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OSP SMA 2006 Bagian Kedua No 2

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Misalkan $m$ bilangan asli yang memenuhi $1003 < m < 2006$. Diberikan himpunan bilangan asli $S = \{1, 2, 3,\ldots, m\}$, berapa banyak anggota $S$ harus dipilih agar selalu terdapat paling sedikit satu pasang anggota terpilih yang hasil tambahnya 2006?

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