Combinatorial Problems in Mathematical Competitions
This 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 anda arithmetic sequence Assume belong blue line segment chessboard chessman China Mathematical Competition circle circular permutation cogwheel common complete graph completes the proof conclusion holds containing denote the number diagonal lines distinct coloring distinct objects divided divisible element subsets equals equation exactly Example exists Fibonacci sequence figure 9 finite Firstly geometric sequence given condition grid Hence inclusion-exclusion principle integer solutions Latin square least line segments connecting line segments meeting mathematical induction Mathematical Olympiad method monochromatic triangle multiple mutually acquainted nonnegative integer number of balls number of distinct number of elements obtain perfect square persons Pigeonhole Principle players polygon positive integers prove real numbers rectangle recurrence relation red line segments red points red sides required number required smallest satisfies the condition satisfying the following satisfying the given straight lines subsets Suppose teams triples unit squares vertex vertices wins