Intelligence test(s)

[Prime Junta]

Here's a really, really nasty one. It took me days to figure this one out; let's see if any of you guys can do better.

A certain country that's not too keen on the Geneva conventions operates a prison far from the public eye. It's run by a sadistic and despotic warden, who also likes puzzles.

One day the warden called the 100 prisoners in his charge to the yard, and made them a little speech.

"Listen up, bitches! I'm getting bored here, so I've thought of a little entertainment.
"There's an unused cell in this prison. It contains a regular old wall clock, which is broken. The arms on it will never move of their own accord.
"Now, one day from now, you'll all be locked into your cells. You won't be able to talk to each other, send any messages to each other, or communicate with each other in any way.
"Then, I'll send a guard to pick one of you at random and take you to the cell with the clock.
"There, you'll have to turn the clock forward a half an hour, or back a half an hour -- your choice.
"After that, you'll be returned to your cell. Eventually, the guard will pick another random prisoner -- could be someone who's already been picked before -- and take him to the cell, with the same instructions.
"At any time, when leaving the cell with the clock, any one of you can ask to see me, in order to say to me: 'Every prisoner has been in the cell with the clock at least once.'
"If this statement is true, you'll all go free. Buh-bye. Have a good life, all that commotion.
"If this statement is false, you'll all be hanged, after which there will be a party, to which you're not invited.
"You have one day to discuss the situation between yourselves, after which the entertainment will commence.
"Any questions?"

So, here's the question:

Which strategy should the prisoners choose in order to be certain that they'll go free?

Quick summary of the salient facts:
* 100 prisoners.
* Cell with a stopped clock.
* Prisoners will be taken at random into the cell, and MUST turn the clock back OR forward a half an hour.
* No other communication allowed between them.
* Prisoners may be called into the cell more than once.
* What should they do to know that each prisoner has been in the cell at least once?

 

[POLYGON]

Does the prisoners know what time the clock is set initially?

 

[Bartacus]

Just keep doing this till their time is up -> If one of the prisoners has a life sentence, it's a problem off course.

edit: The first test -> Does anyone knows the next ones:

15 P in a R T
13 L in a B D
6 B to an O in C
12 S of the Z

I have solved everything else and I just want to find out the other answers.

 

[Prime Junta]

Does the prisoners know what time the clock is set initially?

No, they don't.

 

[Prime Junta]

Just keep doing this till their time is up -> If one of the prisoners has a life sentence, it's a problem off course.

That's a creative solution, but unfortunately these are all either lifers or condemned to death, so that's a non-starter in this case.

 

[VPeric]

12 S of the Z

Spoiler

12 Signs of the Zodiac

PJ - yeah, it's a tough one. Gonna have to give it a serious bit of thought one of these days.

 

[Bartacus]

Thanks VP! Now just 3 away from a perfect score.
Btw, I had to let it be explained to me what you're spoiler meant.

15 p of a r t is this:

Spoiler

15 players of a rugby team

 

[woges]

Does that clock have a day counter on it?

 

[Prime Junta]

No. It's an ordinary wall clock, with an hour hand, minute hand, 12 hour marks, and no other indicators.

 

[woges]

So it's impossible to be sure of counting above 24 from the first guy that enters?

 

[POLYGON]

Here's the best I thought of:
each prisoner should memorize the time the clock was set at the first time he enters, then he should move it forward half an hour,
then he will move it backwards the second time then keep moving the clock to the opposite direction fro the last time he enterd(1st forward, 2nd backward,3rd forward, etc...)
The first prisoner to find the clock at the time he memorized for three times should know that every prisoner has been inside at least once??????

explanation:say the 1st prisoner entered and found it 12 and moved it to 12:30
second will move it to 1
if the first is back again he will move it back to 12:30
so it's as if he didn't do anything, so it will never reach 12 again unless 48 prisoners have passed by

 

[woges]

I was thinking the first 2 times a prisoner entered he'd move it forward then alternate so you don't lose the bit of info that somebody has entered then once you hit around 200 half hours you know everyone's been in. It has holes because of that 12hr face though.

 

[Prime Junta]

So it's impossible to be sure of counting above 24 from the first guy that enters?

That's correct.

 

[Prime Junta]

Here's the best I thought of:
each prisoner should memorize the time the clock was set at the first time he enters, then he should move it forward half an hour,
then he will move it backwards the second time then keep moving the clock to the opposite direction fro the last time he enterd(1st forward, 2nd backward,3rd forward, etc...)
The first prisoner to find the clock at the time he memorized for three times should know that every prisoner has been inside at least once??????

explanation:say the 1st prisoner entered and found it 12 and moved it to 12:30
second will move it to 1
if the first is back again he will move it back to 12:30
so it's as if he didn't do anything, so it will never reach 12 again unless 48 prisoners have passed by

That won't work, because there are 100 prisoners.

Suppose the clock starts at 12.
Suppose the first 24 prisoners are called in in order, and then prisoner #1 is called in again -- it's at 12, and he'll move it back a notch.
Now, suppose prisoners 2-24 are called in twice, after which prisoner #25 is called in. Then prisoner #1 is called in again. It'll again be at 12, and now prisoner #1 will move it forward.
Then suppose prisoners 2-24 are called in twice, after which prisoner #1 is called in again. It'll be at 12 the third time, but only prisoners 1-25 will have been in the room. You can get the clock back to 12 any number of times with just 25 prisoners.

 

[woges]

even and 1/2 past even = on (positive)
odd and 1/2 past odd = off (negative)

Pick one man as counter he's the only man to turn the clock to an 'on' (or positive) state. The rest turn the clock to an off (or negative) state if it's the first time they have seen it on (otherwise they leave it). The counter (person) then counts to 100 'turn ons' and you're done. That solves that counting problem i saw before anyway.

 

[Lucky Day]

Oh i am sorry, i didnt know it was a scam.

yeah! quit scamming me, you scamming guy, you.

 

[VPeric]

(otherwise they leave it).

Thing is, they _have_ to move the clock, they can't leave it as-is.

 

[Arhu]

Thing is, they _have_ to move the clock, they can't leave it as-is.

They _can_ if they follow woges' instructions. They simply leave it in the state they found it in if it's not the first time they've seen it on. Example: If it's 12:30, they move it back to 12:00. If it's 12:00, they move it forward to 12:30. Both mean "on". Only the counter is allowed to move it to an "on state" from an "off state", effectively counting all 100 prisoners, because everyone else can change the status only once (from on to off, the first time they see it on).

To me that sounds like a possible solution, even if it means that on average everyone needs to go to the clock 100 times.

 

[VPeric]

Ah, "otherwise they leave it in the same state." Missed the implied bit there.

 

[Prime Junta]

even and 1/2 past even = on (positive)
odd and 1/2 past odd = off (negative)

Pick one man as counter he's the only man to turn the clock to an 'on' (or positive) state. The rest turn the clock to an off (or negative) state if it's the first time they have seen it on (otherwise they leave it). The counter (person) then counts to 100 'turn ons' and you're done. That solves that counting problem i saw before anyway.

We have a winner! Bravo, that was quick -- and this one is a real beast.