Combinatorics · Partitions · Products · Extremal problems
The numbers \(1, 2, 3, 4, 5, 6, 7, 8\) are split into three disjoint nonempty sets. Let \(P_{1}\), \(P_{2}\) and \(P_{3}\) be the products of the numbers in the first, the second and the third set, respectively, and let \(P\) be the largest of these three numbers. Determine the smallest possible value of \(P\).
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Serbian Municipal Competition 2026, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source