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"let's make a deal" Marbles


Best Answer bubbled, 20 May 2014 - 12:47 PM

Let's add one more caveat then....

After the first person choises, you have the option to redistribute the marbles again.

Spoiler for My solution

Go to the full post


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14 replies to this topic

#1 BMAD

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Posted 17 May 2014 - 03:03 AM

you are a contestant on a game show competing against another person. There are four jars each containing 20 marbles.  At the start, one jar has all blue marbles, another has only green marbles, a third has white marbles, and the last has black marbles.  You see which jar has which at the beginning (the other contestant does not).
 
You may redistribute the marbles however you like except three conditions must persist:
  • every jar must contain at least 1 marble,
  • every marble must be in a jar,
  • no jar may contain more than 50 marbles.  

Once the redistribution occurs, you and the other person will be blindfolded and jars shuffled and randomly placed on the table.  They will pick one jar first then you will pick one from the remaining three.  The marbles in each jar are then counted and scored according to their values:

  • blue = 1
  • green = 3
  • white = 5
  • black = 10

Two questions:

  1. What would be the best configuration of marbles that would most help assist you in winning?
  2. What is the probability you would win this game?

 


Edited by BMAD, 17 May 2014 - 03:03 AM.

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#2 bonanova

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Posted 17 May 2014 - 10:00 AM

Spoiler for Red herrings / missing info?


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#3 BMAD

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Posted 17 May 2014 - 10:55 PM

Spoiler for Red herrings / missing info?

Each jar feels identical (since you and your contestant are blindfolded the look shouldn't matter)

No matter how many marbles they weigh an imperceptible difference

The other person only knows the amount of jars and the starting count and colors in each jar and of course knows the value of each marble.

I did leave this part out, you are only blindfolded after the first person picks their jar and then the jars are shuffled again while you are blindfolded.

The jars are not transparent


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#4 bonanova

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Posted 18 May 2014 - 01:06 PM

OK I'll have to think about it some more.

It seems impossible to implement a strategy.

You're blindfolded and grab one of three jars your opponent didn't pick.

 

Now, to state that problem in a way that will allow a solution ....


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#5 BMAD

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Posted 18 May 2014 - 07:12 PM

Let's add one more caveat then....

After the first person choises, you have the option to redistribute the marbles again.
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#6 bubbled

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Posted 20 May 2014 - 12:47 PM   Best Answer

Let's add one more caveat then....

After the first person choises, you have the option to redistribute the marbles again.

Spoiler for My solution


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#7 dgreening

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Posted 30 May 2014 - 04:12 PM

Spoiler for I've dabbled with various strategies:

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#8 dgreening

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Posted 30 May 2014 - 04:26 PM

One more question:
Does it matter how many points you win by?? [say you were paid $1 per point]; or
Is winning by 1 point as valuable as winning by 20 points?
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#9 BMAD

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Posted 01 June 2014 - 04:56 AM

Winning is winning
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#10 dgreening

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Posted 02 June 2014 - 05:25 PM

Winning is winning

In that case, I think bubbled has the optimum strategy.


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