Question

Gar the Magician wrote each of the numbers from 1  to 7, one on each of seven cards, and placed them in his hat. He offered the hat to two other magicians, Kan and Roo. Kan took, at random, 3  cards from the hat and Roo took 2  cards (so that there were 2  cards left in the hat). Kan told Roo: "I can deduce that the sum of the numbers of your cards is even". What was the sum of the numbers on Kan's cards?

Answer 1

Kan must know for sure that Roo's cards are either both even or both odd. The only way he can be sure of this is if he's selected the three even cards leaving Roo only odd-numbered cards. Therefore Kan has cards 2, 4  and 6  and the sum of his cards is 12.