Junior Mathematics

“We Have A Problem”

Note: The last day for buying books from this website is the 13th of December 2023. After that date we will cease selling books for the foreseeable future. Books ordered on or before the 13th of December will still be sent out.

This resource book contains the questions and model solutions for the University of Otago Junior Mathematics Competition from 2006 to 2015.

Each question has been edited onto a single page so that teachers may photocopy questions as desired. Occasionally students may need more space than is provided, and they will certainly need rough paper at times. The solutions are placed immediately next to the questions, but sometimes they take more than one page. They may also be copied if desired. The solutions given are generally more detailed than those which could be expected from students working under exam conditions. They are not the only possible solutions, nor do we claim that they are necessarily the best.

As some of the questions are “difficult”, teachers intending to use them should attempt them first to provide familiarity just in case a student comes up with an unexpected but valid solution to a particular problem.

It is hoped that this booklet will be a useful resource for all students, not just those who intend sitting the competition.

  • Copies of "We Have A Problem" are available for purchase. This book is designed to support the mathematical processes strand from Mathematics in the New Zealand Curriculum.
  • The price for this book is $NZ30 per copy.
  • Payment is required with the order as we have tried to keep the costs to a minimum by not involving the financial wizards with their invoices etc. A receipt will be sent with your books.
  • The book contains all the questions over the period 2006 to 2015.
  • Each question has been edited onto a single page so that teachers may photocopy questions as desired. This means that the questions may be handed out to classes (or individual students) as exercises or homework sheets.
  • The questions should provide useful problem-solving material for all students in years 9 to 11, not just those who sit the competition.
  • The questions will be useful throughout the year, and not just as preparation for the competition.
  • Detailed answers are provided!
  • The book is primarily useful for the second part of the competition, as the contents of the book pre-date the competition having two parts.

Online order form for use by schools (NZ only)

Online order form for use by individuals with New Zealand addresses

Online order form for use by individuals with overseas addresses

Please ensure you know exactly what you are ordering - if you want books aimed at year 7 and 8 students see below.

(Five companion booklets of questions from the Problem Challenge Competition, designed for Intermediate school students, are also available — see Problem Challenge. These booklets contain an Introduction to Problem Solving, along with many references.)


“Ten of the Best” and "A Decade of Problems"

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