How Old Are the Guys? Math Puzzle

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How Old Are the Guys? Math Puzzle

Anton, Boyd, Chester, Dwight, and Eugene have the following to say about each others' ages.

Anton	Eugene is 27.
Boyd	I am 81.
Chester	Boyd is 61.
Dwight	Anton is 57. What Chester says is false.
Eugene	Boyd is older than Anton. Dwight is 30 years younger than Chester.

None of the guys is younger than 10 or older than 99.

Remarks made by anyone 50 or older are true, unless the age he gives is a perfect square.

Remarks made by anyone who is under 50 are false, unless his age is a perfect cube.

What are the ages of all of them?

Thanks to E.R. Emmet

Click to find the answer to this math puzzle.

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