|Lawrence Ip > Maths Olympics Training Guide|
The highlight of the MUMS calendar
is the annual Maths Olympics. One of the best things you can do in the lead-up
to this great event is to engage in the training that up until now has only been
practised by one or two teams every year. I do not pretend to offer the final
word when it comes to training methods for the Maths Olympics, but I will try
to give a glimpse into the methods my team has used in the past seven years we
have competed. What worked for us may not necessarily work for your team. Try
them and see!
Before we begin, you may want to read the following explanation of the difference between the Maths Olympics and the International Mathematical Olympiad, often known as the maths olympiad.
First, a few words about the Maths Olympics itself. It's a maths relay with
teams of five people. The team is split up into two groups on opposite sides
of Theatre A with a runner relaying a question from the marker to the groups.
Only one side may work on any one question and you can't work on the next
question until you've either solved the previous question or given up on it.
There's no penalty for wrong answers so you can guess as much as you want. Calculators
aren't permitted for this contest - you're going to have to use old-fashioned
pencil and paper!
Even if you don't feel like competing, come along and spectate. The start has
always been a great sight - all runners simultaneously hustling for that first
question. It can also be really funny seeing friends of yours being really
pumped up after solving questions, or really flustered while attempting them!
If that's not enough there's a spectator competition as well - questions already
attempted by all the teams are put up on an overhead and spectators who solve
them win chocolates for their efforts. For those who prefer to just sit back
and watch, you'll find that the compere hurls sweets into the crowd at
Some tipsThe following tips offer some ways to improve your performance and also enjoyment in the Maths Olympics (to a level even higher than what it already would be!).
Enter early. You won't enjoy it as much if you're not competing! Due to the finite size of the lecture theatre, only about 28 teams can enter. In some years, almost 50 teams have submitted entries, only for many to be turned away.
Bring along lots of pens and paper. You'll need it!
The runner can and should help. In years gone past, the runner was forbidden from helping with the question solving. However, due to blatant violations of this rule and the difficulty of enforcement, it was repealed. Keep working when the runner goes off, as the answer may have been wrong. One worthwhile tactic is to have the runner running back and forth guessing answers while the rest of the side tries to actually work out the answer.
Don't give up too easily! If you get stuck, read the question carefully, even if you have no idea, spend a minute as it may be easier than it first looks. Questions are usually designed to have a neat solution that doesn't require too much calculation. If you still have no idea, don't be afraid to abandon the question. One easy trap to fall into is to keep on investing more time in a question because it is psychologically difficult to give up on a question once you've spent a significant amount of time on it.
Guess. Always look for the opportunity to guess the answer. For example, consider the following question:
At first you might think,
Hmmm, no obvious pattern... Then you might say,
That wasn't too bad was it? However, another possibly quicker approach would be to notice that the rules imply that f(n) must be either 1, or 1 - 1 = 0. Thus a quick way to do this question would be to guess 0 and when that fails, try 1. Remember that there is no penalty for guessing, you can do it as many times as you like (provided the runner doesn't mind!). So let your legs do the thinking for you!
The team name. A vital part of the Maths Olympics is the ingenious team names that teams come up with every year. Some team names from the past have included,"No Real Solutions", "The Return of the Lemma", "Pythagoras was Wrong!", "We Don't Count", "Meds on Prozac", and "Gottim - Yes". Start thinking now! For those who really want to get into the spirit of things, team mascots, music, costumes and make-up are encouraged. Bring along a cheer squad too.
Lastly, don't take it too seriously. Have fun! Unless you're one of those people who can't stand coming 2nd (the section below is devoted to them!), just sit back and enjoy the spectacle when the other half of your team is working on a problem. Yell and scream a bit! At the end, even if you receive no monetary reward, I guarantee you will have had one of your most entertaining hours at uni.
Advanced Training TechniquesCaution: The methods described are highly dangerous and may result in physical and mental injury. Do not try these at home! Do not try without expert supervision. The author will not be responsible for any loss of property, physical injury or impairment of mental faculties sustained. You have been warned!
This section is for those who are ultra-competitive perfectionists who are satisfied with nothing less than coming first, or failing that, to perform at their absolute best.
Treat it seriously! You must learn to ignore all your friends who say that you're mad. Treat it as a badge of honour! At least one team in the past has gone to extraordinary lengths to ensure that nothing will stop them. In fact, the current (at the time of writing) president of MUMS has often been heard to say that 50 hours of training is his target (he's been known to achieve this too).
Pick your team early. Nothing is more important than having the right team, and nothing is more frustrating than finding that your plans for the ideal team have been thwarted due to someone having previous commitments to a rival team. So what makes a good team?
Optimise your running order. The ideal first runner is a rugby player. Readers who have witnessed the mad rush to pick up the first question will understand why. Most teams aren't lucky enough to find a mathematically gifted rugby player, but it helps to have someone who can negotiate a dense crowd. The next few runners should be in decreasing order of speed. It's no good having a fast runner if they don't get the chance to run! However there is a trade off here - it may be better to have the fitter runners run later when there's likely to more questions that may require a lot of guessing (because the increased difficulty makes it difficult to solve any other way).
Manage your time well. Why do you need a time management strategy? The most important reason is that it is easy to spend too much time on a question. Psychologically, it is difficult to abandon a question after having spent a lot of time on it. It is all very well to invest a lot of time in a question if you end up solving it, but it leaves you vulnerable to various risks:
This has the several advantages:
It's also important to only implement this strategy if you have trained with it. Because people are reluctant to abandon questions after having spent a lot of time on it, every team member must be convinced that on average, this strategy works well. This confidence in the strategy can only come through successful implementation in practice.
Train physically. Mens sana in corpore sano - a healthy mind
in a healthy body. For the really dedicated, there is the physical training.
Contrary to popular belief, the primary reason for training physically is not
to reduce the time taken to run up and the down the stairs. The real reason
is so that the runner can contribute towards solving the questions as well.
Thinking requires lots of oxygen to reach the brain and those who have competed
in the maths olympics before will realise that it is very difficult to think
when you are tired from running and the blood is coursing through your brain.
You can only avoid this by being fit and training especially to counteract this
problem. Some of the members of my team used to practise doing questions and
then running up and down
The second reason to train physically is to enable exhaustive (both in the mathematical and physical sense!) guessing as a technique to solve problems. There have been times when we guessed the answer to a question after about 8 attempts. To be able to do this, the runner needs to be extremely fit.
It's also important to practise going down stairs. Going up stairs is relatively easy, as long as your legs are strong enough, you just go up 2-3 steps at a time, depending on the length of your stride.
Going down is much more involved. First, going down stairs one step at a time is very slow, because you are limited by how fast you can physically move your legs. The solution? Go down the stairs 2 steps at a time! This produces dramatic speedups but requires training months in advance. Because of the speed at which you go down the stairs, much skill is needed to avoid injury. Skill is also needed to maintain a smooth descent for greatest speed. To develop the necessary technique, practise descending slowly and smoothly in a controlled manner and then gradually increase the speed until you can just glide down the stairs at full pelt.
For those who are interested, there are physiological reasons why you need to train specifically to go down stairs. Most of the exercise that we normally do is concentric exercise, where the muscles exert force and contract in the process. Descending stairs requires eccentric exercise, where the muscles exert force and lengthen in the process. Because we don't normally do eccentric exercise (except in some more exotic sports) even very fit people who could run comfortably up many flights of stairs would have very sore muscles if they tried to run back down those stairs. For those who are interested, there has been recent research conducted by Proske and Morgan at Monash University into this. See http://www.monash.edu.au/pubs/montage/Montage_97-01/p8-9.html.
Train with more difficult problems. By choosing difficult problems, you have the chance to practise teamwork, communication and the division of different parts of problems amongst team members. With easy problems, the communication overhead makes it not worthwhile. Also difficult problems give you the opportunity to practise passing questions.
You now have all the tools that you need to compete in the Maths Olympics either to have fun, or to win. If you think of innovations, or disagree with some of my suggestions, feel free to write to me.
Go get 'em guys!!
(written in 1998)
About the author:
Lawrence Ip competed in Maths Olympics from 1991 through 1997, first competing when he was in year 11 at school. He captained the winning team in 1992, 1994, 1995 and 1997. Since retiring from competition he has spent the last 5 years pursuing a PhD in quantum computing at UC Berkeley. He often dreams of making a comeback but in moments of reason realises he is too old for this kind of thing.
Postscript, an overdue acknowledgement:
Although I was the one who wrote this training guide, the development of these training methods was not a solo effort. My main collaborator was Chaitanya Rao. At the time this guide was first written he was too shy to have his contributions recognised.