If the arrangement is
ABC or BAC
And
If they knew all the statements in the form of “I know whether x or not x” and if Anna was logical (and so would realize the only way for no-one to be embarrassed and know the youngest at the same time is to ultimately keep silent). And Bob and Charlie too (meaning they would realize that they need to state their information.)
Then:
Since if ABC then A is the oldest and does not state this. B states C is not older than A and the configuration could be ABC, BAC, ACB for their minds. C states that C is not in the middle and the only possible configurations are ABC or BAC. This way they know C is the youngest however A and B’s position is not known.
Or
If Anna being logical keeps completely silent about anything the logician tells her. If BAC they will know C is younger than A and is not in the middle. This reveals his position. Although A would know B’s age B would not be embarrassed because he wouldn’t know this fact and for Charlie it can either be BAC or ABC in his eyes.
Then
Zorro is a good logician.
Zorro is a not good logician if the youngest be:
BOB or ALICE because ACB means that they would work out A is the oldest if they were to work out B even if A doesn’t state her information- one has to know C is younger than A and in the middle to know B. For CAB there are insufficient clues for the position B. If BCA it has to be known that A is younger than C and C is in the middle but then they can deduce B is the oldest. Finally if CBA it means again A has to be known to be younger than C but still A’s position is not specified.