how many different integers can be expressed as the sum of three distinct numbers from the set {3 10 17 24 31 38 45 52}?
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Firstly we have to find three such numbers whose sum can be one of the number from the set.
The question asked is how many such three numbers are present.
From the given set it is evident that the minimum number that can be obtained from sum of three numbers is 30(3 + 10 + 17). Similarly the maximum number obtained will be 135(38 + 45 + 52).
So you can see the numbers are having a common difference of 7.
Therefore total numbers equals to (135 - 30)/7 + 1 = 105/7 + 1 = 15+1 = 16 [Ans].
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