GAME THEORY
Q1.
3 people are in a prison together. All wear either a red or a blue hat, but they do not know the color of their hat (in fact all wear red hats). No communication allowed.
The guard tells them that he will ring a bell every hour and if somebody knows that he is wearing a red hat, he or she can leave. (ETA: the guard also tells them that anyone ( Read more... )
3 people are in a prison together. All wear either a red or a blue hat, but they do not know the color of their hat (in fact all wear red hats). No communication allowed.
The guard tells them that he will ring a bell every hour and if somebody knows that he is wearing a red hat, he or she can leave. (ETA: the guard also tells them that anyone ( Read more... )
Comments 23
If there are N persons, they will all leave after N hrs.
Obviously true for N=1.
Suppose the assertion is true when N=n. Consider the case where there are n+1 persons, each will see that there are n persons wearing red hats and conclude that all will leave in the nth hour. At the nth hour, nothing happens, each then conclude that he is also wearing a red hat, hence all will leave in the n+1 th hour.
Hence by induction, true for all N.
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