Competition Details

Here is a summary of the details of our competitions. Click on the buttons below to skip to different sections. Last edited 30 January, 2016.

The curriculum - what students will be expected to know

  • The level of content in questions will follow the NZQA curricula for the corresponding year levels.
  • If additional knowledge is required for a particular question, all relevant information will be provided so that no student is disadvantaged.
  • Students may assume basic results depending on the level of the question.
    • Basic geometry such as angle relationships, basic number theory such as divisibility, basic algebra such as factorisation, and basic combinatorics such as the pigeonhole principle may be used without proof
    • More advanced results, not commonly encountered by students of the corresponding level, such as the midpoint-of-arc lemma, Fermat's little theorem, AM-GM or the Cauchy-Schwarz inequality, and graph theory, are not expected and should not be required for a problem.
    • Other results, such as factorisation identities not commonly encountered in the high school curriculum, should be substantiated with proof where possible.

Monthly Competitions

Entries and due dates

  • Problems will be released on the first day of the month.
  • Entries are due at 23:59 on the last day of the months.
  • Entries should be typed up or scanned then emailed to Please include student name, school and school year.
  • Entries arriving later than the due date will not be marked.

Problem details (significantly changed, effective August 2015)

  • There are six problems of generally increasing difficulty. All students can attempt all problems.
  • Questions 1 and 2 are "answer only" questions (worth 3 marks each).
    • Only the answer is required, but working is welcome.
    • A correct answer will score 3 points; an incorrect answer will score 0 points.
  • Questions 3, 4, 5 and 6 are "working" questions (worth 5 marks each).
    • Students are expected to provide clear written explanation of their work.
    • The correct answer will earn at most 1 point; the other 4 points are allocated based on the student's working.
  • Students can work on the problems all throughout the month, with no time restriction. However, they must not receive any assistance from anyone, including teachers, parents, friends, siblings or anyone else. Students must work on the problems individually and without collaboration.
  • Creative/inventive solutions will perform better than brute-force solutions, and will get special mentions in our solutions!


  • Students are pooled into three divisions:
    • Junior (Years 7-8)
    • Intermediate (Years 9-11)
    • Senior (Years 12-13)
  • Divisions are for determining prizewinners only, and there are no restrictions on which problems a student can work on.
  • Students are eligible for prizes from only their division or a higher division.
  • Students who win prizes will be contacted by email for proof of identity (scanned image of school ID), and postage address.
  • Students are assigned to the correct division automatically on their first submission.
    • If a student wins a prize twice in the same division, they will be automatically moved to the next division after receiving their second prize.
    • If the student is already in the Senior division, they will still continue to be eligible for prizes.

New Zealand Mathematical Olympiad

The official regulations for the NZMO can be found here.


  • Students may register either through their school or individually (to take the NZMO at an alternative testing centre).
  • The cost of registration is $2.00 per student.

The competition

  • Duration: 90 minutes
  • Examination conditions:
    • No cheating, communication or collaboration is permitted.
    • No calculators or any electronic devices are permitted, except for a wristwatch that does not have memory storage or computational capabilities.
    • Closed book: no textbooks or notes are permitted.

Problem details

  • There are four divisions. In ascending order of difficulty:
    • Junior, aimed at Years 7-8
    • Intermediate, aimed at Years 9-11
    • Senior, aimed at Years 12-13
    • Olympiad, aimed at students in any year level that have, at any point in the past, attended the NZMOC Residential January Maths Camp.
  • There will be a different paper for each division.
  • Students may take a paper of a higher division, but must not take a paper of a lower division. This will result in an "unofficial" result, because their participation in an easier division will disadvantage other students in that division.
    • Examples of unofficial entries: (1) A Year 12 student takes the Intermediate paper. (2) A Year 11 student who has previously attended the NZMOC Maths Camp takes the Intermediate paper. (3) A Year 11 student who has previously attended the NZMOC Maths Camp takes the Senior paper.
  • Junior, Intermediate and Senior: each paper will have six problems, with marks allocated for a total of 60 marks.
  • Olympiad: there will be three problems, with 7 marks each for a total of 21 marks.
  • All working is expected for all questions. A correct answer (if one is required) will earn at most one point.

Marking and prizes

  • Every valid submission will be marked, but statements which cannot be interpreted (due to illegibility or poor explanation) will be ignored.
  • Clear explanation is expected for every key step of the solution.
  • Students are eligible for prizes from their division only, unless they wish to compete in a higher division.
  • Medals will be presented for the top students of each division (gold, silver and bronze medals).
  • Certificates will be presented to all students:
    • Gold/Silver/Bronze,
    • Honourable Mention,
    • Highly Commended, and
    • Commended.
  • Badges and other prizes (such as books, t-shirts, Rubik's cubes) may also be presented to accomplished students.
  • Special awards, for example the Golden Pen Award (for the most convoluted yet completely correct solution) and the Ingenuity Award (for the most inventive, creative solution), may also be awarded.