Details about the selection problems

Here is the post on the NZMOC site, and if you are really lazy, here are the problems (registration form is in the same file).

Due date: September 24, 2014

Send to: NZ Mathematics Olympiads, The University of Auckland, Department of Mathematics, Private Bag 92019, Auckland 1142, New Zealand

For clarifications, you can email Michael Albert directly ( or leave comments on this post and we'll contact him on your behalf.

Anyone can try these questions, but please note that selection is dependent on several conditions, which can be found at the bottom of page 2 in the attached document.

What? Selection? For what? What camp?

Okay, from the beginning: there is this massive, international, incredibly well-recognised high school competition called the International Mathematical Olympiad (IMO). New Zealand has been represented in the IMO since 1988. But among all the high school students in NZ, only six can participate in the IMO. The entire selection process in NZ (administered by the NZMOC, not us, the NZMOSA) is spread out over a few months of training, competitions and testing:

  1. First, students attempt selection problems - this is what this post is about. Anyone can attempt this.
  2. From these students, around 20 to 30 students are selected to attend the NZ Maths Olympiad Residential Camp (in Auckland in January 2015).
  3. At the camp, students spend about a week learning, practising, and preparing for a final Squad Selection Test.
  4. The test selects 12 people from the camp for further training through Term 1. Throughout this time, they also do a few international Olympiads (including the British Mathematical Olympiad, Australian Mathematical Olympiad, and Asia Pacific Mathematics Olympiad) and assignments which are all taken into account when selecting the final NZIMO team of 6 people (and one non-travelling reserve).
  5. This team continues training for a few months, and no further selection occurs.
  6. In July, the NZIMO team travels to and competes in the IMO, which will be in Chiang Mai, Thailand, in 2015.

So... do you think you're up for the challenge? Give these problems a shot - you'll have to explain as much of your working and thinking as possible, but don't worry too much: we will try to give you some guidance over the next few months about coming up with and writing proofs.

Good luck, and have fun!!