New Zealand Maths Olympiad Committee online

2010 March Problems

Chris — Thu, 04 Mar 2010 10:34:18 +0000

The March problems are intended to help students prepare for the 2010 camp selection problems, used to choose students to attend our week-long residential training camp in Christchurch in January.

In recent years the camp selection problems have been known as the “September Problems”, as they were made available in September. This year we’re going to trial moving the selection problems earlier in the year, releasing them in July and moving the due date to August. This will allow more time for pre-camp training, building up to Round One of the British Mathematical Olympiad in December.

The solutions will be posted in about two month’s time, but can be obtained before then by email if you write to me with evidence that you’ve tried the problems seriously.

Good luck!

- Chris

(Looking for something more challenging? Try the squad number theory assignment.)

2010 Squad Assignment One: Number Theory

Chris — Fri, 26 Feb 2010 02:47:04 +0000

This year’s team selection will be based on three competitions (the BMO2, the AMO, and the APMO) and four assignments: one on each of the four Olympiad areas of algebra, combinatorics, geometry and number theory.

Here is the squad’s first assignment, on number theory. The problems are taken from a variety of sources; these will be acknowledged in the solutions, which I’ll post in a month’s time, together with the second assignment. Following our usual practice, you can get the solutions before then if you write to me with evidence that you’ve made a serious attempt.

Enjoy!

- Chris

Australian Mathematical Olympiad – New Zealand results

Chris — Fri, 26 Feb 2010 02:13:07 +0000

This year for the first time New Zealand was invited to participate in the Australian Mathematical Olympiad, held earlier this month. Our squad of thirteen performed very well, netting a total of eleven awards: one gold, seven silver and three bronze.

Our award winners were:

Malcolm Granville (Auckland Grammar School), Gold
Scott Zhang (Auckland International College), Silver
Edward Wang (Hillcrest High School), Silver
Robert Zhang (Auckland Grammar School), Silver
Tom Yan (Auckland Grammar School), Silver
Byung-Cheol Cho (Auckland Grammar School), Silver
Stephen Mackereth (King’s College), Silver
Michael Wang (Macleans College), Silver
Benedict Morrissey (Garin College), Bronze
Ha Young Shin (Christchurch Boys’ High School), Bronze
Boyd Siripornpitak (Christ’s College), Bronze

Congratulations to all! Full results can be found on the Australian Mathematics Trust’s site.

- Chris

British Mathematical Olympiad Round 2 – New Zealand results

Chris — Fri, 26 Feb 2010 02:11:42 +0000

Late last month the training squad took part in round two of the British Mathematical Olympiad. The top two results from New Zealand (scores out of 40) were

Malcolm Granville, Auckland Grammar School (30)
Robert Zhang, Auckland Grammar School (18).

Congratulations to both, and especially to Malcolm, whose score puts him among the top five (and in fact second equal!) on the leading scores table at the BMOC site.

- Chris

2010 IMO Squad

Chris — Wed, 20 Jan 2010 05:33:32 +0000

New Zealand’s training squad for the 2010 International Mathematical Olympiad was announced last Friday. The final team of six to travel to Astana, Kazakhstan will be decided in April.

The squad members are:

Byung-Cheol Cho, Auckland Grammar School
Malcolm Granville, Auckland Grammar School
Chiao Lin, Columba College
Stephen Mackereth, King’s College
Benedict Morrissey, Garin College
Ha Young Shin, Christchurch Boys’ High School
Boyd Siripornpitak, Christ’s College
Luke Tian, Auckland Grammar School
Edward Wang, Hillcrest High School
Michael Wang, Macleans College
Tom Yan, Auckland Grammar School
Robert Zhang, Auckland Grammar School
Sicong Zhang, Auckland International College.

The team will be accompanied by:

Dr Christopher Tuffley, Massey University (Leader)
Ilya Chevyrev, University of Auckland (Deputy Leader)
Alan Parris, Linwood College (Manager).

The training squad for the 2010 IMO.

2010 January Camp

Chris — Wed, 20 Jan 2010 05:03:43 +0000

The 2010 January Camp was held last week at Rangi Ruru Girls’ School in Christchurch, attended by 24 students from throughout New Zealand. Below are some images from the week.

Arkadii Slinko (U of Auckland) proving the rearrangement inequality in a senior algebra lecture.

Thomas Li explains the solution to a problem to a student during evening question time.

Malcolm Granville presenting his solution to one of the afternoon's problems during discussion time.

Fierce competition at the foosball table during afternoon tea.

Ha Young Shin presents a solution, watched over by challenger Stephen Mackereth, during Wednesday’s
“Math Battle” (known here as “Mathematical Rugby”).

Students working together during evening question time.

Crunch time: Friday's squad selection test.

For your amusement (integer sequences)

Michael — Tue, 15 Dec 2009 01:59:10 +0000

Neil Sloane, who is the father of the encyclopedia of integer sequences, has produced a paper, which highlights seven of them. There are no problems to solve there (other than some hard open ones!), but lots of interesting stuff. For example, you might like to try and prove the following result before reading it:

Consider the sequence defined as follows a(1) = 1, a(2) = 2, and for n >= 3, a(n) is the smallest positive integer not yet in the sequence such that gcd(a(n), a(n-1)) > 1. Prove that every positive integer eventually appears in the sequence.

Michael

BMO Round 1 – New Zealand results

Chris — Mon, 14 Dec 2009 21:50:24 +0000

Seventeen students from New Zealand took part in Round 1 of the British Mathematical Olympiad this month; our top six (scores out of 60) were

Malcolm Granville, Auckland Grammar School (59)
Sicong (Scott) Zhang, Auckland International College (46)
Tom Yan, Auckland Grammar School (42)
Yuan (Edward) Wang, Hillcrest High School (39)
Stephen Mackereth, King’s College (38)
Ha Young Shin, Christchurch Boys’ High School (33).

Congratulations to all these students, and especially to Malcolm and Scott, whose names appear among the top 23 overall on the BMOC site.

A big thanks goes to the BMOC, for allowing us to take part.

Chris

British Math Olympiad Round I

Michael — Wed, 09 Dec 2009 20:36:21 +0000

A number of students from New Zealand recently took part in round 1 of the British Mathematics Olympiad. Results will be available later in December, or early in January. In the mean time you might enjoy looking at the problems, or possibly the solutions (in video form) featuring a mystery guest star in question 6.

Michael

Chrystal’s Algebra

Michael — Wed, 09 Dec 2009 20:31:18 +0000

A classic (pre 1900) textbook on algebra by Chrystal has recently been scanned and made available electronically. Volume 1 is not likely to be of much interest for training purposes but chapters 23 and 24 (on combinatorics), 32 through 34 (continued fractions), and 35 (number theory), of volume 2 are. However, be warned, the scanned PDF is about 30M, so don’t try this on a slow or expensive connection!

Michael