The 16 inhabitants of Knightsland are either knights or knaves (always tell the truth or always lie). Some, or all of them, meet every Sunday at the local restaurant and sit around a circular table, in equal distances from each other, in order to discuss their pending matters and then have lunch. Not all of them are always present. Also in the current meeting, not everyone was present. Jason, who is impatient and always in a hurry to finish things off and start eating, says: “We are already 11, so let’s start”. Harry, who was sitting right opposite to him, says: “No, we are not 11, we are 12 – apparently you don’t know how to count!!” The two of them were just about to start fighting but were calmed down by their left and right neighbors. Brandon, who was sitting calmly, says: “Calm down gentlemen; there were times in the past when we were even fewer! In fact, our today’s number is a product of two numbers, of which the smaller is the number we were in our smallest meeting!” Finally their gathering went out of control and any of the present members was blaming his adjacent neighbors for being liars.
How many Knightslanders were gathered this time and what is the smallest number that they ever in the past?
I understand we have 3 statements that can be either true or false, so we have to make a truth table.
The only thing I managed to deduce is that since Harry is sitting opposite to Jason, their current number is even. Furthermore, since Harry and Jason were calmed down by their right and left neighbors, assuming these are different for each, their current number is minimum 6. If Brandon was sitting calmly, can we also assume he was not one of the neighbors (who were trying to calm down the others)?
Anyway, I don't know how to continue... logic is not my favorite topic!
Any help is much appreciated!