# More Mathematical Morsels

## Ross Honsberger

## Preface

Entitling this book *More Mathematical Morsels* has the advantage of immediately informing anyone who is acquainted with my *Mathematical Morsels* just what kind of book to expect. If it hadn't been for the earlier volume, the present collection might well have been called Gleanings From Crux Mathematicorum, referring to a wonderful undergraduate problems journal that was founded in Ottawa, Canada, in 1975 by Leo Sauv6 and Fred Maskell. Except for a few miscellaneous cases, I encountered all the problems discussed here in Crux Mathematicorum. Of particular interest and value are the many slates of problems given by Murray Klamkin in his regular column "Olympiad Corner" during the years 1979-1986. There is much for every level of mathematics scholar to enjoy in Crux Mathematicorum - the examples touched on here represent only a small fraction of the good things to be found there.

In this collection we shall be concerned only with elementary problems, and, of those, only ones that aren't too long or complicated. Needless to say, I hope that each of them contains something exciting - a surprising result, an intriguing approach, a stroke of ingenuity. They are not presented in any attempt to be instructive, but solely in the hope of giving enjoyment-an elegant or ingenious argument can be a beautiful thing.

In vindication of the original contributors to Crux Mathematicorum, it should be noted that I have written up these brief essays to suit myself, and have generally raided their work as I pleased; consequently, I have only myself to blame for all the faults in the result.

I remember reading somewhere years ago that J.L.Synge declared that *"The mind is at its best when at play"*. I have
always felt there might be something to this idea and so I hope that you will approach these vignettes as mathematical entertainment.

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