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53rd UNSW Mathematics Competition (1 Viewer)
- Thread starter Kevink98
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rumbleroar
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i have heaps of friends doing it and saw the maths paper
wtf LOL
wtf LOL
Kurosaki
True Fail Kid
I got 2 questions out, the two easy ones lol (the inequalities one and the combinatorics question).
I misread the circle geometry question but apparently it was easy if you transposed it onto the coordinate axes and applied coordinate geometry.
Most of my friends got 3-4 out of the 6 out, and one of them managed to do 5 of them!
Time to quit maths.
I misread the circle geometry question but apparently it was easy if you transposed it onto the coordinate axes and applied coordinate geometry.
Most of my friends got 3-4 out of the 6 out, and one of them managed to do 5 of them!
Time to quit maths.
How'd you do the inequalities??
I tried that for about 20 minutes then gave up...
I got n + k - 1 for the first one, combinatorics question as well using mod, and I had to rush question 5... did it shiftily though using binary... By any chance do you know the answer for question 5b? I got 171 but it's probably wrong... Didn't even touch the geometry haha.
I tried that for about 20 minutes then gave up...
I got n + k - 1 for the first one, combinatorics question as well using mod, and I had to rush question 5... did it shiftily though using binary... By any chance do you know the answer for question 5b? I got 171 but it's probably wrong... Didn't even touch the geometry haha.
Futuremedstudent
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yeah i did it, everyone in my class had to. 20 minutes after the test, we had a topic test on calculus.
The maths comp was hard for most people, i managed to get 3-4 q's.
The maths comp was hard for most people, i managed to get 3-4 q's.
Kurosaki
True Fail Kid
I think that the combinatorics one is 301.
The inequality was alright, so, um
 $ $which is valid as it is equal to 1 $ \\ LHS=(a_1+....+a_n)(\frac{1}{a_1}+......+\frac{1}{a_n}) \\ = (1+\frac{a_1}{a_2}+.....\frac{a_1}{a_n}) + (1+\frac{a_2}{a_1}+....\frac{a_2}{a_n})+....(1+\frac{a_n}{a_1}+.....+\frac{a_n}{a_{n-1}})=n + (\frac{a_1}{a_2}+\frac{a_2}{a_1})+(\frac{a_1}{a_3}+\frac{3}{1})+.......)
For each pair of
, apply the AM-GM inequality for two variables. This makes 
. Now, there are }{2})
pairs (we need to choose 2 distinct integers for these pairs, and the number of ways we do this corresponds to the number of pairs.
So then
 + n \\ =n^2 )
As required.
The inequality was alright, so, um
For each pair of
So then
As required.
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Futuremedstudent
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cos i'm accelerated, so they make everyone do it! I attempted up to 3-4, before it got too tough.
Kurosaki
True Fail Kid
Ah nice, 3/4U?
Futuremedstudent
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i'm in year 10 atm. but this year we do 2 unit prelim, in year 11 we do 3u prelim and 2u hsc and in year 12 we do both 3u and 4u exams.
Damnnnnn, that's a nice proof...I think that the combinatorics one is 301.
The inequality was alright, so, um
For each pair of
So then
As required.
Did anyone get question 6 (senior)? The guy next to me had a whole heap of triangles on his page..
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I managed to get 5 out 
Not sure how rigorous my proofs were though
For the first 1 I got n
Second was just leave the other person with a multiple of 3 counters
Third was as Kurosaki said (there was a similar question in Cambridge 4U harder 3U)
Fourth I just used coordinate geometry letting the first circle be x^2+y^2=1 and the second circle be (x-1)^2+y^2=1 and went from there
Fifth was simply perms and combs, got 301 for the 2nd part but not sure if I'm right
And for the last question I have no idea. Apparently, it was in the junior paper as well. I'd really like to know how to do it.
Not sure how rigorous my proofs were thoughFor the first 1 I got n
Second was just leave the other person with a multiple of 3 counters
Third was as Kurosaki said (there was a similar question in Cambridge 4U harder 3U)
Fourth I just used coordinate geometry letting the first circle be x^2+y^2=1 and the second circle be (x-1)^2+y^2=1 and went from there
Fifth was simply perms and combs, got 301 for the 2nd part but not sure if I'm right
And for the last question I have no idea. Apparently, it was in the junior paper as well. I'd really like to know how to do it.
