Prison Puzzle

WilyTilt · #1 01-31-2007, 05:03 PM

I got inspired by Motorholdem's poker chip puzzle to post this one, which took me days to figure out. It's a bit harder.

Here's the situation. An Arab sultan has arrested 50 men accused of plotting against him, and decided to imprison them for life unless they can figure out a puzzle. All 50 will be separated by day and will never see each other, but every night one of them will be randomly picked and placed in a special cell, where in the corner there is a light bulb. He can turn on or turn off the lightbulb as he likes, and it will remain in that state until the next night. There's no other way to leave any message in the room. The prisoners are allowed one night to discuss a plan before they are separated and the puzzle starts.

The sultan tells them that when one of them can tell him for certain that every single prisoner has been in the room at least once, and can explain why, all of them will be freed. If he's wrong, then all of them will be executed.

Please post answers in white. Enjoy.

Five-Star · #2 01-31-2007, 05:05 PM

if only there was a subforum for PUZZLES AND GAMES..
alas i guess what should have been

djames · #3 01-31-2007, 05:10 PM

Designate person 1 as the only person who turns the light off. This person is never to turn the light on. Instruct each other prisoner to only touch the light once ... the first time they enter the room and see that the light is off, they must turn it on. When the designated person turns off the light for the 49th time, this person should tell the sultan and explain the plan.

WilyTilt · #4 01-31-2007, 05:11 PM

[ QUOTE ]
 Designate person 1 as the only person who turns the light off. This person is never to turn the light on. Instruct each other prisoner to only touch the light once ... the first time they enter the room and see that the light is off, they must turn it on. When the designated person turns off the light for the 49th time, this person should tell the sultan and explain the plan.

[/ QUOTE ]

If you've never heard this puzzle before, you win my deepest respect for being brilliant. [img]/images/graemlins/cool.gif[/img]

djames · #5 01-31-2007, 05:15 PM

Make it harder and ask for the expected number of days until the release of the prisoners...

Even harder still .. what's the probability they are released if they are all exactly 20 years old and all will live to exactly 80 years old (you can use 365 days in each year for simplicity)?

WilyTilt · #6 01-31-2007, 05:28 PM

[ QUOTE ]
Make it harder and ask for the expected number of days until the release of the prisoners...

Even harder still .. what's the probability they are released if they are all exactly 20 years old and all will live to exactly 80 years old (you can use 365 days in each year for simplicity)?

[/ QUOTE ]

Off the top of my head, would figuring out the number of days expected be the following:

49/(x/49) + 49/(x-1/49) ... + 49/(1/49), where x is the number of prisoners who haven't been counted yet.

Or am I missing something?

OneChipWarrior · #7 01-31-2007, 05:31 PM

[ QUOTE ]
 Designate person 1 as the only person who turns the light off. This person is never to turn the light on. Instruct each other prisoner to only touch the light once ... the first time they enter the room and see that the light is off, they must turn it on. When the designated person turns off the light for the 49th time, this person should tell the sultan and explain the plan.

[/ QUOTE ]

This doesnt make any sense to me. How will the designated person turn off the light for the 49th time? I thought you were only in the room to turn on or off the light one time.

deadbody · #8 01-31-2007, 05:34 PM

[ QUOTE ]
 Designate person 1 as the only person who turns the light off. This person is never to turn the light on. Instruct each other prisoner to only touch the light once ... the first time they enter the room and see that the light is off, they must turn it on. When the designated person turns off the light for the 49th time, this person should tell the sultan and explain the plan.

[/ QUOTE ]

How does he know that the same person hasn't been brought in twice. If I was the sultan as soon as I saw that only 1 person was turning the light off I'd start sending people back in a 2nd time before sending in someone else.

Great idea, but it can't work that way.

On sencond look you seem to have that covered, but I am still not sure it'll work that way

WilyTilt · #9 01-31-2007, 05:35 PM

[ QUOTE ]
[ QUOTE ]
 Designate person 1 as the only person who turns the light off. This person is never to turn the light on. Instruct each other prisoner to only touch the light once ... the first time they enter the room and see that the light is off, they must turn it on. When the designated person turns off the light for the 49th time, this person should tell the sultan and explain the plan.

[/ QUOTE ]

This doesnt make any sense to me. How will the designated person turn off the light for the 49th time? I thought you were only in the room to turn on or off the light one time.

[/ QUOTE ]

No, one person is randomly assigned every night, no matter if he's been there before.

TiK · #10 01-31-2007, 05:35 PM

[ QUOTE ]

This doesnt make any sense to me. How will the designated person turn off the light for the 49th time? I thought you were only in the room to turn on or off the light one time.

[/ QUOTE ]

Everybody except for the designated guy is to touch the light switch once and only once (no matter how many times they are brought into the room) and that is to turn the light on if they come in and find it off. The designated guy though is to turn the light off every time he goes into the room to find the light on. Since the 49 people are only turning the light on once, when the guy turns off the light 49 times, everybody will have been in the room once.