# Blog

## The speediest cyclist

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Alice, Bernice and Claire are all speedy bike riders. They decided to race against each other to find out who is fastest cyclist.

They ran three races together. In two races, Alice beat Bernice. In two races, Bernice beat Claire.

Knowing this, is it possible that Claire beat Alice in one race? Could Claire have beaten Alice in two races? What about in all three?

Claire can beat Alice two times, but not three.

If Alice beats Bernice and Bernice beats Claire, then the result must be A, B, C. This must happen in at least one race.

In the other two races, Alice must beat Bernice once, and Bernice must beat Claire once. But these don’t have to be the same race!

In the race where Alice beats Bernice, the order could be C, A, B, and Claire can beat Alice.

In the race where Bernice beats Claire, the order could be B, C, A and once again Claire can beat Alice.

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