Brainteaser #2 again.

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Mrlucky77 wrote on 2010-12-03 22:23

Because I need too add more details and I don't wanna add to the thread cause it's already long.

100 PERFECT LOGICIANS are summoned by some gods as a test of their abilities. The gods paint green paint on one or more logician(s) foreheads. Then the logicians are told three things:

1. At least one logician will have their forehead painted green.

2. As soon as you realize your forehead is painted green, you must leave the room.

3. Everyone in this room is a perfect logician. They have the same knowledge power as you, therefore they do not make mistakes in logic.

However, the gods have a sense of humour and decide to paint EVERYONE'S forehead green.

YOU, the reader, must figure out this.

What happens? What I mean by this is you must describe when a logician or logicians leave the room.

The bonus question is, WHY?

Why do the logicians leave? How do they figure out that their forehead is painted green? Tell me your thought process behind your "What happens" answer.

Quote from Trigger;236367:
Given that you cannot see your own forehead, and that the logicians cannot communicate with each other ("no communication" means, quite literally, nothing -- looks, hand gestures, etc.), it is completely impossible for anything to happen in that room as a result of a logician realizing that his forehead has been marked. You're going to need to provide a LOT more details on this scenario, namely the following:

1. Is there any reflective material in the room?

No, there is no material, only opaque, regular walls.

2. Is the mark detectable by touch?
3. Are the logicians free to move around the room?
4. Is there any communication with the outside world?

Logicians cannot move around, they must sit in their chair and can only look around. The room is isolated, so no, there is no communication at all.

5. What is the mark's color and the logicians' skin color?

The mark is green, so it's visible on all people's foreheads.

6. How close are the logicians' seats to one another (wide circle, narrow circle, etc.)?

All logicians sit in one big circle, but close enough so that one can clearly see another's forehead.

7. What color is the light in the room?

White light.

8. What material are the walls, floor, and ceiling made of?

They're drywalls so yeah. The floor is carpet, the chairs are of wood.

9. Can the logicians do ANYTHING other than sit still and turn their heads to look around? (blinking leads to people suggesting Morse Code...)

The logicians cannot do anything other than sit still and turn their heads to look around. No communication.

HINT: This problem is a LOT EASIER if you imagine it with <100 people instead.

What this means? I won't tell.

Post any questions you have in the thread. PM me your answers.
[SIZE="7"]EDIT: I forgot to add this:[/SIZE]

The gods will turn off the light long enough for any logician to leave the room. The logicians have a few minutes every time the light is turned on to see if anybody has left, and whose foreheads are green/not. They will repeat this process until everyone in the room's foreheads are not green. aka everyone leaves.
Ruquion wrote on 2010-12-03 22:43

Quote from Ruquion:
Although this is a "test" set by the gods, there is no way to clear it.
As perfectly logical individuals, they will just leave the room instantly.

Quote from Mrlucky77:
Nice try, but there is a procedure for this exact situation, where all logicians can decide when to leave and how to determine who does not have a green forehead.

What are the conditions for the Logicians to clear the test?
Also, is it possible for them to see their reflection in the other Logicians' eyes?
WiseAz wrote on 2010-12-04 21:11

Are logicians whose forehead is not painted green allowed to leave the room?
Mrlucky77 wrote on 2010-12-04 21:29

No, they cannot leave the room until all the ones whose forehead is painted green leaves the room. Remember, the logicians cannot die as they are under the supervision of the gods.
WiseAz wrote on 2010-12-04 21:36

Do the lights ever go off for any reason other than when a person leaves?
Time wrote on 2010-12-04 21:55

Oh, it has to be PM...
Mrlucky77 wrote on 2010-12-04 22:25

Quote from WiseAz;237451:
Do the lights ever go off for any reason other than when a person leaves?

Actually, the lights turn of SO people can leave.
psyal wrote on 2010-12-05 00:27

Hey, I edited my solution, but your inbox is full so I can't submit it...
Mrlucky77 wrote on 2010-12-05 00:37

I deleted useless stuff from my inbox. Sorry bout that.
Ruquion wrote on 2010-12-09 12:57

Thought about this for a while, still don't see why my solution is wrong...
Kueh wrote on 2010-12-09 16:13

Users found this page by searching for....jeeze.
Justified wrote on 2010-12-10 13:37

My theory -

Logicians first assume that their forehead is not green. They then work to find out if it is green, or to affirm that it is not.

With 2 logicians...
B assumes that he is not green.
B sees that A is green. Therefore B is not required to be green, and does not leave the room.
--- Same for A.
Since neither person leaves the room, they both know that they are green.

With 3 logicians...
C assumes that he is not green.
C sees that A and B are green. Therefore C is not required to be green, and does not leave the room.
If C is not green, then A and B would only be looking at each other, resulting at the above described scenario in which both leave the room. C is green, therefore the above does not occur since A and B both see two green people.
Since nobody leaves the room, they all know that they are green.

With 4 logicians...
D assumes that he is not green.
D sees that A, B, and C are green. Therefore D is not required to be green, and does not leave the room.
If D is not green, then A, B, and C would only be looking at each other, resulting at the above described scenario in which all three leave the room. D is green, therefore the above does not occur since A, B, and C all see three green people, not two.
Since nobody leaves the room, D knows that he is green.

In essence, a logician removes himself from the population when assuming he is not green. By observing that nobody else leaves, he can be sure that his assumption is wrong. With less than four people, all of them will know at once. With more than three people, only one will.

Seems to have some flaws, but not really in the mood to theorize/work it out any further. I still think it could work up to 100 though.

The thing I don't like about my theory is that all logicians are equal, thus it's impossible for any less than the entire group to come to a conclusion at any given moment, since they are all in identical situations with identical brainpower. Thus, having lights turned off to allow people to leave is unnecessary. Whether this is a flaw in my answer or in the riddle (or both), I don't know.
psyal wrote on 2010-12-10 23:28

The thing is, it is not said anywhere that the logicians are equal. Perfect logician are also able to think faster or slower than other people; the only thing in common is that their logic is flawless.

Also, I believe it says to PM him the answers, so that people can read the thread and still send in answers without having to have seen someone's solution, therefor giving them an advantage.