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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 / dave peck
The team nominates a leader. The group agrees upon the
following rules:
The leader is the only person who will announce that
everyone has visited the switch room. All the prisoners
except for the leader will flip the first switch up when
possible, but only for their first visit to the room.
If the first switch is already up, or they have already
flipped the first switch twice, they will then on flip the
second switch. Only the leader may flip the first switch
down, and if the first switch is already down, then the
leader will flip the second switch. The leader remembers how
many times he has flipped the first switch down. Once the
leader has flipped the first switch down 23 times (once for
each of the other 22 prisoners, and once just in case it
started in the up position), he announces that all have
visited the room. It does not matter how many times a
prisoner has visited the room, in which order the prisoners
were sent or even if the switch was
flipped up by the warden.
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