What a Math Party Game Tells Us About Graph Theory

[gilleain]

Seems like a introduction to the 'Handshaking lemma'?

https://en.wikipedia.org/wiki/Handshaking_lemma

[jstanley]

> At the start, everyone has shaken zero hands, so you all start at an even number. Let’s say Anna and Byron take the initiative and shake each other’s hands. Now they are at one handshake each.

> Caitlin needs to join in, so she shakes Byron’s hand, giving her one handshake, an odd number. But now Byron has two handshakes, and so he’s back to an even number.

The first blunder of the game. Byron was already in a winning position and was under no obligation to shake a hand, but he has allowed Caitlin to capitalise on his stupidity.

[sva_]

It isn't meant to be a competitive game, but a cooperative one

[tarentel]

We interpreted this much differently. I think everyone has to shake hands with an odd number of people not just any single person. It's everyone wins or no one does.

[tromp]

How is playing a losing move in a lost position a blunder? All moves are losing after all...

[ensignavenger]

The solution, when dealing with an odd number of folks, is to do a 'three-way' handshake. Some times you have to think outside the box.

[lupire]

That's 2 per person, or an impossible shake, since a hand is half a pair.

[croes]

Isn't the simplest solution that everybody shakes hand with Byron?

Everybody but Byron has one handshake and Byron has n-1, with n the number of people

[bitslayer]

Depending on your definition of simpler, everyone could just pair off and shake exactly one hand.

[xboxnolifes]

It's the simplest option when n is even (which it is in this case), but fails when n is odd.

[lupire]

The article about how this problem is trivial for N even but impossible for N odd.

[kolmogorov]

While the title is entertaining this doesn’t seem to be a very good candidate for a game at a party.

[lupire]

Title is backwards. graph theory tells us about the party game.