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Imagine a maths exam where you have as much paper as you like AND as much time as you like (almost) AND if you get absolutely no marks whatsoever it doesn't matter in the slightest. That's my type of maths exam.
In the MOG - international maths olympiad for girls - there are 5 questions and 2.5 hours, which is the longest time you will ever spend at school doing one single activity!! I enjoy the sense of freedom- to either get right to the bottom of one puzzle or to flit between all 5 of them - working away at the first until the next one starts to look more interesting...
Something else that marks out the MOG from the other ukmt challenges (eg multiple-choice junior/senior maths challenges where you've just got to get as many answers right as fast as possible) is the focus on presentation and demonstration of complete solutions. When I am writing my workings, I imagine it like a conversation with my piece of paper or a performance of what I am thinking.
If you get a question about a real life situation, then why not try it out? This year's question 3 was about some kind of sudoku. Quinn was told by her friend how many counters were in each row and column of a 5x5 square board (all of these totals had to be different). Quinn's friend could place any number of counters on a board square- from zero to, I suppose, infinity. Were there any situations in which Quinn would not be able to guess correctly how many counters in each square?
I created my own 5x5 board of numbers on my paper and gave myself a set of 10 totals. Then i tried to re-create my sudoku using only the 10 totals. Soon, two things became apparent: Quinn's intellect and patience were streets ahead of my own, and the only board Quinn wouldn't be able to work out would be one where two boards have the same set of 10 row totals.
Questions 1, 2, and 4a made you prove statements about shapes. Sometimes, in the proofs questions, it feels like they've told you the answer in the question, and the examiner knows that it's the right answer so why should you have to tell them, and there's no way that you would have worked out the statement in the question unless you'd been told, so how ironic that you're the one doing the explaining! However, particularly in question 2 it was really useful to have the statement to prove, because it provided an idea of where to start, working out the maths going on behind the shape.
Question 5 was a lot less fun than it looked. 4 girls all had models for different fractions - Bella had "(6p-5)/(3p+6)", Isabella had "(n+1)/n", Christine had something else. Using different values of their constants, each girl could multiply examples of her fraction model together as many times as she liked with the aim of getting an integer answer. Drawn in by the word "integer" (a clean whole number is always pleasant) I thought I'd have a go. However, After working out that Isabella could obtain all integers (bigger than 2) [because 2/(2-1) = 2 and multiplying that by 3/2 = 3, and that X (4/3) = 4 and so on], two successive disasters happened. Firstly, I realised that I'd done the whole next stage of working calling Bella "Christine" (so I had to do tons of scribbling out - yuck). Then, completely missing the fact that actually, Bella (6p-5)/(3p+6) couldn't make any integers at all [because there aren't any values of p that could make a multiple of (6p-5) divisible by a multiple of (3p+6)], my prospects for Bella's integers just kept getting more and more disconcertingly un-integer-like!!
I didn't try 4b until the very end because the diagram, drawn in the question, looked like someone had taken a chessboard and smashed it onto the floor, breaking the black squares but not the white ones. Crazy. Fortunately (thank you UKMT) it was made out of squares and equilateral triangles, all with sides of length 2. X and Y were two points in the middle of two of the squares, and you had to find the distance between them. The first thing that I thought of doing was to draw circles around the squares (regular shapes fit really nicely inside circles - and outside of them, I think that's because tangents to a point are equal). It turned out that length XY was equal to 6 circle radii.
So the MOG ended happily ever after, and I'm now really excited to go through the answers. It's always a true enlightenment to see the clear solutions that your tangled workings could have looked like.
However, I'd still say that getting the answers wrong is just as much fun as getting them right - if anything, it's more creative!!
-Anoushka Sharp, Year 12
In the MOG - international maths olympiad for girls - there are 5 questions and 2.5 hours, which is the longest time you will ever spend at school doing one single activity!! I enjoy the sense of freedom- to either get right to the bottom of one puzzle or to flit between all 5 of them - working away at the first until the next one starts to look more interesting...
Something else that marks out the MOG from the other ukmt challenges (eg multiple-choice junior/senior maths challenges where you've just got to get as many answers right as fast as possible) is the focus on presentation and demonstration of complete solutions. When I am writing my workings, I imagine it like a conversation with my piece of paper or a performance of what I am thinking.
If you get a question about a real life situation, then why not try it out? This year's question 3 was about some kind of sudoku. Quinn was told by her friend how many counters were in each row and column of a 5x5 square board (all of these totals had to be different). Quinn's friend could place any number of counters on a board square- from zero to, I suppose, infinity. Were there any situations in which Quinn would not be able to guess correctly how many counters in each square?
I created my own 5x5 board of numbers on my paper and gave myself a set of 10 totals. Then i tried to re-create my sudoku using only the 10 totals. Soon, two things became apparent: Quinn's intellect and patience were streets ahead of my own, and the only board Quinn wouldn't be able to work out would be one where two boards have the same set of 10 row totals.
Questions 1, 2, and 4a made you prove statements about shapes. Sometimes, in the proofs questions, it feels like they've told you the answer in the question, and the examiner knows that it's the right answer so why should you have to tell them, and there's no way that you would have worked out the statement in the question unless you'd been told, so how ironic that you're the one doing the explaining! However, particularly in question 2 it was really useful to have the statement to prove, because it provided an idea of where to start, working out the maths going on behind the shape.
Question 5 was a lot less fun than it looked. 4 girls all had models for different fractions - Bella had "(6p-5)/(3p+6)", Isabella had "(n+1)/n", Christine had something else. Using different values of their constants, each girl could multiply examples of her fraction model together as many times as she liked with the aim of getting an integer answer. Drawn in by the word "integer" (a clean whole number is always pleasant) I thought I'd have a go. However, After working out that Isabella could obtain all integers (bigger than 2) [because 2/(2-1) = 2 and multiplying that by 3/2 = 3, and that X (4/3) = 4 and so on], two successive disasters happened. Firstly, I realised that I'd done the whole next stage of working calling Bella "Christine" (so I had to do tons of scribbling out - yuck). Then, completely missing the fact that actually, Bella (6p-5)/(3p+6) couldn't make any integers at all [because there aren't any values of p that could make a multiple of (6p-5) divisible by a multiple of (3p+6)], my prospects for Bella's integers just kept getting more and more disconcertingly un-integer-like!!
I didn't try 4b until the very end because the diagram, drawn in the question, looked like someone had taken a chessboard and smashed it onto the floor, breaking the black squares but not the white ones. Crazy. Fortunately (thank you UKMT) it was made out of squares and equilateral triangles, all with sides of length 2. X and Y were two points in the middle of two of the squares, and you had to find the distance between them. The first thing that I thought of doing was to draw circles around the squares (regular shapes fit really nicely inside circles - and outside of them, I think that's because tangents to a point are equal). It turned out that length XY was equal to 6 circle radii.
So the MOG ended happily ever after, and I'm now really excited to go through the answers. It's always a true enlightenment to see the clear solutions that your tangled workings could have looked like.
However, I'd still say that getting the answers wrong is just as much fun as getting them right - if anything, it's more creative!!
-Anoushka Sharp, Year 12
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