Puzzle provided by Noetic Learning Math Contest
There are 7 number cards, each with a number from 1 to 7, in a box.
Henry took out 3 cards and Mathew took out 2 cards. Henry looked at
his 3 cards and said to Mathew, “The sum of the numbers on your 2
cards must be an even number.” Mathew thought for a minute and
said, “Then I know the sum of the numbers on your 3 cards.” What is the
sum of the three numbers on Henry’s cards?
© 2013 National Council of Teachers of Mathematics
http://illuminations.nctm.org
Solution: 12.
The sum of Mathew’s two number cards is an even number. That
tells us that Mathew’s two numbers have to be both even or both
odd. Henry found out this from looking at his cards. That means the
4 cards that don’t belong to Henry have to be all odd or all even.
Therefore, they have to be 1, 3, 5 and7. Henry must have 2,4 and 6.
Therefore, the sum of Henry’s numbers is 12.
© 2013 National Council of Teachers of Mathematics
http://illuminations.nctm.org