Here's my "journey" NZMOC' Heather Macbeth'

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• Here's my "journey" - NZMOC. Heather
  Macbeth.
• My journey to the 2004 International
  Mathematical Olympiad began two and a half years
  earlier, the summer after my third-form year,
  when I attended my first NZMOC January camp. In
  one of the most influential weeks of my life so
  far, I caught a glimpse of what the NZ Maths
  Olympiad program could offer me challenge,
  competition, glory, beautiful mathematics,
  lifelong friendships, and of course the obvious
  reward of a trip to an exciting and faraway place
  in a few years if I worked hard enough in the
  meantime. Within a few days I was hooked by the
  end of the week I had set my goals. I would
  return to camp the next year, 2003, and be picked
  as a reserve for New Zealands IMO team that
  year. In 2004, with two years experience behind
  me, I would be good enough to make the team
  proper, and maybe as a seventh-former in 2005 I
  could win a medal.

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• After a year of weekly trainings and
  independent study, I attended my second January
  camp and, as Id hoped, was made a reserve for
  the 2003 team. This meant that in 2003, as well
  as the usual Monday training and private study, I
  had six months of assignments and exams the
  same training that the team itself received.
  This is designed to develop your ability to solve
  difficult IMO-level problems (as opposed to the
  easy problems encountered at the January camp!)
  The training was a struggle for me but it was
  worthwhile, since it meant that the next year,
  2004, I found the camp and team selection tests
  comparatively easy, and finally was chosen for
  the NZ IMO team.

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• Again I worked through months of training
  books, notes, assignments, tests. For a month
  before I left I counted down the days, and
  finally the day arrived when I met up with the
  other Cantabrians and flew up to Auckland. Two
  weeks of intensive training followed some in
  Auckland, some in Greece. At its worst this was
  a discouraging slog at its best this was the
  most challenging and inspiring maths Ive ever
  seen. Its impossible to feel prepared for the
  IMO, but by the last day or so I began to relax a
  bit and feel calmer.

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• The IMO itself was all Id imagined. The
  exams went well and I won a bronze medal. Greece
  was beautiful, busy, hot and historic. The other
  teams were stimulating company we were
  inseparable from the Irish, and developed
  friendly relations with everyone from Britain to
  Iran and from Luxembourg to (gasp!) Australia.
  The whole trip was as near perfect as it was
  possible to be.

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• So what have I got out of it? Well, a trip,
  obviously. It was my first time in Europe and it
  was really neat for me, having studied Greek
  language, to be able to visit Greece. Secondly,
  lots of friendships. The Maths Olympiad program
  is great for meeting people from all across New
  Zealand and from all over the world. The people
  involved in Olympiad maths tend to be interesting
  and extremely multitalented, and of course they
  share my obsession with maths. Im still in
  touch with half the people I met at my first
  January camp, two and a half years ago.
• Naturally, Im also involved in the Maths
  Olympiad program because I love the maths. The
  problems are beautiful and elegant, and the
  Eureka moment that comes from solving one is
  enough to put me in a good mood for days. I also
  enjoyed the glory that comes from representing
  New Zealand at such a prestigious event my
  fifteen seconds of fame! And being a very
  competitive person, I love the thrill of
  competing at a very high level.

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• For me, though, the best thing about the Maths
  Olympiad program is the challenge. At my first
  January camp, used to being reasonable
  effortlessly top of my classes in maths, I found
  it incredibly stimulating to feel stupid for a
  week or so. Olympiad maths is simply in a
  different league of difficulty from anything
  taught at school there is a huge amount of
  material to learn, and a huge amount of
  experience needs to be gained. When you dont
  find any school work particularly difficult, its
  very appealing to have a goal which takes several
  years of really hard work to accomplish. And
  accomplishing that goal in my case a bronze
  medal makes you feel incredibly satisfied.

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• Where to from here?

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2007

• September problems are out in schools now and are
  on the web at
• www.nzamt.org.nz
• Three digit problems competition 23rd to 26th
  October. Precursor to 2008 NZ Mathematical
  Olympiad competition.

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• New Zealand Mathematical Olympiad
• January Camp Selection Problems
• Junior Problems
• 1. Which fraction 7777777773 , or 8888888882
• 7777777778 8888888887
  is greater? Give reasons.
• 2. Prove that if a(abc) lt 0, then quadratic
  equation ax2bxc 0 has two distinct real
  roots.
• 3. Find a positive integer N whose decimal
  representation contains nine distinct digits such
  that among all the two-digit integers obtained by
  deletion of any seven digits from N there is at
  most one prime number. (If a two-digit integer
  obtained as a result of deletion of seven digits
  starts with a 0, it is considered to be a
  one-digit integer. For example, 07 is 7.)

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• NZMOC January Camp Selection Problems
  Instructions
• 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 13th and 19th of January
  2008. At this Camp the New Zealand squad will be
  selected for the Asia-Pacific Olympiad and
  candidates will be chosen to continue to work in
  the training program prior to selection for the
  NZ team for the IMO competition to be held in
  Spain in July 2008.
• There are two sets of problems junior problems
  and senior problems.
• If you are currently in year 12, or you have
  attended a January camp previously, then you may
  only attempt the senior problems.
• If you are currently up year 11 and you have
  never previously attended a January camp, then
  you may attempt both sets of problems (and your
  results from both sets will be taken into account
  in the selection process).

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• New Zealand Mathematical Olympiad
• January Camp Selection Problems
• Senior Problems
• Some goods, with total weight 18 tonnes, are
  packed in n 35 containers in order to be
  delivered to an orbiting space station. Seven
  shuttles are available to do this, but each can
  deliver no more than 3 tonnes of goods. It is
  known that the shuttles can simultaneously
  deliver any 35 of the n containers. Prove that
  they can simultaneously deliver all the
  containers.
• 2. A brother and a sister cut a round pizza with
  two mutually perpendicular cuts not passing
  through the centre. The boy took the smallest and
  the largest pieces and the girl took the
  remaining two. Who got more pizza? (Or, cant we
  be sure?)

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• New Zealand Maths Olympiad Committee
• Three Digit Problems, 2007
• The competition may be held anytime between
  October 23 and October 26, 2007. The time allowed
  for doing the competition should not be more than
  one hour. Different classes may do the
  competition at different times, even on different
  days.
• The three digit problems are just that. The
  answer to each question is a three digit number,
  i.e. an integer between 100 and 999 inclusive. An
  answer is either correct or incorrect (that is,
  no partial credit for having one or two digits
  correct!)

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• For which three digit number abc is the quantity
• (a - b) X (c - b) as large as possible?
• 2. In a recent test against Italy, the All Blacks
  scored on 21 different occasions. A scoring play
  is one of
• a drop or penalty goal (3 points), a try (5
  points), or a conversion (2points). A conversion
  can only be scored immediately after a successful
  try.
• If M is the greatest number of points that the
  All Blacks might have scored, and m the least
  number
• of points that they might have scored, then what
  is 2M m?
• 3. What is the sum of the prime factors of 33330?
• 4. A geometric sequence is a list of numbers in
  which the ratio of each successive pair of
  numbers is the same (for example 3, 6, 12, 24, .
  . . ).
• If the first three terms of a geometric
  sequence are 64, 96 and 144, then what is its
  first odd term?

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