Prisoners: Cards 1

#1

The prison is overcrowded and the warden wants to free up some space, so he is going to give two prisoners a game. They will be pardoned if they win. The prisoners will know the rules of the game before hand and can discuss a strategy before the game starts. Once the game starts they may not communicate.

The game is as follows:
The first prisoner of the team goes into the warden’s office. The warden randomly shuffles a standard 52 card deck. He then deals all cards onto a table face up. The first prisoner may swap the position of any two cards. The warden then turns all of the cards face down and the first prisoner leaves the room.

The second prisoner enters the wardens office. The warden will name one the 52 cards at random. The second prisoner then has 26 guesses to find this named. After each guess, the guessed card is flipped over.

What strategy should the two prisoners use?

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Prisoner: Cards 2
#2

This is an beautiful riddle. 5/5!!

#3

Are the cards laid out in some sort of ordered fashion? Like a grid or a row or something?

#4

Good question, yes, the card are laid out in a row and the prisoners are informed of this before the games starts

#5

Ah yeah, then:

Summary

Before the game starts our prisoners should agree on some enumeration of the cards such that they are numbered 1-52.

When the warden calls a card the second prisoner should flip over the corresponding numbered card. That is if the warden called the 3 of Clubs and the prisoners agreed that this corresponded to 15 the prisoner should flip over the 15th card. The prisoner will then flip over the card corresponding to the card he flipped over, then flip over the card corresponding to that card etc. This will eventually loop back on it’s self so the 3 of Clubs will be chosen which would point to 15 completing the cycle.

The only issue left is to ensure this cycle is less than 26 cards in length. There can only be one cycle of length greater than 26, this cycle can be cut in half by swapping two cards so that is what prisoner one does.

Another nice puzzle :smile:

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#6

Nice, I had the same solution. This is one of my favorites

#7

Yeah it’s great, especially because at first it seems like without knowledge of the card that’s gonna be called prisoner one can’t take any meaningful action.