A cylindrical box is divided into three equal-volume, pieshaped regions-A, B, and C-by vertical partitions that allow the transfer of energy but not of particles from one region to another. Each region shares a partition with the other two. Each region contains 13 particles, and the system contains 39 energy units, initially all located in region \(\mathrm{A}\). If each particle-partition collision transfers one energy unit, is it possible for the system to evolve to its most probable state in

(a) 18 collisions,

(b) 27 collisions,

(c) 29 collisions?