UKMT Senior Challenge-IX
A box contains seven cards numbered from 301 to 307. Graham picks three cards from the box and then Zoe picks two cards from the remainder. Graham looks at his cards and then says “I know that the sum of the numbers on your cards is even”. What is the sum of the numbers on Graham's cards?
This problem is not original.This problem is part of this set .
The answer is 912.
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1 solution
There are 4 odd numbered and 3 even numbered cards. Since Graham is comfident that whatever combination that Zoe picked, it will always be odd. This can only happen if Graham had taken all the even numbered cards and Zoe are left with all the odd numbered cards.