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RU-ALLRUSSIAN 1974 Problem 13

    Find all three digit decimal numbers a1a2a3\mathrm{a_1a_2a_3} which equal the mean of the six numbers a1a2a3\mathrm{a_1a_2a_3} , a1a3a2\mathrm{a_1a_3a_2} , a2a1a3\mathrm{a_2a_1a_3} , a2a3a1\mathrm{a_2a_3a_1} , a3a1a2\mathrm{a_3a_1a_2} , a3a2a1\mathrm{a_3a_2a_1} .

    Dataset text NuminaMath olympiads. Quoted with source.

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