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UKMT Junior Mathematical Olympiad, 2021

Combinatorics Difficulty 2.0 Junior Prove it United Kingdom

Amy, Bruce, Chris, Donna and Eve had a race. When asked in which order they finished, they all answered with a true and a false statement as follows:

Amy: Bruce came second and I finished in third place.

Bruce: I finished second and Eve was fourth.

Chris: I won and Donna came second.

Donna: I was third and Chris came last.

Eve: I came fourth and Amy won.

In which order did the participants finish?

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