Greedy Pirates
Logic puzzles require you to think. You will have to be logical in your reasoning.
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.
HintStart backwards  what would pirate #4's options be if the first 3 pirates were killed?
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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 11 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 21 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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