you have 45 chameleons on an island dispersed in groups of fifteen. the colors of the three groups are blue, green, and red. when two chameleons of different colors meet, they turn the third color. could you have 14 blue, 15 green, and 16 red? why or why not?
you have 100 prisoners. the warden of the prison has given them the ability to gain their freedom. the warden will take one prisoner at random into a room. the prisoner can flip a lightswitch but nothing else. when a prisoner feels that all of the other prisoners have flipped the switch, he can say that all of the prisoners have flipped the switch. if he is correct, the prisoners will gain their freedom. if he is not, all of the prisoners will spend the rest of their lives in prison. the prisoners can meet and discuss a strategy before the warden of the prison starts bringing prisoners into the room. since the warden will choose the prisoner to visit at random, all prisoners will visit the room. the prisoners will not be able to discuss the room after the warden starts bringing them into the room. how can the prisoners be sure that they will be given their freedom?
i will start you all with these two...
