Lateral Thinking XIV

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Holmes
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Lateral Thinking XIV

Post by Holmes »

Putting aside Lateral Thinking XIII (recommended, there are 2 problems to solve yet.), I found this really nice Logic - Problem. And also, to keep the Lateral Thinking Threads  ;D

Here it is ...

Five pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all extremely intelligent, treacherous and selfish (especially the captain).

The captain always proposes a distribution of the loot. All pirates vote on the proposal, and if half the crew or more go "Aye", the loot is divided as proposed, as no pirate would be willing to take on the captain without superior force on their side.

If the captain fails to obtain support of at least half his crew (which includes himself), he faces a mutiny, and all pirates will turn against him and make him walk the plank. The pirates start over again with the next senior pirate as captain.

What is the maximum number of coins the captain can keep without risking his life?

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Sayumi

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Re: Lateral Thinking XIV

Post by Sayumi »

I knew this one already, so I won't post the answer....  ;)
"It is one of those instances where the reasoner can produce an effect which seems remarkable to his neighbor, because the latter has missed the one little point which is the basis of the deduction."
Sherlock Holmes
sstimson
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Re: Lateral Thinking XIV

Post by sstimson »

This is more of a thought then an answer. I read somewhere about the human needs ( for lack of a better word like misspelled phycisie ) to hand on to the possible. So would the crew mutiny if the Captain ask this question: There are five of us. In order to be at 50% only takes two, So two of you will miss out. However if you all let me have all the treasure then it is possible all of you might get something. But if you do not like that Idea then you need to decide between yourselves which two will get something and which two get nothing

Because if the two who will miss out agree that a possible of maybe getting something is better then a certain of getting nothing, then it is possible that the Captain could get it all. Besides in the future, the Captain must take care of the crew to be successful. And Even if they get nothing now,There is a good chance of getting indirectly something ( like bought food ) later

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S.H.

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Re: Lateral Thinking XIV

Post by S.H. »

Can anyone explain what "superior force" means in the "as no pirate would be willing to take on the captain without superior force on their side."? Thanks!
Holmes
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Re: Lateral Thinking XIV

Post by Holmes »

It´s just part of ther problem, it means that the crew has no guts to do a rebellion, cause the most powerful man in the crew is the captain.
Nothing else.
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Re: Lateral Thinking XIV

Post by ayw »

This puzzle verges on game theory. The assumption that every pirate is greedy and seeks only to maximise his share without cooperating with another pirate is quite profound, because the rules of the game and the pirates' answers would change if one gives the pirates the capability to cut 50-50 (or other mutually maximising) deals with each other, their intelligence in game theory enabling them to do this without communicating. See also sstimson's earlier post.

The answer I think is that...
...the captain of the ship can keep 98 coins.

Explanation: Label pirates according to rank A, B, C, D, E where A is the current captain. Since there is the possibility of mutiny after which the number of pirates is reduced by one with the next highest in rank becoming captain, it is intuitive to approach this problem from the other end, that is, the case where only two pirates remain. The following table shows the distribution of coins which would result in more "aye"s for a given number of pirates left . (y) or (n) indicates whether the pirate of that table column would agree to that distribution.
[tt]Pirates left    A      B      C      D      E 
     2                             100(y)   0(n)
     3                       99(y)   0(n)   1(y)
     4                99(y)   0(n)   1(y)   0(n)
     5         98(y)   0(n)   1(y)   0(n)   1(y)[/tt]
If the pirates were of a different logical (or gaming) disposition then, e.g. Pirate C and E might say (n) in the first round, ousting the captain, and Pirate B sharing 33-33-33 between himself, C and E in the next round. The best way for A to distribute the coins in the first round may then be A1-B33-C33-D0-E33, though I haven't thought this through sufficiently to be sure.


On a lighter note, why are pirates called pirates?
A: because they just arrghhh!  (sorry... :D)
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Re: Lateral Thinking XIV

Post by S.H. »

Argh...I got the answer after ayw did...

My answer is also 98  :(
Sayumi

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Re: Lateral Thinking XIV

Post by Sayumi »

@ayw & S.H.
[spoiler]Yup, that's the answer - at least as far as I know...  we better wait for Holmes to confirm, but I'm pretty sure that this is right![/spoiler]
Btw we've got spoier tags again, so we can stop the (at least for me) slightly annoying coloring of posts....  ;)
"It is one of those instances where the reasoner can produce an effect which seems remarkable to his neighbor, because the latter has missed the one little point which is the basis of the deduction."
Sherlock Holmes
Holmes
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Re: Lateral Thinking XIV

Post by Holmes »

That´s very correct, well done!

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Re: Lateral Thinking XIV

Post by ayw »

Holmes wrote:Welcome back ayw.

Thanks, Holmes  :)

S.H. wrote:Argh...I got the answer after ayw did...

As Shinichi said, there's no winner in deductions, there's only one truth.
.. or something like that  ;)

ps. Sayumi got it loooong before me.  :D
Last edited by ayw on April 1st, 2009, 8:55 am, edited 1 time in total.
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Holmes
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Re: Lateral Thinking XIV

Post by Holmes »

" In deductions there is no winning or losing, there is no being supeior or inferior, because there is only one single truth " - Kudo Shinichi

I have this one deep in my head, will never forget it.

And ayw, Sayumi had already known the answer.

Anyway, I still haven´t found a Lateral Thinking problem extremely difficult so you won´t know how to resolve it, Muahahahaha. Kidding  :P
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Re: Lateral Thinking XIV

Post by S.H. »

I agree with that...But I believe that if one wants to improve, he/she must overcome challenges.  ;)
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Re: Lateral Thinking XIV

Post by bash7353 »

[spoiler]I don't think you can answer this with absolute certainty because who says two of the pirates wouldn't say okay to an offer that gives them only 32 coins...
Assuming the captain proposes something like this:
Captain: 40 coins
Pirate 1: 30 coins
Pirate 2: 30 coins
Pirate 3: 0 coins
Pirate 4: 0 coins

Piarates 1 and 2 have to consider that if - by denying the offer - they cause a mutiny, which results in a captain that proposes an offer in which they get nothing like the "33-33-33-1-0" one that was stated in a previous post.

I wouldn't exactly call it dumb, if 1 and 2 agreed to this...[/spoiler]

Edit: Just added spoiler-tags.
"Vad ska jag annars vara?" - "Det vet jag inte. Det måste du svara på. Men om du släpper allt du tror att du måste, och frågar dig vad du vill... Vad vill du då?"
描いた夢は叶わないことの方が多い
秀れた人を羨んでは自分が嫌になる
浅い眠りに押し潰されそう夜もある
優しい隣人が陰で牙を向いていたり

惰性で観てたテレビ消すみたいに生きることを時々辞めたくなる

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sstimson
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Re: Lateral Thinking XIV

Post by sstimson »

googleearth wrote:[spoiler]I don't think you can answer this with absolute certainty because who says two of the pirates wouldn't say okay to an offer that gives them only 32 coins...
Assuming the captain proposes something like this:
Captain: 40 coins
Pirate 1: 30 coins
Pirate 2: 30 coins
Pirate 3: 0 coins
Pirate 4: 0 coins

Piarates 1 and 2 have to consider that if - by denying the offer - they cause a mutiny, which results in a captain that proposes an offer in which they get nothing like the "33-33-33-1-0" one that was stated in a previous post.

I wouldn't exactly call it dumb, if 1 and 2 agreed to this...[/spoiler]

Edit: Just added spoiler-tags.


Read my earlier post and the question. If the Pirates can talk with each other it is possible in theory for the Captain to get it all. ( I still believe this is the best answer. Can you see Pirates other then the Captain wasting their spoils on like rum and when the BIG Spoils come, the Pirates are unable to do their duty. Think of the Captain like a bank. )

The question ask for THE MOST the Captain can ask for and still be the Captain.

Later
Later

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bash7353
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Re: Lateral Thinking XIV

Post by bash7353 »

sstimson wrote:Read my earlier post and the question. If the Pirates can talk with each other it is possible in theory for the Captain to get it all. ( I still believe this is the best answer. Can you see Pirates other then the Captain wasting their spoils on like rum and when the BIG Spoils come, the Pirates are unable to do their duty. Think of the Captain like a bank. )

The question ask for THE MOST the Captain can ask for and still be the Captain.

Later


[spoiler]I think it's not possible for the captain to get everthing because then, no other pirate would get anything. In that case, they had nothing to lose to they all would vote against the proposal. But then again, some pirates might even be okay with getting only 1 coin:
Captain: 98 coins
Pirate 1: 1 coin
Pirate 2: 1 coin
Pirate 3: 0 coins
Pirate 4: 0 coins[/spoiler]
"Vad ska jag annars vara?" - "Det vet jag inte. Det måste du svara på. Men om du släpper allt du tror att du måste, och frågar dig vad du vill... Vad vill du då?"
描いた夢は叶わないことの方が多い
秀れた人を羨んでは自分が嫌になる
浅い眠りに押し潰されそう夜もある
優しい隣人が陰で牙を向いていたり

惰性で観てたテレビ消すみたいに生きることを時々辞めたくなる

人生は苦痛ですか 成功が全てですか
僕はあなたにあなたに ただ逢いたいだけ
信じたい嘘 効かない薬 帰れないサヨナラ
叫べ叫べ叫べ   逢いたいだけ
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