Two simpler approaches to the same answer: approach (1) Simply put, normal behavior of the host(s) would be: Burne greets the 5 visiting mages Burne apprentice (Prishella) greets the 5 visiting apprentices Therefore answer is 5 approach (2) Each mage and apprentice greets between them everyone but themselves i.e. 10 people Therefore, the possibilities are 10+0, 9+1. 8+2. 7+3, 6+4, 5+5 everyone Burne asked gave a different number, therefore Burne himself must be one of the 5+5 combination If Burne is 5, then his apprentice must be the other 5 of the 5+5 combo.
#2 makes a lot of sense. I definitely think that all this debate just confirms that it was ambiguously worded. O well.