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There are two friends in prison. The warden offers them a chance to live through a game. The game is as follows: tomorrow, the warden will put one friend into room A , which contains 8 balls lined up in a row, each of which is either red or black. He will put the other friend in another room, call it room B, with 8 red balls and 8 black balls. The task is for the the friend in room A to communicate the arrangement of the 8 colored balls in his room to the other friend. If the friend in room B can successfully reconstruct the 8-balls arrangement in room A, both will win their freedom. Otherwise, they forfeit their lives.

There's a catch to this. The friend in room A has to communicate with the person in room B via messengers. The warden will only put 16 messengers in room A, and each messenger can only be instructed to either say 'Black' or 'Red'. It is known that of the 16 messengers, 14 are truth tellers (always correctly convey the message that friend A will send), and 2 are random speakers (will randomly say 'Black' or 'Red' to friend B, regardless of what he is instructed by friend A).

Each of the 16 messengers can only be sent once, and the two friends will not know which messenger is a truth teller, and which is a random speaker. Attempting to figure out which messenger is the truth teller/random speaker is not allowed. Assume that each messenger will only convey only 1 bit of information-'Red' or 'Black'- (so please rule out instructing the messenger to walk fast/slow, talk in high/low voice, sending the messengers in some order depending on their heights, etc. ).

The prisoners are told all the rules of the game as above. They have 1 night to plan a strategy. Please help them determine a strategy that is guaranteed to win the game.

Edited by bushindo
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First 4: Red= red/black or black/red Black= red/red or black/black (each messenger explaining the combination of 2 balls) Next 4: Red= red/black or red/red Black= black/red or black/black (depending on info given by first 4) Last 8: Simply say the color of the balls in order.

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