Puzzler of the week

[Scott MacLean]

This week's puzzler:

This puzzle has been making the rounds of Hungarian mathematicians' parties.

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."

Here's the question:

What is the strategy the prisoners devise?

Last week's puzzler:

A family of four and their dog are trapped on an island, when rising floodwaters tear out the bridge that they had used just a few hours earlier.  When they had just given up hope the son says, "I've got a small boat and oars."

But their joy was short-lived. The manufacturer�s instructions printed on the boat stern tell that the boat can carry only 180 pounds.

The dog is the only one who can swim.

The father weighs 170. The mother says she weighs 130 but it�s more like 155. The son is 90 pounds, the daughter is 80, and the dog is 15.

Here�s the question: is there any way, which the family can be saved? And if so, what�s the fewest number of crossings they have to make to save everybody?

Last week's puzzler answer:

The boy and the girl row over to the mainland. That's 170 pounds. One of them comes back. Doesn't matter which one. The next trip the mother and the dog row to safety. So now we got one of the kids over there, the mother and the dog. But now the other kid comes back. So the only two that have reached safety so far are the mother and the dog. The boy and the girl row over again. One of them comes back. The father rows over. The other kid comes back to the island and now the two kids row to safety together. And then when they get there, they look for the car. That's nine crossings.

_______________________
Scott MacLean
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