This is a puzzle question ....
The warden meets with 23 new prisoners when they arrive. He
tells them, "You may meet today and plan a strategy. But
after today, you will be in isolated cells and will have no
communication with one another.
"In the prison is a switch room, which contains two light
switches labeled A and B, each of which can be in either the
'on' or the 'off' position. I am not telling you their
present positions. The switches are not connected to anything.
"After today, from time to time whenever I feel so inclined,
I will select one prisoner at random and escort him to the
switch room. This prisoner will select one of the two
switches and reverse its position. He must move one, but
only one of the switches. He can't move both but he can't
move none either. Then he'll be led back to his cell.
"No one else will enter the switch room until I lead the
next prisoner there, and he'll be instructed to do the same
thing. I'm going to choose prisoners at random. I may choose
the same guy three times in a row, or I may jump around and
come back.
"But, given enough time, everyone will eventually visit the
switch room as many times as everyone else. At any time
anyone of you may declare to me, 'We have all visited the
switch room.' and be 100% sure.
"If it is true, then you will all be set free. If it is
false, and somebody has not yet visited the switch room, you
will be fed to the alligators."
What is the strategy they come up with so that they can be free?
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Answer Posted / z
the problem is that the leader will never know whether the
switch was up or down at the beggining. So he has to wait
until he will switch it down 23 times(or 45, because if its
only 44 he wont know if the last prisoner has visited the
switch room, its the same thimg).But in case the switch was
down at the beginning he will have to wait forever for the
23th or 45th time and that will never happen. So there's no
way with this solution that he can be absolute sure(except
ofcourse if one day he switches it down for the 23th or 45th
time respectively)
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