Puzzle time

[jon-nyc]

This one took me a little while.

[Klaus]

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...

[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.

[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...

[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?

[jon-nyc]

No, your first statement is not correct.

Hint - first find out how many hands you shook.

[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.

[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?

[Doctor Phibes]

Typical German. You should just ask her.

[jon-nyc]

Yes you are right, Klaus

[Klaus]

It's a pretty neat puzzle.