Maths Problems Thread

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#6. I have seen this :P

Spoiler

A will propose a 98 : 0 : 1 : 0 : 1 split, in other words A gets 98 coins, the C pirate gets 1 coin and D gets 1 coin.

Working backwards:

2 Pirates: D splits the coins 100 : 0 (giving himself all the gold). His vote (50%) is enough to ensure the deal.

3 Pirates: C splits the coins 99 : 0 : 1. E will accept this deal (getting just 1 coin), because he knows that if he rejects the deal there will be only two pirates left, and he gets nothing.

4 Pirates: B splits the coins 99 : 0 : 1 : 0. By the same reasoning as before, D will support this deal. B would not waste a spare coin on C, because C knows that if he rejects the proposal, he will pocket 99 coins once B is thrown overboard. B would also not give a coin to E, because E knows that if he rejects the proposal, he will receive a coin from C in the next round anyway.

5 Pirates: A splits the coins 98 : 0 : 1 : 0 : 1. By offering a gold coin to C (who would otherwise get nothing) he is assured of a deal.

Note: In the final deal A would not give a coin to B, who knows he can pocket 99 coins if he votes against A's proposal and A goes overboard. Likewise, A would not give a coin to D, because D knows that if he votes against the proposal, A will be voted overboard and B will propose to offer D the same single coin as A. All else equal, D would rather see A go overboard and collect his one coin from B.

More questions
#7(easy)
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#8(easy)
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