Colleenz
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Post by Colleenz on Oct 18, 2011 7:36:30 GMT -5
The possibilities for the remaining two members are: FF MF FM So 33% chance the third member is a female. That, and I think I have guessed every other combination so one of my answers should be correct. ![:P](//storage.proboards.com/forum/images/smiley/tongue.png)
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hoops902
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Post by hoops902 on Oct 18, 2011 8:35:54 GMT -5
The possibilities for the remaining two members are: FF MF FM So 33% chance the third member is a female. That, and I think I have guessed every other combination so one of my answers should be correct. ![:P](//storage.proboards.com/forum/images/smiley/tongue.png) Since we're ignoring the signon order and the issues of Rick signing on first, 33% chance of 2 females, 1 male is correct I believe.
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Virgil Showlion
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Post by Virgil Showlion on Oct 18, 2011 12:07:23 GMT -5
We're down to the wire and it's the last call for bets. Colleenz has put all her chips down on 2/3 chance 2M/1F, 1/3 chance 2F/1M. Her left hand is white-knuckling the edge of the betting table while her right hand feeds an endless chain of cigarettes into her quivering lips. Hoops is looking more relaxed in his Hawaii shirt, but even he's feeling the pressure. He's moved his chips from 2/3 1/3 to 3/5 2/5 to 5/8 3/8 back to 2/3 1/3 next to colleenz. He lights up a Cuban and sends a wink Collenz' way. "Luck be two thirds of a man and one third of a lady tonight," he quips. The mysterious "Mr. S" who opened betting by placing all of his chips on 50% 2M/IF 50% 2F/1M is silent and grim. One of those shy types who has faith that the "you" in the problem statement is probably correct. Will his blind faith pay off? Last call. Any more brave souls? Any risk-takers to put their chips in beside Hoops and Colleenz? Any starry-eyed EEers who want to put it all on the line and stack their chips next to Mr. S's? Or any rebels who just know the solution to the problem is out of Hoops', colleenz', and Mr. S's reach and want to venture their own solution? What will you do? ![](http://syonidv.hodginsmedia.com/vsmileys/charmed.png)
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Colleenz
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Post by Colleenz on Oct 18, 2011 14:02:24 GMT -5
That's Colloweenz to you Virgil. I like Halloween! ![:P](//storage.proboards.com/forum/images/smiley/tongue.png)
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Virgil Showlion
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Post by Virgil Showlion on Oct 18, 2011 16:43:26 GMT -5
The wheel slows... the ball hops... boink... boink... rattle... It lands on 50% 2M and 1F, 50% 2F and 1 M! The mysterious Mr. S. picked the winning solution! ;D Indeed, the initial assumption of 50% chance 2 men and 1 woman, 50% chance of two women and 1 man is correct. ![:o](//storage.proboards.com/forum/images/smiley/shocked.png) (I told you this was a tricky one.) The reason why requires a crash course in conditional probability, and there are numerous proofs as to why 50/50 is correct and as to why 67/33 is incorrect. The problem is so tricky, in fact, that many brainteaser sites that present it present the wrong solution (usually 67/33) along with an erroneous proof. I will present one proof and one debunking. One of the simplest to understand proofs is that of symmetry. The fact that Rick is present is precisely equivalent to the statement "at least one male is online" in terms of giving us knowledge about how many male and female members are online. The fact that the male's name is "Rick" is a red herring. It's unimportant. Hence, the three facts we know are: - three members are online (fact A)
- at least one male is online (fact B)
- at least one female is online (fact C)
Intuitively we should realize that the order in which we learn these three facts should not affect the probability of having two females versus one male or vice versa. We know exactly the same amount of information at the end of learning fact A, fact B, and fact C, regardless of which order in which we learn the facts. We should also intuitively realize that the problem is symmetric in "male" and "female" given the three facts. If we swapped "male" for "female" and vice versa, fact B would swap with fact C, but still the facts are the same. Hence whatever probability we calculate for there being x males and y females must also be the probability that there are y males and x females, for any x and y. This symmetry alone combined with the fact that 2M/1F and 2F/1M are the only two combinations that can possibly satisfy facts A, B, and C tells us that the probability of each is 50%. (If this proof is insufficient, I can give a more exhaustive one using conditional probabilities.) Let's also provide one of the 67/33 debunkings. It seems logical that since the problem is symmetric in login order of the members (i.e. the answer doesn't depend on the order in which the members logged in), we can assume without loss of generality that Rick is "member 1", giving us the four possible combinations: R-M-M R-M-F R-F-M R-F-F This is in fact correct. It then also seems logical to eliminate any combination where at least one female is not present (i.e. R-M-M), leaving, R-M-F R-F-M R-F-F and then concluding a 67% probability of 2M and 1F (as Hoops and colloevilunciadeathspawnaweenz did). The problem is that these three remaining combinations are not equally likely. That is, we've botched the application of Bayes' rule. The correct approach is to start with as our four equally-likely configurations after we've locked in Rick as member #1: R-M-M R-M-F R-F-M R-F-F We now (in effect) sample randomly from the remaining two members whose genders are unknown. We sample a 'F'. (This sampling process is completely equivalent to the statement "there is at least one female in the remaining two members". No more and no less information is gained.) Since we know the (unconditional) probabilities of each of the four configurations and the probability of sampling an F given each config, Bayes' rule tells us what the (conditional) probability of each config is. I turns out that p( R-M-M ) = 0, as expected (i.e. you can't sample a female from a male-only config.), but for the remaining three, p( R-M-F ) = 1/4 p( R-F-M ) = 1/4 p( R-F-F ) = 1/2 Or stated more intuitively: the fact that we sampled a female member gives us a higher probability that we sampled it from a female-rich configuration. In this case, the probability of the R-F-F config is exactly the same as the combined probabilities of the R-F-M and R-M-F configs, giving 50%/50% as expected. This proof can also be done more exhaustively (i.e. without relying on login order symmetry and with explicit use of Bayes' rule to move from completely unconditional probabilities to the "after fact B" conditional probabilities that are the starting point for the above analysis. But again, I won't bore you with the details unless you still doubt 50/50 is the correct answer. ![;)](//storage.proboards.com/forum/images/smiley/wink.png)
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Virgil Showlion
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Post by Virgil Showlion on Feb 22, 2012 17:18:07 GMT -5
Problem 63 - Iggy's ChilliSomebody ate Iggy's chilli. ![:(](//storage.proboards.com/forum/images/smiley/sad.png) - Nancy claims that Lassie ate the chilli. - Lassie claims that Toughtimes is surely the chilli-eater. - Toughtimes claims that Lassie is lying. - Swamp swears that she didn't eat the chilli. If only one of the above four statements is true, who ate Iggy's chilli?
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Jaguar
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Post by Jaguar on Feb 22, 2012 17:19:43 GMT -5
Problem 63 - Iggy's ChilliSomebody ate Iggy's chilli. ![:(](//storage.proboards.com/forum/images/smiley/sad.png) - Nancy claims that Lassie ate the chilli. - Lassie claims that Toughtimes is surely the chilli-eater. - Toughtimes claims that Lassie is lying. - Swamp swears that she didn't eat the chilli. If only one of the above four statements is true, who ate Iggy's chilli? MU
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TD2K
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Post by TD2K on Feb 22, 2012 17:25:49 GMT -5
Problem 63 - Iggy's ChilliSomebody ate Iggy's chilli. ![:(](//storage.proboards.com/forum/images/smiley/sad.png) - Nancy claims that Lassie ate the chilli. - Lassie claims that Toughtimes is surely the chilli-eater. - Toughtimes claims that Lassie is lying. - Swamp swears that she didn't eat the chilli. If only one of the above four statements is true, who ate Iggy's chilli? MU ![](http://i239.photobucket.com/albums/ff155/JiminiChristmas/smileys/1-1.gif)
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Virgil Showlion
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Post by Virgil Showlion on Feb 22, 2012 17:27:23 GMT -5
Although the wind issue might support this answer ![](http://syonidv.hodginsmedia.com/vsmileys/actnatural.png) , MU is not the culprit. If he was, both statements 3 and 4 would be true.
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chiver78
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Post by chiver78 on Feb 22, 2012 17:28:50 GMT -5
so how does this game work? do we just post our answers here? I PM'd mine to Virgil, but he's offline. I wanna play! ![:)](//storage.proboards.com/forum/images/smiley/smiley.png)
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ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ
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Post by ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ on Feb 22, 2012 17:31:40 GMT -5
Easy... It was Nancy.
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chiver78
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Post by chiver78 on Feb 22, 2012 17:34:19 GMT -5
no, it was Swamp.
testing the clues with Swamp as the culprit -
F- Nancy claims that Lassie ate the chilli. F- Lassie claims that Toughtimes is surely the chilli-eater. T- Toughtimes claims that Lassie is lying. F- Swamp swears that she didn't eat the chilli.
If only one of the above four statements is true, who ate Iggy's chilli?
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Virgil Showlion
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Post by Virgil Showlion on Feb 22, 2012 17:36:02 GMT -5
Chiver, you can post your answer here, but out of courtesy to others prefix it with " ". ![:)](//storage.proboards.com/forum/images/smiley/smiley.png) It's also helpful if you post a summary of your reasoning.
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chiver78
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Post by chiver78 on Feb 22, 2012 17:36:50 GMT -5
oh, my bad. I was following SL's lead. ![](http://syonidv.hodginsmedia.com/vsmileys/shucks2.png)
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Apple
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Post by Apple on Feb 22, 2012 17:40:46 GMT -5
Chiver is right. Virgil--the reasoning is self explanatory ![:P](//storage.proboards.com/forum/images/smiley/tongue.png)
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chiver78
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Post by chiver78 on Feb 22, 2012 17:43:21 GMT -5
....or did Iggy eat the chili and just blame everyone else? ![](http://syonidv.hodginsmedia.com/vsmileys/duh.png)
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ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ
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Post by ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ on Feb 22, 2012 17:45:31 GMT -5
I"m changing my answer to Swamp. The rest of us (Lassie, TT and Nancy only claim somone else did it) But Swamp "swears" that she didn't eat it. (Since she's a lawyer, she's trying to deflect blame). ![;)](//storage.proboards.com/forum/images/smiley/wink.png)
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NoNamePerson
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Post by NoNamePerson on Feb 22, 2012 21:28:20 GMT -5
I say one of these guys ate the chili ![???](//storage.proboards.com/forum/images/smiley/huh.png)
no, it was Swamp.
testing the clues with Swamp as the culprit -
F- Nancy claims that Lassie ate the chilli. F- Lassie claims that Toughtimes is surely the chilli-eater. T- Toughtimes claims that Lassie is lying. F- Swamp swears that she didn't eat the chilli.If only one of the above four statements is true, who ate Iggy's chilli?
Is this the equivalent of "Who's On First" ![](http://syonidv.hodginsmedia.com/vsmileys/idunno.gif)
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Jaguar
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Post by Jaguar on Feb 22, 2012 21:57:25 GMT -5
Problem 63 - Iggy's ChilliSomebody ate Iggy's chilli. ![:(](//storage.proboards.com/forum/images/smiley/sad.png) - Nancy claims that Lassie ate the chilli. - Lassie claims that Toughtimes is surely the chilli-eater. - Toughtimes claims that Lassie is lying. - Swamp swears that she didn't eat the chilli. If only one of the above four statements is true, who ate Iggy's chilli? Virgil YOU ATE Iggy's chilli . that's my answer and i'm sticking to it. ![](http://syonidv.hodginsmedia.com/vsmileys/raspberries.png)
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Virgil Showlion
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Post by Virgil Showlion on Feb 22, 2012 22:49:38 GMT -5
Actually, if you omit the implicit assumption that only one person was responsible for the great chilli heist, there are multiple correct answers to the problem. *brrrr-aaap*(where on Earth did that come from?) ![:o](//storage.proboards.com/forum/images/smiley/shocked.png)
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ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ
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Post by ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ on Feb 22, 2012 22:59:07 GMT -5
The answer's simple - IGGY ate Iggy's Chili.
Nothing in the question said that one of the four suspects had to be the chili-eater.
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Jaguar
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Post by Jaguar on Feb 22, 2012 23:04:04 GMT -5
Of course Iggy ate her own damn chilli. The rest of you couldn't teleport yourselves there. DUH !!!
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Virgil Showlion
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Post by Virgil Showlion on Feb 23, 2012 11:20:23 GMT -5
Solution to Problem 63 - Iggy's ChilliChiver gets 2 karma for being the first to come up with the correct solution to the problem: Swamp is in fact the chilli thief! ![:o](//storage.proboards.com/forum/images/smiley/shocked.png) A more exhaustive proof holds that: - (2) true implies (4) also true, hence (2) cannot be true
- (2) false implies (3) true, hence (3) must be true
- (3) true means (4) must be false, since only one condition is true
- (4) false means that Swamp is lying, meaning that she ate Iggy's chilli
Of course, Sugilite's theory of MuscleUp involvement can't be fully discounted. And pity the fools who actually eat Iggy's homestyle cookin', which inevitably carries the curse of the five weeks squits. smilies.site blocked due to malware warnings/imgs/food-and-drink/food-and-drink018.gif[/img]
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chiver78
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Post by chiver78 on Feb 23, 2012 15:51:34 GMT -5
I think it might be a typo, Ig. add an "r' in there and see if it makes more sense. ![](http://syonidv.hodginsmedia.com/vsmileys/unwell.png) thanks for the karma, Virgil. ;D
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moon/Laura
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Post by moon/Laura on Feb 23, 2012 16:38:03 GMT -5
well, he DID spell "chili" incorrectly, sooooooo... ![;)](//storage.proboards.com/forum/images/smiley/wink.png)
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ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ
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Post by ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ on Feb 23, 2012 17:02:14 GMT -5
What are you the "word police" ![](http://i239.photobucket.com/albums/ff155/JiminiChristmas/smileys/1-1.gif) (I avoided pointing out Virg's spelling error yesterday after I was called that a few days ago) ![:P](//storage.proboards.com/forum/images/smiley/tongue.png)
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NancysSummerSip
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Post by NancysSummerSip on Feb 23, 2012 17:09:05 GMT -5
Wait, I never post on this thread. How did I get dragged over here into a fight over chili, anyway? ![](http://syonidv.hodginsmedia.com/vsmileys/idunno.gif)
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moon/Laura
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Post by moon/Laura on Feb 23, 2012 17:14:14 GMT -5
What are you the "word police" yep! all party of the awesome (and FREE) services we provide!
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Befferz
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Post by Befferz on Feb 23, 2012 17:37:47 GMT -5
Where's Gramps? ![:P](//storage.proboards.com/forum/images/smiley/tongue.png)
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Virgil Showlion
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Post by Virgil Showlion on Apr 17, 2012 0:14:50 GMT -5
Problem 64 - What's in a Name?The following partial sentences describe well-known board members in a special way. See if you can figure them out! ![:)](//storage.proboards.com/forum/images/smiley/smiley.png) If you do, post the answer to one and only one clue for a karma. ![](http://syonidv.hodginsmedia.com/vsmileys/thumbsup.png) Please leave others for other posters to figure out. If you want a real challenge, try solving the HARD clues before looking at the MEDIUM and EASY clues. HARD1. She usually gets in little idioms to encourage. 2. Isn't generally getting younger. ![:-/](//storage.proboards.com/forum/images/smiley/undecided.png) 3. Acquired parasites & promptly left EE. MEDIUM4. Plastered on mondays. 5. Mostly oversees online nuisances. Bans especially annoying members. 6. Posts before proving. 7. Tall tales. EASY8. Cupid makes exceptions. ![](http://syonidv.hodginsmedia.com/vsmileys/duh.png) 9. The janitor. 10. More moonshine? 11. Mainly moderates half-mad maniacs. 12. Stupid leopards! ![](http://syonidv.hodginsmedia.com/vsmileys/raspberries.png) 13. Trinity's Dogs; 2 Killed* 14. Try harder, you miserable excuses 4 contributors! Higher authorities need genuine entertainment!** 15. Why wear bathing garments? *5 karma to whoever names the poster the clue refers to and also explains the significance of the clue (posters who weren't members on the old MSN needn't try) ![](http://syonidv.hodginsmedia.com/vsmileys/nerdy.png) **refers to the "Am I Alone?" thread
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