What three odd integers have a sum of 30?

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  • What five odd integers have a sum of $30$?

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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.