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Re: HSC 2015 4U Marathon - Advanced Level Just came back from a 3 day camp and saw this, so I may have made some silly mistakes. NOTE: the LAtex takes a bit of time to load, so please be patient $ Suppose that k is higher than h. Then, construct a slice through h parallel to the base of the...

Re: HSC 2015 4U Marathon - Advanced Level If there are any things which i haven't quite made clear pls let me know, then I'll explain when i next log on

Re: HSC 2015 4U Marathon - Advanced Level Since no one is posting their soln, due to everyone being so busy, I'll post mine. there could be more elegant methods, but this was what i came up with when i did the question a couple of weeks back (didn't look for an elegant solution after solvign...

Re: HSC 2015 4U Marathon - Advanced Level Sorry for the lack of latex, on the train home right now and latexing on phone is annoying. the problem is trivial for primes, so i'll just consider the composite numbers Case 1: n = a*b, where a>b>1. Then, since a(b-1)-1>0, then ab-1>a>b>1. Thus, b...

Re: HSC 2015 4U Marathon - Advanced Level Lol, to be fair these people haven't encountered situations where mathematical rigor is of great importance... I do have a rigorous solution, which I can post if requested perhaps tomorrow. You mean whether your solution is 100% valid? No. But I...

Re: HSC 2015 4U Marathon - Advanced Level Or is it the wording of the question that is throwing people off? Here is the exact wording of the question. \text{Given any nine integers, show that it is possible to choose five of them such that their sum is divisible by 5}

Re: HSC 2015 4U Marathon - Advanced Level Should I post a hint?

Re: HSC 2015 4U Marathon - Advanced Level here is a great question I was doing a couple of weeks back. show that in every set of 9 positive integers, a subset of 5 positive integers exists such that the sum of the numbers is divisble by 5.

Re: HSC 2015 4U Marathon - Advanced Level ah okay. Do you have any idea what the general cut off mark for HD is then? For senior? Like for a paper of average difficulty

Re: HSC 2015 4U Marathon - Advanced Level btw realisenothing, how many points did u score? I believe you scored a HD in that comp? I just want to get a general idea of the cut off marks lol.

Re: HSC 2015 4U Marathon - Advanced Level of course, but as you said q1s are typically easier lol. I think q6 was quite interesting as well, which involved the use of the chinese remainder theorem but my latexing skills arent good enough for me to post the question. Perhapsthere is someone...

Re: HSC 2015 4U Marathon - Advanced Level yeah that was the basic idea behind my method during the exam (proving that there had to be at least 38 points if the claim was false).

Re: HSC 2015 4U Marathon - Advanced Level Ah sorry, mistyped the question, it should be, Around a spherical planet, there are 37 satellites. Prove that, there exists a point on the surface such that at most 17 satellites are visible

Re: HSC 2015 4U Marathon - Advanced Level Here's the first question from a paper called the UNSW mathematics competition for this year, (not the ICAS but a 3 hour exam). Around a spherical planet, there are 37 satellites. Prove that, for any point on the planet, there are at most 17 satellites...

Re: HSC 2015 4U Marathon - Advanced Level given that i have interpreted the question correctly, d1= {1,3,6,8} results in dn = 2 if n even or 6 if n odd. d1{2 and 7} results in dn=6 for even n and 2 for odd n. d1{4,5,9} have dn =0 for all n>1.

Re: HSC 2015 4U Marathon - Advanced Level $haven't seen this thread in a long time! $ $Okay, here's what I get for this q. note that all numbers are k mod 9, where k = 0--> 8. $ $so (n+1)^{(n+1)} +(-n)^n $ [text\]{is congruent to}$ (k+1)^{k+1} +(-k)^k mod 9 $where k = 0--> 8.$ $ $testing...

Re: HSC 2015 4U Marathon Thank you, for some reason he isn't convinced though, apparently his tutor said otherwise

Re: HSC 2015 4U Marathon Hey Seanieg, or Sy or whoever sees this, my friend claims that if sin(2a)*sin(2b)*cosa + sin(2a)sin(a)cos(2b)= sin(2b)sin(2a)cos(b)+sin(2b)sin(b)cos(2a) because the lhs is basically the rhs except with the a and b switched, this automatically means that a must equal b...

Re: HSC 2015 4U Marathon - Advanced Level Assuming that the symbol means "for x between and including 0, and 1", I get an integer answer. Is it an integer answer? I'd like post my solution, but only if I'm sure that there's no sillies.

Re: HSC 2015 4U Marathon - Advanced Level sorry but can you explain what the question is asking for? I don't know what that last symbol is supposed to mean.