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Re: HSC 2016 MX2 Combinatorics Marathon I'm afraid I can't remember exactly where I found it. But if my answer is correct (and I am reasonably confident it is) then you would need to run a simulation about 10^37 times just to get one success. How long are you planning on living?

Re: HSC 2016 MX2 Combinatorics Marathon I found this question on an online forum and they had no definitive answer. But I have worked out an answer that is about 10 to the power of 20 smaller than yours! I believe those factorials you have should actually be in the numerator. And don't forget...

Re: HSC 2016 MX2 Combinatorics Marathon 27 unit-cubes are assembled into a single 3-by-3-by-3 cube. The surface of this larger cube is painted red. The cube falls apart, and a blind man reassembles it. What is the probability that the reassembled cube again has its entire surface painted red?

Link: Extension 2

A link to selective HS trial papers: Extension 1

2 Unit

Here are links to some 2016 Trial papers: 2 Unit Extension 1 Extension 2

If the desire to believe in something supernatural is not expressed in our genes, what exactly explains the cargo god phenomenon? I notice you didn't say "That is neglecting some of the positive advancements made by those BECAUSE they held to a viewpoint other than of paganism." Advancements...

Indeed - a vastly improved one. (Assuming another nonsense religion hadn't filled the void - viz. the cargo gods - but given human nature that would probably be too much to hope for) Hopefully one day scientists will eradicate the malignant god gene.

It's not mentioned in the 3U syllabus, but you can still use it and I'm pretty sure most teachers teach it.

There is no physical evidence for a god, and "extraordinary claims require extraordinary proof". Until there is evidence of existence, I do not feel the need to justify its non-existence any more than you should feel the need to justify the non-existence of the FSM, Ahura Mazda or leprechauns...

500 claimed witnesses. You do know that there are no original manuscripts of the bible in existence don't you. The earliest surviving copy of the text describing the "resurrection" exists in a museum in Egypt. It clearly shows that the story of Jesus' ascension to heaven was added later, with...

Yes - that is my conclusion. And what part of your 'proof' cannot be applied to the existence of the Zoroastrian god and it's "prophet" Zarathustra?

I watch the worried expressions appearing on students' faces.

If he existed at all. Similarly, the christian god is a mass murderer, killing millions in the old testament. And he promoted rape. And in the new testament also became schizophrenic. The resemblance is uncanny. Thank effing christ it is pure fiction.

Hitler?? Where TF do you get that from? And I seriously hope your profile photo of that revolting individual does not reflect your viewpoint.

Re: HSC 2016 MX2 Combinatorics Marathon But doesn't the number of passengers affect the answer? There is a 1/n chance that the first person gets the right seat, and in that case so will the last person. This is before considering the chance that the last person gets the right seat when the...

My path is determined by me and chance. Nothing else.

Re: HSC 2016 MX2 Combinatorics Marathon By 'arbitrarily large' do mean that an additive probability of 1/n can be assumed to be zero?

It is the orthocentre and centroid which form new circles. The given circle IS the circumcircle regardless of the position of P, so the locus of the circumcentre is just the centre of this circle. The incentre gives two arcs of different circles, depending on whether P lies on the major or minor...