Combinatorics · Forbidden sums · Pairings · Selection with constraints · Uniqueness
In how many ways can \(1000\) numbers be chosen from the set \(\{1, 2, \dots, 1999\}\) so that no two of the chosen numbers have sum \(1999\) or sum \(2000\)?
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Serbian Municipal Competition 2000, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source