## Hungarian Problem Book IIIGyörgy Hajós, Andy Liu, G. Neukomm, János Surányi This book contains the problems and solutions of a famous Hungarian mathematics competition for high school students, from 1929 to 1943. The competition is the oldest in the world, and started in 1894. Two earlier volumes in this series contain the papers up to 1928, and further volumes are planned. The current edition adds a lot of background material which is helpful for solving the problems therein and beyond. Multiple solutions to each problem are exhibited, often with discussions of necessary background material or further remarks. This feature will increase the appeal of the book to experienced mathematicians as well as the beginners for whom it is primarily intended. |

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### Contents

Eötvös Mathematics Competition Problems | 1 |

Combinatorics Problems | 9 |

Number Theory Problems | 33 |

Algebra Problems | 49 |

Geometry Problems Part I | 61 |

Geometry Problems Part II | 99 |

137 | |

### Common terms and phrases

acute altitude angle assume bisector Book called Chapter circle common competition complex congruent consider contradiction defined denote desired Determine distance divides divisible draw edges elements equal equilateral triangle exactly exists expression extension Exterior Angle factors Figure finite follows Geometry give given graph greater Hence holds induction Inequality infinite inside interior intersect joining least length lies Mathematical maximum mean median midpoint multiple Note objects opposite pairs parallel parallelogram perpendicular plane positive integers prime Principle Problem Proof properties Prove real numbers rectangles relation represent respectively result Second Solution shown in Figure sides similar Similarly Solution squares Suppose symmetry tangent term Theorem third triangle ABC true vector vertex vertices ZCAB