Post #288,503
7/8/07 6:30:57 PM
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"The Cordial Dinner Party"
I submitted this (lifted from an old Scientific American if I recall aright) to the "Car Talk" guys a dozen years ago. I don't think they ever used it. Anyway, here it is, retrieved from my files this afternoon and suitably paraphrased:
Five husband-and-wife couples meet for dinner at the local Applebee's (they are the sole guests that night) and exchange greetings at the outset. After dinner one of the party, a LAN administrator, asks each of the other diners to tell him with whom they shook hands. Three facts emerge from this survey:
1. No one shook his or her spouse's hand.
2. No one shook his or her own hand. (Duh!)
3. Each respondent shook a different number of hands, and no one shook hands with the same person more than once.
Question: With how many people did the LAN administrator's spouse shake hands?
cordially,
Die Welt ist alles, was der Fall ist.
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Post #288,511
7/8/07 8:13:37 PM
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Doesn't seem to work.
But I'm terrible at these things...
10 people, so there's a 10x10 truth table. Conditions 1 and 2 imply that each person could shake hands with at most 8 people. That leaves 9 unique combinations (8 to 0). So there would have to be a duplicate to cover all 10 people, wouldn't there?
Then there's the problem of figuring out which one is the wife of the LAN administrator. Unless we accept that it's impossible for a LAN administrator to be married. ;-)
Cheers,
Scott.
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Post #288,521
7/8/07 9:28:07 PM
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you're picking it up at the wrong end
The piquancy of the puzzle lies in one's gut reaction that insufficient information has been provided for the solution. Read the terms carefully and then return to your truth table.
cordially,
Die Welt ist alles, was der Fall ist.
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Post #288,522
7/8/07 9:38:15 PM
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Re: you're picking it up at the wrong end
The answer lies obviously in fact that if one person shakes a certain number of hands, that affects how many other people can shake. I'm too tired to figure it out from there, though.
Regards,
-scott anderson
"Welcome to Rivendell, Mr. Anderson..."
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Post #288,516
7/8/07 8:43:27 PM
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I think CarTalk used this one
... or one like it, 2-3 years ago.
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Post #288,518
7/8/07 8:54:35 PM
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Re: I think CarTalk used this one
They did? Those bastards! I never got the "CarTalk" beanie!
Read terms carefully.
cordially,
Die Welt ist alles, was der Fall ist.
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Post #288,528
7/8/07 10:05:52 PM
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Among the missing information:
Siblings, relatives (even generational) == already intimately acquainted.
Social conventions are inextricable from the situation, prima facie -- else nose-rubbing would have been an option, as well as ...
For no one to have shaken the same number of hands, a one might postulate the number of kin pairings (including possible ex-es)-- but that would render merely a probability (n! reasoning) and not properly fill a Truth table.
(Likely Mr. Fibonacci would spawn a better diagrammatic exercise, as more information dribbled in?)
This one seems akin to one ~ about a boy in car accident, now in surgery; the surgeon exclaims, That's my Son!! (yet the surgeon is not the father, per intro.)
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Post #288,572
7/9/07 12:55:18 PM
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General solutions get you a 50% tip. (137 kB Img.)
[image|http://imgs.xkcd.com/comics/np_complete.png|0|NP Complete|414|640]
:-)
Cheers,
Scott.
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Post #288,595
7/9/07 10:36:46 PM
7/9/07 10:38:56 PM
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I think I know the gimmic
Spoiler: The guy asking the questions didn't actually answer the questions. So he and his wife are either anti-social twits or germophobes.\n1 2 3 4 5 6 7 8 9 10\n1 Y Y Y Y Y Y Y Y\n2 Y Y Y Y Y Y Y\n3 Y Y Y Y Y Y\n4 Y Y Y Y Y\n5 Y Y Y Y\n6 Y Y Y\n7 Y Y\n8 Y\n9 LAN admin\n10 LAN admin's wife |
Not so cordial after all, I must say. ===
Kip Hawley is still an idiot.
===
Purveyor of Doc Hope's [link|http://DocHope.com|fresh-baked dog biscuits and pet treats].
[link|http://DocHope.com|http://DocHope.com]
Edited by drewk
July 9, 2007, 10:38:56 PM EDT
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Post #288,599
7/10/07 1:14:59 AM
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so close...yet so very far away
You grasped one important point...but you should have used the tips of the thumb and forefinger rather than the entire grubby fist.
I'll post the solution tomorrow evening.
cordially,
Die Welt ist alles, was der Fall ist.
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Post #288,663
7/10/07 8:59:54 PM
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Hmmm ...
Since no one shook his own or his spouse's hand, the highest number possible is 8.
Including 0, this leaves only 9 possible counts, so the surveyor was not also a respondant.
Is there any reason his spouse couldn't have been any one of the other people.
Hmmm ... nope, not getting it.
===
Kip Hawley is still an idiot.
===
Purveyor of Doc Hope's [link|http://DocHope.com|fresh-baked dog biscuits and pet treats].
[link|http://DocHope.com|http://DocHope.com]
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Post #288,665
7/10/07 9:20:50 PM
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Think polygyny.
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Post #288,604
7/10/07 6:41:44 AM
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the lan admin is a broad
her spouse only shook handswith the guys, 4 and grabbed the ass of the other 4 wimmen
thanx,
bill
Quantum materiae materietur marmota monax si marmota monax materiam possit materiari?
Any opinions expressed by me are mine alone, posted from my home computer, on my own time as a free american and do not reflect the opinions of any person or company that I have had professional relations with in the past 51 years. meep
reach me at [link|mailto:bill.oxley@cox.net|mailto:bill.oxley@cox.net]
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Post #288,670
7/10/07 10:09:42 PM
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"The Cordial Dinner Party" explained, sort of
As I noted earlier the piquancy of the problem has to do with one's gut reaction that there is not enough information provided in order to reach a solution. Compounding this is the natural inclination to pick it up by the wrong end: to commence, that is, rather than to conclude with the identity of the LAN administrator's spouse. A deep breath and a moment's thought will (and indeed did, in the initial response by Another_Scott) between them yield the following preliminary elements about our ten dinner guests:
1. The maximum possible number of handshakes, since selves and spouses are excluded, is 8.
2. By the same token the minimum number of possible handshakes under the term set forth is that roundest of all numbers, 0.
3. Accordingly the various diners shook 8, 7, 6, 5, 4, 3, 2, 1 and no hands for a total of nine unique combinations.
4. This means that two of the diners must have shaken the same number of hands. Since everyone the LAN administrator polled (recall that in framing the puzzle we were at pains to specify that he asked each of the other guests, not himself) responded with a different figure, the LAN guy hisself must have shaken the same number of hands as one of the others. It will be useful for you to put this point aside for the moment without, however, forgetting it entirely.
We have established that someone in the party shook eight hands. We will arbitrarily call this individual "A1" and his/her spouse "A2," maintaining this convention for the other four couples (hence "B1," "B2," "C1," "C2," etc). This means that every member of couples B, C, D and E shook at least one hand (that of the worthy and personable A1) but no more than seven. Having accounted for nine diners we are left with just one candidate for the no-handshakes slot, and this must needs be that pariah, A2.
We turn our attention next to the individual (otherwise unknown except that the pool of suspects is now eight rather than ten) who shook seven hands, and we will call this sociable individual B1. Now we know that each member of the three other couples all shook at least two hands (A1 and B1) but no more than six, and that B1's spouse, the shy and awkward B2, is the only possible candidate for the single-handshake spot, this presumably unwelcome contact having been bestowed by the relentlessly friendly A1.
A pattern emerges:
Couple A: 8 paired with 0
Couple B: 7 paired with 1
Couple C: 6 paired with 2
Couple D: 5 paired with 3
Couple E: 4 paired with 4
Since we had previously determined (at this time be good enough to retrieve preliminary conclusion #4 above) that the LAN administrator shared the same number of handshakes with one other member of the party, that other is, QED, his spouse, and the answer is 4. For right-brain types, [link|http://homepage.mac.com/rcareaga/Sites/aus_pix/handshakes.jpg|table here.]
cordially,
Die Welt ist alles, was der Fall ist.
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