Pirate Problem
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8 members have voted
January 17th, 2019 at 5:56:16 AM
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Thought I’d toss out a math question I’ve heard given in interviews.
There are five pirates: captain, first mate, second mate, third mate and fourth mate. The pirates are rational actors and have the following preferences:
1) Pirates prefer to live rather than die.
2) So long as life not in jeopardy, Pirates prefer more gold rather than less.
3) All else being equal, Pirates prefer to make other Pirates walk the plank (killing them) than not.
Pirates follow the strict pirate code for sharing booty. The highest ranking pirate makes a proposal about how to share the booty and then everyone votes. If a majority (more than half) vote in favor of the plan, the booty is shared that way. Otherwise, the pirate that made the proposal has to walk the plank, and the next highest pirate makes a proposal.
The five pirates just made a score of 100 gold pieces.
How will the 100 gold pieces be shared?
Answers in spoilers please.
There are five pirates: captain, first mate, second mate, third mate and fourth mate. The pirates are rational actors and have the following preferences:
1) Pirates prefer to live rather than die.
2) So long as life not in jeopardy, Pirates prefer more gold rather than less.
3) All else being equal, Pirates prefer to make other Pirates walk the plank (killing them) than not.
Pirates follow the strict pirate code for sharing booty. The highest ranking pirate makes a proposal about how to share the booty and then everyone votes. If a majority (more than half) vote in favor of the plan, the booty is shared that way. Otherwise, the pirate that made the proposal has to walk the plank, and the next highest pirate makes a proposal.
The five pirates just made a score of 100 gold pieces.
How will the 100 gold pieces be shared?
Answers in spoilers please.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
January 17th, 2019 at 7:22:59 AM
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This is one of my favorite logic puzzles, but I ask it with 1,000 coins and I reorder the priorities as follows:
1) So long as life not in jeopardy, Pirates prefer more gold rather than less.
2) All else being equal, Pirates prefer to make other Pirates walk the plank (killing them) than not.
3) Pirates prefer to live rather than die.
Where this might make a difference is if a pirate is put in a position where he gets no gold either way. Would he give up his own life to have another pirate walk the plank? Under my rules the answer is "yes."
I'll put a 24-hour delay on myself to give the rest of the forum a chance to enjoy it.
1) So long as life not in jeopardy, Pirates prefer more gold rather than less.
2) All else being equal, Pirates prefer to make other Pirates walk the plank (killing them) than not.
3) Pirates prefer to live rather than die.
Where this might make a difference is if a pirate is put in a position where he gets no gold either way. Would he give up his own life to have another pirate walk the plank? Under my rules the answer is "yes."
I'll put a 24-hour delay on myself to give the rest of the forum a chance to enjoy it.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 17th, 2019 at 7:42:01 AM
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the first and second mate get 50 each.
We assume the first party always votes for the plan. To get then majority the captain needs two more votes. He offers 50 and 50 to the two mates. If either of those two vote against the plan they know the captainis going to die. The first mate prefers life over death and then gold. The only thing the first mate can do is offer the 2nd and third mates 50 each. The second mate knows that if the first mate gets killed then he will get no gold as he will have to offer the third and fourth mates all of the gold. Therefore the 1st and 2nd mates will accept 50 each from the captain and win the vote 3 to 2, and everyone lives. It says everyone votes so i presume it includes the person offering the deal.
We assume the first party always votes for the plan. To get then majority the captain needs two more votes. He offers 50 and 50 to the two mates. If either of those two vote against the plan they know the captainis going to die. The first mate prefers life over death and then gold. The only thing the first mate can do is offer the 2nd and third mates 50 each. The second mate knows that if the first mate gets killed then he will get no gold as he will have to offer the third and fourth mates all of the gold. Therefore the 1st and 2nd mates will accept 50 each from the captain and win the vote 3 to 2, and everyone lives. It says everyone votes so i presume it includes the person offering the deal.
Maybe?
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You want the truth! You can't handle the truth!
January 17th, 2019 at 9:51:44 AM
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Quote: unJonThought I’d toss out a math question I’ve heard given in interviews.
There are five pirates: captain, first mate, second mate, third mate and fourth mate. The pirates are rational actors and have the following preferences:
1) Pirates prefer to live rather than die.
2) So long as life not in jeopardy, Pirates prefer more gold rather than less.
3) All else being equal, Pirates prefer to make other Pirates walk the plank (killing them) than not.
Pirates follow the strict pirate code for sharing booty. The highest ranking pirate makes a proposal about how to share the booty and then everyone votes. If a majority (more than half) vote in favor of the plan, the booty is shared that way. Otherwise, the pirate that made the proposal has to walk the plank, and the next highest pirate makes a proposal.
The five pirates just made a score of 100 gold pieces.
How will the 100 gold pieces be shared?
Answers in spoilers please.
My initial guess is that the Captain proposes a three way split. The booty would be divided 32/34/34, with the Captain getting the small share. The first mate and second mate would also get offers. If the First Mate turns on the Capt, he will still have to deal with proposing the same split to three other pirates, who all have an incentive to vote it down. If the Second Mate turns on the Captain, then turns on the First Mate, he will be left making a proposal to two others who have an incentive to vote him down to get a 50/50 share by making him walk the plank. They both can do no better.
What happens if, should it get to four voters, there is a tie? Does the proposer walk the plank?
Simplicity is the ultimate sophistication - Leonardo da Vinci
January 17th, 2019 at 10:46:14 AM
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Quote: AyecarumbaWhat happens if, should it get to four voters, there is a tie? Does the proposer walk the plank?
Yes. Majority means over 50%.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 17th, 2019 at 1:19:48 PM
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I've never heard this one before and I have not looked it up on the internet. Here is my off-the-top-of-my-head answer.
The five pirates are captain, 1st mate, 2nd mate, 3rd mate and 4th mate.
Third mate does not want the decision to slide down to him, because 4th mate will always vote no on his decision, kill the 3rd mate and take all the money.
2nd mate wants the decision to slide down to him, he can propose that 100% of the money go to himself and third mate must vote for it to save his own life. Thus 2nd mate has the potential to win 100% of the loot, leaving 3rd mate and 4th mate with zero.
First mate knows all of the above. If the decision come to him he can keep 98 gold pieces and give 1 each to the 3rd and 4th mates, That's a better deal for 3rd and 4th mate then they would get from 2nd mate, so they would accept this and vote yes to prevent 2nd mate from getting the decision.
Therefore, Captain can split the money 96 for him, 0 for 1st and 2nd mates and 2 each for 3rd and 4th mates. That is the best deal that the 3rd and 4th mates will get, therefore they will vote yes.
The five pirates are captain, 1st mate, 2nd mate, 3rd mate and 4th mate.
Third mate does not want the decision to slide down to him, because 4th mate will always vote no on his decision, kill the 3rd mate and take all the money.
2nd mate wants the decision to slide down to him, he can propose that 100% of the money go to himself and third mate must vote for it to save his own life. Thus 2nd mate has the potential to win 100% of the loot, leaving 3rd mate and 4th mate with zero.
First mate knows all of the above. If the decision come to him he can keep 98 gold pieces and give 1 each to the 3rd and 4th mates, That's a better deal for 3rd and 4th mate then they would get from 2nd mate, so they would accept this and vote yes to prevent 2nd mate from getting the decision.
Therefore, Captain can split the money 96 for him, 0 for 1st and 2nd mates and 2 each for 3rd and 4th mates. That is the best deal that the 3rd and 4th mates will get, therefore they will vote yes.
Last edited by: gordonm888 on Jan 17, 2019
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
January 17th, 2019 at 4:39:46 PM
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Quote: gordonm888I've never heard this one before and I have not looked it up on the internet. Here is my off-the-top-of-my-head answer.
The five pirates are captain, 1st mate, 2nd mate, 3rd mate and 4th mate.
Third mate does not want the decision to slide down to him, because 4th mate will always vote no on his decision, kill the 3rd mate and take all the money.
2nd mate wants the decision to slide down to him, he can propose that 100% of the money go to himself and third mate must vote for it to save his own life. Thus 2nd mate has the potential to win 100% of the loot, leaving 3rd mate and 4th mate with zero.
First mate knows all of the above. If the decision come to him he can keep 98 gold pieces and give 1 each to the 3rd and 4th mates, That's a better deal for 3rd and 4th mate then they would get from 2nd mate, so they would accept this and vote yes to prevent 2nd mate from getting the decision.
Therefore, Captain can split the money 96 for him, 0 for 1st and 2nd mates and 2 each for 3rd and 4th mates. That is the best deal that the 3rd and 4th mates will get, therefore they will vote yes.
...that's not the best deal for the Fourth Mate. He has a chance to split 50/50 with the third mate, or take it all.
Simplicity is the ultimate sophistication - Leonardo da Vinci
January 17th, 2019 at 5:32:51 PM
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. This is really close!Quote: gordonm888I've never heard this one before and I have not looked it up on the internet. Here is my off-the-top-of-my-head answer.
The five pirates are captain, 1st mate, 2nd mate, 3rd mate and 4th mate.
Third mate does not want the decision to slide down to him, because 4th mate will always vote no on his decision, kill the 3rd mate and take all the money.
2nd mate wants the decision to slide down to him, he can propose that 100% of the money go to himself and third mate must vote for it to save his own life. Thus 2nd mate has the potential to win 100% of the loot, leaving 3rd mate and 4th mate with zero.
First mate knows all of the above. If the decision come to him he can keep 98 gold pieces and give 1 each to the 3rd and 4th mates, That's a better deal for 3rd and 4th mate then they would get from 2nd mate, so they would accept this and vote yes to prevent 2nd mate from getting the decision.
Therefore, Captain can split the money 96 for him, 0 for 1st and 2nd mates and 2 each for 3rd and 4th mates. That is the best deal that the 3rd and 4th mates will get, therefore they will vote yes.
Error in the last step. Captain can save a gold piece.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
January 17th, 2019 at 11:23:37 PM
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Quote: gordonm888I've never heard this one before and I have not looked it up on the internet. Here is my off-the-top-of-my-head answer.
The five pirates are captain, 1st mate, 2nd mate, 3rd mate and 4th mate.
Third mate does not want the decision to slide down to him, because 4th mate will always vote no on his decision, kill the 3rd mate and take all the money.
2nd mate wants the decision to slide down to him, he can propose that 100% of the money go to himself and third mate must vote for it to save his own life. Thus 2nd mate has the potential to win 100% of the loot, leaving 3rd mate and 4th mate with zero.
First mate knows all of the above. If the decision come to him he can keep 98 gold pieces and give 1 each to the 3rd and 4th mates, That's a better deal for 3rd and 4th mate then they would get from 2nd mate, so they would accept this and vote yes to prevent 2nd mate from getting the decision.
Therefore, Captain can split the money 96 for him, 0 for 1st and 2nd mates and 2 each for 3rd and 4th mates. That is the best deal that the 3rd and 4th mates will get, therefore they will vote yes.
Under the rules that earlier people have to offer strictly more money, for instance if 2nd offers no money to 3rd, wizard's question says they'd rather die and kill off another pirate if they're going to get no money. Thus the figures for each round have to be larger than those on offer later.
3rd mate knows if it gets to him he gets no money as 4th will vote against him.
2nd mate has to offer 3rd mate some money (this is where wizard's rule starts to change things) so 2nd can keep 99 and offer 1 to 3rd mate to get his vote.
1st mate now has to offer more to 3rd and 4th to get their votes, so keeps 97 and gives 2 to 3rd and 1 to 4th.
Similarly captain has to offer even more, so 3 to 3rd and 2 to 4th, so can only keep 95.
If the rules were as originally stated 2nd mate wouldn't have to offer any money (as 3rd would prefer to live). However the captain still has to offer 2 to 3rd and 4th (to beat the later offer) so keeps 96.
January 18th, 2019 at 8:58:15 AM
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Quote: charliepatrickQuote: gordonm888I've never heard this one before and I have not looked it up on the internet. Here is my off-the-top-of-my-head answer.
The five pirates are captain, 1st mate, 2nd mate, 3rd mate and 4th mate.
Third mate does not want the decision to slide down to him, because 4th mate will always vote no on his decision, kill the 3rd mate and take all the money.
2nd mate wants the decision to slide down to him, he can propose that 100% of the money go to himself and third mate must vote for it to save his own life. Thus 2nd mate has the potential to win 100% of the loot, leaving 3rd mate and 4th mate with zero.
First mate knows all of the above. If the decision come to him he can keep 98 gold pieces and give 1 each to the 3rd and 4th mates, That's a better deal for 3rd and 4th mate then they would get from 2nd mate, so they would accept this and vote yes to prevent 2nd mate from getting the decision.
Therefore, Captain can split the money 96 for him, 0 for 1st and 2nd mates and 2 each for 3rd and 4th mates. That is the best deal that the 3rd and 4th mates will get, therefore they will vote yes.
Under the rules that earlier people have to offer strictly more money, for instance if 2nd offers no money to 3rd, wizard's question says they'd rather die and kill off another pirate if they're going to get no money. Thus the figures for each round have to be larger than those on offer later.
3rd mate knows if it gets to him he gets no money as 4th will vote against him.
2nd mate has to offer 3rd mate some money (this is where wizard's rule starts to change things) so 2nd can keep 99 and offer 1 to 3rd mate to get his vote.
1st mate now has to offer more to 3rd and 4th to get their votes, so keeps 97 and gives 2 to 3rd and 1 to 4th.
Similarly captain has to offer even more, so 3 to 3rd and 2 to 4th, so can only keep 95.
If the rules were as originally stated 2nd mate wouldn't have to offer any money (as 3rd would prefer to live). However the captain still has to offer 2 to 3rd and 4th (to beat the later offer) so keeps 96.
Doesn't he turn down all offers since he actually has a chance to kill everyone else and keep 100% for himself? Why would he accept 2 when he can have 100?
Simplicity is the ultimate sophistication - Leonardo da Vinci
January 18th, 2019 at 9:24:33 AM
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Quote: AyecarumbaQuote: charliepatrickQuote: gordonm888I've never heard this one before and I have not looked it up on the internet. Here is my off-the-top-of-my-head answer.
The five pirates are captain, 1st mate, 2nd mate, 3rd mate and 4th mate.
Third mate does not want the decision to slide down to him, because 4th mate will always vote no on his decision, kill the 3rd mate and take all the money.
2nd mate wants the decision to slide down to him, he can propose that 100% of the money go to himself and third mate must vote for it to save his own life. Thus 2nd mate has the potential to win 100% of the loot, leaving 3rd mate and 4th mate with zero.
First mate knows all of the above. If the decision come to him he can keep 98 gold pieces and give 1 each to the 3rd and 4th mates, That's a better deal for 3rd and 4th mate then they would get from 2nd mate, so they would accept this and vote yes to prevent 2nd mate from getting the decision.
Therefore, Captain can split the money 96 for him, 0 for 1st and 2nd mates and 2 each for 3rd and 4th mates. That is the best deal that the 3rd and 4th mates will get, therefore they will vote yes.
Under the rules that earlier people have to offer strictly more money, for instance if 2nd offers no money to 3rd, wizard's question says they'd rather die and kill off another pirate if they're going to get no money. Thus the figures for each round have to be larger than those on offer later.
3rd mate knows if it gets to him he gets no money as 4th will vote against him.
2nd mate has to offer 3rd mate some money (this is where wizard's rule starts to change things) so 2nd can keep 99 and offer 1 to 3rd mate to get his vote.
1st mate now has to offer more to 3rd and 4th to get their votes, so keeps 97 and gives 2 to 3rd and 1 to 4th.
Similarly captain has to offer even more, so 3 to 3rd and 2 to 4th, so can only keep 95.
If the rules were as originally stated 2nd mate wouldn't have to offer any money (as 3rd would prefer to live). However the captain still has to offer 2 to 3rd and 4th (to beat the later offer) so keeps 96.Doesn't he turn down all offers since he actually has a chance to kill everyone else and keep 100% for himself? Why would he accept 2 when he can have 100?
When it gets down to the 2nd mate, 3rd mate, and 4th mate, the offer should be 99, 1, 0. 2nd obviously takes the offer. 3rd takes it because he would rather get 1 and live than get 0 and die when it gets down to him and the 4th mate. Even if he can manage to get the captain and 1st mate killed, he will get stuck with 0 gold. Instead, he takes the first offer of 2. The first offer should be 97, 0, 1, 0, 2.
I heart Crystal Math.
January 18th, 2019 at 11:24:17 AM
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Quote: AyecarumbaQuote: charliepatrickQuote: gordonm888I've never heard this one before and I have not looked it up on the internet. Here is my off-the-top-of-my-head answer.
The five pirates are captain, 1st mate, 2nd mate, 3rd mate and 4th mate.
Third mate does not want the decision to slide down to him, because 4th mate will always vote no on his decision, kill the 3rd mate and take all the money.
2nd mate wants the decision to slide down to him, he can propose that 100% of the money go to himself and third mate must vote for it to save his own life. Thus 2nd mate has the potential to win 100% of the loot, leaving 3rd mate and 4th mate with zero.
First mate knows all of the above. If the decision come to him he can keep 98 gold pieces and give 1 each to the 3rd and 4th mates, That's a better deal for 3rd and 4th mate then they would get from 2nd mate, so they would accept this and vote yes to prevent 2nd mate from getting the decision.
Therefore, Captain can split the money 96 for him, 0 for 1st and 2nd mates and 2 each for 3rd and 4th mates. That is the best deal that the 3rd and 4th mates will get, therefore they will vote yes.
Under the rules that earlier people have to offer strictly more money, for instance if 2nd offers no money to 3rd, wizard's question says they'd rather die and kill off another pirate if they're going to get no money. Thus the figures for each round have to be larger than those on offer later.
3rd mate knows if it gets to him he gets no money as 4th will vote against him.
2nd mate has to offer 3rd mate some money (this is where wizard's rule starts to change things) so 2nd can keep 99 and offer 1 to 3rd mate to get his vote.
1st mate now has to offer more to 3rd and 4th to get their votes, so keeps 97 and gives 2 to 3rd and 1 to 4th.
Similarly captain has to offer even more, so 3 to 3rd and 2 to 4th, so can only keep 95.
If the rules were as originally stated 2nd mate wouldn't have to offer any money (as 3rd would prefer to live). However the captain still has to offer 2 to 3rd and 4th (to beat the later offer) so keeps 96.Doesn't he turn down all offers since he actually has a chance to kill everyone else and keep 100% for himself? Why would he accept 2 when he can have 100?
The 4th mate knows that it will never get down to the 3rd mate making the decision -because the 3rd mate knows that he will walk the plank if he makes the decision. So the 4th mate knows that the 3rd mate will always approve any decision of the 2nd mate to avoid making the decision himself and walking the plank himself. The 2nd mate knows this, so the 2nd mate can decide to keep all 100 golds and the the 3rd mate will vote for that decision. Thus, the 4th mate knows that he will get no gold coins if the Captain and First Mate both walk the plank.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
January 18th, 2019 at 11:38:54 AM
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Absurd. Pirate ships were egalitarian. A captain received one extra share but was voted into office and could be voted out of office. Walking the plank was usually a prank played upon newly seized captives. A pirate vessel's strength was in numbers and lives were not to be sqandered.Quote: unJonAnswers in spoilers please.
So much for historically inaccurate math.
January 18th, 2019 at 11:43:04 AM
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Quote: CrystalMathQuote: AyecarumbaQuote: charliepatrickQuote: gordonm888I've never heard this one before and I have not looked it up on the internet. Here is my off-the-top-of-my-head answer.
The five pirates are captain, 1st mate, 2nd mate, 3rd mate and 4th mate.
Third mate does not want the decision to slide down to him, because 4th mate will always vote no on his decision, kill the 3rd mate and take all the money.
2nd mate wants the decision to slide down to him, he can propose that 100% of the money go to himself and third mate must vote for it to save his own life. Thus 2nd mate has the potential to win 100% of the loot, leaving 3rd mate and 4th mate with zero.
First mate knows all of the above. If the decision come to him he can keep 98 gold pieces and give 1 each to the 3rd and 4th mates, That's a better deal for 3rd and 4th mate then they would get from 2nd mate, so they would accept this and vote yes to prevent 2nd mate from getting the decision.
Therefore, Captain can split the money 96 for him, 0 for 1st and 2nd mates and 2 each for 3rd and 4th mates. That is the best deal that the 3rd and 4th mates will get, therefore they will vote yes.
Under the rules that earlier people have to offer strictly more money, for instance if 2nd offers no money to 3rd, wizard's question says they'd rather die and kill off another pirate if they're going to get no money. Thus the figures for each round have to be larger than those on offer later.
3rd mate knows if it gets to him he gets no money as 4th will vote against him.
2nd mate has to offer 3rd mate some money (this is where wizard's rule starts to change things) so 2nd can keep 99 and offer 1 to 3rd mate to get his vote.
1st mate now has to offer more to 3rd and 4th to get their votes, so keeps 97 and gives 2 to 3rd and 1 to 4th.
Similarly captain has to offer even more, so 3 to 3rd and 2 to 4th, so can only keep 95.
If the rules were as originally stated 2nd mate wouldn't have to offer any money (as 3rd would prefer to live). However the captain still has to offer 2 to 3rd and 4th (to beat the later offer) so keeps 96.Doesn't he turn down all offers since he actually has a chance to kill everyone else and keep 100% for himself? Why would he accept 2 when he can have 100?When it gets down to the 2nd mate, 3rd mate, and 4th mate, the offer should be 99, 1, 0. 2nd obviously takes the offer. 3rd takes it because he would rather get 1 and live than get 0 and die when it gets down to him and the 4th mate. Even if he can manage to get the captain and 1st mate killed, he will get stuck with 0 gold. Instead, he takes the first offer of 2. The first offer should be 97, 0, 1, 0, 2.
The 3rd mate knows that he will walk the plank if 2nd mate walks the plank, because no matter what 3rd mate proposes the 4th mate will vote no -causing the 3rd mate to walk the plank and leaving all 100 gold pieces with the 4th mate. Thus, the 2nd mate can offer 100,0,0 and 3rd mate must vote yes in order to stay alive.
However, I beleive the 3rd mate must be incentivized to vote withe the Captain or 1st mate. 3rd mate can always get zero gold pieces and live by letting Captain and 1st mate walk the plank and then voting in support of whatever decision the 2nd mate makes. And remember the problem statement says that all things being equal, the pirates would prefer that other pirates walk the plank so if Captain or 1st mate offer him zero gold pieces they why should 3rd mate vote in support of their decision? Thus, I still think it is true that 3rd mate will not vote in support of a decision by either the Captain or the 1st mate unless he receives more than zero gold pieces. Captain and 1st mate realize this as well, so 1st mate would offer 1 gold piece and therefore Captain must offer 2 gold pieces.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
January 18th, 2019 at 11:43:10 AM
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Quote: FleaStiffAbsurd. Pirate ships were egalitarian. A captain received one extra share but was voted into office and could be voted out of office. Walking the plank was usually a prank played upon newly seized captives. A pirate vessel's strength was in numbers and lives were not to be sqandered.
So much for historically inaccurate math.
Yeah, and Pirates live in Pittsburgh.
Beware, I work for the dark side.... We have cookies
January 18th, 2019 at 11:50:18 AM
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Quote: gordonm888
The 4th mate knows that it will never get down to the 3rd mate making the decision -because the 3rd mate knows that he will walk the plank if he makes the decision. So the 4th mate knows that the 3rd mate will always approve any decision of the 2nd mate to avoid making the decision himself and walking the plank himself. The 2nd mate knows this, so the 2nd mate can decide to keep all 100 golds and the the 3rd mate will vote for that decision. Thus, the 4th mate knows that he will get no gold coins if the Captain and First Mate both walk the plank.
I suspect the answer depends on how you interpret the set of rules. As I understand it wizard is saying if anyone is destined to get no money then they will vote to eliminate a previous player even if it means they themselves will subsequently die.Quote: Wizard...Where this might make a difference is if a pirate is put in a position where he gets no gold either way. Would he give up his own life to have another pirate walk the plank? Under my rules the answer is "yes." ...
On re-reading this I am now beginning to wonder whether wizard's interpretation is incorrect as surely a pirate getting no money in this round round but living is better than [eliminating a pirate and] going to the next round and then dying.Quote: Wizard...3) Pirates prefer to live rather than die...
Thus if someone was destined to die in the next round they would be happy with no money in the previous one. Under wizard's interpretation in the earlier round would have to offer them 1 to receive their vote.
January 18th, 2019 at 12:27:22 PM
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Interesting discussion.
My meta-level analysis is that when Charlie and/or Crystal have disagreed with me in the past, they have almost always been right and I have been wrong. And UnJon has shown he is a very sharp guy and he disagrees with me too.
So, even though I think my analysis is consistent and I believe I'm correct, I think that I am wrong with more than 50% probability.
My meta-level analysis is that when Charlie and/or Crystal have disagreed with me in the past, they have almost always been right and I have been wrong. And UnJon has shown he is a very sharp guy and he disagrees with me too.
So, even though I think my analysis is consistent and I believe I'm correct, I think that I am wrong with more than 50% probability.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
January 18th, 2019 at 1:28:57 PM
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^ Actually I originally agreed with your answer but then read wizard's intrepretation of the rules and then came up with a slightly different answer. However I can now see a different answer (suggested in another reply)...
- {. . . 3 4} 4th will reject any offer, 3rd dies if they get to this round.
- {. . 2 3 4} 100-0-0 3rd will accept no money just to live, so 2nd can keep all to himself.
- {. 1 2 3 4} 98-0-1-1 3rd and 4th are happy to let #1 die unless they're offered money. 3rd will not accept no money so has to be offered 1, similarly 4th also has to be offered 1. Note that 2 receives no money in this scenario.
- {C 1 2 3 4} 97-0-1-2-0 or 97-0-1-0-2 This time 2nd is happy to accept 1 (as otherwise he'll get none next round). Similarly 3 or 4 are each happy to accept 2, the captain can choose either.
January 18th, 2019 at 1:36:41 PM
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Quote: charliepatrick^ Actually I originally agreed with your answer but then read wizard's intrepretation of the rules and then came up with a slightly different answer. However I can now see a different answer (suggested in another reply)...
So the captain can keep 97. My mistake was not realising that you could offer #2 1 unit in the first round.
- {. . . 3 4} 4th will reject any offer, 3rd dies if they get to this round.
- {. . 2 3 4} 100-0-0 3rd will accept no money just to live, so 2nd can keep all to himself.
- {. 1 2 3 4} 98-0-1-1 3rd and 4th are happy to let #1 die unless they're offered money. 3rd will not accept no money so has to be offered 1, similarly 4th also has to be offered 1. Note that 2 receives no money in this scenario.
- {C 1 2 3 4} 97-0-1-2-0 or 97-0-1-0-2 This time 2nd is happy to accept 1 (as otherwise he'll get none next round). Similarly 3 or 4 are each happy to accept 2, the captain can choose either.
Ahh, yes, the key is Captain offering money to 2nd mate rather than to 3rd (or 4th).. I had missed that. I now am persuaded that this is the correct answer.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
January 18th, 2019 at 1:55:20 PM
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I was just coming here to post that exact thing.Quote: gordonm888Quote: charliepatrick^ Actually I originally agreed with your answer but then read wizard's intrepretation of the rules and then came up with a slightly different answer. However I can now see a different answer (suggested in another reply)...
So the captain can keep 97. My mistake was not realising that you could offer #2 1 unit in the first round.
- {. . . 3 4} 4th will reject any offer, 3rd dies if they get to this round.
- {. . 2 3 4} 100-0-0 3rd will accept no money just to live, so 2nd can keep all to himself.
- {. 1 2 3 4} 98-0-1-1 3rd and 4th are happy to let #1 die unless they're offered money. 3rd will not accept no money so has to be offered 1, similarly 4th also has to be offered 1. Note that 2 receives no money in this scenario.
- {C 1 2 3 4} 97-0-1-2-0 or 97-0-1-0-2 This time 2nd is happy to accept 1 (as otherwise he'll get none next round). Similarly 3 or 4 are each happy to accept 2, the captain can choose either.
Ahh, yes, the key is Captain offering money to 2nd mate rather than to 3rd (or 4th).. I had missed that. I now am persuaded that this is the correct answer.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
January 18th, 2019 at 2:42:36 PM
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Quote: charliepatrickOn re-reading this I am now beginning to wonder whether wizard's interpretation is incorrect as surely a pirate getting no money in this round round but living is better than [eliminating a pirate and] going to the next round and then dying.
Haven't you heard that pirates are "bloodthirsty?" This is the way it was told when I first heard this many years ago. It also leads to a cleaner solution, in my opinion.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 18th, 2019 at 3:28:45 PM
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Agree!Quote: Wizard....pirates are "bloodthirsty?"...leads to a cleaner solution....
- {. . . 3 4} #4 will reject any offer, #3 dies if they get to this round.
- {. . 2 3 4} 99-1-0 #3 now needs 1, else will just kill off #2.
- {. 1 2 3 4} 97-0-2-1 #3 and #4 are happy to let #1 die unless they're offered more money than they'd get in the next round. Note that #2 still receives no money in this scenario and #4 is only offered 1.
- {C 1 2 3 4} 97-0-1-0-2 This time #2 is happy to accept 1 (as otherwise he'll get none next round). However only #4 is happy to accept 2. So it's neater in that there's a unique solution as the captain no longer can choose either.
January 18th, 2019 at 7:42:40 PM
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Quote: charliepatrickAgree!
So the captain can still keep 97 but only has one choice of who to offer 2 to, i.e. a cleaner solution.
- {. . . 3 4} #4 will reject any offer, #3 dies if they get to this round.
- {. . 2 3 4} 99-1-0 #3 now needs 1, else will just kill off #2.
- {. 1 2 3 4} 97-0-2-1 #3 and #4 are happy to let #1 die unless they're offered more money than they'd get in the next round. Note that #2 still receives no money in this scenario and #4 is only offered 1.
- {C 1 2 3 4} 97-0-1-0-2 This time #2 is happy to accept 1 (as otherwise he'll get none next round). However only #4 is happy to accept 2. So it's neater in that there's a unique solution as the captain no longer can choose either.
- {. . . 3 4} #4 will reject any offer, #3 dies if they get to this round.
- {. . 2 3 4} 99-1-0 #3 now needs 1, else will just kill off #2.
I think this last item is not quite correct . The offer should be 100-0-0 because #3 will die if #2 dies so #3 will always vote to accept #2's offer, therefore no gold coins to #3 need to be offered.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
January 18th, 2019 at 9:05:25 PM
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Quote: gordonm888Quote: charliepatrickAgree!
So the captain can still keep 97 but only has one choice of who to offer 2 to, i.e. a cleaner solution.
- {. . . 3 4} #4 will reject any offer, #3 dies if they get to this round.
- {. . 2 3 4} 99-1-0 #3 now needs 1, else will just kill off #2.
- {. 1 2 3 4} 97-0-2-1 #3 and #4 are happy to let #1 die unless they're offered more money than they'd get in the next round. Note that #2 still receives no money in this scenario and #4 is only offered 1.
- {C 1 2 3 4} 97-0-1-0-2 This time #2 is happy to accept 1 (as otherwise he'll get none next round). However only #4 is happy to accept 2. So it's neater in that there's a unique solution as the captain no longer can choose either.
- {. . . 3 4} #4 will reject any offer, #3 dies if they get to this round.
- {. . 2 3 4} 99-1-0 #3 now needs 1, else will just kill off #2.
I think this last item is not quite correct . The offer should be 100-0-0 because #3 will die if #2 dies so #3 will always vote to accept #2's offer, therefore no gold coins to #3 need to be offered.
The Wizard rearranged the order of the rules vs what I presented. Per Wiz’s “suicidal pirate rules” #3 is happy to give his own life so long as he gets to kill #2 first. So #2 has to give him a gold piece. The way I presented the rules, your analysis is correct because #3 people refers survival foremost.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
January 19th, 2019 at 2:13:25 PM
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Quote: unJonQuote: gordonm888Quote: charliepatrickAgree!
So the captain can still keep 97 but only has one choice of who to offer 2 to, i.e. a cleaner solution.
- {. . . 3 4} #4 will reject any offer, #3 dies if they get to this round.
- {. . 2 3 4} 99-1-0 #3 now needs 1, else will just kill off #2.
- {. 1 2 3 4} 97-0-2-1 #3 and #4 are happy to let #1 die unless they're offered more money than they'd get in the next round. Note that #2 still receives no money in this scenario and #4 is only offered 1.
- {C 1 2 3 4} 97-0-1-0-2 This time #2 is happy to accept 1 (as otherwise he'll get none next round). However only #4 is happy to accept 2. So it's neater in that there's a unique solution as the captain no longer can choose either.
- {. . . 3 4} #4 will reject any offer, #3 dies if they get to this round.
- {. . 2 3 4} 99-1-0 #3 now needs 1, else will just kill off #2.
I think this last item is not quite correct . The offer should be 100-0-0 because #3 will die if #2 dies so #3 will always vote to accept #2's offer, therefore no gold coins to #3 need to be offered.The Wizard rearranged the order of the rules vs what I presented. Per Wiz’s “suicidal pirate rules” #3 is happy to give his own life so long as he gets to kill #2 first. So #2 has to give him a gold piece. The way I presented the rules, your analysis is correct because #3 people refers survival foremost.
LOL, when in doubt, read the rules! I admit that I was using UnJon's rules since he was OP -as evidenced by the fact that I kept referring to 100 gold pieces rather than the 1,000 gold pieces in Wizard's version. Anyway, this was a fun puzzle to work as a community. Well done, all.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
