The premise is incoherent. As noted, they all see legislators with long noses and know how many they have seen, so there is nothing special about the day the Truon came visiting.

Second, they all know they are liars, nose or no nose, so they should have resigned immediately.

The only way the puzzle makes any sense is (1) the liars have a blind spot about their lies, and nobody ever gets on their case about the lies (nose or no nose), and (2) the legislature hasn't been meeting very long. The Truon just happened to show up before they would all have resigned anyway. So, you can't tell how many there were, because you don't know when they first met.

The blue-eyed islanders have the second problem.