Algebra · Sign choices · Parity · Sums of consecutive integers · Explicit constructions
Each of the numbers \(1, 2, \dots, 1995\) is to be given a sign \(+\) or \(-\). How should the signs be chosen so that the value of
\[ \pm 1 \pm 2 \pm \cdots \pm 1995 \]
is as close to zero as possible?
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Serbian Regional Competition (Okruzno takmicenje) 1995, high school grade I, problem 3. The 1995 regional paper was not split into categories. Organized by the Mathematical Society of Serbia (DMS).