Ms Math's kindergarten class has 16 registered students. The classroom has a very large number, N, of play blocks which satisfies the conditions:
(a) If 16, 15, or 14 students are present in the class, then in each case all the blocks can be distributed in equal numbers to each student, and
(b) There are three integers 0 < x < y < z < 14 such that when x, y, or z students are present and the blocks are distributed in equal numbers to each student, there are exactly three blocks left over.
Find the sum of the distinct prime divisors of the least possible value of N satisfying the above conditions.
A knight remembers another
banquet he had
"Oh, that was another really nice banquet; all the liars and the knights of the kingdom were there, even the village fool. We all ate and drank and at the end of it, the king asked each one of us to make a few statements about a few other people, meaning, to say if they are liars or knights. The same number of statements were said about each one of us, and each one made the same statements that the one before him made. I just don't remember what the village fool said this time.
"That's ok", you say, "you can know what he said even without trying to remember it."
How can he do that?