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What order

A plane was returning from the Olympic Games with five athletes who placed first through fifth in an event. They made the following statements:
A: “I was not the last”
B: “C was the third”
C: “A was behind E”
D: “E was second”
E: “D was not the first.”
On account of modesty or for some other reason, the gold and silver medallists lied. The three worst athletes told the truth.
What order did they all place in?
A`s statement must be true; if he is lying, he is last and he is also first or second, which is contradictory. So A is third or fourth. If D is telling the truth, E is lying and D is first and is lying, which is contradictory. So E is not second, and D is first or second. If E is lying, D is first and E is second. But D is lying when he says E is second. Therefore, E is telling the truth, which makes him third, fourth or fifth. D is not the first, but second. Only B or C can be first. If B is not first, since he is also not second he is telling the truth, and C is third, and cannot be first either, which is impossible. Then B is first and C is not third. C, being neither first nor second, is telling the truth that A is behind E. E is third, A is fourth, and C is fifth. The athletes places in order; B,D,E,A,C.

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