SOLUTION: A group of students disagree, and think that there must be a set of 3 consecutive numbers whose sum is not a multiple of 3. Use sound mathematical reasoning to convince them that t
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Question 281406: A group of students disagree, and think that there must be a set of 3 consecutive numbers whose sum is not a multiple of 3. Use sound mathematical reasoning to convince them that they must be wrong. Answer by dabanfield(803) (Show Source):
You can put this solution on YOUR website! Let x be the smallest of the three integers. Then the next two consecutive integers are x+1 and x+2.
Their sum then is:
x + (x+1) + (x+2) =
3x + 3 =
3*(x+1)
Since the above has a factor of 3 the sum is always divisible by 3.
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