Puzzle time
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wrote on 14 Apr 2020, 13:17 last edited by
Klaus and Mrs. Klaus went to a reception with ten other couples; each person shook hands with everyone he or she did not know. (Obviously, this took place before the COVID-19 epidemic.) Later, Klaus asked each of the other 21 partygoers with how many people they shook hands, and got a different answer every time.
With how many people did Mrs Klaus shake hands?
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wrote on 14 Apr 2020, 13:19 last edited by
Zero. Klaus played piano after which she was shunned.
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wrote on 14 Apr 2020, 13:21 last edited by
Is 20 too obvious of an answer? Probably.
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wrote on 14 Apr 2020, 13:48 last edited by
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wrote on 14 Apr 2020, 15:46 last edited by Klaus
Question: Do you assume that the two persons in each couple know each other?
Sounds like a rather unrealistic assumption, but I want to be sure. -
wrote on 14 Apr 2020, 16:05 last edited by
Also, does a person shake his own hand (since we can safely assume that everone knows him- or herself)?
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wrote on 14 Apr 2020, 16:10 last edited by Doctor Phibes
Are these all university couples? If so, it would probably be quite hard for them to shake their own hands since they'll be so busy patting themselves on the back
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wrote on 14 Apr 2020, 16:11 last edited by
Klaus - they don’t shake their own hand or that of their pairing.
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wrote on 14 Apr 2020, 16:22 last edited by
@Mik said in Puzzle time:
Zero. Klaus played piano after which she was shunned.
Klaus expressed the desire for "she" to be used as
hisher preferred pronoun? Makes sense, I just wanted to confirm. -
wrote on 14 Apr 2020, 16:27 last edited by
I think 20 must be too obvious, so if we take the "and got a difference answer every time" key phrase, that means even individuals WITHIN a couple have difference answers, which means we need to find all the various valid combos out there...leaving Mrs. Klaus shaking 10 hands.
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wrote on 14 Apr 2020, 16:32 last edited by
It doesn't matter. They will all be dead from corona virus in a few weeks.
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wrote on 14 Apr 2020, 16:44 last edited by
Can’t just throw out a number, you have to say why
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wrote on 14 Apr 2020, 16:44 last edited by
This one took me a little while.
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wrote on 14 Apr 2020, 20:21 last edited by
OK, let's see.
Since there are at most 20 people anyone can shake hands with, the different numbers of the other 21 partygoers must be the numbers from 0 to 20...
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wrote on 14 Apr 2020, 20:24 last edited by Klaus
What I don't understand is how Ms. Klaus plays any designated role in your puzzle that would allow me to distinguish her from anyone else.
Let's say we name the other 21 persons p-0 to p-20, whereby p-0 shook 0 hands, p-1 shook 1 hands etc.
Ms. Klaus could be any p-i without raising a contradiction.
So, let's say Ms. Klaus is p-7 and shook hands with 7 other people. If the puzzle is well-designed, that should lead to some kind of contradiction. But I don't see a contradiction.
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wrote on 14 Apr 2020, 20:33 last edited by Klaus
Hm, wait a minute.
The guy with the 20 handshakes, p-20 must have shaken Ms. Klaus hand because he shook everyone's hand except his own partner's.
So Ms. Klaus cannot be p-0. And p-20's partner must be p-0, by the same argument.
Presumably this is the base case of some kind of inductive argument...
But on the other hand, what prevents Ms. Klaus from being p-20? Hmm...
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wrote on 14 Apr 2020, 20:41 last edited by Klaus
Ah, I think I got it.
p-20 must have shaken my hand and hence cannot be Ms. Klaus.
p-20's partner must have been p-0, who can hence also not be Ms. Klaus.p-19 must have shaken my hand, too, because he didn't shake p-0's hand, hence p-19 cannot be Ms. Klaus either.
By the same argument as above, p-19's partner is p-1, who also cannot be Ms. Klaus.If we continue in the same way until p-11 and p-9, we see that the only number that is left is p-10.
Ms. Klaus shook 10 hands.
Correct?
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wrote on 14 Apr 2020, 20:53 last edited by
No, your first statement is not correct.
Hint - first find out how many hands you shook.
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wrote on 14 Apr 2020, 20:58 last edited by Klaus
Oh, I see. I think my solution is still correct.
p-20 must be married to p-0, ..., p-11 must be married to p-9.
Hence my wife can't be any of p-0,...,p-9 or p-11 to p-20, because I'm not among the ones they are married to.
That leaves only the p-10 spot for her.
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wrote on 14 Apr 2020, 21:13 last edited by Klaus
Here's the full solution.
p-0 : {}
p-1 : {p-20}
p-2 : {p-19,p-20}
...
p-9 : {p-12,....,p-20}
p-10 = Ms. Klaus : {p-11,...,p-20}
p-11 : {Mr. Klaus, Ms. Klaus, p-12, ..., p-20}
p-12 : {Mr. Klaus, Ms. Klaus, p-9, p-11, p-13, ..., p-20}
p-13 : {Mr. Klaus, Ms. Klaus, p-8, p-9, p-11,p-12, p-14, ..., p-20}
...
p-20: {Mr. Klaus, Ms. Klaus, p-1, .., p-9, p-11,...,p-19}
Mr. Klaus: {p-11,...,p-20}Is this not correct?
