I've been asked the following question:

What three odd integers from the set {1,3,5,7,9,11,13,15} that when summed together equals to 30? Note that any integer can be used more than once.

Is there any possibility to solve these kind of questions with some formulae? Note I have gone through the answers for making it with 5 numbers.

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    $\begingroup$ adding odd number of odd numbers can never get you an even number $\endgroup$ – AgentS Apr 9 '15 at 13:29
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    $\begingroup$ Odd numbers can be written $2k+1$. So $(2a+1)+(2b+1)+(2c+1)=2(a+b+c+1)+1=30$. So when can this occur? $\endgroup$ – Eleven-Eleven Apr 9 '15 at 13:33
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    $\begingroup$ I dint think I understand adding three odd numbers gives an odd number $\endgroup$ – Karl Apr 9 '15 at 13:34
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    $\begingroup$ This was asked on Puzzling.SE yesterday. There are many non-base 10 solutions. puzzling.stackexchange.com/questions/11729/fill-the-holes $\endgroup$ – Golden Dragon Apr 9 '15 at 13:35
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    $\begingroup$ The version on puzzling.SE does not specify "odd integers", it merely specifies the digits of each number. If the base is odd, the last three numbers in the set are even. $\endgroup$ – David K Apr 9 '15 at 13:56

Note that all the elements of the set are odd.

Hence, even if we repeat, we have, w.l.o.g, the following cases

(i) Odd $x$ + Odd $x$ + Odd $y$ = Even+Odd=Odd

(ii) Odd $x$ + Odd $y$ + Odd $z$ = Odd

(iii) Odd $x$ + Odd $x$ + Odd $x$ = Even+Odd=Odd

.... while $30$ is even.

I actually remember this question which is rumored to be from an IAS exam and no one could solve it except the topper. That's actually a false rumor.

The only way you can get $30$ is by doing it in a mathematically incorrect way (by a "trick"), like $7.5+9.5+13=30$

Other than that, this question simply is a bogus question.

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