Combinatorics · Pigeonhole · Arithmetic progressions · Pairing
Let \(A\) be a subset of the set \(\{1, 4, 7, \dots, 1996\}\) containing exactly \(335\) elements. Prove that \(A\) contains two distinct numbers whose sum equals \(2000\).
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Serbian Municipal Competition 1996, high school grade I, problem 3. Organized by the Mathematical Society of Serbia (DMS).