subhojit saha
2004-10-07 16:34:37 |
switches puzzle
This one was recently given on Car Talk, and it's been making the rounds right now also...
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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nikki
2004-10-07 17:00:06 |
Re: switches puzzle
First of all, please read the FAQ page. Under the first subject, "Are there any rules to this site?" you will see the following paragraph:
"We also ask that you refrain from posting problems on the forums, since that upsets the overall structure of the site."
I understand you are new and probably didn't realize this. Now that you know, please don't do it again. Thank you.
Second, there is already a very similar problem on this site. It is called "Smart prisoners always get a break" In the future, before properly submitting a problem through the queue, it is a good idea to see if a similar problem exists.
Have fun here! =) |
