23 囚犯問題 - 拼圖

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.'

"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."

There exists a strategy such that, if the prisoners adopt it,
they are guaranteed to be set free (given enough time). What
is the strategy?

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