Bay 12 Games Forum

Please login or register.

Login with username, password and session length
Advanced search  
Pages: 1 ... 20 21 [22] 23 24 ... 36

Author Topic: The questions, riddles and puzzles thread  (Read 37918 times)

irmo

  • Bay Watcher
    • View Profile
Re: The questions, riddles and puzzles thread
« Reply #315 on: March 28, 2011, 05:45:55 pm »

I think we can assume that pirate #1 will go "Oh hey, I be the only one left. All for me, and screw yer democracy, ye drunken hallucination. Ye don't get a vote."

Sure, and I assume the pirates would agree to a plan that gives everyone a share. But by a strict reading of the rules they can't do that.
Logged

ed boy

  • Bay Watcher
    • View Profile
Re: The questions, riddles and puzzles thread
« Reply #316 on: March 29, 2011, 03:32:30 am »

Apologies. In the event that there is only one pirate left, he just takes all the dubloons for himself.
Logged

ed boy

  • Bay Watcher
    • View Profile
Re: The questions, riddles and puzzles thread
« Reply #317 on: March 29, 2011, 11:08:31 am »

On the pirate question, it helps to think inductively.
Let us use the following notation:
(a,b,c,...)
where a is the numbe of dubloons for pirate 1, b is the number for pirate 2, etc.

If there is only 1 pirate, he takes all the dubloons.
(100)

If there are two pirates, then pirate 2 has to propose a plan. If pirate 2 offers pirate 1 anything less than 100 dubloons, pirate 1 will vote no, kill pirate 2, and keep the dubloons. Therefore, if there are only two pirates, pirate 1 will end up with all the dubloons, and both pirates will remain alive.
(100,0)

If there are three pirates, then pirate 3 needs to propose a plan. He wants to surivive, so he wants to get two votes from the other two pirates. The only such plan he can come up with is to give pirate 1 all the dubloons. If either of the pirates vote no, then they end up in the two-pirates position, where 1 gets everything and 2 gets nothing. Both the pirates will therefore vote yes.
(100,0,0)

If there are four pirates, then pirate 4 needs to get at least two votes. Pirates 2 and 3 would get nothing in the 3-pirate situation, so he doesn't need to offer them anything to get their vote. he can keep the rest of the dubloons to himself.
(0,0,0,100)

In all subsequent numbers of pirates, if there are N pirates, pirate N can keep all the dubloons to themselves as they will have N-2 votes from the pirates would would get nothing anyway if they voted no.

That is what would happen if the pirates vote yes whenever voting yes or no has the same outcome for them. What would happen if they were to vote no is that situation?
Logged

Earthquake Damage

  • Bay Watcher
    • View Profile
Re: The questions, riddles and puzzles thread
« Reply #318 on: March 29, 2011, 12:01:28 pm »

What would happen if they were to vote no is that situation?

They wouldn't, because their first priority is survival.
Logged

ed boy

  • Bay Watcher
    • View Profile
Re: The questions, riddles and puzzles thread
« Reply #319 on: March 29, 2011, 12:06:00 pm »

Their first priority is their own survival. Their new thought process would be as such:
-If voting one way would result in their death and voting the other would not, they will vote to avoid dying
-Otherwise, they will vote in the way that maximizes the number of dubloons they get
-If both options offer the same number of dubloons, they vote no
Logged

Earthquake Damage

  • Bay Watcher
    • View Profile
Re: The questions, riddles and puzzles thread
« Reply #320 on: March 29, 2011, 12:18:28 pm »

Their first priority is their own survival. Their new thought process would be as such:
-If voting one way would result in their death and voting the other would not, they will vote to avoid dying
-Otherwise, they will vote in the way that maximizes the number of dubloons they get
-If both options offer the same number of dubloons, they vote no

On pirate N's turn, pirate N-1 will vote yes.  Why?  Because if pirate N dies, it becomes N-1's turn.  And so forth.  By voting no when they will neither win any doubloons or die in that round, they ensure their deaths in future rounds.
Logged

ed boy

  • Bay Watcher
    • View Profile
Re: The questions, riddles and puzzles thread
« Reply #321 on: March 29, 2011, 12:29:17 pm »

They consider more than the current round when they make their voting decision.

Try starting with the single pirate case and working your way up.
Logged

Earthquake Damage

  • Bay Watcher
    • View Profile
Re: The questions, riddles and puzzles thread
« Reply #322 on: March 29, 2011, 01:50:59 pm »

They consider more than the current round when they make their voting decision.

Try starting with the single pirate case and working your way up.

Please explain, then, why they would all suicidally vote no.  I'd love to hear how that either ensures their survival (it doesn't, except for pirate 1) or maximizes their piece of the pie (it doesn't, except for pirate 1).
Logged

Sowelu

  • Bay Watcher
  • I am offishially a penguin.
    • View Profile
Re: The questions, riddles and puzzles thread
« Reply #323 on: March 29, 2011, 02:57:30 pm »

If there are four pirates, then pirate 4 needs to get at least two votes. Pirates 2 and 3 would get nothing in the 3-pirate situation, so he doesn't need to offer them anything to get their vote. he can keep the rest of the dubloons to himself.
(0,0,0,100)

In all subsequent numbers of pirates, if there are N pirates, pirate N can keep all the dubloons to themselves as they will have N-2 votes from the pirates would would get nothing anyway if they voted no.

Let's say N=5, and pirate N wants to keep all the cash.  Pirate 1 always votes no, because if he can kill off everyone else, he gets all the cash himself.  N=2 and N=3 know they will never get anything, so they always vote yes. N=4 knows that if N=5 bites the dust, HE gets all the money.  So, pirate 5 must give all his money to pirates 1 or 4 to survive.

Actually, no.  Pirate 1 knows that he never gets any money either, doesn't he?  Because it'll never go past the N=3 case.
Logged
Some things were made for one thing, for me / that one thing is the sea~
His servers are going to be powered by goat blood and moonlight.
Oh, a biomass/24 hour solar facility. How green!

ed boy

  • Bay Watcher
    • View Profile
Re: The questions, riddles and puzzles thread
« Reply #324 on: March 29, 2011, 04:20:28 pm »

They consider more than the current round when they make their voting decision.

Try starting with the single pirate case and working your way up.

Please explain, then, why they would all suicidally vote no.
I mae no such claim.
Logged

Strife26

  • Bay Watcher
    • View Profile
Re: The questions, riddles and puzzles thread
« Reply #325 on: March 31, 2011, 06:04:48 am »

Spoiler (click to show/hide)
Logged
Even the avatars expire eventually.

ed boy

  • Bay Watcher
    • View Profile
Re: The questions, riddles and puzzles thread
« Reply #326 on: March 31, 2011, 09:24:24 am »

Am I right in thinking that it is an eight digit number with 135 in it somewhere?
Logged

Strife26

  • Bay Watcher
    • View Profile
Re: The questions, riddles and puzzles thread
« Reply #327 on: March 31, 2011, 09:41:58 am »

You would be incorrect in that assumption. It is not an eight digit number.



A third of 135 is a fourth of the way right though.
Logged
Even the avatars expire eventually.

Heliogabalus

  • Bay Watcher
    • View Profile
Re: The questions, riddles and puzzles thread
« Reply #328 on: March 31, 2011, 09:59:17 am »

1745 AD
Logged

Caesar

  • Bay Watcher
    • View Profile
Re: The questions, riddles and puzzles thread
« Reply #329 on: March 31, 2011, 10:01:49 am »

Pi?
Logged
Spider Overhaul
Adding realistic spiders to Dwarf Fortress. (Discontinued.)

Godhood VIII
The latest installment in the Godhood roleplaying game series.
Pages: 1 ... 20 21 [22] 23 24 ... 36