## The art and craft of problem solvingThis text on mathematical problem solving provides a comprehensive outline of "problemsolving-ology," concentrating on strategy and tactics. It discusses a number of standard mathematical subjects such as combinatorics and calculus from a problem solver's perspective. |

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#### Review: The Art and Craft of Problem Solving

User Review - Krollo - GoodreadsI'm a bit new to Olympiad maths, but this book has given me a decent overview. I especially liked the combinatorics but all of it was pretty good. We'll see how I'll do in BMO1, but it's not fair to blame my failures on this book! Fnarr fnarr... Read full review

#### Review: The Art and Craft of Problem Solving

User Review - Kaylee - GoodreadsYay for math! And yay for a math book with so much variety! And yay for a math book with so much approachability! Boo for problems without an answer key. I don't want to have to sit at my computer while I do math just so I can check my answers. Read full review

### Contents

Chapter | 7 |

Strategies for Investigating Problems | 15 |

Fundamental Tactics for Solving Problems | 68 |

Copyright | |

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### Common terms and phrases

algebra algorithm AM-GM AM-GM inequality argument assume cards circle coefﬁcients color complex numbers compute conjecture Consider contains contradiction converges count crux move deﬁne deﬁnition degree denote difﬁculty divisor easy edges equal equation Eulerian path exactly example extreme principle factor ﬁgure ﬁnd ﬁnite ﬁrst ﬁxed formula function geometric series graph greatest common divisor Hamiltonian paths ideas inequality inﬁnite integer coefﬁcients lattice points leam least element locker look mathematical mean value theorem modulo monic monic polynomial multiple non-negative notation Notice number theory pairs parity partitions path pattem penultimate step perfect square permutation pigeonhole principle pigeons plane polygon polynomial positive integer possible prime problem solving Problems and Exercises proof Prove Putnam real numbers rectangle reﬂection rooks roots of unity satisﬁes sequence Show simple Solution speciﬁc strategy subsets symmetry tactic theorem tool triangle true USAMO variables vector vertex vertices words zero