N pirates are dividing the loot of M gold coins. They don't trust each other etc. and have the following rules (only):
- most senior one starts by proposing a distribution of the coins between robbers
- a vote is held whether this is accepted, ties are broken by the senior guy
- if it is rejected, the senior guy is hanged and new proposal by the second-in-command.
solution: the 2 youngest always reject so they can divide the M coins between themselves?
The second youngest will probably end up with most of the coins, but the youngest will demand at least round_up(M/N) coins
that is my guess :p
edit:
this works if N = 3
Let me think...
If N = 4, the second oldest don't want to die I guess, so he will bribe the 2 youngest
so he gets zero, and the other 2 get N/2, oldest one dies
I need to think about this some more, very interesting puzzle!
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edit2, very interesting...
N=1: (obvious)
=> P1 gets M
N=2: P1 breaks the ties, so he can just take it all
=> P1 gets M, P2 gets 0
N=3: P1 wants to live, so he need at least one of the pirates to accept his proposal.
The only way he can achieve that is by colluding with P2 or P3 and giving him all the coins.
No idea who would collude, but I am guessing P2 and P3 will start to lower their bid to make sure P1 picks them, it's a race to the bottom
I don't have a solution for this... Maybe P1 ends up with M-1 and P2 or P3 gets one coin
On the other hand, P2 can bribe P3 to hang P1 so he has a better chance to get some coins. He promises to give P2 some coins to collude with him so doesn't end up with zero coins (which would be the normal case for N=2)
But in that case, P1 will offer P3 all his coins, if he wants to live. It is also possible P1 offers P2 all of his coins, but this seems less likely, because P2 would get all the coins anyway for the case N=2, so he would demand additional coins or a service from P1.
=> It will be cheaper for P1 to just give all his coins to P3 (I think)
N=4: P1 wants to live, but P2, P3 and P4 can collude to take him out. they need all 3 votes though, so everybody needs to gain
P2 just doesn't want to die in N=3, so he will offer P3 and P4 an equal amount of coins (M/2), I think.
another option is that P4 bribes 2 other people to collude with him, possible P2 (because he would get zero coins in all other scenarios) and P3 or P4.
although I think in the end, P3 or P4 would again end up with all of the coins, because they think about the situation for N=3 and due to the same reasoning, I think P4 will end up with all the coins
=> P1 colludes with P2 and P4 to support him, P4 gets all the coins
same for N=5, 6, ...
So, I think that, as long as N =/= 2, the youngest will end up with all the coins and nobody dies
If N = 2 the oldest one gets them all
edit3:
found this on
wikipedia:
The pirates do not trust each other, and will neither make nor honor any promises between pirates apart from a proposed distribution plan that gives a whole number of gold coins to each pirate.
This changes things a lot