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A set of six distinct positive integers has a mean of 8, a median of 8 and no term greater than 13. What is the least possible value of any term in the set?

 Mar 1, 2016
 #1
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first we have 8*6 as the total value of the set of number (no.)

and we have 8 as the medium of the set of no.,so the middle two no. is 8*2=16, as each of the set no. is unqiue, so the middle to number is 6 and 10, _ _ 6 10 _ _ and as each no is not greater than 13 , the greatest no. is 13, so we have _ _ 6 10 _ 13 by subtraction, we have 48-13-16=19, we can have 9 between 10 and 13 , then 10 leave , we can make the least number by subtracting 8 from 10 , so we get 2 finally, 

 Mar 1, 2016
 #2
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sorry one mistake  for my previous post, it should be 19-12 instead of 9 , so we have 12 in the middle of 10 and 13, and 7 is leave, so the least no can be on=btain by subtracting 5 from 7 so , the least no is still 2, the set of no is 2 5 6 10 12 13.

 Mar 1, 2016
 #3
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there is smaller one:

13+12+9+7+6+1 = 48

Solveit  Mar 1, 2016

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