Pirates. (1 Viewer)

[Sy123]

I keep trying, even with small numbers, I the pirates keep dying.
One argument that I had was (after deriving it by first experimenting with 50 Pirates and 10 GOld). At 200 pirates, 100 of them recieve gold, and 100 do not, and Pirate #3 would then think, "if I can eliminate #1 and #2, then I can be pirate king, have enough gold to give myself enough supporters AND at the same time give myself 2 gold (because I would have enough to do so)"

So I will say for now that my second shot is 198 pirates remain.

(And to prevent another loop of that happening, where the new #3 has the same thoughts as the old one, he should recognise, that if he does it, then he will start up a loop of the same thing happening, and he will get killed eventually)

 

[seanieg89]

DAFUQ has been the closest logically, but neither 198 or 200 are correct. Though as a hint, if it gets down to 200 pirates, it will go no further!

 

[DAFUQ]

DAFUQ has been the closest logically, but neither 198 or 200 are correct. Though as a hint, if it gets down to 200 pirates, it will go no further!

oh i think i know y now. i forgot about their priorities

 

[DAFUQ]

so its 202

 

[Sy123]

I got 201.

Since when there are 201 pirates remaining after everyone killed the head pirate since there were 500 pirates since he couldnt satisfy everyone.

Now there are 201 pirates left, and the head pirate gives to everyone 1 piece of gold except himself, so there are 100 people with gold that will vote for the distribution, AND the head pirate himself who will vote for the distribution to spare his own life.

 

[DAFUQ]

I got 201.

Since when there are 201 pirates remaining after everyone killed the head pirate since there were 500 pirates since he couldnt satisfy everyone.

Now there are 201 pirates left, and the head pirate gives to everyone 1 piece of gold except himself, so there are 100 people with gold that will vote for the distribution, AND the head pirate himself who will vote for the distribution to spare his own life.

101/201 > 101/202

 

[seanieg89]

I won't confirm whether 202 is the correct answer until tomorrow to give more people a chance to do it .

 

[Sy123]

101/201 > 101/202

dangnabbit.

I think you have got it then.
Im still happy I got the concept of the head pirate not giving to himself by myself.

(unless we are both wrong)

 

[DAFUQ]

I won't confirm whether 202 is the correct answer until tomorrow to give more people a chance to do it .

alright. thanks for sharing us the problem.
i reckon the logic is more important than the answer.

 

[seanieg89]

alright. thanks for sharing us the problem.
i reckon the logic is more important than the answer.

No worries. Yep, the logic is definitely more important than the answer.

 

[Obvious]

The first pirate receives all of the money?

Edit: I'll try and type out my logic but I'm getting really tired.

Edit 2: Fuck it, I'll do it tomorrow morning.

Edit 3: I think I may be wrong. I'll post what I have so far though. A hint would be welcome.

The problem with the previous answer (202), is that the first 298 pirates, being perfect logicians, will not vote in the manner described in that scenario because it guarantees their collective deaths. As their first priority is survival, if they disintegrate into a rabble and just vote out every pirate king on the basis of not receiving any coins, then they will all eventually be elected and killed.

Moving on from this, it follows that 250 of these top ranking pirates must vote for a higher ranking king pirate regardless of the fact that most of them will not receive any money in order to stay alive.

Now I hope that you can better appreciate how much of a mind fuck this is. I've considered a few scenarios, and I can't really say that any of them are optimal.

 

[seanieg89]

The first pirate receives all of the money?

Edit: I'll try and type out my logic but I'm getting really tired.

Edit 2: Fuck it, I'll do it tomorrow morning.

Edit 3: I think I may be wrong. I'll post what I have so far though. A hint would be welcome.

The problem with the previous answer (202), is that the first 298 pirates, being perfect logicians, will not vote in the manner described in that scenario because it guarantees their collective deaths. As their first priority is survival, if they disintegrate into a rabble and just vote out every pirate king on the basis of not receiving any coins, then they will all eventually be elected and killed.

Moving on from this, it follows that 250 of these top ranking pirates must vote for a higher ranking king pirate regardless of the fact that most of them will not receive any money in order to stay alive.

Now I hope that you can better appreciate how much of a mind fuck this is. I've considered a few scenarios, and I can't really say that any of them are optimal.

Bingo. The first pirate does NOT receive all the money, but the solution is significantly > 202 pirates for the reason you mentioned. Survival plays a major role in the higher ranked pirates decisions. I will post a soln later tonight if no-one else does.

 

[Obvious]

I give up. Post the answer or PM it to me please .

 

[D94]

I believe it's 299.

The first 100 ranked pirates (after a certain number of votes and kills) will know that they are next in line to get killed, so since survival is the primal role, then they will not take a share in the gold. That leaves 199 pirates left. Now, 1 pirate will know that if he decides to vote in disagreement to the distribution then he will be next in line, so he votes in favour of the decision. That leaves 198 pirates left. If we have 99 who vote in favour and 99 who vote against, then there are not more than 1/2 who vote against, thus leaving 299. We then give gold to those 100 who voted in favour of the distribution. In other words, top 100 survive and don't get gold, 100 who get gold, and 99 who don't get gold, which = 299.

/mostlikelywrong

 

[Obvious]

The pirates will vote for the decision ONLY when they survive and are given the maximum possible combination of kills and money. It's some sort of optimization problem, but it's very hairy so I assume there's a trick that I've failed to see.

Edit: Is it 404 remaining pirates with the pirate king taking all of the money?

 

[seanieg89]

The answer is > than all those posted, but nothing silly like 500. I will write a (hopefully!) clear solution in a couple of hours .

 

[Obvious]

Quick! Before I begin tearing my hair out!

 

[RANK 1]

is it 499?

 

[DAFUQ]

is it 499?

it probably is.

im guessing you also have to work backwords.
eg, only pirate #499 and #500 alive. then #499 can take all the gold. in a sense, #500 is worth 0, #499 is worth 100
now include pirate #498. have to give pirate #500 1gold, and retain the other 99 for himself. #498 worth 99
include #497 (4 pirates now). #497 gives #500 1gold and #498 99gold #497 worth 0
include #496. gives #500 and #497 1 gold each. then keep the rest #496 worth 98
and so on.. ull c a pattern in terms of the worth of each pirate

Once it hits #298 (i think), #298 and below are worth 0, so now we start from front and quit going backwards.

EDIT: i think its #297 actually

 

[seanieg89]

Answer is 456 pirates remaining (I am pretty sure). Sorry for the delay in posting a proof, have been busy doing things around the house. It will be up soon.