Computer Science/Maths logic question help needed :)

How would you go about solving a problem like this?

How do pirates divide their treasure?

A group of 7 pirates has 100 gold coins. They have to decide amongst themselves how to divide the treasure, but must abide by pirate rules:So, what division should the most senior pirate suggest to the other six?

If you're asking just because you want to know the answer, take a look at
http://www.ox.ac.uk/admissions/undergraduate/applying-to-oxford/interviews/sample-interview-questions#asolution

Here's my reasoning process (given that you'd like to know how people may tackle the problem, rather than just the solution) :+)

First, let's consider what an equal share of gold would look like for each pirate. 100/7 = 14.29.. or so. We will assume that amounts of gold must be integers, since we all know pirates deal in physical gold coins. Therefore, the senior pirate cannot propose such a division of gold – but they wouldn't in any case, as according to the rules of pirates, pirates are ruthlessly logical and seek only to maximise their own ends. The senior pirate can do better than that.

In order for a motion to pass, half or more of the pirates must agree including the SP. Therefore, the SP must propose the best possible outcome for 4 out of 7 pirates, including themself. If the SP proposes that they themself will receive a larger share of gold than the 3 other pirates that must vote in favour with the motion, then the motion will not pass, as the pirates are pure logical entities, and there is no reason that they would vote in favour of a motion that leaves them with a lower share than they potentially could receive if they throw the SP overboard and begin again.

Therefore, in order for the SP to maximise their gold share whilst appeasing half or more of the 7 pirates, the gold must be split equally between 4 – the SP, and 3 other pirates of their choice in order to make up the 4 out of 7 needed for the motion to pass. It does not matter that the other 3 pirates receive nothing, as their votes will be in the minority. 100/4 = 25.

Ergo; the senior pirate must suggest that 4 pirates including themself receive 25 gold each. The motion will pass, and the SP (being a pirate and therefore in accordance with pirate rules) will have maximised their share of the gold as far as is possible.

For some reason I can't see the answer on my computer :/
Would you mind copying it for me??

"The solution involves looking at what happens with only 2 pirates, and working up from there.(We assume that the most senior pirate has the letter A. Others will be B, C, D etc, depending on how many there are in the group.)2 PiratesPirate A suggests he gets all the gold. He votes for it, so it carries.Pirate A gets 100 coins, pirate B gets 0.3 PiratesPirate A knows that if he’s thrown overboard, pirate C would get nothing (as the situation would revert to the two pirate example above, with pirate C promoted to pirate B). So if pirate A bribes pirate C with 1 coin, pirate C will vote in favour.Pirate A gets 99 coins, pirate B gets 0, pirate C gets 1.4 PiratesPirate A knows that if he dies, then pirate C gets nothing (again, it will become the 3 pirate case, and pirate C will be promoted to pirate B), so he needs 1 coin to bribe him.Pirate A gets 99 coins, pirate B gets 0, pirate C gets 1, pirate D gets 0.5 PiratesNow Pirate A needs 3 votes, so he must bribe each of the pirates who would get 0 coins if he dies with 1 coin each.Pirate A gets 98 coins, pirate B gets 0, pirate B gets 1, pirate D gets 0, pirate E gets 1.6 PiratesSame story: bribe pirate B and pirate D.Pirate A gets 98 coins, pirate B gets 0, pirate C gets 1, pirate D gets 0, pirate E gets 1, pirate F gets 0.7 PiratesIn this final stage (although you can continue indefinitely!) the senior pirate has to get 4 votes, so must bribe 3 pirates… might as well bribe the 3 that have the most to lose if he dies (ie, pirates C, E and G). Pirate A gets 97 coins, pirates C, E and G get 1 coin each, and the others get nothing."