Comments on: Speaking of Puzzles…

By: Conrad M

Conrad M — Sat, 25 Feb 2006 19:58:49 +0000

I was thinking of larger shares at first and was confused by the 98/1/1 split of the coins, but it makes sense if you try and argue against it. Pirate 4 will say no to anything seeing as he becomes in charge if the vote is against P5 proposal. This puts pirate 3 in the same boat if Pirate four is in charge, so pirate 3 knows that Pirate 4, if in charge will seek to please pirate 2 or 1. With each pirate thinking of the alternatives, the only one that stands to gain more than the proposal is the next in command. If you try to do a split that favours the next in command, you’re a dead man because they will still gain more by voting against as will the others. You die, they take over…. So really, 98 0 1 0 1, would guarantee 5’s survival if the other pirates were smart. HOWEVER, in the real world, with human nature involved, you crap on the next in command this way and offer more to a lower ranked person down the line…….you’re a dead man anyway.

If I was pirate 5, I would just do the old “Hey look over there….sneak a coin” routine over and over until there were just a few left, then say “ahh, you guys go ahead and work it out for yourselves”

By: Michael H.

Michael H. — Mon, 27 Jun 2005 15:18:01 +0000

If Pirate 5 thinks he can get more than 20 coins he’s a dead man for sure. It’s worth a few coins to get back at the person who ripped you off!

By: David

David — Tue, 21 Jun 2005 13:06:46 +0000

Pirates 1 and 2 can expect 20 gold coins each, but barely more if no one is killed. If Pirate 5 wants to have P1 and P2Âºs favors, heÂºd better give 30 to P1 30 to P2 and keep 40 for himself. P3 and P4 get 0 but P1 and 2 are happy as they got more than what a fair share would get them if P5 were killed (that’d be 25 coins)

But then again, P5 could run away with the gold coins…

By: Ram

Ram — Thu, 01 Jan 1970 00:00:00 +0000

I don’t understand why any of them will accept any situation the seniormost proposes. Whatever he proposes its best to kill him isn’t so the average money per person increases. Or am i not getting the point. I hate these kinda puzzles.

By: Yazad

Yazad — Thu, 01 Jan 1970 00:00:00 +0000

I remember this puzzle. It’s a damn unfair world

For those who are breaking their heads, try solving this backwards. If there were only 2 pirates what would the seniormost propose? (It’s easy)

Only 3 pirates then what? And so forth.

By: Girish Maiya

Girish Maiya — Thu, 01 Jan 1970 00:00:00 +0000

Not sure if I’m right, but Pirate 5 will keep 98 coins, Pirate 2 will get 1 coin and Pirate 1 will get 1 coin.

As for reasoning: if there are 2 pirates left, then Pirate 1 gets nothing (pirate two keeps everything and is 50% of the remaining pirates, so the proposal passes)
Pirate 3, who values his life, knows this and therefore offers Pirate 1 a single gold coin. Pirate 1 would take this because the alternative is to get nothing and together Pirates 3 and 1 are greater than 50% of the remaining pirates. In this case, Pirate 2 gets nothing.
Pirate 4 knows this and therefore offers Pirate 2 a single gold coin. Pirate 2 will take this, because the alternative is that he gets nothing and Pirates 4 & 2 are 50% of the remaining pirates. Pirate 3 & 1 get nothing.
Pirate 5 knows this and offers Pirate 1 and 2 a single coin each. They can’t do better than that.

Am I close?

Girish

By: Vijay Ganti

Vijay Ganti — Thu, 01 Jan 1970 00:00:00 +0000

& the answer is

98 ,0 , 0, 1, 1.

This to me is a representatiion of what is happening in the technology world executive compensation. It pays to be either a head honcho or being the engineering worker bee is optimal for subsistence. All you guys in the middle are truly squeezed out of existence.

By: MadMan

MadMan — Thu, 01 Jan 1970 00:00:00 +0000

You got it from here, didn't you?

By: Ravikiran Rao

Ravikiran Rao — Thu, 01 Jan 1970 00:00:00 +0000

Look I know that my readers are the smartest people in the world. It should then follow that I did not ask this question to test your skills at cracking mathematical induction.

Yes, if you insist on following the logic of mathematical induction, that is the answer you’ll get. Small correction – the answer should be

98 0 1 0 1

Pirate 5 is better off giving the gold coin to Pirate 3 instead of Pirate 2 because he knows that Pirate 2 will get a coin even under Pirate 4’s distribution, so Pirate 5 can’t be sure of 2’s vote even if he is given the coin. On the other hand, Pirate 3’s vote is assured.

But all this is beside the point. There is something completely wrong about the smug assumptions that we are making about rationality here.

Let me give a hint. My “irrational” behaviour can get magically transformed into rational behaviour if you know that I will display that “irrational” behaviour.

And vice versa.

By: pradeepr

pradeepr — Thu, 01 Jan 1970 00:00:00 +0000

This also reminds me of the Cuban missile crisis between the US and USSR.
Basically, both sides had pointed nuclear missiles towards each other and the question was who was going to back down first. If both sides/agents were rational, both would have agreed to back down.
But it was USSR which capitulated first.

In the private negotiations, apparently Kennedy was advised to wear dishevelled clothes, unkempt hair etc. and generally appear stressed and make irrational statements.

The thing is this irrationality was actually rational in that USSR had to obviously back down from a nuclear standoff against an irrational person.