And three dead points have to "change hats". One less survivor means adding one to the total of dead points. A survivor converts to four pharisees and vice versa. So the number of pharisees in a position with one survivor is 4n - 4.īrenda: The key to the proof is that each additional survivor reduces the number of pharisees by four.īrenda: Yes. Now, of the 4n-2 dead spots, two will be "closest neighbors" of the survivor. Linda: Each survivor will be an unplayed move.īrenda: Right. A beginning position has 3n liberties, meaning a maximum of 3n extra spots, dead or alive, minus any survivors. The maximum number of dead spots would be 4n-2, which would occur in a position with a single survivor.īrenda: Each move adds a spot but uses up a liberty. Wingnut: A pharisee is a dead spot which is not one of the two closest neighbors of any survivor.īrenda: Yes, I'm beginning to recall the proof. Wingnut: The proof is simple but would be distracting.īrenda: It has something to do with pharisees, does it not? I mean, any move involves adding back a cannibal.īrenda: And I don't believe we could have more survivors than original spots. Now what even number would that be? Zero, two, four?īrenda: I don't suppose you could ever have zero survivors. You want an even number of survivors as we have just verified. Wingnut: Well, back to our sprouts position. Wingnut: Well, he's the WGOSA president, or so I understand. Linda: Are you talking about the gentleman continually loading up on desserts?īrenda: He buys another dessert every time he loses a chess game! Wingnut: See the old fat guy losing chess game after chess game?īrenda: That man has been ogling me for the past 45 minutes! Wingnut: Speaking of whom, that's him over there. I'm sure the guy running that would allow me to make changes as needed. If I wanted to post a sprouts article I think I would just send it to the WGOSA website. Wingnut: Interestingly, the original Swarthmore post which purports to demonstrate that fact contains a blunder.īrenda: Perhaps that is not so surprising, Wingnut, since the Swarthmore posts cannot be edited once posted. Later, when I have some time, I will work out to my own satisfaction how the cannibal parity changes with each move. That eventuality will prove that he has made the final move, since the current position has an odd number of cannibals. Linda: So the player to move in the position we are now examining needs the final position to contain an even number of cannibals (survivors). The parity goes from odd to even to odd to even and so forth, or vice versa. One or three cannibals are added, or a single cannibal is subtracted.
Wingnut: Well, as you can work out for yourself, any move to a position always changes the parity of the number of cannibals. Wingnut: A spot with exactly one line attached would always allow another move. Any starting position and any exhausted position consists of all cannibals. Linda: So we are presently examining a position with three cannibals. Wingnut: A cannibal is a spot with zero or two lines attached. Does the player to move need an even or an odd number of survivors? Utilizing Conway notation, I've got Wingnut serving 3+. Brenda, what would be a good first move?īrenda: I'm sure I don't know, but I hope Linda is taking notes. This is going to be a normal game, not a misere game. Now I'm going to take this napkin here and draw three spots. Wingnut is never cuter than when he explicates his favorite game.
Sit down and let Wingnut teach us some sprouts theory. Let's acquire mochas and discuss some sprouts.īrenda: I've already ordered the mochas, and here they come now. Plus, I don't own a set of tiny wrenches.
Wingnut: I'm afraid chess and quantum mechanics are both too difficult for my limited brain. All the physicists in this town play chess and when they're not playing chess, they seem to spend their time trying to wring new meaning out of the quantum mechanical formalism. Wingnut: This place seems to have been invaded by chess players.īrenda: Chess players and physicists.