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Pre-Championship Rehearsal - Logic Puzzles

At last month's rehearsal, four top athletes competed in two 400-metre qualifiers.

As the results were expected to be mislaid, various notes were taken to ensure the accuracy of the overall placings:

No one finished both races in the same position.
In both races, Sam beat the runner whose surname was Watson.
Billie Taylor came third in the second race, and Pat came last in the first race.
In the second race, the athlete whose surname was Arnold won, and the athlete whose surname was Bowler came last.
In the first race, Billie beat Jamie, but Jamie beat Sam.
Can you determine who finished where in each of the races?

Puzzle Copyright © Kevin Stone

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