Three spies, suspected as double agents, speak as follows when questioned:

Albert: “Bertie is a mole.”
Bertie: “Cedric is a mole.”
Cedric: “Bertie is lying.”

Assuming that moles lie, other agents tell the truth, and there is just one mole among the three, determine:

1.) Who is the mole?
2.) If, on the other hand there are two moles present, who are they?

Bill, Ken, and Mark are, not necessarily in this order, a quarterback, a receiver, and a kicker.  The kicker, who is the shortest of the three, is a bachelor.  Bill, who is Ken’s father-in-law, is taller than the receiver.

Who plays in which position?

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?

There are three boxes, one contains only apples, one contains only oranges, and one contains both apples and oranges.  The boxes have been incorrectly labeled such that no label identifies the actual contents of the box it labels.  Opening just one box, and without looking in the box, you take out one piece of fruit.  By looking at the fruit, how can you immediately label all of the boxes correctly.

Which box did you open and how can you be sure to label all boxes correctly?

A girl was sitting in her hotel room when she heard a knock on the door. She opened the door and found that a man was standing outside.
The man said, “Oh! I am really sorry, I thought this was my room.”
He then walked through the corridor to the elevator. The girl did not know the man. She closed her door and called the security asking them to apprehend the man.
What made her suspicious of that man? He might have been genuinely mistaken.

Suppose there are twin brothers; one which always tells the truth and one which always lies.  What single yes/no question could you ask to either brother to figure out which one is which?

Assume 9 is twice 5; how will you write 6 times 5 in the same system of notation?

What is the four-digit number in which the first digit is one-third the second, the third is the sum of the first and second, and the last is three times the second?