MARP Editor Cutthroat Puzzle

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Weehawk
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MARP Editor Cutthroat Puzzle

Post by Weehawk »

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Zwaxy has decided to reward his editorial staff by giving them 10 priceless jewels to be distributed among them through the following procedure: each editor, starting with the senior-most will be given the opportunity to propose a distribution scheme to the group. The editors will then vote on whether to accept the proposal or to reject it. If the proposal is rejected, the editor who made it will be eliminated from the process, and forced to play Pot-o-Gold for 12 straight hours. The process will then continue without that editor, the next senior taking his turn. In order to pass, a proposal needs a majority of the editors still involved voting for it with ties broken by the senior editor (who proposed it).

Given that:

1) The editors each want to keep as many jewels for themselves as possible, without regard to the others.

2) The editors all really hate Pot-o-Gold.

3) The editors are all intelligent enough to deduce the optimal distribution for themselves at every stage of the process.

What distribution should the senior-most editor propose, and why? Since I don’t know the exact seniority standing of all the editors, and some of them may have been appointed on the same day, we will simply refer to them as Editor1 (the senior-most), Editor2, Editor3, Editor4, Editor5, Editor6, and Editor7 (the junior-most).

For the first person to respond with the correct answer, I have a choice (and therefore everyone is eligible!) of a Golden Era Game of the Week t-shirt:

ImageImage

or a Robotron 2084 t-shirt:

Image

On the Robotron shirts, I only have one Medium, and one Large, so those are your choices.

Post your answers to the thread, but you only get one shot.

Also, if you are familiar with this puzzle in another form, please excuse yourself.
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Post by Zhorik »

Highlight text if want to see my solution:
We'll solve it recursively (and assume the players are thinking this way):

If it gets down to the last 2 editors, Editor6 will propose getting all 10 jewels for himself, and then beat Editor7 on tiebreak. So Editor7 clearly doesn't want it to go to the last 2 editors, so any proposal before this that gives him at least 1 jewel is better.

So if there are only 3 editors left, Editor5 should propose giving himself 9 jewels, Editor6 0 jewels, and Editor7 1 jewel, which will pass if Editor7 is looking out for his best interest.

Editor4 can see the weakness of Editor6 if things continue, so if only 4 editors are left he can propose a distribution of Editor4 9 jewels, Editor5 0 jewels, Editor6 1 jewel, and Editor7 0 jewels.

Similarly Editor3 should propose Editor3 8 jewels, Editor4 0 jewels, Editor5 1 jewel, Editor6 0 jewels, and Editor7 1 jewel.

Continuing the logic recursively, Editor1 should propose:

Editor1 = 7 jewels
Editor2 = 0 jewels
Editor3 = 1 jewel
Editor4 = 0 jewels
Editor5 = 1 jewel
Editor6 = 0 jewels
Editor7 = 1 jewel
-gastrainga
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Weehawk
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Post by Weehawk »

George has it.

He chooses the Large Robotron and points out that this was much easier than beating BBH's score on the game. :wink:

BBH, you want the Medium, since nobody earned it by beating you?
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Post by BBH »

Weehawk wrote:BBH, you want the Medium, since nobody earned it by beating you?
I'm torn... I like free shit but it really wouldn't be a perfect fit :X
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Post by Weehawk »

BBH wrote:
Weehawk wrote:BBH, you want the Medium, since nobody earned it by beating you?
I'm torn... I like free shit but it really wouldn't be a perfect fit :X
Are you saying you need a Large for the length...I know you don't need it for the width.

If you're insisting on Small you're in for a rough life. I used to actually rant a little about that. "If it's the smallest they sell, why do they call it Medium?"
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Post by BBH »

Weehawk wrote:If you're insisting on Small you're in for a rough life. I used to actually rant a little about that. "If it's the smallest they sell, why do they call it Medium?"
haha naw. k, Medium it is then :D
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