Algebra · Systems of linear equations · Pairwise sums · Ordering arguments · Extremal elements
Find five real numbers whose pairwise sums are
\[ 0,\; 2,\; 4,\; 5,\; 7,\; 9,\; 10,\; 12,\; 14,\; 17 . \]
(Five numbers form exactly ten pairs, and ten values are listed; the sums may be listed in any order.)
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Serbian Republic Competition (Republicko takmicenje) 1997, high school grade I, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source