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HS just teaches you to do basic calculations quickly and pretty much directly apply some simple theorems in the various topics. The calculus you do in HS is nowhere near rigorous and nor should it be, for the sake of actually being able to solve some decent real world problems within only a...

Re: HSC 2016 4U Marathon Bingo :).

Quite a lot of background is needed to understand Wiles' proof at any greater depth than the absolute "top level overview".

Still untrue. Given a square matrix A, there is a unique solution to Ax=y IFF A is invertible. (Prove this!) A matrix can fail to be invertible even if no two of its rows are scalar multiples of each other. Eg/...

fun game :). back to work for me!

http://lichess.org/rhRFc3nx

still looking?

Re: HSC 2016 4U Marathon Pretty much just using properties of inequality and induction. Out-of-HSC techniques don't come into it at all unless you approach it in a really weird way.

Re: HSC 2016 4U Marathon Your first method needs to be tidied up a bit to work. What is a_1? For any particular a_1 you can choose A and B in lots of different ways. You need to show that for ANY such choice, a_2 must be equal to a_1, or the sequence must violate the properties that iterating f...

Re: HSC 2016 4U Marathon Find all functions f:N->N such that f(n)+f(f(n))=2n. (N is the set of positive integers). You might find induction useful to justify your answer.

Use N for knight, K means king in chess notation. Yeah would move king in response to that ofc.

http://lichess.org/Q3tdQtwv whoever gets here first. I'm a bit high so my play won't be amazing either.

still looking for games?

Re: HSC 2016 4U Marathon \frac{z-w}{z+w}=ki\Rightarrow z=w\frac{1+ki}{1-ki}\Rightarrow |z|=|w|\frac{|1+ki|}{|1-ki|}=|w|.

Anyone for games in a bit?

If you host a quick game on lichess in the next couple of mins, I will play. Otherwise I really need to get to work.

Endgames are so fun dude. It feels the most like maths to me because it boils down to reducing a problem to problems you already know how to solve. Also, playing lots of endgames really helps understanding of which pieces are good in which positions / good vs bad pawn structures etc. Most...

Yeah, without him having king activity the endgame was completely hopeless. Even if he did activate his king earlier, it would be a pretty uphill battle a pawn down and knight vs bishop in that position. Thanks dude, am a bit rusty tactically (esp in short games) but am still reasonably solid...

Me too haha, gotta get back to work. Will be looking for more games later.

http://lichess.org/0w3pgp5j