  It is known that the formation of apparent horizons with non-spherical
topology is possible in higher-dimensional spacetimes. One of these is the
black ring horizon with $S^1\times S^{D-3}$ topology where $D$ is the spacetime
dimension number. In this paper, we investigate the black ring horizon
formation in systems with $n$-particles. We analyze two kinds of system: the
high-energy $n$-particle system and the momentarily-static $n$-black-hole
initial data. In the high-energy particle system, we prove that the black ring
horizon does not exist at the instant of collision for any $n$. But there
remains a possibility that the black ring forms after the collision and this
result is not sufficient. Because calculating the metric of this system after
the collision is difficult, we consider the momentarily-static $n$-black-hole
initial data that can be regarded as a simplified $n$-particle model and
numerically solve the black ring horizon that surrounds all the particles. Our
results show that there is the minimum particle number that is necessary for
the black ring formation and this number depends on $D$. Although many particle
number is required in five-dimensions, $n=4$ is sufficient for the black ring
formation in the $D\ge 7$ cases. The black ring formation becomes easier for
larger $D$. We provide a plausible physical interpretation of our results and
discuss the validity of Ida and Nakao's conjecture for the horizon formation in
higher-dimensions. Finally we briefly discuss the probable methods of producing
the black rings in accelerators.
