Math Riddles

Question: A man wanted to enter and exclusive club, but did not know the password to get in. He waited by the door and listened. The doorman said "Twelve" and the other man said "Six" and was let in. A second member came up and the doorman said "Six" to which the member replied "Three" and was let in. The man went up and the doorman said to him "Ten" the doorman said "Five" but was not let in. Why?

Question: Joe deals himself and his friend John some cards from a deck of cards (not the same amount). If John gives Joe some cards Joe will have 4 times as many cards as John. If Joe gives John the same number of cards he will have 3 times as many cards as John.

How many cards does each man have and how many cards do they trade?

Question: If you have a rope around a soccer ball and the moon, which rope would have to increase in length more to create a one meter gap between the rope and the soccer ball/moon?

Question: The warden of a circular jail is extremely hyper one day so he begins running around opening cells. The jail has 100 cells numbered from 1 to 100. He runs in a circle and opens all of the cells. Next he runs around and closes every 2nd cell (starting with cell 2, 4, 6 , etc.). If a cell is open he closes it and if a cell is closed he opens it. When he finishes running by all 100 cells he opens/closes every 3rd cell (starting with 3, 6, 9, 12 etc.), then every 4th cell (starting with 4, 8, 12, etc.) and so on. He does this until he goes around and only changes the 100th cell.

When he is done what cells will be open?

Question: There are 100 passengers boarding a 100 passenger airplane. When passenger 1 gets onto the plane, he is dissoriented, so he randomly picks a seat. Each of the remaining passengers (2, 3, 4, etc.) get onto the plane and take their seat if it is available or picks one of the remaining seats at random if it is not.

What is the chance that the last passenger (passenger 100) will get his seat?