100 prisoners are stuck in the prison in solitary cells. The warden of the prison got bored one day and offered them a challenge. He will put one prisoner per day, selected at random (a prisoner can be selected more than once), into a special room with a light bulb and a switch which controls the bulb. No other prisoners can see or control the light bulb. The prisoner in the special room can either turn on the bulb, turn off the bulb or do nothing. On any day, the prisoners can stop this process and say "Every prisoner has been in the special room at least once". If that happens to be true, all the prisoners will be set free. If it is false, then all the prisoners will be executed. The prisoners are given some time to discuss and figure out a solution. How do they ensure they all go free?
A boy and a girl are sitting on the porch.
"I'm a boy," says the child with black hair.
"I'm a girl," says the child with red hair.
If at least one of them is lying, who is which?
A bag contains 64 balls of eight different colours. There are eight of each colour (including red). What is the least number you would have to pick, without looking, to be sure of selecting 3 red balls?
The first person saw the bridge step on it and crossed,
the second person saw the bridge did not step on it but crossed,
the third person did not see the bridge did not step on it but crossed.
Who are these people?