Preface

W. J. Blundon was born February 20, 1916, in St. Anthony, Newfoundland. Most of his professional life was devoted to Newfoundland education, and among the various positions he held were those of teacher, school supervisor and professor. From 1948 to 1976, he was Head of the Department of Mathematics and Statistics at Memorial University. He retired in 1979, and passed away on March 25, 1990.

Although his main research interest was packing and covering problems, Professor Blundon did a substantial amount of work in number theory and geometry, particularly, in the problem-solving venue. He was an ardent disciple of elegance in mathematical expression, often rewriting a proposal or solution several times in order to meet his own exacting standards. His efforts in this regard led one editor to comment on the “pure and austere elegance” of his solutions. Professor Blundon’s enthusiasm and ingenuity inspired both students and faculty. His interest in problem-solving continued even after his retirement. His frequent visits to the department to enjoy a cup of coffee and discuss the latest problems were greatly anticipated.

Professor Blundon was highly respected in the mathematical community. He served on the Board of Directors of the Canadian Mathematical Society for eight years, and for three years he was Chairman of the Canadian Mathematical Olympiad Committee. He was an original member of the Mathematics Committee of the Atlantic Provinces Council on the Sciences (APICS) and, in his honour, the APICS Mathematics Committee instituted the annual Blundon Lecture in 1981. His contribution to problem-solving has also been recognized by the Department of Mathematics and Statistics at Memorial University and by the Canadian Mathematical Society, who sponsor the annual W. J. Blundon Mathematics Competition for Newfoundland high school students.

We have attempted to bring together in this manuscript all of Professor Blundon’s problem-solving work. We hope that this collection is complete, but since Professor Blundon made a great many contributions to many different journals, it would not surprise us to learn that some have been missed. Please bring any such omissions to our attention!

Students who work through this manuscript will gain a great deal of insight into how to attack problems in geometry and in number theory. Of course, the best advice we can give is this. “Try the problem first on your own. Only if you are stuck (which will be often, as many of the problems are difficult) should you read through the solution.” In addition, we hope that all readers will gain an appreciation for Professor Blundon’s unique style.

As for the organization of the book, each of the four sections (Geometry, Geometric Inequalities, Number Theory, Miscellaneous), has problems listed roughly in ascending order of difficulty with complete references given for all problems. In addition, it should be noted that we have freely edited some of the solutions. For example, we felt that extra explanation was needed in some cases, while in others, comments not directly relevant to the solution (although interesting) have been omitted.

Much thanks is given to Linda Bartholomew and Kaaren May, two very dedicated assistants, who not only did an exhaustive search of the literature but also prepared a rough draft of the manuscript. We would also like to thank Bruce Shawyer whose strong support was invaluable and who helped secure the first summer grant to get the project started. Special thanks go to Edgar Goodaire without whose involvement the project could never have been completed. He first helped to secure a second grant to enable the remainder of the material to be collected, and then brought the attention of this work to the Mathematics and Statistics Committee of APICS who kindly, indeed eagerly, agreed to act as publishers (and provide the necessary financing). In addition, he has acted as the liaison with the printers, Wilfred Laurier University Press, and has even assisted with the LATEX technology that was necessary in order to get the material into publishable form. A final word of thanks goes to the publishers of all the referenced journals who have kindly allowed us to reproduce relevant material from their various volumes.

R.H. Eddy and M.M. Parmenter

Department of Mathematics and Statistics,
Memorial University of Newfoundland
St. John’s, Newfoundland
Canada A1C 5S7
May, 1994