## Mathematical gems |

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### Contents

CHAPTER PAGE 1 Three Surprises from Combinatorics and Number Theory | 1 |

Four Minor Gems from Geometry | 10 |

A Problem in CheckerJumping | 23 |

Copyright | |

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### Common terms and phrases

1-factor a x b rectangle Accordingly Amer attainable score beads BICENTRIC POLYGONS black edges bricks circumcenter circumcircle circumsphere collinear column complete graph composite solutions configuration congruent Consequently consider contains contradiction copies deleted diagonal digits distance can occur divides dominoes eight-point circle endpoints equal exceed Figure gives graph G harmonic bricks harmonic series hexominoes implying incircle integer intersection isosceles 6-point isosceles tetrahedron key multiple Klarner L-tromino lattice point layers least line ax Math Mathematical monomino Monthly natural numbers necklaces number of vertices obtain odd block odd components odd number odd prime pack the line packable pair Paul Erdos perimeter plane polycubes polyominoes prime number problem proof proved quadrilateral red edges relatively prime result segments sides Similarly Slothouber-Graatsma Puzzle spheres subset Suppose tangent tetrahedron tetrominoes theorem total number tromino unattainable unit cubes vertex Wilson's theorem yields