The problem looks particularly simple. But notice that you have a shortage of an equation. You have three things to find - the three normal forces. And you have only two equations - one for translational equilibrium of the rod and one for the rotational equilibrium. So what's the problem?

I asked this at several places and they blatantly said that the system is not solvable. But to me, non-solvability means non-uniqueness. I am not able to understand how is the system non-unique. Am I not providing all the required information? It's also surprising that the same set of information works properly with a two support system. What's happening in the transition from two to three?