Brain Teasers
1. You are one of 20 prisoners on death row with the execution date set for tomorrow.
Your king is a ruthless man who comes to your cell today and tells you:
"I'll give you prisoners a chance to go free tomorrow. You will all stand in a row (queue) before the executioner and we will put a hat on your head, either a red or a black one. Of course you will not be able to see the color of your own hat; you will only be able to see the prisoners in front of you with their hats on; you will not be allowed to look back or communicate together in any way (talking, touching.....)
(The prisoner in the back will be able to see the 19 prisoners in front of him or her. The one just ahead will be able to see 18 and so on).
Starting with the last person in the row (the one who can see everybody in front of him), each will be asked a simple question: WHAT IS THE COLOR OF YOUR HAT?
Each person will be only allowed to answer "BLACK" or "RED". If any person says anything else you will ALL be executed immediately.
If a prisoner guesses the right color of the hat on his own head he is set free, otherwise he is put to death. Then I will move on to the one in front of him and ask him the same question and so on ...
Well, good luck tomorrow, HA HA HA HA HA HA!"
Now since you all can communicate freely during the night, can you find a way to guarantee the freedom of some prisoners tomorrow? How many?
2.  Three boxes are all labelled incorrectly, and you must get the labels right. The labels on the boxes read as follows:
[box 1] nails
[box 2] screws
[box 3] nails and screws
To get the information that you need to move the labels to the correct boxes, you may remove a single item from one of the boxes. You may not look into the boxes, nor pick them up and shake them, etc.
Can this be done? If so, how? If not, why not?