1. (4 points) You are one of P recently arrested prisoners. The warden, a derang
ID: 3746747 • Letter: 1
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1. (4 points) You are one of P recently arrested prisoners. The warden, a deranged computer engineer, makes the following announcement: . You may meet together today and plan a strategy, but after today you will be in isolated cells and have no communication with one another. . I have set up a "switch room" which contains a light switch, which is either on or off. The switch is not connected to anything. select one prisoner at random to enter the "switch room." This prisoner may throw the switch (from on to off, or vice-versa), or may leave the switch unchanged. Nobody else will ever enter this room. . Each prisoner will visit the switch room arbitrarily often. More precisely, for any N, eventually each of you will visit the switch room at least N times.Explanation / Answer
(a) Choose a leader from P. Consider he/she has the responsibility of switching OFF. And everybody else should switch ON, only once (if it is OFF), or else leave it as it is (unchanged). Everybody else other than the leader, are leaving the switch unchanged on their subsequent visits, and when the switch is already ON.
Now, the leader if switches OFF for atleast P times, he can declare 'We have all visited the switch room atleast once'.
This is because, everybody is switching ON only once, and if the leader switches off P times, this happens because, everybody visited the room atleast once, and switched on the light.
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