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A Problem Even The Wizard Can't Solve (I hope!)
| October 25th, 2011 at 4:36:45 PM permalink | |
| statman Member since: Sep 25, 2011 Threads: 12 Posts: 95 | This post is not intended as a challenge to the Wizard; it is an attempt to get at DorothyGale, one of my most outspoken admirers, without anyone else stepping in and spilling the beans, as they did in "How's The Weather in Nerdville?" It is a classic problem, and those who have arrived at the correct answer can be counted on one hand, one foot, one ear, and one nose. Even the original proponent, Sir Arthur Eddington, didn't get it right. If A, B, C and D each speak the truth once in three times (independently), and A affirms that B denies that C declares that D is a liar, what is the probability that D was speaking the truth? I hope DorothyGale will be the first to respond and show her mettle. Perhaps this will do the trick: DorothyGale looked in her mirror and it broke! She went to the hardware store and got a plastic mirror and put in on the wall. She looked in it - it melted! She went to the hardware store and got a mirror made of polished aluminum. It would neither break nor melt. She put it on the wall. She looked in it and the mirror cried "What the Hell is THAT, got down off the wall and kicked her in the ass. Over to you, Dorothy. A fool is someone whose pencil wears out before its eraser does. - Marilyn Vos Savant |
| October 25th, 2011 at 5:05:24 PM permalink | |
| dwheatley Member since: Nov 16, 2009 Threads: 10 Posts: 550 | Arf. What did D say that would get the others in such a huff? And who names their kid C? Wisdom is the quality that keeps you out of situations where you would otherwise need it |
| October 25th, 2011 at 5:11:06 PM permalink | |
| weaselman Member since: Jul 11, 2010 Threads: 17 Posts: 1924 |
Yes, he did. "When two people always agree one of them is unnecessary" |
| October 25th, 2011 at 5:15:40 PM permalink | |
| MathExtremist Member since: Aug 31, 2010 Threads: 46 Posts: 2521 |
If you want to communicate with DorothyGale in private, do so. This is a public forum and you posted a puzzler in the math section. You should expect replies. I get a number less than 1/3 but more than 30%, conditional on D actually saying something to begin with (if D is silent, the probability is zero; EDIT, actually we have to assume that everyone says something, and furthermore that the statement of the problem is true 100% of the time.). I'm being intentionally vague so as not to give away the solution. But my first question to you is: Can you solve it? "In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice."
-- Girolamo Cardano, 1563 |
| October 25th, 2011 at 5:24:49 PM permalink | |
| dwheatley Member since: Nov 16, 2009 Threads: 10 Posts: 550 | The answer(s) can be found in a number of books on probability. Apparently the good Knight made a certain assumption based on who is saying exactly what that led him to one answer, when a more straightforward assumption leads to another answer. This statement is false. Wisdom is the quality that keeps you out of situations where you would otherwise need it |
| October 25th, 2011 at 5:35:02 PM permalink | |
| MathExtremist Member since: Aug 31, 2010 Threads: 46 Posts: 2521 |
Which one -- the last one or the one above it? :) "In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice."
-- Girolamo Cardano, 1563 |
| October 25th, 2011 at 5:42:56 PM permalink | |
| weaselman Member since: Jul 11, 2010 Threads: 17 Posts: 1924 |
Actually, Eddigton's assumption was fairly straightforward if you ask me, it was also the only one that agrees with the rules of the predicate calculus. Also, don't forget, he is the one, who formulated the problem. If he says his assumption is correct, it is correct :) "When two people always agree one of them is unnecessary" |
| October 25th, 2011 at 6:41:10 PM permalink | |
| DorothyGale Member since: Nov 23, 2009 Threads: 40 Posts: 615 | I have to admit I am at once flattered by your attention and at the same time so very sad for you ... --Ms. D. Resident OZ-like entity ... |
| October 25th, 2011 at 6:53:08 PM permalink | |
| MathExtremist Member since: Aug 31, 2010 Threads: 46 Posts: 2521 |
Having just read up on it, the answer does indeed depend on the assumptions you make. Specifically, if you assume each party makes a relevant statement (as I did), you end up with a different answer than if you make no assumptions about who spoke and/or about what. However, in the latter case it would seem Eddington didn't go far enough: as I said earlier, if D has said nothing, the probability of D having spoken the truth is zero. "In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice."
-- Girolamo Cardano, 1563 |
| October 25th, 2011 at 8:12:10 PM permalink | |
| Mosca Member since: Dec 14, 2009 Threads: 74 Posts: 1628 | They each speak the truth one in three times. I think that's the answer right there. NO KILL I |
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