Bonus question: 4 bonus marks] A pirate ship has a captain and five crew. One da
ID: 2930189 • Letter: B
Question
Bonus question: 4 bonus marks] A pirate ship has a captain and five crew. One day they raid a passing vessel and make off with a chest containing 33 gold bars. Since 33 is not a multiple of 6, they decide that a democratic way of dividing the gold is best They nmber themselves 1 through 6, with the captain being number 1 and the sailor who swabs the deck being number 6. The highest numbered pirate makes a proposal about how to divide the gold, and the group votes on it. If the proposa is supported by at least half of the pirates, then the gold is divided as suggested. Otherwise, the proposer is killed and the process is repeated in the smaller group. of the group are aware that: (a) All pirates are greedy, and wil vote against any proposal if, by waiting, they could get more gold later in the process (b) All pirates are bloodthirsty, and will vote against any proposal in which they could get the same amount of gold later because it means the proposer is killed (c) All pirates have perfect logic skills. Suppose you are pirate number 6. What do you propose? Does it matter?Explanation / Answer
To understand the answer, we need to reduce this problem to only 2 pirates. So what happens if there are only 2 pirates. Pirate 2 can easily propose that he gets all the 33 gold coins. Since he constitutes 50% of the pirates, the proposal has to be accepted leaving Pirate 1 with nothing.
Now let’s look at 3 pirates situation, Pirate 3 knows that if his proposal does not get accepted, then pirate 2 will get all the gold and pirate 1 will get nothing. So he decides to bribe pirate 1 with one gold coin. Pirate 1 knows that one gold coin is better than nothing so he has to back pirate 3. Pirate 3 proposes {pirate 1, pirate 2, pirate 3} {1, 0, 32}. Since pirate 1 and 3 will vote for it, it will be accepted.
If there are 4 pirates, pirate 4 needs to get one more pirate to vote for his proposal. Pirate 4 realizes that if he dies, pirate 2 will get nothing (according to the proposal with 3 pirates) so he can easily bribe pirate 2 with one gold coin to get his vote. So the distribution will be {0, 1, 0, 32}.
Smart right? Now can you figure out the distribution with 5 pirates? Let’s see. Pirate 5 needs 2 votes and he knows that if he dies, pirate 1 and 3 will get nothing. He can easily bribe pirates 1 and 3 with one gold coin each to get their vote. In the end, he proposes {1, 0, 1, 0, 31}. This proposal will get accepted and provide the maximum amount of gold to pirate 5.