Combinatorics · Partitions · Difference sets · Case analysis
The numbers \(1, 2, 3, 4, 5\) are divided into two groups so that each group contains at least one of them. Prove that one of the groups contains two numbers whose difference also belongs to that same group.
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Serbian Municipal Competition 1998, high school grade I, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source