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.
This problem is taken from the UKMT Mathematical Challenges.