Captain Hook was delighted to perform, revealing he'd always dreamed of being part of a pirate rock band.
Later that evening during showtime, Hook had quite enough of this foolishness and storms onto the stage, bent on stealing the microphone, but much to his surprise, Jake offers Hook the microphone and suggests that he sing to the audience. Hook was determined to ruin the show so he'll never have to hear Jake's song ever again, but Jake and his friends soon become aware of Hook's plot and bested the sneaky captain's many attempts to ruin the show. While Jake and his crew practice for their performance, Captain Hook and his scurvy crew soon arrive at Pirate Rock. Marina left to gather the rest of friends to watch them perform at Pirate Rock. Marina enjoys the song so much that she suggests that Jake and his friends could perform a show on Pirate Rock, much to the pirates' delight. Hint 3: Try proving the proposition by induction.Marina overheard Jake and his crew performing their song after besting Captain Hook in a brief race. Hint 2: Formulate a proposition with the pattern found. You may find it helpful to add more rows. Hint 1: Write out the above solutions in a table and try to look for a pattern. The final outcome is therefore:Īs an extension problem, can you say something about the general case of n pirates? And if so, can you prove it by induction? If we allocate a single coin to each of them, they will vote in favour of our proposal (since the alternative sees them receive zero coins without the ability to change anything). We can see from the above scenario with four pirates that pirates 3 and 5 can be most easily bribed. We have finally worked our way back up to the original problem. Therefore, pirate 2 only needs to give 1 coin to pirate 4 to ensure their vote and therefore a winning proposal. Since they are intelligent and rational, they know that if this proposal fails and only three pirates remain they will end up with nothing (and most importantly can do nothing to stop this). Little does she know, danger and adventure lie right under her nosequite literally. Although she is by nature a steady, responsible sort of person, Jenny longs for adventure, even danger. With four pirates remaining, the key vote lies with pirate 4. Turtle Rock is where sixteen-year-old Jenny Snow goes to sit and listen to her iPod and think about the tedium that is her life. Therefore, pirate 3 needs to only sacrifice 1 coin to pirate 5 to ensure a winning vote and does not need to give anything to pirate 3. Pirate 4 knows that they will receive 100 coins in the next round of voting and so will vote against any proposal made here. If there are three pirates remaining, pirate 3 needs only give pirate 5 a single coin and they will already be better off. Outcome for two pirates (4, 5) = (100, 0) If pirates 4 and 5 are the only one remaining, pirate 4 can simply propose that they have all 100 coins and given only one vote is required for the plan to triumph, they can vote in favour and receive all of the treasure. We start by numbering the pirates from 1 (tallest) to 5 (shortest) and work backwards through the problem. Since pirates are generally known to be bloodthirsty, if a pirate will get the same number of coins if voting for or against a proposal, they will choose to vote against so that the proposer is thrown overboard.Īssuming that all 5 pirates are intelligent, rational, greedy, and do not wish to die, what will happen? Otherwise, the pirate proposing the scheme is thrown overboard, and the process is repeated with the pirates that remain. If 50% or more of the pirates vote for it, then the coins will be shared that way.
#ROCKS PIRATES HOW TO#
The tallest pirate proposes how to share the coins, and ALL pirates (including the tallest) vote for or against it. They decide to split the coins using the following scheme: Five pirates of different heights have a treasure of 100 gold coins, which they plan to share amongst themselves.
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