Magician's hat
Weekly problem 12 - 2007
Kan the magician can tell Roo that his cards add up to an even number. What is the sum of Kan's cards?
Kan the magician can tell Roo that his cards add up to an even number. What is the sum of Kan's cards?
Age
11 to 14
Challenge level
Problem
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?
If you liked this problem, here is an NRICH problem which is based on similar mathematical ideas.
Student Solutions
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
$12$.