What is the sum of the three smallest integers with the same mean, median, and range?
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Let the numbers be a , b , c . Clearly 2 a + c = b or else the median will not equal the range. Therefore we can represent the numbers as b − x , b , b + x . Now note that 2 x = b or else the range will not equal the median. Therefore the numbers are 2 1 b , b , 2 3 b . The smallest integer b that makes all these values integer is clearly b = 2 , so our numbers are 1 , 2 , 3 and the answer is 1 + 2 + 3 = 6 .