Money Money
5 people of varying ages have to split $100.
They decide to split the money using this scheme:
The oldest person proposes how to share the money, and ALL people (including the oldest) vote for or against it.
If 50% or more of the people vote for it, then the money will be shared that way. Otherwise, the person proposing the scheme will be considered out, and the process is repeated with the people that remain.
As people tend to be a mean bunch, if a person would get the same number of money if he voted for or against a proposal, he will vote against so that the person who proposed the plan will be out.
Assuming that all 5 people are intelligent, rational, greedy, and do not wish to die, what will happen?
Concatenate the ratios of A : B : C : D : E as ABCDE
For example if it was 2 : 6 : 24 : 42 : 0 then it would be 2624420
This is part of the Set .
Note: not my own problem
The answer is 980101.
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1 solution
The oldest person will propose a 98 : 0 : 1 : 0 : 1 split, in other words the oldest person gets 98 $$$$$, the middle person gets 1 $$$$$ and the youngest gets 1 $$$$$.
Let us name the people (from oldest to youngest): Alex, Billy, Colin, Duncan and Eddie.
Working backwards:
2 People: Duncan splits the $$$$$ 100 : 0 (giving himself all the gold). His vote (50%) is enough to ensure the deal.
3 People: Colin splits the $$$$$ 99 : 0 : 1. Eddie will accept this deal (getting just 1 $$$$$), because he knows that if he rejects the deal there will be only two people left, and he gets nothing.
4 People: Billy splits the $$$$$ 99 : 0 : 1 : 0. By the same reasoning as before, Duncan will support this deal. Billy would not waste a spare $$$$$ on Colin, because Colin knows that if he rejects the proposal, he will pocket 99 $$$$$ once Billy is thrown overboard. Billy would also not give a $$$$$ to Eddie, because Eddie knows that if he rejects the proposal, he will receive a $$$$$ from Colin in the next round anyway.
5 People: Alex splits the $$$$$ 98 : 0 : 1 : 0 : 1. By offering a gold $$$$$ to Colin (who would otherwise get nothing) he is assured of a deal.
(Note: In the final deal Alex would not give a $$$$$ to Billy, who knows he can pocket 99 $$$$$ if he votes against Alex's proposal and Alex goes overboard. Likewise, Alex would not give a $$$$$ to Duncan, because Duncan knows that if he votes against the proposal, Alex will be voted overboard and Billy will propose to offer Duncan the same single $$$$$ as Alex. All else equal, Duncan would rather see Alex go overboard and collect his one $$$$$ from Billy.)