15 Mar '12 04:50>
Originally posted by ThomasterWell, it says this in the puzzle "a. a successful division or b. a reason to shoot the person who proposed it?"
Ok, I'll use that assumption now. The one who proposes cannot vote, and a tie means death (for some reason).
My backwards induction now is as follows:
720 (no voting)
720 - 720 (1 vs 0)
720 - 720 -720 (2 vs 0)
1440 - 720 - 720 - 0 (2 vs 1)
2160 - 0 - 720 -720 - 0 (3 vs 1)
3600 - 0 - 0 - 720 - 0 - 0 (3 vs 2)
5040 - 0 - 0 - 0 - 0 - 0 - 0 (4 vs 2)
So the oldest one can give himself all the money.
So there are actually two assumptions: one for a tie being an agreement and another for tie being death of the proposer. So you can have one or two different answers.
(Using the assumption that a tie is an agreement) I have this:
1260-1260-1260-1260-0-0-0
(Using the assumption that a tie means death) I have this:
0-0-0-0-0-0-720
0-0-0-0-0-719-721
0-0-0-0-718-720-722
0-0-0-717-719-721-723
0-0-716-718-720-722-724
0-715-717-719-721-723-725
714-716-718-720-722-724-726
Actually, the first answer I gave could work for both assumptions.
1260-1260-1260-1260-0-0-0