What is Problem Challenge?

Problem Challenge is a mathematics problem solving competition aimed primarily at children in years 7 and 8 but may be of interest to mathematically gifted children in year 6. It has been offered to schools throughout New Zealand for the past 33 years. The response to the competition has been overwhelmingly positive. Almost one million New Zealand children have participated in the competition over the years.

Most schools with year 7 and 8 children, and some with year 6 children, are on our mailing list and will automatically receive an invitation, in mid-February, to take part in the competition.

Registration is now open (Online registration).
Not sure whether your school is on our mailing list? You can check here.

The competition has been organised by John Curran and John Shanks, retired members of the Department of Mathematics and Statistics at the University of Otago, with huge administrative help from Leanne Kirk. However John Curran and Leanne retired from the competition at the end of 2023; John Shanks will attempt to run it from 2024...

The value of such problem solving competitions is well recognized overseas. For example, similar schemes are run in Australia, Britain and the United States. Here the New Zealand Curriculum, Mathematics Standards (years 1-8), considers various ways in which effective mathematics teaching can provide quality programmes. Amongst other components, problem-centred activities are highlighted. The document states Cross-national comparisons show that students in high-performing countries spend a large proportion of their class time solving problems. The students do so individually as well as co-operatively. The problems we pose allow children to practise and learn such simple strategies as guessing and checking, drawing a diagram, making lists, looking for patterns, classifying, etc. Although children answer the questions individually on our sets there is ample opportunity for co-operative practise using our resources.

How does it work?

Children participating in the competition attempt to answer five questions in 30 minutes on each of five problem sheets, which are done about a month apart. They do the problems individually but they can share their answers and strategies in small groups afterwards.

Note that all three levels (years 6, 7 and 8) attempt the same problem set although there are separate awards for each of those levels.

The problems are generally aimed at more able children. However, we hope to keep the first question or two reasonably straightforward, so that all children entered can have some success. Many schools that have taken part before will have a good idea of the standard involved. Here are two recent example sets as a guide.

Rules of the competition
Glossary of common mathematical words

As a general rule, teachers may wish to enter children for whom they feel a score of say 3 out of 5 is an attainable goal. We felt the problems set last year were about the right level of difficulty, so we will be aiming for much the same standard this year. For schools that want more information, there are five books available that give questions and solutions from the first 24 years of the competition. These books can be obtained by completing the order form.

What must the teacher do?

For each of the 5 problem sets that you receive, you will have to photocopy (or otherwise make available) sufficient copies of the problem sheet for the participants from your school, and administer the challenge on the day specified (or as near as possible).

You must mark the pupil responses (using the solutions provided) and return collated results to us, as well as keeping a record of your results (using your own spreadsheet or on a form provided).

  • Results are returned to us on-line. Further details of this together with a log-in code for your school will be supplied with the first set of problems.
  • All competition material, including sets, solutions and letters, will be emailed to schools or made available on the website.
  • Certificates will be provided in electronic form for schools to print.
It is important that administrators have reliable internet access.

How does your school benefit?

The problem sets may be used later as a resource for other children in any way the teacher wishes. For example, small groups could solve the problems co-operatively together, talking through the various strategies that could be applied to each question.

For each set you will receive a summary of the overall results, so that you can evaluate your pupils’ progress. In the past we have received very favourable feedback on the benefit of this. (Individual school results will not be collated or publicised so will remain strictly confidential to you.) Overall results from previous years can be seen here.

All children taking part will receive a certificate of participation. Those in about the top 10% in each year will receive certificates of excellence and those in the next 25% or so will receive certificates of merit. Where schools have provided on-line results, the childrens’ names will already be on the certificates.

Each year $25 book tokens are awarded to children in the top 1% or so of the competition. Note that book tokens are normally given to a maximum of 20% of the entries from each school.

When is Problem Challenge held?

As in previous years there will be a Problem Challenge each month from April to August, spaced at about five week intervals. This year’s administration days can be found here. However, as in the past, there is some flexibility in these dates and no school is precluded from entry on account of the timing. This is explained more fully if you enter.

How much does it cost and how do you enter?

The entry fee consists of $20 per school plus $0.40 per child entered (including GST). We will be mailing all Intermediate schools each February asking for entries: at that stage, if you wish to take part, you will need to register on-line and arrange to pay the registration fee (by credit card or University invoice).

We hope you will join Problem Challenge and enjoy the questions we set!!

John Shanks
Department of Mathematics
University of Otago

The Final Challenge

Children who do particularly well in Problem Challenge during the year are invited to enter a final multi-choice competition in late October. Note that, because of limited resources and in fairness to all, we regret that only those who reach a specified total number of problems correct (regardless of absence, sickness, etc) will be eligible to enter.

Final Challenge provides a great challenge for the very able, and there are more substantial prizes for the best performers at both Years. The competition consists of 10 multiple-choice questions, with five options per question, together with 10 questions that require explicit answers. The problems are similar in style to the usual Problem Challenge questions but generally of a standard comparable to question 5 on the Problem Sets or harder.

  • Children have one hour in which to attempt the questions.
  • The use of calculators is not permitted.
  • Each multi-choice question answered correctly gains 4 marks (with 1 mark deducted for each wrong answer), while the other ten questions are worth 6 marks each, making a possible total of 100.

The date for Final Challenge is Thursday 17 October.

Prize-winners for previous years can be seen here.


Problem Challenge
Department of Mathematics
University of Otago
PO Box 56, Dunedin.

Phone: (03) 479 7759

Email regarding books: pcbooks@maths.otago.ac.nz
Email regarding the competition: pc.maths@otago.ac.nz

Mailing list

Most schools with year 7 and 8 children are on our mailing list and automatically receive an invitation to take part in the competition in mid-February each year. You can check here to see whether your school is on our mailing list. If your school is not there then please use the form below to request that your school be added.

If you haven’t received an invitation by late February you can download a registration form at that time.

To contact us email, write or fax to the above, or you can fill in your query here:

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