Originally posted by smartarin
5 greedy yet intelligent brothers (all different ages) have to take a decision of how they should divide 50 precious diamonds inherited from their gangster father, among themselves. They set a rule. The eldest brother will propose a solution and all (including the proposer) will vote 'yes' or 'no' for this. If the number of 'yes' is more than or equal to 5 ...[text shortened]... mbers. Assuming that everyone wants to stay with the family, how will the division happen?
There is the additional problem, apparently not considered by some, that if less than 50% do not accept, the older brother is out, and the process starts again. This is why I disagree with 48,0,1,0,1. These are gangsters, and the problem allows for them to kick out the older brother, so the older brother should sacrifice himself to get anything at all. Consider that if the older brother is kicked out, then 50 diamonds are shared among 4 brothers, and, if no acceptable solution, than 50 diamonds shared among 3 brothers, and so on. The second youngest brother seems in the cat-bird's seat, as he can't be kicked out if he votes for his own solution (two brothers left, he is 50
, and his vote becomes increasing more important if there is no solution. It is in the younger brothers' interest, vote no until they are guaranteed a large portion.
The oldest brother is the most screwed, with the second youngest brother the most advantageous if the process gets to him. It wouldn't, of course.
For example, if 4 brothers vote no on the first round, than the 4 have more for themselves. If in the next round, 3 brothers vote no, they have more for themselves. In the round with the three brothers, the third youngest brother will be wise to 25, 0, 25, up to 49,0,1 as if the youngest brother votes no, along with the second youngest brother, than in the next round the second youngest brother can propose 50,0 and still have 50%.
So, I say the most likely event is first round: reject, second round: reject, third round, accept.