A pattern can be seen in the solution that the result will be equal to (n/2)*m . May be I am missing any mathematical concept behind this reason. Can anyone provide me the mathematical logic behind the solution? Why is this working?

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A pattern can be seen in the solution that the result will be equal to (n/2)*m . May be I am missing any mathematical concept behind this reason. Can anyone provide me the mathematical logic behind the solution? Why is this working?

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lets take an example for n=12 and m=3.

So 1,2,3,7,8,9 will have -ve sign and 4,5,6,10,11,12 will have positive sign

Now if you look carefully you can see that a n/2 pairs consisting of one +ve and one -ve numbers are formed such that their addition is equal to m

here,

4 — 1 = 3

5 — 2 = 3

6 — 3 = 3

10 — 7 = 3

11 — 8 = 3

12 — 9 = 3

Therefore n/2 pairs will be formed having sum of both numbers as m. Hence the answer is (n/2)*m

Thank you very much

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