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Sweet, well I will probably be free this evening if you are (or anyone else).

Yeah I don't like to play sub 5 mins for that reason (except super casually in certain moods). Am pretty bad at 5 too mostly because I manage time poorly.

Yeah fair enough dude. Am nothing special myself. I think I could get to a decent club level if I made a focused effort on improving certain aspects of my game and sharpened up my rusty tactics but as it stands now I am woefully inconsistent. What time controls of lightning? I mostly just play...

Has Integrand played people on these forums? I never see his games so I actually have no idea what level he is.

Re: HSC 2016 Complex Numbers Marathon Thanks to all your extensive counting practice from the combinatorics marathon!

Don't waste time trying to memorise openings, just learn the basic rules of thumb. You will improve much faster by plugging tactical leaks first. (And endgames so you know how to convert won games).

Went to an amazing lecture on this by Venkatesh last year. Fascinating problem.

Note that "strong" induction is a bit of a misnomer, regular induction is exactly as strong in the sense that assuming the "principle/axiom of induction" allows you to prove the "principle/axiom of strong induction". To see this let S(n) be a sequence of propositions about positive integers and...

Re: HSC 2016 MX2 Combinatorics Marathon Yep. :). The ideas in both proofs are very similar though, even if superficially they look a bit different.

Re: HSC 2016 MX2 Combinatorics Marathon Ah nice yeah, I forgot that you posted that solution here :).

Re: HSC 2016 MX2 Combinatorics Marathon Will also have a crack at your related Q (finding the PDF of the sequence lengths, rather than just the expectation of the lengths.) I remember you asking that before and me being stumped (because my solution to the expectation problem exploited...

Re: HSC 2016 MX2 Combinatorics Marathon This question is exactly the same, which is why I re-asked it :p. It had been a while so new people might not have seen it. Also it was previously phrased in the unweighted case, I still have the solution I tex'd. The method looks like it will carry...

Re: HSC 2016 MX2 Combinatorics Marathon Yep :). Want to justify this for everyone else's sake? You might also find it fun to think about what happens if the coin is biased and has heads probability p in (0,1). (Idk if it still works out nicely and won't have time to check until after uni...

Yep, since it's 2x2 they clearly want you to just equate entries and make the deductions from there. The same result is true in higher dimensions too, and can be proved as follows: Every n x n matrix over R has a complex eigenvalue. (From its characteristic polynomial and the fundamental...

I don't really "practice" chess much anymore, although if I enter a Canberra tournament sometime soon I will train for that. For now though I just play now and then and stave rust away by doing that.

Still playing a ton of melee (ssbm). Anyone with any kind of usb controller who wants to play online, hit me up. Here is a pretty sexy combo video:

Re: HSC 2016 MX2 Combinatorics Marathon Yep, the profit grows much faster than n. Will provide more hints if it goes unsolved for a while.

Re: HSC 2016 MX2 Combinatorics Marathon Care to justify this more if you stand by it? I think you can afford to pay a lot more than that. Eg in the simple n=1 case we are flipping coins till we get a tails. The probability of a coinflipping sequence terminating precisely after k flips is...

Re: HSC 2016 MX2 Combinatorics Marathon You are offered (at a price!) to flip a fair coin repeatedly until you flip n tails in a row. (n some positive integer). At the end, you are given $k where k is the number of total flips you had (including the n tails). Up to what price are you willing...