天真
发表于 2025-3-23 12:29:22
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憎恶
发表于 2025-3-23 15:35:30
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射手座
发表于 2025-3-23 20:15:31
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个人长篇演说
发表于 2025-3-23 23:24:43
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Prologue
发表于 2025-3-24 03:58:32
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deface
发表于 2025-3-24 07:54:37
Number Theory and CombinatoricsMany Olympiad problems refer to arrays of numbers. Let us start with some examples.
阴谋小团体
发表于 2025-3-24 13:41:50
Algebra. Factor (.+2.−3.).+(.+2.−3.).+(.+2.−3.).... Observe that (.+2.−3.)+(.+2.−3.)+(.+2.−3.)=0. Because .+.+.=0 implies ..+..+..=3., we obtain
OREX
发表于 2025-3-24 14:55:37
Geometry and Trigonometry. Let . be a convex quadrilateral. Prove that.. Let . be the point of intersection of the diagonals . and .. We have .+.>. and .+.>.; thus .+.>.+.. Similarly, .+.>. and .+.>.; thus .+.>.+.. It follows that. For the second inequality, note that .<.+. and .<.+.; hence. Analogously,. and the result follows by adding these inequalities.
健壮
发表于 2025-3-24 22:48:23
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柔声地说
发表于 2025-3-25 00:22:25
professors and Mathematical Olympiad coaches, the text will be invaluable to teachers, students, and puzzle enthusiasts. The advanced reader is challenged to find alternative solutions and extensions of the proposed problems. .978-0-8176-8253-8