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Guest Message by DevFuse

# nice dice

Best Answer plasmid, 10 July 2014 - 05:21 AM

Looks like you've mostly solved your own puzzle

And no one tried to argue that it's impossible because there are only 6*6*4*4 = 576 ways to orient the dice, while there are 6! = 720 ways to arrange the prisoners, so the dice can't encode all possible arrangements of prisoners.

Spoiler for Well, here's my implementation

Go to the full post

13 replies to this topic

### #1 TimeSpaceLightForce

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Posted 07 July 2014 - 06:56 PM

Everyday, six prisoners: numbered #1 #2 #3 #4 #5 #6 were randomly
locked-up inside six prison cells: [1] [2] [3] [4] [5] [6]...

No one have any information about the other locked-up prisoners.
They do not have any means of communications once inside the closed room.

During a dinner the warden offered the prisoners to participate in a game of chance.
Anyone who can guess all the prisoner's # in every prison cell correctly
shall be freed together with one of the other prisoners he selects.
If the guess is wrong, both of them shall be hanged.
Anyone who wont guess will be hanged.

For accepting his challenge he would grant the prisoners request that
one of the prison cells must contain a boxed dice to play and share.
Provided they can only send it once to other cell and received it once
from other cell with the assistance of prison guard.

The six prisoners talked it over and all agreed to take the challenge.
On the next day they were all  locked-up with  blindfold ..
but they were all saved by the dice.

How can this be done?

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### #2 k-man

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Posted 07 July 2014 - 07:49 PM

Interesting puzzle.

I have some clarifying questions:

1) Do the prisoners know the number of their own cell? I would guess yes, but better ask than guess.

2) When you say that "they can only send it once to other cell and received it once from other cell" do you mean there is only one pass of dice allowed? Or each prisoner can do a single pass for a total of 6 passes of the dice?

3) Can the prisoner with the dice specify the cell number of the prisoner number that shall receive the dice from him?

4) What is the significance of the blindfold? They obviously need to be able to set the dice to something specific and read the dice. Some people may be able to feel the numbers on the dice using their fingers, but not all people can do that reliably.

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### #3 TimeSpaceLightForce

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Posted 07 July 2014 - 10:13 PM

Thanks for clarifying and interest k-man..

1) No, not on the challenge day.

2) They are allowed 6 passes.

3) The dice holder can specify the prison cell or  the prisoner number (not in OP but Ok)

4) They can take off the blinders when inside the cells (hope the lights are on)

It is a matter of freedom and doom and everyone should be very efficient.

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### #4 k-man

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Posted 07 July 2014 - 11:03 PM

Thanks for clarifying, but it seems that something is still missing...

Spoiler for

Also, if prisoner #1 guessed correctly and wants to save prisoner #2, who guessed incorrectly or refused to guess what happens to prisoner #2?

Edited by k-man, 07 July 2014 - 11:09 PM.

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### #5 TimeSpaceLightForce

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Posted 08 July 2014 - 02:49 AM

Interesting puzzle.

I have some clarifying questions:

1) Do the prisoners know the number of their own cell? I would guess yes, but better ask than guess.

2) When you say that "they can only send it once to other cell and received it once from other cell" do you mean there is only one pass of dice allowed? Or each prisoner can do a single pass for a total of 6 passes of the dice?

3) Can the prisoner with the dice specify the cell number of the prisoner number that shall receive the dice from him?

4) What is the significance of the blindfold? They obviously need to be able to set the dice to something specific and read the dice. Some people may be able to feel the numbers on the dice using their fingers, but not all people can do that reliably.

Correction: Post #3
1) No, not on the start of challenge day.

Spoiler for

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### #6 TimeSpaceLightForce

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Posted 08 July 2014 - 04:35 AM

@ K-man: what missing is..

When done  with dice one prisoner will volunteer to see the warden,
select a partner to be saved and guess correctly for their freedom..
then the next prisoner shall do the same..until all of them are free.

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### #7 plasmid

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Posted 08 July 2014 - 05:07 AM

The picture has a box that can hold two dice, and has an orientation so that if someone were to hand you the box then you could distinctly talk about "the die on the side with the D" versus "the die on the side with the E", and define faces of the dice as "pointing toward the DNE" or "pointing toward the lion" when you send or receive the box. Is that what the prisoners will get in the puzzle?

When a prisoner receives the dice, will he be told how many other prisoners have already had the dice?

After the first prisoner guesses and two prisoners get released or get hanged, do the remaining four prisoners only need to guess which cells the remaining four prisoners are in, or do they also need to guess about the two prisoners that are now gone?

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### #8 TimeSpaceLightForce

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Posted 08 July 2014 - 05:45 AM

@ plasmid:

1) Is that what the prisoners will get in the puzzle? ...Exactly!

2)When a prisoner receives the dice, will he be told how many other prisoners have already had the dice?

The written guess of the 3 savers should be like:

Ex:

[1]#2

[2]#5

[3]#1

[4]#4

[5}#6

[6}#3

Edited by TimeSpaceLightForce, 08 July 2014 - 05:46 AM.

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### #9 TimeSpaceLightForce

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Posted 08 July 2014 - 07:37 AM

@ plasmid:

2)When a prisoner receives the dice, will he be told how many other prisoners have already had the dice?

ans: The dice might carry that information..

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### #10 TimeSpaceLightForce

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Posted 08 July 2014 - 09:41 AM

Spoiler for the plan

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