Handshakes

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StuartR
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Handshakes

Post by StuartR »

I enjoyed this puzzle in the Christmas edition of New Scientist. I'm pretty sure I have the answer right, but it won't be published till next year...
New Scientist wrote: A married couple, Noel and Holly, invite four other couples over for drinks. It's a rather formal affair, but as everyone in the group is a mathematician they don't want to do more handshaking than is necessary. Each person only shakes hands with the people they haven't met before.

As the brandy begins to flow, Noel asks everyone at the party how many hands they shook, and he receives nine different answers. How many people did Holly shake hands with?
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Rudi
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Re: Handshakes

Post by Rudi »

Spoiler
There may be maths involved to calculate the answer, but my gut says that none of the answers can be verified if the brandy was already flowing freely! :xhumbug:
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Leif
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Re: Handshakes

Post by Leif »

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None. As joint host, she would know everyone already. But I'm not certain :grin:
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HansV
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Re: Handshakes

Post by HansV »

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My answer is that Holly shook hands with 4 people, just like Noel himself.

Although mathematicians can be rather autistic (I am one myself :grin:), I assume that they know their own partner, so the maximum number of handshakes per person is 8, and the minimum is 0 of course.
Since Noel hears 9 different answers, he must have heard each of 0, 1, 2, ..., 8 once.
One person has shaken 8 hands, i.e. everyone except his/her partner. As a consequence, all those others have shaken at least 1 hand, and hence the partner of the first person must be the one who has shaken none.
Then, there is someone who has shaken 7 hands: everyone except the partner of the first person and his/her own partner. These 7 have shaken at least 2 hands, so the partner of this second person must be the one who has shaken only 1 hand.
Continuing this way, we have a couple of which one has shaken 6 hands, and the other only 2.
Then a couple of which one has shaken 5 hands, and the other 3.
In the final couple, both partners have shaken 4 hands. This MUST be Holly and Noel, otherwise Noel would have received 4 twice as an answer.
S1407.png
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StuartR
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Re: Handshakes

Post by StuartR »

Hans, that is exactly the answer that I came up with, and following the same logic.
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Leif
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Re: Handshakes

Post by Leif »

Thanks Hans (and Stuart for posting) - that makes perfect sense!
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Re: Handshakes

Post by StuartR »

I think it's a delightful puzzle because at first it seems as though there can't be enough information
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Re: Handshakes

Post by Rudi »

I'm still more interested in the brandy? Any calculation to determine what brand of brandy was flowing? :xgrin:
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Re: Handshakes

Post by HansV »

You have to calculate the direction and speed of the wind first...
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StuartR
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Re: Handshakes

Post by StuartR »

The nutters on my Facebook page kept making all sorts of weird suggestions for this one, so I had to post:
Stuart's Facebook page wrote: OK folks. Since so many of you are struggling. Here are the assumptions that I am aware of having made:
• Every couple consists of two people who are capable of shaking hands
• The two people in each couple have met each other, and therefore do not shake hands
• Each handshake involves exactly two people, never more or less
• Every handshake is transitive. If A shakes hands with B, then B shakes hands with A
• Each person correctly reports the number of handshakes they have been involved in
Can anyone here think of any more assumptions that I might have forgotten to document for them?
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HansV
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Re: Handshakes

Post by HansV »

I think that's it.
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Re: Handshakes

Post by BobArch2 »

Rudi wrote:I'm still more interested in the brandy? Any calculation to determine what brand of brandy was flowing? :xgrin:
I totally agree with Rudi ! You have my vote big guy! :xgrin:
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Rudi
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Re: Handshakes

Post by Rudi »

    
On a similar, but different topic...

Q: How many mathematicians does it take to screw in a light bulb?

A: It only takes one mathematician to screw in a light bulb.

Proof:
SC023.jpg
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Re: Handshakes

Post by BobH »

Most excellent proof, Rudi!
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StuartR
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Re: Handshakes

Post by StuartR »

That seems right to me Rudi
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