Post by: the.watchman on May 05, 2010, 05:14:55 pm
I didn't do so well IMO but it was fun! :)
Post by: appianway on May 05, 2010, 05:20:10 pm
Meh. I failed hardcore. The questions weren't actually hard, but I answered barely anything in the time and made heaps of careless mistakes. There's no way with the amount that I answered that I can actually get anything. Hope EvangelionZeta or the.watchman do though!
Post by: the.watchman on May 05, 2010, 05:24:08 pm
The fact that you posted a thread about it instead of forgetting you even sat it contradicts the "I didn't do so well" statement.
Meh. I failed hardcore. The questions weren't actually hard, but I answered barely anything in the time and made heaps of careless mistakes. There's no way with the amount that I answered that I can actually get anything. Hope EvangelionZeta or the.watchman do though!
That's not a fair statement, I am merely interested to see how much I failed in comparison to the others on VN :P
I know, the questions seemed kinda easier this year, but I still couldn't successfully answer most of them...
Post by: appianway on May 05, 2010, 05:34:40 pm
Oh, and you failed less than I did. So that's how you did in comparison to VN people.
Post by: the.watchman on May 05, 2010, 05:46:03 pm
Oh, and you failed less than I did. So that's how you did in comparison to VN people.
Very funny... :P
Anyone else?
Post by: the.watchman on May 05, 2010, 06:02:43 pm
Post by: AzureBlue on May 05, 2010, 06:09:56 pm
Really? Outstanding for three full questions? That's cool!Also, you tend to do better if you have 3 full solutions, then if you made progress on all 7 questions but didn't get a solution. (as stated on the cover sheet). That's why I failed today, I think. I don't know why I always do better against the cohort above me than the cohort below me. Technically, above is stronger...
Maybe they only seemed easy in comparison to physics, but you could work out most of them logically.Yes, MUMC is slightly different to the others. More logic. :)
Post by: appianway on May 05, 2010, 06:16:00 pm
Post by: luken93 on May 05, 2010, 07:47:59 pm
Anyway, I'm tryin to remember the questions, post solutions if you think you got em haha
1. The number of snaps on a chocolate bar
2. The arrangement around the circle 1, 2, 3 ... 2n
3.
4. The consecutive 18 numbers
5. Sum of the digits of 9n
6. The convex tetrahedron intersecting at x and y
7.
8. The polyhedron that haad different sized areas with a sphere inside
I think i got 1, some of 2, some of 3, some of 5, some of 8???
Oh well, all over for another year
Post by: TrueTears on May 05, 2010, 07:49:57 pm
Post by: appianway on May 05, 2010, 08:02:41 pm
Post by: luken93 on May 05, 2010, 08:12:13 pm
Hmm for the half marks, I had solutions but I don't think my proofs were as rigorous as they could've been. So I fully answered about 4 of the questions, but I only think one of the questions had a really rigorous bulletproof proof.yeh thats what i reckon, i so wanted to say WELL IT IS OKAY, YOU MADE THE QUESTIONS SO WHY DO I NEED TO PROVE TO YOU THAT THE QUESTION CAN BE DONE WHEN YOU MADE IT
got a bit cranky halfway through aha
Post by: luken93 on May 05, 2010, 08:14:20 pm
Hehe, I stole the question sheet, I'll post them up in a tick here:haha so did i, forgot all about it. you can upload it, otherwise I will waste the night procrastinating instead of rote learning like I should be :P
TO COME
Post by: TrueTears on May 05, 2010, 08:15:38 pm
LOL WDF THIS QUESTIONS IS IN ART N CRAFT HAHA it was a basic combinatorics Q rofl
(2) Find all the arrangements of the numbersaround a circle so that the difference between any two numbers next to each other is at most 2.
Post by: EvangelionZeta on May 05, 2010, 08:18:09 pm
Colin Lu got all 8 questions fully. =)
Post by: the.watchman on May 05, 2010, 08:24:48 pm
(1) Let s be the number of snaps required to break an
(2) Find all the arrangements of the numbers
(3) For positive integers
(4) Prove that among any 18 consecutive positive three-digit numbers, there must be at least one number divisible by the sum of its digits.
(5) Let N be a number whose digits when read from left to right form a strictly increasing sequence. The numbers 234 and 13479 are examples of such numbers. Find all possible values of the sum of the digits of 9N.
(6) Let ABCD be a convex quadrilateral (a quadrilateral is convex if and only if the two diagonals intersect at a point that is in the interior of the quadrilateral). Let diagonals AC and BD meet at the point X and let AB meet CD at Y. Suppose that triangles ABC, BCD, AXD have equal area. Prove that triangles YBC and ABD have equal area.
(7) In the equation:
both c and n are integers,
(8) A polyhedron is a geometric solid in three dimensions with flat faces and straight edges. If the faces are painted black and white, such that every white face is surrounded by black faces (surrounding faces must share an edge with the faces they surround), but the total area of the white faces exceeds the total area of the black faces, prove that one can't inscribe a sphere in the polyhedron.
Post by: luken93 on May 05, 2010, 08:26:13 pm
This is correct isn't it?
Post by: the.watchman on May 05, 2010, 08:26:54 pm
Eh, I got 1, 2 and 4, got half answers for 3 and 5 (including some made up premises...), wrote bs for 6 and 7 and didn't touch 8. Spent the last ten minutes writing out the "What a piece of work is a man!" speech on my last page.
Colin Lu got all 8 questions fully. =)
Wow, that guy must be amazing...
I almost did as much as you, but my techniques were horrid (almost resorted to 'proof by elimination of impossible cases'...)
q1. [tex](m \times n) - 1 = s
This is correct isn't it?
Absolutely :)
Post by: luken93 on May 05, 2010, 08:31:27 pm
woohoo, that was my goal, get one question right :)Eh, I got 1, 2 and 4, got half answers for 3 and 5 (including some made up premises...), wrote bs for 6 and 7 and didn't touch 8. Spent the last ten minutes writing out the "What a piece of work is a man!" speech on my last page.
Colin Lu got all 8 questions fully. =)
Wow, that guy must be amazing...
I almost did as much as you, but my techniques were horrid (almost resorted to 'proof by elimination of impossible cases'...)q1. [tex](m \times n) - 1 = s
This is correct isn't it?
Absolutely :)
Post by: the.watchman on May 05, 2010, 08:33:47 pm
Considering that I knew the answer for one of the questions, but had no idea about the process, would I get any marks for just putting a bogus explanation and the answer? I thought of doing that, but in the end I just left that question blank...
Post by: luken93 on May 05, 2010, 08:44:48 pm
I am interested to know:well thats what i thought, but then if they say prove that im guessing you need some sort of equation or similar to prove it?
Considering that I knew the answer for one of the questions, but had no idea about the process, would I get any marks for just putting a bogus explanation and the answer? I thought of doing that, but in the end I just left that question blank...
also, was q5 all sum to equal 9? i showed 3 random numbers and explained why i used them, however i doubt i will get full marks.
Post by: the.watchman on May 05, 2010, 08:46:55 pm
I am interested to know:also, was q5 all sum to equal 9? i showed 3 random numbers and explained why i used them, however i doubt i will get full marks.
Considering that I knew the answer for one of the questions, but had no idea about the process, would I get any marks for just putting a bogus explanation and the answer? I thought of doing that, but in the end I just left that question blank...
That's the exact question I was thinking of
It's pretty obvious that it's 9, but how to prove it for all cases?
So I attempted a full proof and failed dismally
Post by: luken93 on May 05, 2010, 08:58:21 pm
wat did that collin lu write then evangelion?I am interested to know:also, was q5 all sum to equal 9? i showed 3 random numbers and explained why i used them, however i doubt i will get full marks.
Considering that I knew the answer for one of the questions, but had no idea about the process, would I get any marks for just putting a bogus explanation and the answer? I thought of doing that, but in the end I just left that question blank...
That's the exact question I was thinking of
It's pretty obvious that it's 9, but how to prove it for all cases?
So I attempted a full proof and failed dismally
Post by: EvangelionZeta on May 05, 2010, 09:20:52 pm
wat did that collin lu write then evangelion?I am interested to know:also, was q5 all sum to equal 9? i showed 3 random numbers and explained why i used them, however i doubt i will get full marks.
Considering that I knew the answer for one of the questions, but had no idea about the process, would I get any marks for just putting a bogus explanation and the answer? I thought of doing that, but in the end I just left that question blank...
That's the exact question I was thinking of
It's pretty obvious that it's 9, but how to prove it for all cases?
So I attempted a full proof and failed dismally
No idea - didn't ask. D:
Post by: AzureBlue on May 05, 2010, 09:26:39 pm
Hehe, I stole the question sheet, here are the questions:Thanks :) Wow, 5/8 are proof questions and no chessboard/domino combinatorics question this year for the first time in ages. Actually looks like a quite accessible paper though, I'll sit the paper this weekend and see how I go. :D
Also, was the question sheet released at 1pm (ie. you can take it home anytime after 1pm today) or is it released in 3 days? LOL for AMO, the questions are banned for discussion for a whole month >:(
Post by: luken93 on May 05, 2010, 09:35:11 pm
Yeh compared to last year it seemed alot easier to understand, but alot harder to justify you reasonsHehe, I stole the question sheet, here are the questions:Thanks :) Wow, 5/8 are proof questions and no chessboard/domino combinatorics question this year for the first time in ages. Actually looks like a quite accessible paper though, I'll sit the paper this weekend and see how I go. :D
Post by: appianway on May 05, 2010, 09:41:33 pm
Post by: AzureBlue on May 05, 2010, 09:43:16 pm
I don't think it was different mathematically (although I didn't sit last year's senior so I can't compare), but rather, you didn't need much prior knowledge. You didn't need theorems or to know much about factorial-esque stuff.Correct. That tends to be the case with MUMCs - it's all about logic, you don't need to know obscure theorems or anything, whereas you sometimes do for AMOs or harder ones, though most things are able to be manipulated by simpler but useful theorems and a touch of ingenuity!
Post by: luken93 on May 05, 2010, 10:04:28 pm
Also, do you get a certificate of partic, credit, distinc etc?
Only 2 kids did it at our school, but dont wanna accept a "participation" award at assembly ahaha
Post by: kyzoo on May 05, 2010, 10:47:04 pm
I'm pretty sure I got full solutions for 2, 3, and 4.
I got the wrong answer for question 1 LOL, misinterpreted question >.<. I only realised this after talking to 3 other ppl who did the comp (Colin Lu, Evangelion, and a person from another school).
I got the answer for question 5, but like, I must have set up the equation wrong since Colin Lu told me the sum of the digits worked out to be 9, and I got something with like 20 variables.
I tried doing question 6, made some progrss, but ultimately didn't get the answer
I didn't touch question 7 or 8
...
Overall, I think I performed the same as I did last year.
Post by: luken93 on May 05, 2010, 10:53:08 pm
and how did you do 2, 3, 4 with proper answers?
Post by: kyzoo on May 05, 2010, 10:56:21 pm
3 - If you solve the question, then you already have the proof
4 - Prove that any number whose digits sum up to a multiple of 9, will be divisible by 9.
Post by: TrueTears on May 05, 2010, 11:36:33 pm
you got a prize tho last year didnt you?Q2 is a basic combinatorics question, i personally wouldn't do a proof, i'd maybe try a combinatorial argument to create an isomorphism which would most likely solve it.
and how did you do 2, 3, 4 with proper answers?
Post by: kyzoo on May 05, 2010, 11:47:51 pm
you got a prize tho last year didnt you?Q2 is a basic combinatorics question, i personally wouldn't do a proof, i'd maybe try a combinatorial argument to create an isomorphism which would most likely solve it.
and how did you do 2, 3, 4 with proper answers?
....
LOL what's a "combinatorial argument" and what's an "isomorphism"
Post by: TrueTears on May 05, 2010, 11:56:16 pm
the one i've always remembered when i learnt combinatorial arguments is this example:
prove the summation identity
for
one could do a algebraic 'proof' but one can also avoid the use of any rigorous/formal maths and simply try an "combinatorial argument" like this:
say n = 17 and r = 10 then we have:
now my combinatorial argument will be like this:
Let us consider all 11 member committees formed from a group of 18 people, fix one of the 18 people, say some one called E. The 11 member committees can be broken down into two mutually exclusive types: those with Eand those without. How many include E? Having already chosen E, we are free to chose 10 more people from the remaining pool of 17, so we got:
Then just replace 17 with n and 10 with r and do the same combinatorial argument thus "proving" the equality.
can u see how a combinatorial argument is like a "story" which basically requires a bit of wishful thinking to create ur OWN problem which yields the result, rather than using known identities to prove the result.
for example, create a combinatorial argument for 7 x 8 = 56
what does it mean? well it could mean that there are 7 choices of pasta and 8 choices of pizza so there are 56 ways of choosing a pasta dinner with pizza.
other types of isomorphisms or "bijections" could be like generating functions and combinatorics
you could have a very complex combinatorics questions but simply represent it with an expression like (1+x^2+x^4+...)(1+x^3+x^5+...) or something whose indices could represent different combinations.
another type of basic isomorphic relationship could be in basic linear algebra, where you can view a matrix using different methods such as using the column picture of a matrix or a row picture, both yield different equations but when solved, they represent the exact same thing.
Post by: AzureBlue on May 06, 2010, 07:08:32 am
What are the prizes anyway, is it purely on the top 10/20/30 etc or is it the amount of marks?Nope, there's first three places, then about top 10-15 get outstanding award, then the next 15 get cert of merit. Rest get participation I think (which is around the other thousand people).
Also, do you get a certificate of partic, credit, distinc etc?
Only 2 kids did it at our school, but dont wanna accept a "participation" award at assembly ahaha
Post by: the.watchman on May 06, 2010, 08:08:05 am
What are the prizes anyway, is it purely on the top 10/20/30 etc or is it the amount of marks?Nope, there's first three places, then about top 10-15 get outstanding award, then the next 15 get cert of merit. Rest get participation I think (which is around the other thousand people).
Also, do you get a certificate of partic, credit, distinc etc?
Only 2 kids did it at our school, but dont wanna accept a "participation" award at assembly ahaha
So what sort of score do you reckon is needed to get a merit certificate?
Post by: AzureBlue on May 06, 2010, 01:48:20 pm
Don't know, I've personally never gotten one before (I either get outstanding or nothing). I reckon that it's about 2.5-3 questions though. Depends on the difficulty of the paper.So what sort of score do you reckon is needed to get a merit certificate?What are the prizes anyway, is it purely on the top 10/20/30 etc or is it the amount of marks?Nope, there's first three places, then about top 10-15 get outstanding award, then the next 15 get cert of merit. Rest get participation I think (which is around the other thousand people).
Also, do you get a certificate of partic, credit, distinc etc?
Only 2 kids did it at our school, but dont wanna accept a "participation" award at assembly ahaha
Post by: the.watchman on May 06, 2010, 01:50:02 pm
Don't know, I've personally never gotten one before (I either get outstanding or nothing). I reckon that it's about 2.5-3 questions though. Depends on the difficulty of the paper.So what sort of score do you reckon is needed to get a merit certificate?What are the prizes anyway, is it purely on the top 10/20/30 etc or is it the amount of marks?Nope, there's first three places, then about top 10-15 get outstanding award, then the next 15 get cert of merit. Rest get participation I think (which is around the other thousand people).
Also, do you get a certificate of partic, credit, distinc etc?
Only 2 kids did it at our school, but dont wanna accept a "participation" award at assembly ahaha
I see, thanks!
Post by: AzureBlue on May 06, 2010, 01:54:15 pm
Post by: the.watchman on May 06, 2010, 01:55:53 pm
Yesterday night, I attempted the questions again (without any help except a hint in one of the questions). I solved all of them. GRRRRR. :( I guess I have to work more carefully and faster next time.
Lol, good job! :)
Post by: luken93 on May 29, 2010, 07:36:25 pm
and i dont think id even get 10 marks :(
anyway, here's the link
http://www.mathscomp.ms.unimelb.edu.au/archive/2010SS.pdf
Post by: AzureBlue on May 29, 2010, 08:50:21 pm
SOLUTIONS ARE OUTapart from the intermediate section for some reason... :P
and i dont think id even get 10 marks :(
anyway, here's the link
http://www.mathscomp.ms.unimelb.edu.au/archive/2010SS.pdf
Post by: luken93 on July 28, 2010, 10:35:28 pm