If there are two, both kill their husbands the second night because they only see one cheater and there were no shots on the first night. If there are three, all three kill their husbands the third night because they all saw two cheaters and there were no shots on the second night. And so on. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846852) |
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Date: April 27th, 2026 12:11 PM Author: peeface this seems to be built on a bigoted premise that all wives are women (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846634) |
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Date: April 27th, 2026 1:55 PM Author: oomox Oh no how heteronormative of me (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846873) |
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Date: April 27th, 2026 1:56 PM Author: oomox NEXT QUESTION: This one is a more common version of the hat problem, and the solution isn't as obscure/mathy.
There are 100 prisoners in a for-profit prison in a brand new SmartCity. Their sadistic AI warden decides to play a game. The prisoners will stand in a line on a ramp, each of them able to see all of the prisoners in front of them. A Red or Blue hat will be placed on each person's head. As in the last case, they can't see their own, just those of the people in front of them. Starting at the back of the line, each person will have to guess whether he has a Red or Blue hat. If he's wrong, he's executed; if he's right, he gets an upgrade from jail to the VR data harvesting labs where at least you get to play games. Everyone can hear the guesses of everyone before him.
They can strategize about it beforehand. How can they ensure the maximum survival possible of the group? |
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Date: April 27th, 2026 2:00 PM Author: niggerstomper59 (✅🍑) There is no restriction on the set of hats? (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846893) |
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Date: April 27th, 2026 2:01 PM Author: oomox Any hat can be red or blue. No set distribution; could be all one color or split in any way. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846897) |
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Date: April 27th, 2026 2:25 PM Author: niggerstomper59 (✅🍑) I don't think there is a way they can all be guaranteed to survive, the last in the line (i.e. the first to guess) has no path to obtain information about his own hat, but he can see all the other hats in front of him and he is the first to guess so he ought in principle be able to find a way to signal the information he has to the other 99 players in a way that they can sequentially use and pass forward (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846973) |
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Date: April 27th, 2026 2:28 PM Author: niggerstomper59 (✅🍑) are they restricted in what they can say e.g. only "red" or "blue" to guess their own hat, or can they also say other things? e.g. if each player is permitted to speak a number, they can allocate 1 and 0 to each other colors and each plater add up the hats they see in front of them and pass that information forward so that X(p)-X(p-1) = 0 or 1 so that each player can know the color of their own hat but the last in the line cannot do this and so may croak |
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Date: April 27th, 2026 2:29 PM Author: oomox 🎯🎯🎯
So what info should they agree on beforehand for the first guy encode in his guess?
Each guess = just "red" or "blue," no numbers or additional info. |
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Date: April 27th, 2026 2:07 PM Author: The Penis Can they use encoding beyond the literal words red or blue? Like can they agree to say the words louder, with weird accents etc. to mean different things? (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846926) |
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Date: April 27th, 2026 2:08 PM Author: non stop prop op from israel (gunneratttt) also, are they aware of a prisoner guesses wrong and is executed? (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846927) |
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Date: April 27th, 2026 2:11 PM Author: oomox They hear the guesses before theirs for sure, and it doesn't matter if they hear the results of the guesses. For drama let's say they do.
edit: The result doesn't matter *if* we assume they're perfectly rational actors, which we are. If we stipulate that they may make mistakes, it does matter. |
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Date: April 27th, 2026 2:18 PM Author: The Penis What if they agree beforehand that the first prisoner’s word is not a sincere guess but a code bit where “Red” means even parity and “Blue” means odd parity? That doesn't technically violate literally Red/Blue (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846950) |
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Date: April 27th, 2026 2:26 PM Author: oomox Crrrr! SOLUTION: The first prisoner's answer reflects whether he sees an even number of [designated color] hats or an odd number. He has a 50% chance of survival and then everyone else can get theirs right for sure based on that first answer and the answers of those that go before him.
(If there's the possibility that the prisoners make mistakes deducing from the answers before them, I guess we do need the results to be audible to everyone.) |
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Date: April 27th, 2026 2:25 PM Author: non stop prop op from israel (gunneratttt) if they can hear the results of the guess it works similarly to card counting. they could assign the hats a binary 1 or 0 and then communicate the count by assigning each color even or odd. e.g. red = 1, blue = 0, guessing red = even, guessing blue = odd.
if the last prisioner sees 40 red hats he would announce even. if the next prisoner sees 40 red hats he knows his is blue. then each prisoner follows suit.
i guess knowing the result of the guess isn't necessary if we assume the prisoners execute this perfectly. it would be necessary to confirm the accuracy of the count if someone makes a mistake. if they execute it perfectly, 99 prisoners are sure to live. the last guy is 50/50 regardless. i assume for the purposes of the hypo he will cooperate with the strategy even though he won't benefit personally? |
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Date: April 27th, 2026 2:27 PM Author: oomox All exactly correct! We do need to hear the results if they might make mistakes. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846981) |
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Date: April 27th, 2026 2:09 PM Author: oomox Nope no extra info, just red/blue. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846928) |
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Date: April 27th, 2026 2:13 PM Author: The Penis What about exploiting the ambiguity in the phrase "guess whether he has a Red or Blue hat"? This is probably fighting the hypo, because it seems the intended puzzle is saying the only valid outputs are "red" or blue" “whether he has a Red or Blue hat” can be read loosely as asking him to answer the question “Do you have a red-or-blue hat?” I guess that probably violates "no extra info, just red/blue", but I think its a funny way to do it (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846941) |
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Date: April 27th, 2026 2:20 PM Author: oomox Oh yeah "guessing" just means each of them says "red" or "blue" and receives the consequence (death if it's not the color of his hat, transfer if it is) from the warden. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846958) |
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Date: April 27th, 2026 2:21 PM Author: The Penis I can't stop Fighting the Hypo. I have Poor Abstraction Discipline (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846959) |
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Date: April 27th, 2026 2:27 PM Author: richard clock first guy should say the color that has the most number of hats to help the other bros out. actually i guess he needs to come up with a way to convey more info than that but idk what it is (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49846980) |
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Date: April 27th, 2026 2:34 PM Author: oomox Not quite which one has more because imagine the front guy is red and everyone behind him is blue. Back guy says "blue," second-to-back still doesn't know what color he has. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49847001) |
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Date: April 27th, 2026 2:43 PM Author: non stop prop op from israel (gunneratttt) this solution would ensure >50% of the people survive. if the majority of hats are red, last guy announces red, and everyone follows suit.
this might be the best answer in a real world scenario considering human fallibility and how unlikely it would be for the last prisoner to make an accurate count. |
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Date: April 27th, 2026 4:30 PM Author: oomox NEXT QUESTION: Slumlord CSLG goes on an insecurity-fueled rampage and tracks down 50 POASTERS who said mean things about him on the bort. He imprisons them in some of his UNITS. He tells them all that there is a single room in the basement, which he menacingly calls "The Playroom," containing nothing but a switch and corresponding tacky chandelier. Every day after work and before infidelity, he heads over to his UNITS and uses a (pseudo)RNG website to choose a poaster to escort to The Playroom. The poaster can see if the light is on and off, and they can choose to toggle the switch or not.
At any point when summoned to go to The Playroom, a poaster can tell CSLG: "Every poaster has been to The Playroom." If they're correct, he'll set everyone free. If they're wrong, everyone is executed and CSLG sells the UNITS to SpacePorn to make into real playrooms. Sick stuff.
CSLG gives the poasters a chance to coordinate a plan before bringing them to their separate units, warning them that they'll never see each other again unless someone correctly tells him that they've all been to The Playroom. He tells them that the first poaster will be SUMMONED that night. What's their plan to get out alive? |
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Date: April 27th, 2026 5:03 PM Author: non stop prop op from israel (gunneratttt) what do you mean by psusdo rng? does it eliminate people that haven't gone before or is it completely random? because then the 50th night the poaster who goes 50th would be the last. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49847337) |
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Date: April 27th, 2026 5:15 PM Author: oomox Completely random. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49847368) |
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Date: April 27th, 2026 5:22 PM Author: non stop prop op from israel (gunneratttt) with 50 poasters selected randomly the probability of all being selected is pretty high after a year. they should just agree to YOLO after a year.
im stumped. the only way i can think of to come to a certain answer is to brute force it, but that could take decades, and there's no way all 50 balding middle adged poasters all last that long. |
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Date: April 27th, 2026 5:08 PM Author: richard clock can the guy in the playroom toggle the switch any number of times? if so, assign a number to each resident and when they are in the playroom, have them toggle the switch the number of times assigned to them.
if they can only do it once, tell the residents to toggle the switch only if this is their first time to the playroom. then you can keep track of how many first timers have gone until everyone has paid a visit |
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Date: April 27th, 2026 5:15 PM Author: non stop prop op from israel (gunneratttt) why would it matter how many times its toggled? the prisoners on see the playroom on their own and can't communicate with the others. the next prisoner to see it only could tell if its on or off, not how many times it was switched? (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49847366) |
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Date: April 27th, 2026 5:23 PM Author: oomox Doesn't matter how many times they toggle it; the other prisoners don't see it real-time. They're just deciding if the light will be on or off when they leave.
Expand on your second idea. How would you keep track? |
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Date: April 27th, 2026 5:33 PM Author: richard clock i thought there was one poster (you) who could see if the light was on or off. is this not right? maybe i read this too fast (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49847413) |
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Date: April 27th, 2026 5:31 PM Author: 345 (🧐) first guy turns it off
for every other guy, they will turn it on if they have never flipped the switch. if it's already on, they do nothing.
whenever first guy comes around again, he turns it off. at some point he will have done this N-1 times
will take a very long time but uh guarantees everyone should get to go home within 10000k days or so
it's something like this + minus the requirement of the "first guy" (since they dont know who goes first) and instead getting everyone to agree on the special man |
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Date: April 27th, 2026 5:39 PM Author: non stop prop op from israel (gunneratttt) i was thinking the same thing but you just assign one poaster as the counter. if he goes in first he would turn it off. but that would take longer that than than the remaining life expectancy of the 50 poasters. and they don't even know if all the poasters remain, including the counter (or first oick in your version). (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49847429) |
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Date: April 27th, 2026 5:48 PM Author: 345 (🧐) there's only one piece of information (the switch) and technically nothing guarantees they will ever get out period since people are called at random
unless it's something goofy like "just put ur hand on the light bulb lol" |
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Date: April 27th, 2026 5:43 PM Author: oomox Crrrrr! The correction at the end is crucial.
SOLUTION: The group designates a Counter. Everyone except for the Counter interacts with The Playroom as follows: If it's your first time in there and the light is off, turn the light on. Otherwise, do nothing.
The Counter interacts with The Playroom as follows: If the light is on, turn it off and add a tally to the POASTERS count. When you've recorded 49 fellow poasters, the next time you're summoned, you can tell CSLG you're ready to bounce. And yeah it will probably take a while. |
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Date: April 27th, 2026 5:47 PM Author: The Penis But how do they figure out that the switch is initially set to "off"? (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2...id#49847457) |
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Date: April 27th, 2026 5:49 PM Author: non stop prop op from israel (gunneratttt) it would take a decade and potentially beyond the range humans can live and also requires all 50 poasters to remain alive, which is a near statistical certainty will not occur.
best bet is wait a year and yolo that everyone has gone, which is near certain by then. |