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Re: Chess thread? Mini-tournament tonight anyone? Register interest here. If there is enough, I will organise something and it will probably start 10ish.

Finally solved it properly, but it would take far too long for me to type up my own solution. I found one online that is pretty similar to mine (in fact it does some things in a tidier way). http://mks.mff.cuni.cz/kalva/short/soln/sh00g7.html

Intelligent guy with a MUCH better ability to communicate than most people who are as good as him. Recommended!

Re: HSC 2013 4U Marathon You are close to the right idea, the key is that < z-tw, z-tw > is non-negative. Expand this expression out and you will get what you want :). The final part of the question should be easier once you interpret it correctly.

Pretty much this, this kind of question is a great example of why rigour is important in mathematics. I have been out all day so I STILL haven't looked at this properly, but will do so tomorrow and post whatever I can come up with.

Re: HSC 2013 4U Marathon Why is < tw , z > smaller than < z , z >? Seems correct if you can justify this step :).

Re: HSC 2013 4U Marathon Why does \langle tw,z\rangle \in \mathbb{R} imply that tw=z?

Not quite sure what you mean by forming 3 pentagons around the triangle. In any case, a complete solution must include proof that 8 is NOT possible.

Ah yes, we probably can't obtain 8 then, I will think about this more later.

Nice! A straighforward proof we can't do better that 8: Consider the set of all PAIRS of girls. These pairs can be ordered by distance. The closest pair of girls must shoot each other => at least two girls must die. I think 8 is correct, I will try to do the "random fuzzing" tomorrow to obtain...

Re: Chess thread? it only goes up to 30 but that should suffice. http://lichess.org/3sgxz6p1

Re: Chess thread? okay, will create now.

No worries, we all have moments of blindness.

Re: Chess thread? Yep, can we pick and stick to a time limit? How long do you feel like?

Re: Chess thread? You around Demento?

BGH=BCD, corresponding angles. And BCD=180-BAD as we already know that ABCD is cyclic.

An upturned cone is a cone with vertex pointing downwards. The angle determines the shape of the cone, so is of course very relevant. It might be very skinny or very fat. Semivertical angle being 45 means that it is exactly in between these extremes.

Nope, no reference to HGCD. BAD + HGB = 180, so ABGH has a pair of opposite angles which are supplementary. This is one characterisation of cyclic quads. Not sure what you mean by "H and G is cyclic for a pair of points in the circumference"...

All you need is a quadrilateral with a pair of opposite angles supplementary :).

HGB=DCB=180-BAD => ABGH concyclic. Try to justify each step yourself.