AI. Census Taker's Puzzle

The solution to the problem of the Three Gods: one always tells the truth; one always lies; one sometimes lies and sometimes tells the truth. When asked which is which, the one of the left says the one in the middle is the god of truth. The one in the middle says he sometimes lies and sometimes tells the truth. And the god on the right says the god in the middle is the god of falsehood. Who is who?

 
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The Math Factor
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