  We give a model of the higher-dimensional spherically symmetric gravitational
collapse of a dust cloud in Einstein-Gauss-Bonnet gravity. A simple formulation
of the basic equations is given for the spacetime $M \approx M^2 \times
K^{n-2}$ with a perfect fluid and a cosmological constant. This is a
generalization of the Misner-Sharp formalism of the four-dimensional
spherically symmetric spacetime with a perfect fluid in general relativity. The
whole picture and the final fate of the gravitational collapse of a dust cloud
differ greatly between the cases with $n=5$ and $n \ge 6$. There are two
families of solutions, which we call plus-branch and the minus-branch
solutions. Bounce inevitably occurs in the plus-branch solution for $n \ge 6$,
and consequently singularities cannot be formed. Since there is no trapped
surface in the plus-branch solution, the singularity formed in the case of
$n=5$ must be naked. In the minus-branch solution, naked singularities are
massless for $n \ge 6$, while massive naked singularities are possible for
$n=5$. In the homogeneous collapse represented by the flat
Friedmann-Robertson-Walker solution, the singularity formed is spacelike for $n
\ge 6$, while it is ingoing-null for $n=5$. In the inhomogeneous collapse with
smooth initial data, the strong cosmic censorship hypothesis holds for $n \ge
10$ and for $n=9$ depending on the parameters in the initial data, while a
naked singularity is always formed for $5 \le n \le 8$. These naked
singularities can be globally naked when the initial surface radius of the dust
cloud is fine-tuned, and then the weak cosmic censorship hypothesis is
violated.
