Logic and sets · Inequality grids · Constraint puzzles · Uniqueness

Problem 2, 1998

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Write each of the numbers \(1, 2, 3, \dots, 9\) into exactly one of the nine shapes in the figure - odd numbers into the triangles, even numbers into the squares - so that all \(12\) of the inequality signs shown are satisfied. In how many ways can this be done?

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Serbian Municipal Competition 1998, high school grade I, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source