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Summer Maths Puzzles - Monday 19 August - Pirate Payouts

Pirate Payouts

2019 pirates are on board the Pirate Ship Ptolomy with a treasure chest containing 10,000 gold pieces.  The pirates are ranked from 1 (the most junior) to 2019 the senior pirate.  The most senior pirate must propose a plan for how to divide the gold.  The pirates will then vote on the plan.  If the majority (or exactly half if there is an even number as the most senior pirate has the casting vote) agree then the plan is accepted and that is how the gold is divided.  If the plan is not accepted then the most senior pirate is thrown overboard and it’s up to the next most senior pirate to propose their plan.  The pirates, although ruthless, are perfectly rational and will abide by the rules.

How much should the Senior Pirate offer and to whom in order to secure the most gold for herself. 

Hint:  Consider first the case when there are two pirates 1 and 2 and use this to predict what would happen when there are 3 pirates 1, 2 and 3 and so on…


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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons