Combinatorial Problems in Mathematical CompetitionsThis book focuses on combinatorial problems in mathematical competitions. It provides basic knowledge on how to solve combinatorial problems in mathematical competitions, and also introduces important solutions to combinatorial problems and some typical problems with often-used solutions. Some enlightening and novel examples and exercises are well chosen in this book. With this book, readers can explore, analyze and summarize the ideas and methods of solving combinatorial problems. Their mathematical culture and ability will be improved remarkably after reading this book. |
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5-digit numbers a₁ a₂ arithmetic sequence Assume b₁ b₂ blue line segment C₁ Cauchy's inequality chessboard chessman China Mathematical Competition circle combinatorial complete graph completes the proof containing corresponding denote the number diagonal lines digit distinct coloring distinct objects divided divisible equals equation exactly Example exists figure finite geometric sequence given condition grid Hence induction integer solutions Latin square least line segments connecting line segments meeting M₁ mathematical induction Mathematical Olympiad method monochromatic triangle multiple mutually acquainted n₁ number of balls number of distinct number of elements obtain pairs perfect square persons Pigeonhole Principle players positive integers problem prove r₁ Ramsey's theorem real numbers rectangle recurrence relation red line segments red points red sides required number S₁ S₂ satisfies the condition satisfying the following satisfying the given straight lines subsets Suppose teams triples unit squares vertex vertices x₁