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A Game of Pirates


Best Answer m00li, 24 May 2014 - 11:03 PM

Spoiler for I agree plasmid but not completely.
Go to the full post


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11 replies to this topic

#1 Yoruichi-san

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Posted 16 May 2014 - 08:57 PM

It seems the harmonic function that represents my activity on BD has finally crossed the x-axis once again...;P I recently came across an extension to an old favorite that I'd like to share. The original variant has been posted here several times probably but for those who don't know it, here is a recap:

 

Season 1 Recap:

 

There are 5 pirates that must split 100 gold coins among themselves.  They do so following the following protocol:

 

1.  The captain presents his proposal on how to distribute the coins.

2.  The living pirates, including the captain, take a vote on whether to pass or reject the proposal.  In case of a tie, the captain has the breaking vote.

3.  If the proposal passes, the coins are divided according to it.  If it is rejected, the captain walks the plank and the first mate becomes captain, the second mate (if they are called that?) becomes first mate, the third mate becomes second, etc, and return to step 1.

 

Assume the pirates are all perfectly rational, do not trust each other, and prioritize in the following order:

1.  They want to survive.

2.  They want to maximize their personal loot.

3.  They want to see others walk the plank.

 

What is the captain's proposal?

 

 

Barring the cliffhanger ending, the logical next extension, then...

 

 

Season 2 recap:

 

Same as above but with n pirates, where n<100.

 

 

And finally, the new extension...

 

Season 3 spoilers:

 

What if n>100?

 


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Women are definitely stronger. We are [Fe]males, after all...

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<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

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#2 Yoruichi-san

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Posted 17 May 2014 - 05:12 PM

Correction:  for parts 2 and 3, the cutoff should be n<200 and n>200, respectively.  I was in too much of a hurry typing things up, sorry.


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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page! Episode 3 is finally here!

When life hands me lemons, I make invisible ink.

#3 bonanova

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Posted 23 May 2014 - 02:14 AM

Y-San, I researched the first version of this puzzle.
It's challenging, even after reading the correct strategy.
I'm very interested to see what is suggested for the current version.

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#4 m00li

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Posted 23 May 2014 - 02:45 AM

Spoiler for skip alternates


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#5 plasmid

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Posted 24 May 2014 - 02:52 AM

Spoiler for @m00li (or anyone else who cares to click =P)


Edited by plasmid, 24 May 2014 - 05:49 AM.

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#6 m00li

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Posted 24 May 2014 - 08:41 AM

Spoiler for @m00li (or anyone else who cares to click =P)

 
No plasmid. What you are stating will work only if condition 3 is relaxed
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#7 plasmid

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Posted 24 May 2014 - 05:46 PM

Condition 1 overrides condition 3. The pirates would want to live if possible, so if enough of them cooperate then they should be able to override the initial 202 pirates who want to see them walk the plank.

 

Spoiler for consider the following argument


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#8 m00li

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Posted 24 May 2014 - 11:03 PM   Best Answer

Spoiler for I agree plasmid but not completely.

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#9 Yoruichi-san

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Posted 28 May 2014 - 10:54 PM

Spoiler for I agree plasmid but not completely.

 

Correct on your analysis of parts 1 and 2, but for part 3...one thing to consider...

 

Spoiler for ...


  • 0
Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page! Episode 3 is finally here!

When life hands me lemons, I make invisible ink.

#10 Yoruichi-san

Yoruichi-san

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Posted 29 May 2014 - 01:16 AM

 

Spoiler for I agree plasmid but not completely.

 

Correct on your analysis of parts 1 and 2, but for part 3...one thing to consider...

 

Spoiler for ...

 

 

Lol, nvm, I was reading the wrong post...(again with the whole rushing things thing  :wacko: .  Anyways, great job  :thumbsup: .


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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page! Episode 3 is finally here!

When life hands me lemons, I make invisible ink.




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