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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

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14 replies to this topic

#11 bonanova

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Posted 06 June 2014 - 04:35 PM

 

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?

 

 

 

The solution contains the assumption:

 

I'm assuming that during the redistribution phase, I will know whether my opponent chose jar 1, 2, 3 or 4.

 

I am trying to reconcile that with the red portion of the OP


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#12 bubbled

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Posted 08 June 2014 - 11:45 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?

 

 

 

The solution contains the assumption:

 

I'm assuming that during the redistribution phase, I will know whether my opponent chose jar 1, 2, 3 or 4.

 

I am trying to reconcile that with the red portion of the OP

 

I was with you as to there being no way to gain an advantage until BMAD added this to the terms of the problem:

 

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

 

Given, that you get to redistribute the marbles, it is reasonable to assume you can tell which jar was chosen and then act accordingly.


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#13 bonanova

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Posted 09 June 2014 - 12:37 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?

 

The solution contains the assumption:

 

I'm assuming that during the redistribution phase, I will know whether my opponent chose jar 1, 2, 3 or 4.

 

I am trying to reconcile that with the red portion of the OP

 

 

I was with you as to there being no way to gain an advantage until BMAD added this to the terms of the problem:

 

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

 

Given, that you get to redistribute the marbles, it is reasonable to assume you can tell which jar was chosen and then act accordingly.

 

 


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

 

 

With this order of events:

  1. I fill the jars the way I want them
  2. Because the jars are not transparent my opponent has no clue about their contents
  3. My opponent picks one
  4. I know which one he picked, either because I was watching
    or because I now have access to all the remaining jars and marbles.
  5. I re-fill the jars the way I want them.
  6. I am blindfolded
  7. The jars are shuffled
  8. I pick one, while blindfolded

there is a strategy.


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

#14 bubbled

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Posted 09 June 2014 - 08:11 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?

 

The solution contains the assumption:

 

I'm assuming that during the redistribution phase, I will know whether my opponent chose jar 1, 2, 3 or 4.

 

I am trying to reconcile that with the red portion of the OP

 

 

I was with you as to there being no way to gain an advantage until BMAD added this to the terms of the problem:

 

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

 

Given, that you get to redistribute the marbles, it is reasonable to assume you can tell which jar was chosen and then act accordingly.

 

 


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

 

 

With this order of events:

  1. I fill the jars the way I want them
  2. Because the jars are not transparent my opponent has no clue about their contents
  3. My opponent picks one
  4. I know which one he picked, either because I was watching
    or because I now have access to all the remaining jars and marbles.
  5. I re-fill the jars the way I want them.
  6. I am blindfolded
  7. The jars are shuffled
  8. I pick one, while blindfolded

there is a strategy.

 

Yes. Your breakdown is exactly how I interpreted the problem after the clarifications. Do you disagree with my strategy?


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#15 bonanova

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Posted 09 June 2014 - 04:30 PM

No.


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




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