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A \\emph{$\\Q$-trivial Bott manifold} of dimension $2n$ is a Bott manifold whose cohomology ring is isomorphic to that of $(\\CP^1)^n$ with $\\Q$-coefficients. We find all diffeomorphism types of $\\Q$-trivial Bott manifolds and show that they are distinguished by their cohomology rings with $\\Z$-coefficients. 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