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 Forum index » Diversions » Perplex City Puzzle Cards » PXC: Black Puzzle Cards
[Puzzle] Black #213: We be Rational Pirates! Arr!
Moderators: AnthraX101, bagsbee, BrianEnigma, cassandra, Giskard, lhall, Mikeyj, myf, poozle, RobMagus, xnbomb
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European Chris
Unfictologist


Joined: 19 Jul 2005
Posts: 1264
Location: London's trendy Whitechapel

 		[Puzzle] Black #213: We be Rational Pirates! Arr!
This is the text of a black card given at Cubefest 2005 as a spoiler of the next wave of cards:

Quote:
AVAST! 'Tis said by landlubbers that there were once five scurvy pirate dogs, stranded on an island. They'd a rich bounty o' 100 gold doubloons, and vowed to spilt the plunder according t' pirate custom. That custom tells us that the, oldest, scurviest pirate gets to propose a spilt between all five o' them, and then all five take a vote 'Aye' for the spilt-even if t' other ha;f vote 'nay'-it goes ahead. But if over half vote 'nay' well, the pirate dog who proposed the spilt had 'is gizzard slit, and the the next oldest pirate gets to have a try with the othe three, and so on.

THE QUESTION IS...me hearties, if you were the oldest scurviuest pirate o' the fiev of them, the first to propose the split, what would ye propose so that ye'd get the most money possible, and also get t' live? What would ye give to each o' the other pirates? (dogs that they are, ye can give 'em all different amounts-even nothing!) Arrr!
[/quote]
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PostPosted: Sat Sep 10, 2005 10:58 pm
Last edited by European Chris on Sun Sep 11, 2005 12:16 pm; edited 1 time in total
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ZoomZoom
Boot

Joined: 12 Nov 2004
Posts: 21
Location: Cambridge, UK

 		My first solve (after months of lurking)
Spoiler (Rollover to View):

Starting from the bottom, with 2 pirates the split is 100/0, and youngest gets nothing.

With 3 pirates the split can be 99/0/1, as if youngest voted nay he will get nothing

With 4 pirates, 98/0/0/2 will pass, as if youngest voted nay he will get 1.

98/0/1/1/0 will pass, as the pirates getting 1 will get 0 if they vote nay.

Assumptions:
There are no deals/bargains between pirates (i.e. No 2+3 agree to share 50 each next time etc.)
Pirates are completely logical
Pirates want the most treasure possible


PostPosted: Sun Sep 11, 2005 9:13 am
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chippy
Entrenched


Joined: 19 Feb 2005
Posts: 789
Location: Leeds, UK

 		photo of card here:
http://www.flickr.com/photos/chippee/42402823/

i think someone picked up the paper, which was getting a bit soggy, but there may be a scan later

PostPosted: Mon Sep 12, 2005 8:49 am
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Curlytek
Veteran


Joined: 30 Jul 2005
Posts: 112
Location: Melbourne, Australia

 		The pirates may not be completely logical, but they are certainly rational (Arrrgggh!). As an aside, it is international pirates day this coming Sunday...a great day to shiver your timbers and hoist ye mainsails.

P.S. I like your answer Zoomzoom, good work.

PostPosted: Mon Sep 12, 2005 8:09 pm
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y2kbozo
Decorated


Joined: 28 Sep 2002
Posts: 252

 		An alternate solution...
Here is another possible solution:
Spoiler (Rollover to View):
Starting from the bottom, with 2 pirates the split is 100/0, the youngest gets nothing.

With 3 pirates the split is 99/0/1, if the youngest votes nay he will get nothing

With 4 pirates the split 99/0/1/0 will pass, as if 2nd youngest votes nay he will get nothing. (In the other solution, at this step the oldest only gets 98, which is not the maximum, so I believe this is the correct split for 4.)

With 5 pirates 98/0/1/0/1 will pass, as the pirates getting 1 will get nothing if they vote nay. (In the other solution where the 2nd youngest gets 1, it is unsure how he would vote if he thought the next step was 99/0/1/0.)


PostPosted: Mon Sep 12, 2005 11:06 pm
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mattyb
Kilroy

Joined: 25 Aug 2005
Posts: 2
Location: Brighton, UK

 		I would say...

Spoiler (Rollover to View):
Wouldn't the most logical solution be to propose a 34/33/33/0/0 split? If you only offer the next 2 most senior pirates 1 each, wouldn't they vote no, sure that they would get more on the next voting round?


PostPosted: Fri Sep 16, 2005 3:32 pm
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ZoomZoom
Boot

Joined: 12 Nov 2004
Posts: 21
Location: Cambridge, UK
mattyb wrote:
I would say...

Spoiler (Rollover to View):
Wouldn't the most logical solution be to propose a 34/33/33/0/0 split? If you only offer the next 2 most senior pirates 1 each, wouldn't they vote no, sure that they would get more on the next voting round?


By consiedering the next round first, as detailed in the soloutions in above posts, you can see that they will accept the split.

34/33/33/0/0 will not work as No.2 says no because he can get more next round.

and btw, I accept the modified soloution proposed, thx (slight slip up in my logic)

PostPosted: Fri Sep 16, 2005 6:30 pm
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oliverkeers13
Entrenched


Joined: 23 May 2005
Posts: 917
Location: London, UK

 		Actually, the solution is
Spoiler (Rollover to View):
98, 0, 0, 1, 1. This is because if the youngest two vote nay, they'll get nothing. the middle two are overpowered.
At least in my opinion
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PostPosted: Fri Sep 16, 2005 7:19 pm
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rkn_technician
Guest


 		[Puzzle] Black #213: We be Rational Pirates! Arr!
http://www.techinterview.org/Solutions/fog0000000102.html gives a full explanation.

PostPosted: Sun Oct 23, 2005 1:08 pm
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Hunting4Treasure
Unfettered


Joined: 06 Aug 2005
Posts: 385
Location: Tampa Bay Area, FL USA

 		Re: [Puzzle] Black #213: We be Rational Pirates! Arr!
rkn_technician wrote:
http://www.techinterview.org/Solutions/fog0000000102.html gives a full explanation.

Holy cow! How long is a typical interview for this company? Shocked

Anyway, put a fork in this one... It's done!
Thanks, rkn_tech! Wink
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PostPosted: Sun Oct 23, 2005 8:04 pm
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chichiri
Decorated

Joined: 31 Oct 2005
Posts: 207

 		confirmed

no da

PostPosted: Thu Nov 24, 2005 11:03 am
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Dysper
Boot

Joined: 09 Sep 2005
Posts: 33

 		It was hard reading all that stuff and then the conclusion was written backwards to our purposes Sad

Spoiler (Rollover to View):
oldest to youngest=98, 0, 1, 0, 1

_________________
There, that ought to do it Wink

PostPosted: Tue Nov 29, 2005 11:35 am
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Guest
Guest


 		Stupid Bloody Pirates...
This is beginning to annoy me...

Pirate 1 offer 2 of the other 1 dubloon and 2 zilch.
Pirate 2, offered 1 coin, for arguments sake, thinks 'Bugger this, if I vote 'Nay' we can kill the old git and the rest of the gang will know I won't be satisfied with just one coin. Arr.'
Pirate 3, offered nothing, thinks 'Well, if we're voting in order of age and the older, wiser pirate offered 1 coin thinks we can get a better deal by offing pirate 1, I'll vote 'Nay' also. Arr.'
Pirate 4 or 5, whoever else is offered nothing will naturally say 'Nay' too. Pirate 1 dies - let's redistribute the wealth, me hearties.

That, my PXC chums is mo funkin' fo logic!

The solve suggested is crud. I thank you for your time. Enjoy your weak lemon drinks...

PostPosted: Mon Feb 06, 2006 1:38 pm
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w0lfwoman
Boot


Joined: 31 Mar 2006
Posts: 24
Location: coast of california

 		the cost of life
I rather agree it is bunk. A pirate would have to be on watch all the time if he tried to keep all the treasure cuz it would be worth it to off him to take it later. If he wanted at least someone to watch his back, he better have been fair to a majority of the others, that is why I opt for the 34/33/33/0/0.

Logic aside...The others would never be satisfied with a doubloon apiece for two of them.

PostPosted: Wed Apr 12, 2006 6:50 pm
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baf
Boot

Joined: 29 Mar 2006
Posts: 46

 		These are PIRATES! They aren't interested in being fair! They're just out to take as much as they can get away with. If pirates 2 and 3 are happy with 34/33/33/0/0, won't they be even happier with offing the senior pirate and taking 50/50/0/0? Or, alternately, 49/49/1/1 -- everyone aside from pirate 1 would like that better than 34/33/33/0/0. And if there's any distribution that all the other pirates like better than your proposal, why on earth would they accept your proposal?

The answer, of course, is that they're not stupid. They know full well that if they reject your proposal, they might face a worse offer from the next guy. But that doesn't mean you have to give them a fair split. It just means you have to give them a better split than what the next guy is going to offer.

But the guy after you isn't worried about getting less from his own proposal. In fact, no matter what you offer him, he can offer himself at least as much. So he doesn't every have any motivation to accept your proposal, does he? So why offer him anything?

PostPosted: Wed Apr 12, 2006 7:52 pm
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