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I am confused Trebla. Is the above relevant to the question, or is it just to demonstrate to goobi what happens when you multiply two summations?

Re: 2012 HSC MX2 Marathon First part split the integral as two terms then the integral with the i in it cancels out due to the sine function and we are left with 2x integral of f(x)cos(x). Second part use the property f(x) = f(a-x), add the two integrals, the icos(x) term cancels and the...

They are two different things because we don't care about the output purely. We care about the dice from which the number came. What you simply did when you counted the {1A,1B} and {1B,1A} case is that you implied 'non-commutativity' in a sense when counting the sets, which is incorrect in...

Why would {1A,1B} and {1B,1A} be counted as two separate things?

From where did you get this question?

Is this a proper question with a fairly elementary solution, or are you just asking us out of curiosity?

How does having 6x6 not count having the same number on each side? It does. Just consider the Cartesian Product: http://en.wikipedia.org/wiki/Cartesian_product {1,2,3,4,5,6} X {1,2,3,4,5,6} ==> 36 elements in the set of pairs.

Because most of us are thinking too deeply, having the burden of knowledge, so things get over-complicated unnecessarily.

There is no elementary way of finding a closed-form solution.

Not necessarily. What if OP was given the question from his/her teacher in a revision booklet or something as such?

It is a typesetting language called TeX (Latex).

I have made a silly error. Suppose we have a set of N arbitrary numbers and added any two elements of the set, then the probability of having an even total approaches 2/3 as N --> infinity. However, this is not applicable to this problem because we are taking the sum of the elements of the...

From where did you get this question and its answer? Because the "Even totals" already amount to 2/3 of the total cases, let alone including those that exceed 7.

Let's look at all the ways we can get an even total: - Odd + Odd = Even. - Even + Even = Even - Even + Odd = Odd + Even = Odd. So this makes 2/3 of all cases, since we have the same number of odd (1,3,5) as we do even (2,4,6). So we have: There are 6 x 6 combinations in total (First die...

hayabusaboston, fortune_cookie is very competent with Mathematics, and I am very confident that he/she would have known what to do without your 'idea'.

Since when did -4+1 = -1?

Why so keen for an answer, is there a trick to it?

Yeah I just thought of it randomly. Sorry if it was too much trouble. I honestly expected a more elementary solution easily found by the average MX2 student =/

Consider a straight line and a piece of string with length L. In what shape should the string be made to maximise the area bounded by the straight line and the string, given that the string must touch the line at least once? Give proof.

Are you sure there is a unique solution?