Problem:
Two integers have a sum of . When two more integers are added to the first two integers the sum is . Finally when two more integers are added to the sum of the previous four integers the sum is . What is the minimum number of even integers among the integers?
Answer Choices:
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Solution:
The sum of two integers is even if they are both even or both odd. The sum of two integers is odd if one is even and one is odd. Only the middle two integers have an odd sum, namely . Hence at least integer must be even. A list satisfying the given conditions in which there is only one even integer is .
The problems on this page are the property of the MAA's American Mathematics Competitions