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TR-MO 2025 Problem 4

    a1,a2,…,a2025a_1, a_2, \ldots, a_{2025} gerçel sayılar olmak üzere, her 1≤i<j≤20251 \le i < j \le 2025 için, birinci tahtaya 1−∣ai−aj∣1 - |a_i - a_j| sayısı, ikinci tahtaya ∣ai+aj∣−1|a_i + a_j| - 1 sayısı yazılıyor. Hangi (a1,a2,⋯ ,a2025)(a_1, a_2, \cdots, a_{2025}) 2025-lileri için, her gerçel sayı her iki tahtaya da eşit sayıda yazılır?

    Official text Turkish Mathematical Olympiad 2025 official paper, page 2. 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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