### Brain Teasers

# Greedy Pirates

Five pirates are trying to split up 1000 gold pieces. The rules are as follows:

Pirate #1 must divide the gold up in such a way that a majority of the pirates (including himself) agree to. If he does not get a majority vote, he will be killed, and pirate #2 will get to propose a solution to the remaining 3 pirates, and the same rules will follow. This continues until someone comes up with a plan that earns a majority vote.

What is the most amount of gold pieces that pirate #1 can keep to himself, and what would his proposal be?

The pirates are infinitely greedy, infinitely ruthless (the more dead pirates the better), and infinitely intelligent.

Pirate #1 must divide the gold up in such a way that a majority of the pirates (including himself) agree to. If he does not get a majority vote, he will be killed, and pirate #2 will get to propose a solution to the remaining 3 pirates, and the same rules will follow. This continues until someone comes up with a plan that earns a majority vote.

What is the most amount of gold pieces that pirate #1 can keep to himself, and what would his proposal be?

The pirates are infinitely greedy, infinitely ruthless (the more dead pirates the better), and infinitely intelligent.

### Hint

Start backwards - what would pirate #4's options be if the first 3 pirates were killed?### Answer

Like the hint says, start backwards:If there are two pirates left (#4 & #5), #4 has no options. No matter what he proposes, pirate #5 will disagree, resulting in a 1-1 vote (no majority). #5 will kill #4 and will keep all of the gold.

Now say there are 3 pirates left. #4 has to agree with whatever #3 decides, because if he doesn't #3 will be killed (because #5 won't vote for #3's proposal no matter what it is). #3 will just propose that he keep all of the gold and will get a 2-1 vote in his favor.

Now if there are 4 pirates left:

#3 won't vote for #2's proposal because if #2's fails, #3 will get all of the gold. #4 and #5 know that they will get nothing if the decision goes to #3, so they will vote for #2's proposal if he gives them one gold piece each. Therefore, #2 would keep 998 gold, and #4 and #5 would each get one gold.

So let's wrap this up:

Pirate #1 needs 2 other votes. He will not get a vote from #2 because #2 will get 998 gold if #1's plan fails.

#1 offers #3 one gold piece to vote for him, which #3 will accept (if it gets to #2's plan, #3 will get nothing).

#1 then offers #4 or #5 (doesn't matter which) two gold pieces, which is more than they would get with #2's plan.

So #1 can end up with 997 gold pieces, with #3 getting one piece and #4 or #5 getting two pieces.

...whew!

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