Louis A. Graham

For decades, professionals in applied mathematics and mathematical puzzle fans from all over the world supplied provocative problems to the puzzle columns of the Graham Dial. Upon the appearance of an interesting problem, readers wrote in to the Dial suggesting new approaches to the solution, some greatly simplifying the problem and others broadening its scope. This collection presents 52 of the finest problems, all featuring the "surprise attack" and abounding in imaginative and interesting solutions.The problems involve measurement of geometrical spaces, probabilities, distances, number systems other than the decimal, interesting number relations, relative motion, and the discovery of the simplest solution through purely logical means. Solutions involve such techniques as arithmetic, algebra and geometry, number theory, statistics, networks, and inversion. Several approaches to the solution accompany each problem, and even the best of these represent not the ideal solution but only the most satisfying -- so far.

Ingenious Mathematical Problems and Methods is a comprehensive book that delves into the world of mathematics and provides a plethora of challenging problems and innovative methods to solve them. Written by Louis A. Graham, a renowned mathematician, this book is an excellent resource for students, teachers, and anyone interested in mathematics.The book covers a wide range of topics, including algebra, geometry, trigonometry, number theory, and calculus. It is divided into two parts, with the first part focusing on problems and the second part on methods. The problems presented in the book are diverse and range from simple to complex, with varying degrees of difficulty.The methods presented in the book are equally diverse, and the author has taken care to provide clear and concise explanations for each method. Some of the methods covered in the book include the use of symmetry, algebraic manipulation, geometric reasoning, and combinatorial analysis.Throughout the book, the author emphasizes the importance of problem-solving skills and critical thinking. He provides numerous examples and exercises to help readers develop these skills and gain a deeper understanding of the concepts presented in the book.Overall, Ingenious Mathematical Problems and Methods is an excellent resource for anyone looking to improve their mathematical skills and learn innovative problem-solving methods. It is a must-read for students, teachers, and anyone who loves mathematics.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.

Wenn ich auf meine iiber 25-jahrige Arbeit als Leiter einer mathema- tischen Kolumne im "Graham Dial" zurUckblicke, so sehe ich gerade in den iiberraschenden Problemlasungen der Leser die schanste Aner- kennung fiir meine Bemiihungen. Die Mehrzahl der Aufgaben waren Originalbeitrage, und in den meisten Fallen waren die pramierten Lasungen der Leser besser als die Lasung des Problemstellers. Haufig wurden durch solche Lasungen neue Aspekte des Problems erkennbar, oder es wurden neue interessante Zusammenhange erschlossen. In diesem Buch bringen wir eine Auswahl von Problemen, bei denen der erwahnte Dberraschungseffekt bei der Lasung besonders deutlich wird. Dies auGert sich etwa durch einen ungewahnlichen La- sungsansatz, der nicht nur zur Vereinfachung der Lasung beitragt, son- dem auch zu einer erweiterten Sicht des Problems fiihrt und zum Teil von einem esoterischen Hauch begleitet ist, der vielen Mathematiker- herzen so lieb ist. Eine technische Bemerkung: Nach jeder Problemstellung wird die Losung durch dieses Wort in fetten Buchstaben angekiindigt. Wer also die Aufgabe selbstandig lasen machte, soli an dieser Stelle das Buch besser zuklappen und erst spater die Lasungen vergleichen. Zur Auflockerung des Textes dienen die eingestreuten illustrierten Verse!, die von Lesem stammen, und in amiisanter Weise eine bekannte Formel in Gedichtform darstellen. L. A. Graham 1) Diese wurden, urn den originellen Reiz nicht zu zerstoren, in der englischen Sprache belassen (Anrn. des Obersetzers) V Inhaltsverzeichnis Das Linsen-Nomogramm ...... . 2 Pick beim Grundstucksmakler ........ 3 Geldwechseln beim Einkauf . ......, 10 4 Bierdeckelgeometrie ..... . 15 17 5 Mathematik am Briefmarkenautomat . 6 Die gekreuzten Leitern ....... . 21 7 Die unaufmerksame Sekretarin .