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I think this could have been worded slightly more clearly. I took the view that for each of the three numbers being considered three of the statements were true (and three of them false), and that seemed to work.

This Python program runs in 35ms.

Solution:The sum of the three numbers is 1135.The three numbers themselves are:

It wasn’t clear to me if candidate numbers should contain exactly one digit 3. I considered numbers with multiple 3 digits in my program, and, as it turns out they could have been excluded at the start.