Jenny's logic
Weekly Problem 52 - 2009
How did Jenny figure out that Tom's cards added to an even number?
How did Jenny figure out that Tom's cards added to an even number?
Age
11 to 14
Challenge level
Problem
Jenny and Tom have a set of cards numbered 1-7. Jenny chose three cards at random, and Tom chose two of the remaining cards. Jenny told Tom: "I can deduce that the sum of the numbers of your cards is even". What was the sum of the numbers on Jenny's cards?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: 2, 4 and 6
Jenny must know for sure that Tom's cards are either both even or both odd.
1 2 3 4 5 6 7
4 odd numbers and 3 even numbers
So Jenny must have taken the 3 evens and left the 4 odds