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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Comments
Wow very good!
I like it!
I like it!
Very clever - I want more like this.
I have three words for that. LONG and CONFUSING.
I realize that this one is tough to explain, but it is definitely one of my all-time favorites.
I'm still confuse
Apr 27, 2002
A Classic! Thanks for the memories.
Awesome, well thought out.
Wow! Nice teaser! I'm pretty new to Briangle, but so far enjoying lots of your teasers. Keep it up, love'd to see more.
good teaser, but if pirates are infiately greedy couldn't P5 do a high split kicking P4&P3 into P1&P2's swords in the confusion P5 could stab P1&P2 thus keeping the money for himself?
Yes maybe. But maybe also in the confusion the gold gets knocked overboard and eaten by a whale who for some reason enjoys eating rare metals.
so what would the first propose? All you said was backward.
Great Teaser! It is hard to put the answer into words, but this really is simple if you think about it long enough. This is definitely going in to myy favorites. Thanks a lot!
Can someone tell me why #4 would agree to #3 saying 1000 gold to himself? If the pirates are infinitely ruthless, then #4 will end up with 1 extra pirate killed, 0 gold if he votes against #3, or end up with 0 gold if he votes for #3. I am interpreting infinitely ruthless to mean the pirates get satisfaction from money first, and then killing other pirates second.
#4 would agree to #3, because if he doesn't, then #3 will get killed. Once #3 is killed, it's just #4 and #5. Because #5 wants all the gold, he won't accept any proposition that #4 makes, therefore killing #4, and keeping all the gold. That's why #4 would agree to #3. That way, he doesn't die.
Personally, I would just think it easier just to break out into a feud.
Personally, I would just think it easier just to break out into a feud.
one of my favourites...
Good teaser. It'd work only in theory though. If pirates are infinitely smart, they would not agree on these rules in first place, or each would try to be #1 to call.
Also, the first assumption in answer is when only two pirates are left, #4 would be thrown/killed. Really! I'd say it'd depend on who is stronger. Lets say, both are equally strong, then it'd be good idea to split the pot rather than killing each other.
Also, the first assumption in answer is when only two pirates are left, #4 would be thrown/killed. Really! I'd say it'd depend on who is stronger. Lets say, both are equally strong, then it'd be good idea to split the pot rather than killing each other.
Don't ruin it by overthinking it. Just admire the puzzle for it's creativity, and don't pick it apart.
This is one of my top 5 teasers. Love, love, love this kind of puzzle.
Impossible to come up with a definitive answer. There could be multiple correct answers. Considering they were all greedy and ruthless, they would likely all end up killing each other in a shootout.
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