These problems will be used by the NZMOC to select students for its International Mathematical Olympiad Training Camp to be held in Christchurch between the 15th and 21st of January 2006. At this Camp a group will be selected to choose the New Zealand team for the next IMO competition to be held in Slovenia in July 2006. Cost of this camp is $250, airfares etc included in this as some sponsorship is available.

Students submitting solutions should be intending to remain in school in 2006. (see Regulation 2.2 of the IMO below). They should also hold New Zealand Passports or have New Zealand Residence status.

Regulation 2.2 of the 47th IMO:
2.2 Contestants must not be formally enrolled in a University (or similar post-secondary institution) and they must have been born on or
after July 21 1986.

Students are allowed up to ten full days to attempt these problems.
Solutions along with a completed Student Form should be sent to:-
Michael Albert
Department of Computer Science
University of Otago
PO Box 56
Dunedin

Arriving no later than 14th October 2005

Selection for the camp is based on the top twelve or so students and the remaining students made up of those who are eligible for another camp in 2007. This means some junior students will be selected. Students will be notified whether or not they have been selected for the Camp by the end of November.

Calculators and computers should not be used to assist in solving these problems.
A reasoned argument should be given for your answer to each question.
All solutions must be your own work.

Note that, twelve questions are given to present a variety of topics. It is not necessary to solve all of them. So please send your solutions even if you are sure that you haven't got everything right. Make sure you name each page so we can identify your work. Fill out the form and attach it to your answers.

Good Luck.