One of them thinking games...

[Beattie]

5 robbers robbed 100 piece of diamonds(same quality and size, weight?).

Now they need to divide 100 among 5 of them.

First they are randomly given numbers 1-5. The person who gets 1 will first start to make proposal, then 2, 3 ,4,5.

If by any chance, they reach a simple majority on No.1?s proposal. Then the deal is done. Same rule apply to No.2,3,4

Note: By any chance, if there is equal or more than 50% of people disagree with the proposal, the guy who made proposal will be killed. There is no hang jury here.

Note: 5 robbers are equally smart, if they know max they can get, they will agree with proposal. There is no favor involved in this case. The robbers are all selfish. They only care what they can get.



Question: How does No.1 guy?s proposal can get max number of diamonds and save his life too?

*edit: the dude that sent it to me said he translated it bad and it should be a simple majority

 

[royaldank]

Huh?

Wouldn't they each just get 20?

 

[tk149]

Do they need unanimous agreement? If it's just majority rules, #1 should offer #2 and #3 one-third, and keep one-third for himself.

 

[Beattie]

I would assume it's unanimous.

As for the thing about each getting 20, wouldnt they each get more if they were to "conspire" somehow to kill other people off?

 

[TwinkleToes77]

#1 shoots em all and takes all the diamonds like a real criminal would do.!

 

[conjur]

Originally posted by: TwinkleToes77
#1 shoots em all and takes all the diamonds like a real criminal would do.!

teh winnAr!

 

[FoBoT]

20 each is the obvious answer which means it is incorrect

there is a way for #1 guy to get more than 20, otherwise this wouldn't be a thinking game/riddle

 

[TooOne21]

No two diamonds are the same...

 

[AbsolutDealage]

This post looks like it was run through google translator about 10 times.

 

[Beattie]

Originally posted by: AbsolutDealage
This post looks like it was run through google translator about 10 times.

it was sent to me by a chinese guy at work.

 

[GagHalfrunt]

I think tk149 has it. Nothing says they all have to get a share, only that more than 50% have to agree with the distribution. The first person is hooked, he needs to offer something that at least 2 of the others agree with or he's dead. He must offer more than 20 each as nobody will agree with that deal. Simply by refusing they can kill him and get 25 each. If all the players are smart nobody can get more than 1/3rd. If the 1st player offers a distro that keeps 3 players in the game and stiffs the other 2 it's in the best interest of the guys getting 33% to accept.

 

[DrPizza]

I don't think the problem was stated correctly...
If it was, then anything other than 20 apiece risks death.

(Because, even if he offered me 25 to be quiet, I'd disagree with him realizing that those getting a smaller than 20 cut would disagree with him... thus, I could tip the scales in favor of his death, and the 100 being split 4 ways.)

 

[GagHalfrunt]

Originally posted by: DrPizza
I don't think the problem was stated correctly...
If it was, then anything other than 20 apiece risks death.

(Because, even if he offered me 25 to be quiet, I'd disagree with him realizing that those getting a smaller than 20 cut would disagree with him... thus, I could tip the scales in favor of his death, and the 100 being split 4 ways.)

But you only thought it halfway through. You wouldn't agree to getting 20 because you knew by disagreeing you could get more. You also would not agree to 25 because you could also get more. But if offered 34? You couldn't get more than that. If player 1 offers a 32-34-34-0-0 split it's the best deal that 2 and 3 could possibly get and they'd need to take it. 3 players agree, the 2 getting stiffed disagree, the deal passes, player 1 survives.

 

[element]

Originally posted by: DrPizza
I don't think the problem was stated correctly...
If it was, then anything other than 20 apiece risks death.

(Because, even if he offered me 25 to be quiet, I'd disagree with him realizing that those getting a smaller than 20 cut would disagree with him... thus, I could tip the scales in favor of his death, and the 100 being split 4 ways.)

Even if #1 offers all 20, the others can say no to the deal just to have him killed and have 1 less to distribute to.

Therefore he should offer to split 3 ways between he, #2 and #3

 

[elGatoXL]

But you only thought it halfway through. You wouldn't agree to getting 20 because you knew by disagreeing you could get more. You also would not agree to 25 because you could also get more. But if offered 34? You couldn't get more than that. If player 1 offers a 32-34-34-0-0 split it's the best deal that 2 and 3 could possibly get and they'd need to take it. 3 players agree, the 2 getting stiffed disagree, the deal passes, player 1 survives.

But if they all disagree in that situation, #1 is removed and #2 can offer 50-50-0-0. #2 and #3 get 50. Much better than 34. If this is not aggreed upon, the same senerio would trickle down until #4 amd #5 are the only ones left. Both would get 50-50. So it's in #3's best interest to take #2's 50-50-0-0 proposal.

I think.

[edit: Nevermind. Thought it was just more than 50% disagreement = death. The equal kills my theory. ]

 

[Luagsch]

nr 1, 2,3 and 4 get 25. nr 5 gets nothing. if they don't agree nr5 will get 100 diamonds and the rest will be dead.

 

[AbsolutDealage]

Originally posted by: DrPizza
I don't think the problem was stated correctly...
If it was, then anything other than 20 apiece risks death.

(Because, even if he offered me 25 to be quiet, I'd disagree with him realizing that those getting a smaller than 20 cut would disagree with him... thus, I could tip the scales in favor of his death, and the 100 being split 4 ways.)

OK, you have to work backwards.

#5 - will never agree with anyone, because he has no risk, and could end up with all the diamonds

#4 - If there are 2 people left, he will have to give all the diamonds to #5 or he is dead. If there are 3 people left, he will agree with anything above 0, because he knows he gets nothing if #3 dies.

#3 - If there are 3 people left, he will have to split it 0-100-0.

#2 - If there are 4 people left, He dies. If there are 5 people left, he will agree with anything.

So, you essentially have a sure thing vote on 2, and number 3 and 4 will agree with anything above 0. My breakdown is: 98/0/1/1/0.

 

[Luagsch]

Originally posted by: elGatoXL

But you only thought it halfway through. You wouldn't agree to getting 20 because you knew by disagreeing you could get more. You also would not agree to 25 because you could also get more. But if offered 34? You couldn't get more than that. If player 1 offers a 32-34-34-0-0 split it's the best deal that 2 and 3 could possibly get and they'd need to take it. 3 players agree, the 2 getting stiffed disagree, the deal passes, player 1 survives.

But if they all disagree in that situation, #1 is removed and #2 can offer 50-50-0-0. #2 and #3 get 50. Much better than 34. If this is not aggreed upon, the same senerio would trickle down until #4 amd #5 are the only ones left. Both would get 50-50. So it's in #3's best interest to take #2's 50-50-0-0 proposal.

I think.

if there is equal or more than 50% of people disagree with the proposal, the guy who made proposal will be killed

EDIT you're dead :beer:

 

[elGatoXL]

EDIT you're dead :beer:

Yeah, just caught that.

 

[GagHalfrunt]

Upon further review:

If player 1 offers 32-34-34 player 2 accepts and players 3-4-5 decline. It's the best deal that 2 can get, but 3 has more options. Therefore 1 can't offer that split as it's death.

What's interesting is that player 2 is completely screwed if player one is killed. At that point there's not a single deal he can offer that doesn't get him killed without him giving up all the diamonds. Player 2 is FORCED to agree to any deal player 1 proposes. On the surface it seems like his best case scenario is 33 diamonds it's actually walking away with his life.

If player one offers a 49-1-50-0-0 split

1: Cannot getmore than 50, tosses 2 a single diamond
2: Gets away with a single diamond and his life, that's his best outcome
3: Can't get more than 50 under any scenario, so must take the deal
4: disagrees
5: disagrees

 

[Luagsch]

ok... another try.
nr5 will always refuse, cause nomatter what if 1 and 2 are dead he just kills 3 and 4 with his vote and gets 100 diamonds. so the last person that could make a proposal so that everybody lives is 2. 2 could propose 100 for him and 0 for 3,4 and 5. if they refuse 3 and 4 are dead and 5 gets all the diamonds.

cause of this the proposal nr 1 can make is 97 for him, 1 for nr 2,3 and 4 and nothing for nr.5. if they don't agree they will be left with nr.2 's proposal and then 3 and 4 would get nothing if they want to survive.

so nr.1: 97
nr.2: 1
nr.3: 1
nr.4: 1
nr.5: 0

EDIT nr 2 refuses nomatter what cause he sees his chance, so nr1 needs nr 5's vote.
so
so nr.1: 97
nr.2: 0
nr.3: 1
nr.4: 1
nr.5: 1

 

[GagHalfrunt]

Originally posted by: Luagsch
ok... another try.
nr5 will always refuse, cause nomatter what if 1 and 2 are dead he just kills 3 and 4 with his vote and gets 100 diamonds. so the last person that could make a proposal so that everybody lives is 2. 2 could propose 100 for him and 0 for 3,4 and 5. if they refuse 3 and 4 are dead and 5 gets all the diamonds.

cause of this the proposal nr 1 can make is 97 for him, 1 for nr 2,3 and 4 and nothing for nr.5. if they don't agree they will be left with nr.2 's proposal and then 3 and 4 would get nothing if they want to survive.

so nr.1: 97
nr.2: 1
nr.3: 1
nr.4: 1
nr.5: 0

That is so far off it's amazing a human being came up with it.

 

[FrOsTxxbYtE]

Originally posted by: royaldank
Huh?

Wouldn't they each just get 20?

 

[OulOat]

Dude, the answer is simple, take all the diamonds and offer everyone else 0 (or offer #2 and #4 one diamond each if they value their life less than a diamond). #2 and #4 will agree. #3 and #5 will disagree. You = profit!!!! I'm da winnAr!!!! I leave it to you to figure out why this combo works.

Edit-----


















SPOILER--------------------------------------------------
























#3 and #5 will disagree with every proposal that's not theirs. Why?

 

[Luagsch]

Originally posted by: GagHalfrunt

Originally posted by: Luagsch
ok... another try.
nr5 will always refuse, cause nomatter what if 1 and 2 are dead he just kills 3 and 4 with his vote and gets 100 diamonds. so the last person that could make a proposal so that everybody lives is 2. 2 could propose 100 for him and 0 for 3,4 and 5. if they refuse 3 and 4 are dead and 5 gets all the diamonds.

cause of this the proposal nr 1 can make is 97 for him, 1 for nr 2,3 and 4 and nothing for nr.5. if they don't agree they will be left with nr.2 's proposal and then 3 and 4 would get nothing if they want to survive.

so nr.1: 97
nr.2: 1
nr.3: 1
nr.4: 1
nr.5: 0

That is so far off it's amazing a human being came up with it.

LMAO, yeah, it wa stupid. see the EDIT