Puzzle time
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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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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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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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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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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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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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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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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?
Sounds like a rather unrealistic assumption, but I want to be sure.
