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Re: HSC 2013 4U Marathon The answer is 4 digits long. I've verified it. It shouldn't be tedious to compute -- I did it quickly using only the operations available on a standard BOS-approved calculator. Part ii) perhaps requires slightly more logical reasoning than you'd get in an HSC paper...

Re: HSC 2013 4U Marathon Here's a tricky little perms & combs for y'all. $ i) There are 5 varieties of fruit available (strawberry, apple, pear, grape, melon). I want to buy at least 1 fruit and at most 12 fruit. In how many ways can I do this? (e.g. one such purchase could be 2 strawberries...

Re: HSC 2013 4U Marathon Doing them on paper, won't TeX up every step. i) 0, 1, 2, 5, 12 ii) $ R.T.P. $P_{k+2}P_k - P_{k+1}^2 = (-1)^{k+1}$, having assumed that $P_{k+1}P_{k-1} - P_k^2 = (-1)^{k}$. Express everything in terms of $P_k, P_{k-1}$ by using the recurrence, then you get -RHS =...

IT, SDD and IPT? I would be worried about the scaling of these subjects =\ your other 3 scale well fine though.

What do people think of the number of questions on the MX2 exam for the 3hr time limit? I often felt like the need to get marks on questions 1-6 (which generally require little creativity, and let's face it, can more or less be rote learned) meant that I rarely had time to really dig in to those...

='( this makes me so sad. Year 12 doesn't have to be a year that you throw away just to get into your desired uni course. It doesn't have to be a stage of your life where you "simply have to rote" stuff. It's possible to achieve your aims without compromising on everything else. Also, the...

This question was on a selection exam for the Australian informatics olympiad team many years ago. There's a pile of diamonds in front of you -- 30 fake diamonds and 2 real diamonds. Each fake diamond weighs 10g. The 2 real diamonds weigh 5g and 15g respectively. You have a set of scales...

For every line of working you do, reread it and concentrate really hard on understanding exactly what you did. Whenever possible, substitute values back in. If your working feels flaky at all or you think that you might have made a silly mistake, redo the whole question without referring to...

UNSW, obvs...

If he's good at all those subjects, I don't see why he can't... you don't need to be AMAZING at any of your subjects to get 99.95, you only need to be good at all of them. Most people are let down by a specific subject (often English, coz it's the only compulsory one). Mid band 6's in all those...

Re: HSC 2013 4U Marathon iii) Let the two letters be a and b. In exactly half the permutations, a will come before b. There are n! total permutations, therefore a can come before b in n!/2 ways. (this seems very obvious to me, so I'm not sure how much more mathematically it must be phrased. If...

Re: HSC 2013 4U Marathon $i) $\sum_{k=1}^{n} k^3 = \frac{1}{4} \sum_{k=1}^{n} 4k^3 = \frac{1}{4} \sum_{k=1}^{n} k^2(k+1)^2 - k^2(k-1)^2$. On expansion, all terms except the last will cancel, leaving the RHS. $ $ii) T_n = $\frac{n(n+1)}{2}$ (using arithmetic series). \therefore \quad $T_n^2$ =...

The computer science + engineering school at UNSW is running a number of summer workshops in computing. The registration deadline might have already passed tho. http://www.computing.unsw.edu.au/school-programs/summer-workshops.html

Went skydiving (technically still during my exams but whatever), got a full time job, started exercising regularly and eating healthier, got a credit card, drove down to Canberra to give a lecture at ANU for the olympiad kids at their summer camp and broke down on the highway and got to see an...

Good job, 3/4 is correct. My method involved taking the maximum of min(A,B) where A and B were two linear functions, and this maximum existed at x=3/4. I lost the rest of the working though :(

i find that i only get that sensation of feeling full when I eat oily or fatty foods (like last night's christmas eve dinner... mmmmm...). with healthy/unprocessed foods, i can eat a plateful and still feel hungry afterwards. effy, yep.

I wanted to combine adv. maths and computer science at UNSW, but they don't offer that. I'll settle for B.Sc (CompSci) / B.Sc (Mathematics), but I'll try to mess around with the degree program so that I end up doing roughly the same coursework as the adv. maths students.

Yeah I'm expecting an exact ratio. This question's probably been floating around in various forms for a while, but I got it from one of the final exams for the algorithms course at UNSW.

Jeremy convinces Marie to play the following game on two identical rectangular cakes. Jeremy will cut the first cake into two pieces, perhaps evenly, perhaps not. After seeing the cut, Marie will decide whether she will choose first or allow Jeremy to do so. If she goes first, she will take the...

Re: What absurd things have people done in your school due to competition and rivalry Definitely this. Ranks aren't important if everyone does well.