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I was told that 2961 isnt that bad if you teach yourself some of the 1901 stuff before the start of the course, which Id plan to do anyway so I can get away with skipping some of the lectures :P And some close friends of mine who did logic and foundations say it became really boring after a...

You can do it by just counting it. So if you think about it, the nPk = n(n-1)(n-2)...(n-k+1) right? Thats pretty easy to justify; n possibilities for the first, n-1 for the second, ... n-k+1 for the kth. So thats nPk. Now the question is, whats the relationship between nPk and nCk? Now if you...

Have you seen the counting argument version?

Yup thats exactly right. You construct a number that has at least one digit different from every number on the list (precisely, it differs from the kth number on the list in the kth digit), giving a contradiction coz then it couldn't be on the list.

Alright its pretty late but still, time for largarithmic does cardinality! Basically we want to come up with an idea for what it means for a set to have "the same size" as another set. Now this is pretty obvious for finite sets: {1,2,3} has the same number of elements as {2,3,4}, for instance...

Nah I meant like, an actual mathematical proof that uses sorta really abstract "symmetry". Can't really think of an example right now though :P I really like number theory too, in particular arguments from polynomials and stuff when they get involved. Something I really enjoyed proving at one...

I don't think there's any one particular thing that I love above all others - but I guess I really like really beautiful symmetric arguments, can't think of an amazing example right now. But something that IS amazing: diagonalisation arguments. I mean the very idea that "some infinities are...

Re: 2012 HSC MX1 Marathon You've answered a slightly different question - I said *sum* of distinct integer powers of phi - you can't have differences. But if you could, yeah that still works ^^ And I believe that theorem is actually pretty easy to prove (you can induct with a pretty simple...

Re: 2012 HSC MX1 Marathon Uses the first property only - don't need anything to do with fibonacci numbers. Try it, its a fun question :)

Re: 2012 HSC MX1 Marathon really cool fact (kinda unrelated but alright...) you know every positive integer can be written as sum of distinct integer powers of phi? e.g. 1 = \phi^0 2 = \phi^0 + \phi^{-1} + \phi^{-2} 3 = \phi^1 + \phi^0 + \phi^{-2} 4 = \phi^2 + \phi^0 + \phi^{-2} (where \phi...

I don't know whether you're a troll or not, but could you please shut up about IQ? Natural intelligence counts a tiny amount in life for most of us; the most of it is hard work and learning how to learn. And to the extent of it does, your intelligence is proven by what you actually do - and no I...

No, that isnt a situation that corresponds with the actual question. The reason is in giving the sides vectors you havent given them directions. For the angles between Z1 and Z2 to actually be alpha, you need Z3 = Z1-Z2 or Z3 = Z2-Z1. If you want Z3=Z1+Z2 (so that it actually corresponds to the...

gogogogogo!

Re: 2012 HSC MX2 Marathon Hey your thing says HSC 2011, are you doing science / advanced maths this year and if so at which uni? Also may as well post a question. Dunno how suitable thing one is but its neat: Part (A). Trapezium ABCD is given with AB parallel to CD. Let diagonals AC and BD...

Re: 2012 HSC MX2 Marathon You dont actually need to use an infinite series. You can use the following fact (prove it for yourself its easy): If \frac{a}{b} = \frac{c}{d}, then both these are also equal to \frac{a+c}{b+d}. Then if R_i and G_i denote the red area/green area within the ith...

Re: 2012 HSC MX2 Marathon Doesn't matter because of dimensionality. Like, what does "radius one" mean? It means, "radius one UNIT" where that unit is something you chose. You could have, the outer radius is radius "one inch" for instance, or could be "two centimetres": but if its radius "two...

Re: 2012 HSC MX2 Marathon cool problem!!! Anyway here's how I'd do it. Observation: each circle has half the radius as the one before it. Proof: Clearly all the circles, since the diagram has rotational symmetry, have the same centre; call this O. Now let a vertex of say the biggest...

Re: 2012 HSC MX2 Marathon Theres basically no agreed standard for what "N" means... I usually just write N_0 or N^+ (dunno how to do blackboard bold on this), in a way that would be pretty unambiguous. Someone give a problem!

wrarrr tesseract

Alright, that quantity i/-k represents the vector CA divided by the vector CB, right? Now if A,B,C is isosceles right angled at C, that means that the length CA = the length CB, right? I.e. |CA| = |CB|, i.e. |CA/CB| = 1 right? So you have to get |i/-k| = 1, coz CA/CB = i/-k if CA and CB are...