## Which Way Did the Bicycle Go?: And Other Intriguing Mathematical MysteriesThis book contains the best problems selected from over 25 years of the Problem of the Week at Macalester College. This collection will give students, teachers, and university professors a chance to experience the pleasure of wrestling with some beautiful problems of elementary mathematics. Readers can compare their sleuthing talents with those of Sherlock Holmes, who made a bad mistake regarding the first problem in the collection: Determine the direction of travel of a bicycle that has left its tracks in a patch of mud. The collection contains a variety of other unusual and interesting problems in geometry, algebra, combinatorics, and number theory. For example, if a pizza is sliced into eight 45-degree wedges meeting at a point other than the center of the pizza, and two people eat alternating wedges, will they get equal amounts of pizza? Or: Is an advertiser's claim that a certain unusual combination lock allows thousands of combinations justified? Complete solutions to the 191 problems are included with problem variations and topics for investigation. |

### What people are saying - Write a review

User Review - Flag as inappropriate

Very interesting, many further informations and generalisations are provided.

User Review - Flag as inappropriate

a perfect investigation book.

### Contents

Plane Geometry | 1 |

Nested Triangles | 7 |

How Many Isosceles Triangles? | 8 |

Triangles from a Triangle | 9 |

Circular Surprises | 10 |

A Ring of Disks | 11 |

If You Lose Your Compass | 12 |

An Ellipse and a Circle | 13 |

The Color of Money | 38 |

Cover the Honeycomb | 39 |

Decimal Diversity | 40 |

Breaking Up Space | 41 |

Count the Tilings | 42 |

Difference Triangles | 43 |

A Veritable Babel | 44 |

ThreeDimensional Geometry | 45 |

A Hexagon in a Circle | 14 |

Find the Rectangles | 15 |

One Quadrilateral Begets Another | 16 |

A Constant Difference | 17 |

Another Area Comparison | 18 |

A Hexagon of Centroids | 19 |

A Short Bisector | 20 |

Miscellaneous 64 Nearest Neighbors | 21 |

Whats the Angle? | 22 |

A Shady Garden Wall | 23 |

Number Theory | 25 |

Theyre There but Where? | 26 |

Reversing Multiples | 27 |

A Very Good Year | 28 |

A Sum of Fractions | 29 |

Theyre in the Money | 30 |

A Necessary Square? | 31 |

Sums and Differences | 32 |

Algebra | 33 |

Powerful Patterns | 34 |

Playing the Stock Market | 35 |

A Shuffling Reconstruction | 36 |

Combinatorics and Graph Theory | 37 |

Traveling among the Pyramids | 46 |

Connect the Dots | 47 |

Painting a Cube | 48 |

Surveying on Earth | 49 |

Miscellaneous | 51 |

A Complicated Constant | 52 |

An EggDrop Experiment | 53 |

A Messy Desk | 54 |

Throw Your Rings into the Hat | 55 |

Passion Has No Square Root | 56 |

Catch the Counterfeit | 57 |

Divide and Be Conquered | 58 |

An Odd Vector Sum | 59 |

How Many 8s Can a Plane Hold? | 60 |

Plane Geometry | 63 |

Number Theory | 131 |

Algebra | 155 |

Combinatorics and Graph Theory | 165 |

ThreeDimensional Geometry | 189 |

Miscellaneous | 201 |

223 | |

233 | |

### Common terms and phrases

AABC ABCD Alice and Bob Alice's altitudes angle arithmetic progression assume bisector blits Bob's boxes cards centroid chords coin colors configuration congruent corners cube cubelets denote diagonal diagram digits disk distance distinct positive squares divides divisible edges equal equation equilateral triangle example Fibonacci FIGURE Find follows formula four geometry graph grid Hamiltonian circuit hexagon hole horizontal inscribed intersection isosceles triangle law of cosines lemma length line segment Macalester College markers Mathematica Mathematical N. G. de Bruijn Note number of vertical pairs palindromic Paul Erdos pennies perpendicular pizza plane points polynomial positive integers possible prime problem appeared problem is due proof prove quadrilateral radius ratio rectangle region rooks rotated sequence Show side-length Similarly slice solution solve Stan Wagon star polygon sum of distinct Suppose tangent theorem tiles total number trominoes vector vertex weighings yields

### References to this book

Mathematical Omnibus: Thirty Lectures on Classic Mathematics D. B. Fuks,Serge Tabachnikov No preview available - 2007 |