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PL-OM 1999 Problem 5

    Niech a1,a2,...,an,b1,b2,...,bna_1, a_2, ..., a_n, b_1, b_2, ..., b_n będą liczbami całkowitymi. Udowodnić, że

    ∑1≤i<j≤n(∣ai−aj∣+∣bi−bj∣)≤∑1≤i,j≤n∣ai−bj∣ .\sum_{1 \leq i < j \leq n} (|a_i - a_j| + |b_i - b_j|) \leq \sum_{1 \leq i,j \leq n} |a_i - b_j|\ .

    Official text Polish Mathematical Olympiad 1999 official paper, page 3. Quoted with source.

    A model read this text from the scan of the paper by OCR, with vision/claude@2.1.318 (claude-opus-5-5). No person has checked it against the paper yet.

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