Lets say, If A was wearing black cap, he can see B and C wearing red caps. since A , B and C are all raising hands B and C could have easily claimed to be wearing red had with simple logic. A with black hat would raise hand looking at B and C, but B and C could raise hands only at looking each other. So B and C could easily conclude that each were raising hands looking at each other. But in this situation since A, B and C are all wearing red hats and all raising hands, A would think B and C were raising hands looking at each other, C would think A and B were raising hands looking at each other and B would think A and C were raising hands looking at each other. None could see black colored cap to comclude that ones cap was red. so as A was more smart than B and C, A claimed to have red cap.