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Mister Norris

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Number of posts : 228
Location : Brazil
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Registration date : 2007-08-26

PostSubject: smartass bandits   Thu Aug 28, 2008 7:33 pm

This is a logic problem that I liked.

5 evil bandits own 100 diamonds, and have to distribute among themselves somehow, not necessarily equaly. They decide to randomly name themselves as 1, 2, 3, 4 and 5. Then they will do propositions in the order of the lowest number to the highest in how exactly to distribute the diamonds (bandit 1 proposes, then bandit 2 proposes, ...).

After the first bandit give his proposition, his mates will each vote for a YES or NO, depending on how the purpose satisfies each of them. If the voting results in a win, game over; if draw or lose, bandit 1 dies by his mates and they do the same with bandit 2, and so on.

Consider that:
- Each bandit is very smart and will surely propose and also vote in the way it's best for him (as many diamonds as possible);
- Each bandit knows that his mates are also very smart;
- Like I said, they're very evil, so if one of them is not sure if the other proposition is good or bad for him, he will vote NO;
- They praise life, so they rather get no diamonds than die.

Who will win the proposition and how are the diamonds gonna be distributed?
Post answers please, cause I wanna laugh!


Last edited by Mister Norris on Wed Sep 03, 2008 11:23 pm; edited 2 times in total
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Nieri

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Number of posts : 91
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Main Char : Lady Nieri - 9x Monk, Curly Brace - 8x Gunslinger
Registration date : 2008-06-25

PostSubject: Re: smartass bandits   Wed Sep 03, 2008 7:27 am

Bandit 1 says, '20 diamonds each, no one dies.' Other bandits agree, even share is fair, no lives taken, best outcome available.
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Angrist



Number of posts : 65
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PostSubject: Re: smartass bandits   Wed Sep 03, 2008 4:42 pm

Nop Nieri, since that proposal would led the other bandits into thinking "20 diamonds for each one if we are 5, more for each one with one less guy " and pum! the first bandit is dead, since remember:

[quote] " - Like I said, they're very evil, so if one of them is not sure if the other proposition is good or bad for him, he will vote NO; "[ /quote]


I'm kind of busy now, but I will give it some thought and reply back later.

Btw Norris, the problem is solved with the five propositions? or can each thief propose more than once if they do not get to an agreement in the first round? because if that's the case... this could go on endlessly Razz

one more thing...they are just allowed to propose over the amount of diamonds each one will get, or they can make proposition over their lives as well, like: "Lets kill two guys and share the diamonds among the three that remains." and... the vote of the proposer counts?
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MysticSpeLL



Number of posts : 155
Age : 29
Location : INDIA
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Main Char : BlazeX 99/70 sinX
r0ughnex 96/64 sniper
Souijuro 95/40 creator lool
kiLL switch 97/65 paladin
Registration date : 2007-12-12

PostSubject: Re: smartass bandits   Wed Sep 03, 2008 6:13 pm

the first bandit will sell all the 100 diamonds and keep the money in bank.Interest will be equally divided among the 5 bandits....and 100 dimonds
affraid
they are RICH now bish lol!
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Mailee



Number of posts : 5
Location : New Brunswick, Canada
Registration date : 2008-08-28

PostSubject: Re: smartass bandits   Wed Sep 03, 2008 7:38 pm

Alright then, here's my take on how all this will turn out.

Bandit 4 and 5 will say no to any deals anyone else makes, ending it in a draw every time, guaranteed. After numbers 1,2, and 3 are dead, Bandits 4 will call this deal off, knowing that whatever he proposes will end up in a draw, getting him killed. Bandit 4 and 5 then fight to the death, and the winner gets all 100 diamonds : )
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Mister Norris

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PostSubject: Re: smartass bandits   Wed Sep 03, 2008 8:07 pm

Angrist, they can't do this forever because if a proposition isn't accepted the proposer will die (if it gets to the 5th bandit he would automatically get all diamonds since he would be the only one alive) =] and the proposition is only on how to distribute diamonds, not to kill


Last edited by Mister Norris on Wed Sep 03, 2008 8:11 pm; edited 1 time in total
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Mister Norris

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PostSubject: Re: smartass bandits   Wed Sep 03, 2008 8:09 pm

btw you all gave wrong answers xD

Oh, and Mailee, please note that the bandit that is proposing won't vote
And that the dead ones won't vote either xD
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Mister Norris

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PostSubject: Re: smartass bandits   Wed Sep 03, 2008 8:18 pm

I'm sorry, i think I wasn't very clear in the rulings of the game, let me edit it.
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Mailee



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PostSubject: Re: smartass bandits   Thu Sep 04, 2008 4:15 pm

I know. That means for Bandit 1, 4 and 5 will end the vote between 2 and 3, making a draw, correct? After that, if those 2 continue to vote no, then it would turn out the same. If they are that evil and that smart, even if Bandit 1 said something like "Ok, I'll take none, and you guys split it, 'cause I don't want to die today" (For example), they could easily still say no, because at least 50 diamonds, or the full 100 if 4 and 5 fight, instead of 25 between the four of them. Or 33 1/3, if you count an even split between 3 of them.
Either way, take this with a grain of salt, I just thought of this and decided it would be fun to post : )

Edit: Said that wrong. This also assumes that the same thing would happen between 2 and 3 with the voting too.
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Mister Norris

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PostSubject: Re: smartass bandits   Thu Sep 04, 2008 4:27 pm

remember that if someone lose his proposition he won't vote in the next one cause he will be dead =]

and there's no "draw", if voting draws the proposer dies;

you said somethings that made sense, still didn't give the answer xD
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Jim



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PostSubject: Re: smartass bandits   Thu Sep 04, 2008 9:11 pm

Let's look at this in reverse.

Given the rules, if 4 and 5 are left, 4 dies and 5 gets 100 diamonds anyway.
5 will say NO... draw, for dies 5 gets everything. Since he is evil, however the main outcome is that 4 dies NOT MATTER WHAT.

Therefore if it is 3, 4 and 5 left:
4 will say YES to anything to preserve his life.
Which means that 3 will say NO to everything preceding, because if he gets to set terms, 4 will have to accept otherwise 4 will die.
This means in a 3, 4, 5 situation: 3 - 100; 4 - 0; 5 - 0; and 4 will accept thus the deal is made.

So in the 2, 3, 4, 5 situation. 2 can offer 2- 98; 3 - 0; 4 - 1; 5 - 1.
Thus offering the local maximum for person 4 and 5, PROVIDING THEY PLAY BY TOTAL LOGIC. Since 4 and 5 get the best deal they can in this situation as 3 will offer them 0 and 4 will accept (from above reasons)

In that case, it is easy for 1 to set the terms...
1 will offer 4 and 5 two diamonds each... keeping 96 for himself.
This is the maximum that 4 and 5 are going to get since 3 will offer them 0.

So 1 proposes this:
1 - 96;
2 - 0;
3 - 0;
4 - 2;
5 - 2;

The votes are:
1 - YES (duh)
2 - NO
3 - NO
4 - YES
5 - YES (due to best outcomes)
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Jim



Number of posts : 205
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PostSubject: Re: smartass bandits   Thu Sep 04, 2008 9:21 pm

A slight optimisation of the solution.

1 - 97 YES
2 - 0 NO
3 - 1 YES
4 - 0 NO
5 - 2 YES

This means that 3 and 5 are in optimal positions and therefore will prevent the slaying of 1.
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Mister Norris

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PostSubject: Re: smartass bandits   Thu Sep 04, 2008 11:33 pm

You almost got everything right, Jim, you just passed the info that the guy dies if the proposition draws that the proposer won't vote, which means,

- if by any chance it gets to 3 voting, 5 will garantee a draw, killing 3, then killing 4 since he's gonna be the only one voting.

- So, 2, smart, knows this, and will take all diamonds to himself (IF GETS TO HIM), so 3 and 4 would unite themselves to save their life.

- everybody then knows that 2 would succeed in taking all diamonds, so 1 decides to let them happy, so the right one would be:

1 proposes:

97 diamonds to himself, 1 to bandit 3, 1 to bandit 4 and 1 to bandit 5 (zero to bandit 2)

3, 4 and 5 know that they will get nothing if bandit 2 proposes, so they will be happy with 1 diamond each.

so 3 votes YES, one vote NO, bandit 1 wins


Last edited by Mister Norris on Thu Sep 04, 2008 11:36 pm; edited 1 time in total
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Mister Norris

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PostSubject: Re: smartass bandits   Thu Sep 04, 2008 11:34 pm

Did i mention you were not invited, Jim? =p
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Nieri

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PostSubject: Re: smartass bandits   Fri Sep 05, 2008 8:37 am

Yeah, when you said they praise life, I figured you meant they would rather not kill if they absolutely didnt have to.
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