Newton's cradle is a classical example of a one-dimensional impact problem. In the early 1980s the naive perception of its behavior was corrected: For example, the impact of a particle does not exactly cause the release of the farthest particle of the target particle train, if the target particles have been just in contact with their own neighbors. It is also known that the naive picture would be correct if the whole process consisted of purely binary collisions. Our systematic study of particle systems with truncated power-law repulsive force shows that the quasibinary collision is recovered in the limit of hard core repulsion, or a very large exponent. In contrast, a discontinuous steplike repulsive force mimicking a hard contact, or a very small exponent, leads to a completely different process: the impacting cluster and the targeted cluster act, respectively, as if they were nondeformable blocks.