> 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.
I'll also add that his comment about winning/losing is a bit off as well.
This isn't a competitive game, it's a cooperative one. Everyone needs to shake an odd number of hands. The game is won, when everyone in the room has shaken an odd number of hands. It's more a puzzle than a game.
There may be additional rules on if disconnected sub graphs are allowed or not, so with an even number of people, the puzzle is trivial to solve.
Everybody but Byron has one handshake and Byron has n-1, with n the number of people
I think the problem with the suggestion is that the solution to the even subgraph may not be under your control? Not sure.
