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LobowolfXXX Inner circle La Famiglia 1196 Posts |
I don't know if this is the objection that Wilbur had in mind or not, but here's the objection I was referring to...
I'm assuming the credited answer here is that the girls are 3, 3, and 8. Because the clever girl needed more information, the question must have been ambiguous; the only 3-factor combination for 72 that has an ambiguous sum is 3, 3, 8 and 6, 6, 2. On the surface level, the additional information that's supposed to be helpful is that he has an oldest daughter; this apparently rules out 6, 6, 2, in which case he'd have two oldest daughters. The objection is that he could have two six-year old daughters and still have an oldest daughter. One might have turned six today, and the other might be turning seven tomorrow. Or even if they're twins, one would still be (minutes) older than the other. The counter to that, though, is that he's a clever guy, and he thought the clue would help the clever girl figure it out, so even though it's not a "pure" bust to the problem, the only way the hint really helps a little is to suggest that the right answer is, indeed, 3, 3, 8. This is what I mean by the problem working on a meta level...it goes beyond the pure mathematical problem that it seemed to be, and is really only rock-solid as a partly psychological problem. Personally, I think this makes it an ever better problem (even though I suspect most people will solve it thinking only of the math, despite the loophole).
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley. "...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us." |
TomasB Inner circle Sweden 1144 Posts |
My thoughts exactly in your last paragraph: The girl knows that the man thinks that this information will help. The only way it can help is if it leads to one answer.
/Tomas |
Michael Daniels Inner circle Isle of Man 1609 Posts |
Yes, I understand now. It makes sense.
But, just to be awkward, 2, 4.5, 8 is another possibility. A girl who was 14 and a half would refer to herself as 14. Mike |
TomasB Inner circle Sweden 1144 Posts |
If that was a possibility, how would the info about one daughter being the oldest help her to know which of 3,3,8 and 2,4.5,8 was the correct answer? It comes down to that we know that that info helped her finding the correct answer.
/Tomas |
Michael Daniels Inner circle Isle of Man 1609 Posts |
She didn't think the man was as clever as she was.
Mike |
landmark Inner circle within a triangle 5194 Posts |
Agree with Lobo--the problem as given has a solution--then this is the only one. But now that we're here, let me propose this problem:
Given that real numbers a, b, c are not a permutation of real numbers d, e, f, and abc=def and abc is not equal to zero, and a+b+c=d+e+f Let N = abc, where N is an integer. Are there solutions possible where at least one of a, b, c, d, e, f are not integers?
Click here to get Gerald Deutsch's Perverse Magic: The First Sixteen Years
All proceeds to Open Heart Magic charity. |
TomasB Inner circle Sweden 1144 Posts |
Michael, I am not sure what you mean. We know that she solved it and got the correct answer. What answer did she give in your case?
/Tomas |
Michael Daniels Inner circle Isle of Man 1609 Posts |
Tomas - she gave the answer 3,3,8.
Recognising that the solution could be either 6, 6, 2, or 3, 3, 8, or 2, 4.5, 8, she asked for more information. When she was told about the oldest daughter, this left her with two options: 3, 3, 8 or 2, 4.5, 8. At this point she doubted the man was clever enough to have thought about the second option, so she plumped for 3, 3, 8. Mike |
TomasB Inner circle Sweden 1144 Posts |
Ahaaa, got it. Clever! So still the same answer.
/Tomas |
TomasB Inner circle Sweden 1144 Posts |
Landmark, yes.
/Tomas |
TomasB Inner circle Sweden 1144 Posts |
I mean, I don't know yet.
/Tomas |
landmark Inner circle within a triangle 5194 Posts |
Quote:
On 2013-02-12 08:29, landmark wrote: Sorry for the terrible grammar. "...where at least one of a, b, c, d, e, f is not an integer?"
Click here to get Gerald Deutsch's Perverse Magic: The First Sixteen Years
All proceeds to Open Heart Magic charity. |
TomasB Inner circle Sweden 1144 Posts |
Do they all have to be positive? I've just assumed they had to be.
/Tomas |
WilburrUK Veteran user 389 Posts |
Well well, I've been away for a few days and not checked back on this. So yes LobowolfXXX was indeed correct about my objection being that even twins have an older and younger member.
Furthermore, I don't buy the solution that the clever man was bound to be trying to help with his clue. After all, we already know that he's the kind of person that would give insufficient information in the first place. So how do we know that he wasn't simply throwing out a red herring to try to trick his unsuspecting victim. And maybe the clever victim second guessed his deception and went for 6,6,2 because she reasoned that he wouldn't give a clue that was still insufficient to solve the riddle unless it was designed to lead her to an incorrect solution. That's the problem with those clever types; they can be quite annoying. I'm reminded of a Martin Gardener article about a similar type of puzzle involving truth-tellers and liars. I'm not sure where his thoughts can be found. But if anyone's interested, I'll try to find out. |
TomasB Inner circle Sweden 1144 Posts |
For a while I didn't think there was a solution to Landmarks problem, but the values below seem to work:
a=1/3 b=1/5 c=15(3+2sqrt(2)) d=1 e=1/15*(334+225sqrt(2)+sqrt(212131+149850sqrt(2))) f=1/15*(334+225sqrt(2)-sqrt(212131+149850sqrt(2))) You can scale all the variables with the same factor for more solutions. /Tomas |
landmark Inner circle within a triangle 5194 Posts |
Strange outcome. The sqrts I expected if there were a solution, because it looked like there would be a quadratic or fourth degree equation to solve, but the actual values seem so arbitrary. I can't figure out where they come from.
Click here to get Gerald Deutsch's Perverse Magic: The First Sixteen Years
All proceeds to Open Heart Magic charity. |
TomasB Inner circle Sweden 1144 Posts |
They _are_ arbitrary. I just picked 1/3 and 1/5 for fun, then forced the others to avoid complex and negative values. There are more solutions than these I think.
/Tomas |
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