Reply
Tue 16 Nov, 2004 05:13 am
10 pirates are ranked in order, first to last. After finding a treasure of 100 gold coins, they are discussing how to divide up the booty. They allow the lowest ranked pirate to divide up the coins, and then they vote on the idea. If the number of pirates that like the division proposal is equal to or greater than the number who dislike it, then the Boss will let it be so. (the proposer of the idea has a vote) Otherwise, the proposer has to walk the plank and the next pirate in line gets to make a proposal.
Question: Supposing pirates are smart, want money, and love life, how many pirates will be forced to walk the plank?
I am not sure what that means. How many are you saying pay the fiddler?
1 walks the plank
when the three middle ranked see the first one die they will then propose that the captian gets it all
pirates are not known for being nice ya know
1 walks the plank
when the three middle ranked see the first one die they will then propose that the captian gets it all
pirates are not known for being nice ya know
oops you said 10 not 5
well same answer really
The answer is 8 pirates walk the plank.
No matter what any of the pirates say, all the others won't be happy unless they are given all the money.
So the first can say whatever he wants, the other still want the money and so he's a goner!!
Same goes right up to the 9th pirate. As he's clever and loves life he tells the captain to take all the money, the captain agrees and he lives. If he tries to take any money for himself, the captain will disagree and he'll die.
Zero walk the plank.
The first pirate arranges the money proportionally to rank, the others see that they will be put in the hotseat if they vote against it.
I believe tryagain is the only one who thought about the riddle. I'm not necessarily saying he is right, but it looks like he began with the question of: Does #1 pirate want it to get down to only 2 left (him and #2)? Does #1 pirate want it to get down to 3 left? Why would any pirate vote for any proposal at all? If voting for that proposal would keep him alive, or if that proposal will give him more money than he would eventually get by voting against it. Start at the beginning and work it backwards
Supposing pirate A is the highest ranked captain and pirate J is the lowest my answer is that nobody walks the plank and the distribution of the money goes like this:
A=8
B=6
C=4
D=2
E=0
F=0
G=0
H=0
I=0
J=80
And.. I think tryagain meant to say this:
A=0
B=1
C=0
D=1
E=0
F=1
G=0
H=1
I=0
J=96
If I am A I don't give J any money.
J is going to vote against any plan, hoping that everyone ahead of him dies. So why waste money on her?
I take it you are J, and pirates die in reversed alphabetical order. And J does not want to be left alone with I who would then take all the money.
Oh shoot, you are right. I forgot about that. And I just wrote a now worthless analysis based on the fact that J would want to be alone with I.
Back to the drawing board. If I am #1 (dropping letter for order) I still don't worry about giving #10 any money.
I think I got it!
The first pirate can keep 96 gold coins.
Assuming the other pirates are all perfectly logical and greedy (that is they would prefer 1 coin to 0 coins) the first pirate needs to give 1 coin each to pirate #3, #5, #7 and #9.
She will get a vote from each pirate that received a coin which (with her own vote) will be 5, enough to get the plan ratified.
I'd vote nay on that deal, expecting a better deal from the next guy.
heh, it appears the first pirate is female.
No you wouldnt (if you were odd numbered) because you know that the other pirates were logical and you would know that if you voted no, you would get nothing.
I figured this by looking from the bottom....
If all the pirates die except for #9 and #10. #9 gets 100 coins and #10 gets nothing. #10 doesn't want this to happen.
-- If it is #9's turn to make a plan
#9 gets 100, #10 get's nothing (all others are dead
-- If it is #8's turn to make a plan (meaning 1-7 are dead)
So #10 wants to keep #8 alive to get anything. Because #8 knows that, if it comes to the point that only #8, #9 and #10 are left alive, #8 only needs to give #10 1 coin (keeping 99 for himself). This means #10 votes for #8 giving #8's plan a majority.
-- If it is #7's turn to make a plan (meaning 1-6 are dead)
Everyone knows that if 8 gets to make a plan, #9 is going to get nothing (see above). This means the #7 can simply offer #9 1 coin (which is better than #9 will get if #7 loses the vote). So #7 and #9 vote yes, meaning the plan wins. and #6 can keep 99 coins
--If it is #6's turn to make a plan.
Well everyone knows that #7's plan means that #8 and #10 get nothing. So #6 can win by giving one coin to #8 and #10 one coin (getting their votes) and keep 98 coins.
Well if you keep this pattern going, #1's plan will win with #3, #5, #7 and #9 all voting for it since #1's plan will give them 1 coin and #2's plan will give them nothing.
I would suggest that no pirate walks the plank. If J divides the coins equally all other pirate have to decide whether to oppose the plan and potentially walk the plank or accept what they have. If they are rational pirates they will "take the money and run."