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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],#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],#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],#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],#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],#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],#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],#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],#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],#49845641) |
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Date: April 27th, 2026 12:34 AM Author: futtbucker (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2],#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],#49845879) |
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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],#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],#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],#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],#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],#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],#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],#49845714) |
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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],#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],#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],#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],#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],#49845775) |
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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],#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],#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],#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],#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],#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],#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],#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],#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 either: - has no remainder when divided by 3 (total = 0, 3, or 6), - has a remainder of 1 when divided by 3 (total = 1 or 4), or - has a remainder of 2 when divided by 3 (total = 2 or 5)
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 the total when divided by 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],#49845754) |
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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],#49845719) |
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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],#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],#49845740) |
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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],#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],#49845759) |
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Date: April 27th, 2026 1:02 AM Author: futtbucker 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],#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],#49845779) |
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Date: April 27th, 2026 1:25 AM Author: futtbucker any riddles that don't involve modulo division? (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2],#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],#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],#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],#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],#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],#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 1:47 AM Author: Juan Eighty (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2],#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: futtbucker 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],#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],#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],#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 starting over at 0 after 2. (http://www.autoadmit.com/thread.php?thread_id=5860893&forum_id=2],#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],#49845884) |
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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],#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],#49846346) |