Riddle #669

Question: Five pirates are parting ways after finding a treasure of 100 pieces of gold. The pirates decide to split it based on a vote. Each pirate, from oldest to youngest, gets to propose a plan on how to split the gold.

If at least 50 percent of the other remaining pirates agree on the plan, that is how they will split the gold. If less than 50 percent of the pirates agree, the pirate who came up with the plan will be thrown overboard. Each pirate is smart, greedy, and wants to throw as many others overboard as possible without reducing the amount of gold they get.

What plan can the first (oldest) pirate propose to live and get as much gold as possible?

Riddle Discussion

By: mikage on 29/6/16

I made an error in my answer. Pirate 5 does not need three votes to win, he only needs two. He can give one gold to pirate 3, and two to either 4 or 5, leaving him 97.

By: mikage on 29/6/16

As explained in previous comments, there are some flaws in the answer.\n\nThe starting point is correct: If there are 2 pirates, the youngest one will deny the oldest pirate's plan and get all the gold. What you forgot to mention is that the oldest pirate will get killed as a result.\n\nIf there are 3 pirates, the oldest pirate is certain his plan will pass, WHATEVER that plan is, because the second pirate will vote for it. If he did not vote for it, he would become the oldest pirate left and be in the situation described above (where he dies). So in a 3 pirate scenario, the oldest pirate takes all the gold.\n\nIf there are 4 pirates, the second pirate will never vote for the plan because he is assured to have all the gold when it is his turn. Even if the first pirate offers to give the second pirate all the gold, the second pirate would prefer killing the oldest AND taking all the gold, so he will refuse the plan. The only way for the oldest pirate to win is to get the votes of pirates 3 and 4. Since they get nothing in the 3-pirate case, he only has to offer 1 gold to them. He therefore gets 98 gold (and pirate 2 gets nothing).\n\nWith 5 pirates, the oldest pirate knows that if his plan is rejected, the second pirate will propose the plan described above, giving the two youngest pirates 1 gold each, and nothing to pirate 3. To win, he needs to offer two gold to pirates 4 and 5, and one gold to pirate 3. He will get 95 gold.

By: prisonmatch on 30/9/15

I think for the solution to be true the statement 'If at least 50 percent of the other REMAINING pirates agree on the plan' should be 'If at least 50 percent of the pirates agree on the plan' else the 4 pirate condition wont work.\nIn the current condition \nIf there are 4 pirates the best plan by oldest is to keep 97 and give 0 to 2nd, 2 to 3rd and 1 coin to 4th. Because in the 3 pirates situation youngest will get nothing and 2nd pirate will get just 1 instead of 2 coins( in 4 pirates condition).\n\nIn the solution given 5th pirate(youngest) will definitely refuse the offer as he is greedy and hope for a better plan by 2nd oldest pirate because in that case too he is at least getting 1 coin and gets to throw 1 overboard. as said by funkychicken. so answer is 97(oldest) 1(3rd pirate) 2 (5th pirate) ,

By: prisonmatch on 30/9/15

I think for the solution to be true the statement 'If at least 50 percent of the other REMAINING pirates agree on the plan' should be 'If at least 50 percent of the pirates agree on the plan' else the 4 pirate condition wont work.\nIn the current condition \nIf there are 4 pirates the best plan by oldest is to keep 97 and give 0 to 2nd, 2 to 3rd and 1 coin to 4th. Because in the 3 pirates situation youngest will get nothing and 2nd pirate will get just 1 instead of 2 coins( in 4 pirates condition).\n\nIn the solution given 5th pirate(youngest) will definitely refuse the offer as he is greedy and hope for a better plan by 2nd oldest pirate because in that case too he is at least getting 1 coin and gets to throw 1 overboard. as said by funkychicken. so answer is 97(oldest) 1(3rd pirate) 2 (5th pirate) ,

By: prisonmatch on 30/9/15

I think for the solution to be true the statement 'If at least 50 percent of the other REMAINING pirates agree on the plan' should be 'If at least 50 percent of the pirates agree on the plan' else the 4 pirate condition wont work.\nIn the current condition \nIf there are 4 pirates the best plan by oldest is to keep 97 and give 0 to 2nd, 2 to 3rd and 1 coin to 4th. Because in the 3 pirates situation youngest will get nothing and 2nd pirate will get just 1 instead of 2 coins( in 4 pirates condition).\n\nIn the solution given 5th pirate(youngest) will definitely refuse the offer as he is greedy and hope for a better plan by 2nd oldest pirate because in that case too he is at least getting 1 coin and gets to throw 1 overboard. as said by funkychicken. so answer is 97(oldest) 1(3rd pirate) 2 (5th pirate) ,

By: MikeHolmes on 18/9/14

4 pirate have to vote, 2 vote is 50percent .\nSo da plan would be..\n''Count to 4 and Eliminate the 4th pirate (count starts from himself) and repeat the process ''.\n THE OLDEST PIRATE Gets all the gold.\nHere, the 2nd,3rd and 5th pirate will vote (because they won't be eliminated ,not yet that is). \nSo what do you think of my answer?

By: McJagger on 26/7/14

One pirate kills everyone. Viola probably solved

By: Twhit on 25/7/14

the three oldest pirates split it.

By: Funkychicken on 8/7/14

There's actually an inconsistency in your logic here. the highest amount that he can get for himself is 97 pieces of gold. The flaw comes in your proposed plan for 4 pirates. Because it has to be voted on by the "remaining" pirates that plan would only be approved of by 1/3rd of the pirates, instead he has to offer 2 pieces of gold to the second youngest pirate to outbid the previous offer. this means that for the oldest pirate to get the most gold he has to offer the 3rd pirate 1 gold piece, and the youngest pirate 2 gold pieces to outbid the offer that would come otherwise.

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