  A Bott manifold is a closed smooth manifold obtained as the total space of an
iterated $\C P^1$-bundle starting with a point, where each $\C P^1$-bundle is
the projectivization of a Whitney sum of two complex line bundles. 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. As a
consequence, we see that the number of diffeomorphism classes in $\Q$-trivial
Bott manifolds of dimension $2n$ is equal to the number of partitions of $n$.
We even show that any cohomology ring isomorphism between two $\Q$-trivial Bott
manifolds is induced by a diffeomorphism.
