A woman went into a bank to cash an insurance refund check. By mistake the teller gave her dollars for cents and cents for dollars. She put the money in her purse but accidentally dropped a nickel on the floor. When she got home, she found that she had exactly twice the amount of the check she had cashed. She didn't have any money in her wallet before going to the bank. What was the exact amount of that check?
The amount must have been $31.63. She received $63.31. After she dropped a nickel there would remain the sum of $63.26, which is twice the amount of the check.
This is impossible to solve, because if I were telling the truth, then I would be lying, which doesn't make sense since I am telling the truth. If I am lying, then what I said was true and that doesn't make sense either.