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Two logicians are on holiday in the Alps when a mad scientist captures them. The mad scientist knocks them unconscious and then tattoos their forheads. When they awake, the mad scientist says with a sneer:

" At least one of your has a tattoo on your forehead. Maybe both of you do...I'm not telling. I will allow you to go free if you have a tattoo on your forehead. All you have to do is walk out that door.

However, if your walk out that door and you do not have a tattoo on your forehead, I will put you to to death. I will leave you in this room, and if you communicate with one another in any way, you will be put to death.

Every day at noon, I will have the door unlocked briefly. You can choose to leave then and only then if you think you have a tattoo on your forehead."

1. Does any one escape? and

2. How long does it take?

3. What is a Logician?

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[1] Yes. They both escape.

[2] They both walk out on Day 2.

[3] A logician is a student or scholar of logic.

Explanation.

On Day 1, each sees the tattoo on the other's forehead. Neither can leave, however. The tattoo each sees might be the only one.

On Day 2, both leave. They both reason that if the other had not seen a tattoo on Day 1, the other would have left [knowing there was at least one tattoo].

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I think they both would leave the first day (assuming they both have tattoos) because one thing I know about tattoos is that they hurt for at least a week, and might even scab over if they don't take care of it. Therefore, they would feel pain on their foreheads, and/or feel a scab :D

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especially on a place like the forehead,

because it's just skin, then bone, without much in between

so it's much more painful to get a tatoo on places like the forehead, knee, ribs, stuff like that

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They  both leave on day 2. The first day each one sees the other doesn’t leave, which proves he himself has a tattoo. Then the next day they both leave. 

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