Logic Puzzles

D is about to answer (he knows his number) but is interrupted by A who knows his number.

Solution:

This puzzle is dumb

Sam wrote:

Solution:

This puzzle is dumb

The Warden

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 1 and 2, each of which can be in either up or the down 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 flip one switch when he visits the switch room, and may only flip one of the switches. Then he'll be led back to his cell.

"No one else will be allowed to alter the switches until I lead the next prisoner into the switch room. 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. I will not touch the switches, if I wanted you dead you would already be dead.

"Given enough time, everyone will eventually visit the switch room the same number of times as everyone else. At any time, anyone 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 all die horribly. You will be carefully monitored, and any attempt to break any of these rules will result in instant death to all of you"

What is the strategy they come up with so that they can be free?

Not-quite-there method:

One of the prisoners is designated as the counter. Each of the others will have one rule to follow: the first time they go in the room and see that switch 2 is in the down position, they will switch it to up. Otherwise they will toggle switch 1. Each time the counter goes in the room and sees switch 2 in the up position he will switch it to down. When he has done this 22 times he knows that either a) all 22 other prisoners have been in and switched 2 to up, or b) Only 21 of the others have been in but switch 2 started in the up position.

Jamie wrote:Think you could be on the right track though Tom. Just that last missing bit of the jig-saw. I think it could be something to do with the fact, that at some point, they'll all have gone in to the room the same number of times. Your solution doesn't seem to make use of that information, but, can't help but feel it's significant, otherwise, why would they mention it?

Solution:

As above, there is one counter and the other 22 follow this procedure: The first *two* times they see switch 2 in the down position, they switch it up. Otherwise they just flip switch 1.

The counter flips switch 2 down every time he sees it up and when he's done that 44 times he knows that everyone else has been in. In fact he knows that most of them have been in at least twice. It's possible that one of them may have only been in once but that's enough.

The flipping of switch 1 is completely irrelevant to tracking the prisoners. It's just there for not flipping switch 2. It would be an equivalent problem to say there's one switch and the prisoners can choose whether to flip it or not each time.