SOLUTION: 1. Is it possible to find four consecutive integers whose sum is 165? why? 2. Is it possible to find two consecutive odd integers when sum is 31? why?

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Question 531849: 1. Is it possible to find four consecutive integers whose sum is 165? why?
2. Is it possible to find two consecutive odd integers when sum is 31? why?
Answer by htmentor(1343) About Me  (Show Source):
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1. Is it possible to find four consecutive integers whose sum is 165? why?
2. Is it possible to find two consecutive odd integers when sum is 31? why?
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1. Let n = the smallest integer. Then the other three are n+1, n+2, n+3
The sum is 4n + 6. Since the sum is even, it can never equal 165.
2. No. The sum of odd integers is always even.