Algebra · Pairwise sums · Systems of equations · Ordering arguments · Double counting
Tina wrote one natural number on each of five slips of paper and refused to say which numbers they were. Sharp-witted Zan talked her into revealing instead all the sums that can be formed from two of the slips. The sums she gave him were
\(17,\; 20,\; 28,\; 14,\; 42,\; 36,\; 28,\; 39,\; 25,\; 31 .\)
Which five numbers did Tina write?
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2001, 1. letnik, category A, problem 2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source