This is the second of two volumes osome higher level problem solving and largely contains material that is not taught imost Westerschools. Like the first volume (A First Step to Mathematical Olympiad Problems), most of the content here was developed initially as aaid for New Zealand students who were hoping to get to aInternational Mathematical Olympiad (IMO).
This original material was presented ithe form of 15 yellow booklets. The first eight of these are the basis of First Step;the remaining seveunderpithis volume. However, it should be noted that there are also new pieces here.The whole of Chapter 3 was not ithe initial yellow booklets neither were many sections and problems that are dotted around the rest of the book.Thiook should help improve the background of students preparing for regional and national mathematics competitiony providing them with theorems, ideas and techniques that they may not have already met. It will also give them suggestions ohow to approach problems that they have not seebefore. But the step to the IMO from regional and national competitions is likely to be a big one and the First and Second Steps should not be considered as a total preparatiofor aIMO. Hopefully though, they are good stepping stones along the way.
But I hope that the book will also be read by both students and teachers who are interested imathematics. There are sufficiently many problems here to while away many happy and frustrating hours, I hope that thiook encourages many readers to simply enjoy mathematics for its owsake and for the pleasure of getting a problem out.
Finally I would like to thank Irene Goodwi(who is now, unfortunately,no longer with us), Lenette Grant and Leanne Kirk for their help to me while the yellow booklets were being prepared and ithe many years since, and to Zhang Ji for her work iturning yellow booklets into Steps.
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