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  Logic
 
Pizza Party
 
Q Four friends left one slice of pizza in the kitchen and went into the next room to play games. During the next half hour, each friend left the room for a few minutes and then returned. At the end of the hour, all four went back into the kitchen and found that the last slice of pizza was gone.

Use the following statements to figure out who ate it. Only one of the following statements is true.

Linda: "Mike ate it."
Mike: "Olive ate it."
Ned: "Who me? Can't be."
Olive: "Mike is lying when he says I ate it."


 
A Ned ate the last slice of pizza. It's impossible for Linda's, Mike's, or Ned's statement to be the only one that is true. (If Linda's statement that Mike ate it is true, then Ned's statement is also true. If Mike's statement that Olive ate it is true, then Ned's statement is also true.) If Ned's statement is true, then no one else's statement can be true. Therefore, Ned's statement is false.

Source: Inspired by brainteaser.com #62.