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Prisoners sorting cards - this puzzle is not for the faint of heart


Best Answer Yoruichi-san, 16 August 2014 - 05:28 AM

 

I had done the same analysis as Barc and concluded that it's probably the correct answer because

Spoiler for

As for coming up with a different strategy
Spoiler for
That said, I bet bonanova's already thought of that and has a solution that still works with those rules despite my argument that attempts to show it's impossible.

 

plasmid gives me too much credit, so I'm going to out myself now and state that this is adapted from genius puzzler who will be credited when the solution is found. This is done to keep Google out of the competition, not that anyone would do that. ;)  Further, I worked on this puzzle until I convinced myself that I could not solve it before looking at the solution. So you guys are the heroes here, not me.

 

Let me add:

  1. plasmid's first paragraph makes me wonder. His mirror point seems valid, and it's possible
    that my adaptation opened a loophole. If so, a slight modification of the OP avoids it:

    The first prisoner solves the puzzle and writes an algorithm on a piece of paper that he leaves in the room.
    In that case, and if there are in fact multiple solutions, then Prisoner 1 selects one that they all will use.
    In that case, any algorithm that gives AKQ will be a correct solution to the puzzle.
    That is, it won't be required that every prisoner would have found the same algorithm (if there are several) and used it.

    Or we could say the prisoners are allowed to discuss a strategy beforehand.

     
  2. I can provide a helpful clue, one that still leaves a very hard problem, if desired.

 

 

Maybe I'm missing something, but I think this might oversimplify the problem.  If I can select a specific direction, I think I can get to AKQ in 6 moves from any initial formation, regardless of the time.

Spoiler for Strategy
Go to the full post


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21 replies to this topic

#1 bonanova

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Posted 13 August 2014 - 06:31 PM

The warden is at it again. The entire prison population will be set free if the inmates can achieve a simple result. They must stack three cards, an Ace, King and Queen, on a table, in that order, with the Ace on top.

Alone and in a closed room, the warden begins the process by placing the three cards face up on a desk in some or all of three bins, appropriately marked Left, Middle, and Right. If they all occupy a single bin, only the top card is visible. If they occupy only two of the bins, then only two cards are visible, and it is impossible to tell which of the two visible cards conceals the third. Of course if they are all in separate bins, all three are visible. How the cards are initially laid out is totally up to the warden, but for the purposes of this puzzle we may assume the placement is random.

At 8:00am on the fateful day, a prisoner chosen at random enters the room and moves one of the visible cards from its bin to a different (possibly empty) bin. That is, from the top of one stack to the top of another (possibly empty) stack. The prisoner then leaves the room and is led back to his cell. He does not communicate in any way with the other inmates. Then at 9:00am, and at one-hour intervals thereafter, a second, third, etc., randomly chosen prisoner enters the room and again moves a single card from the top of one pile to the top of another. A prison guard inspects the cards after each move and informs the warden if at any time the three cards become stacked in a single bin in the desired order: Ace, King, Queen, with Ace on top.

 

The cards must be correctly stacked by the time the 5:00pm prisoner leaves the room, or before, for the prisoners to be released. They are all executed otherwise.

The prisoners are not permitted to work out a strategy beforehand. In fact, the prisoners do not know what they are expected to do until they enter the room. We could say that prisoners enter the room, read the above description of the problem, make their move, and then leave.

What are the prisoners' chances?

We can assume they are smart. Smart enough to be Brain Denizens.


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

#2 Barcallica

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Posted 14 August 2014 - 04:49 AM

Can a prisoner choose not to move anything?

 

also do they know what time it is?


Edited by Barcallica, 14 August 2014 - 04:51 AM.

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#3 plasmid

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Posted 14 August 2014 - 04:59 AM

Must a prisoner commit to moving a card to a particular bin before seeing what's underneath it? Or may he change his mind and pick a different card, or change the chosen card's destination, after seeing what's underneath the card he initially picks up?
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#4 Barcallica

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Posted 14 August 2014 - 05:21 AM

may he change his mind and pick a different card, or change the chosen card's destination, after seeing what's underneath the card he initially picks up?

 

if he may, can he put it back?


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#5 bonanova

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Posted 14 August 2014 - 07:14 AM

Good questions.

The prisoner must make a move. Wait. No, he doesn't. But skipping a move only makes it harder to finish by 5:00pm.
The move is based solely on visible cards.
The move may not be reconsidered based on information gained by making the move.

0. Enter the room.
1. Look at the (visible) cards.
2. Decide which visible card to move and where to move it.
3. Make the move.
4. Leave the room.

Re time of day.
I introduced time of day only to limit the total number of moves.
But you may assume the prisoner has a functioning timepiece.

Gratuitous fact:

Left, Middle and Right are labels whose only function is to enable a description of what a prisoner might see and what move he should then make.


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- Bertrand Russell

#6 Quantum.Mechanic

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Posted 14 August 2014 - 11:53 AM

I just read an equivalent puzzle in a puzzle book, so I'll sit this one out...


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#7 Barcallica

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Posted 15 August 2014 - 08:30 AM

I am stuck.

 

Spoiler for My approach


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#8 bonanova

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Posted 15 August 2014 - 01:01 PM

Nice analysis.
You may have made some assumptions you don't need to make.
Here are some things to consider.

Spoiler for for starters

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- Bertrand Russell

#9 plasmid

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Posted 15 August 2014 - 03:02 PM

I had done the same analysis as Barc and concluded that it's probably the correct answer because
Spoiler for

As for coming up with a different strategy
Spoiler for
That said, I bet bonanova's already thought of that and has a solution that still works with those rules despite my argument that attempts to show it's impossible.
  • 0

#10 bonanova

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Posted 16 August 2014 - 12:22 AM

I had done the same analysis as Barc and concluded that it's probably the correct answer because

Spoiler for

As for coming up with a different strategy
Spoiler for
That said, I bet bonanova's already thought of that and has a solution that still works with those rules despite my argument that attempts to show it's impossible.

 

plasmid gives me too much credit, so I'm going to out myself now and state that this is adapted from genius puzzler who will be credited when the solution is found. This is done to keep Google out of the competition, not that anyone would do that. ;)  Further, I worked on this puzzle until I convinced myself that I could not solve it before looking at the solution. So you guys are the heroes here, not me.

 

Let me add:

  1. plasmid's first paragraph makes me wonder. His mirror point seems valid, and it's possible
    that my adaptation opened a loophole. If so, a slight modification of the OP avoids it:

    The first prisoner solves the puzzle and writes an algorithm on a piece of paper that he leaves in the room.
    In that case, and if there are in fact multiple solutions, then Prisoner 1 selects one that they all will use.
    In that case, any algorithm that gives AKQ will be a correct solution to the puzzle.
    That is, it won't be required that every prisoner would have found the same algorithm (if there are several) and used it.

    Or we could say the prisoners are allowed to discuss a strategy beforehand.

     
  2. I can provide a helpful clue, one that still leaves a very hard problem, if desired.

  • 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




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