### Brain Teasers

# Four People in a Race

John, Paul, George, and Ringo all enter a race, but there is nobody at the finish line to judge the ending. When the judge finally shows up to award the prize for coming in first, these are the statements the four of them make:

John: I was neither first nor last.

Paul: I did not finish last.

George: I won the race!

Ringo: I came in last.

The judge starts to hand George the prize, when Yoko, who was watching the race, says, "Exactly one of these four is lying."

To whom should the judge grant the prize?

John: I was neither first nor last.

Paul: I did not finish last.

George: I won the race!

Ringo: I came in last.

The judge starts to hand George the prize, when Yoko, who was watching the race, says, "Exactly one of these four is lying."

To whom should the judge grant the prize?

### Answer

The prize should go to Paul.If John is lying, then George and Ringo would be telling the truth, which would mean John was not lying, so he can't be the liar.

If Paul was lying, then Ringo would also be lying, so he must be telling the truth, as well.

So we now know that neither John nor Paul finished last. If Ringo was lying, then George would have finished last, which would mean that he was lying, as well. So Ringo can't be lying.

This leaves George as our liar, so we know George did not finish first. Neither did Ringo (he finished last), nor did John (he finished neither first nor last). Therefore, Paul won the race!

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