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Re: 2015 permutation X2 marathon Even though all 13 games aren't necessarily played, you can still pretend that they are all played. In many series such as cricket tests, the dead rubbers are played. So a person can win with 8, 9, 10, .... wins. The best way to convince yourself is to...

Re: 2015 permutation X2 marathon Sorry - my dinner is ready. Perhaps someone else can jump in and answer.

Re: 2015 permutation X2 marathon I just meant that the only probability calculation should be the final calculation.

Re: 2015 permutation X2 marathon (Almost) exactly what I did. Now, someone will typically ask why you consider 13 games for each case when 13 games are not played. Does anyone have that issue?

Re: 2015 permutation X2 marathon Aristotle and Socrates play in the final of the World Championship of Thong Throwing. They each throw a thong, and the person who throws the furthest wins one game. The winner of the championship is the first to win 10 games. Currently, Socrates leads 4 games...

(i) Just count outcomes: There are 2^3 = 8 possibilities for the digits (ignoring order): 124, 125, 174, 175, 824, 825, 874, 875 Two of those have digits that add up to a multiple of 3. 2/8 = 1/4 (ii) What is this "second three-digit number multiple of 3" ?

You can get those substitutions by letting a+b=x, b+c=y and a+c=z, then solving simultaneously for a, b and c.

I derived that as an example of something you could derive. It was not designed to be quoted.

Of course, we are really dividing into groups of 3, 4, 5, 6 and 7.

Re: 2015 permutation X2 marathon Yes, but you need to explain why they follow the Fibonacci sequence. Seeing that the pattern exists is only the first step.

Re: 2015 permutation X2 marathon A subset is any group of any size selected from the original set. That includes the empty set (size zero) and the entire original set. You should already be able to calculate the total number of subsets that can be formed from a set of 12 objects. But...

Re: 2015 permutation X2 marathon You can have any set of just one number. You can't have {2,3}, {2,3,4} or {2,4,6,8,10,11}. You can have {2,4}, {2,4,6,8,10,12}, {1, 9, 12}.

Re: 2015 permutation X2 marathon Sorry - forgot. Edited now.

Re: 2015 permutation X2 marathon Including the empty set, how many subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} do not contain any consecutive integers? Answer: 377 (Since I am not going to count what question we are up to, perhaps we should mark new questions as I have - in the...

Re: 2015 permutation X2 marathon Are you sure about your answer? I am getting 10 more.

Re: 2015 permutation X2 marathon Because your initial move is 1 step OR 2 steps. There are S(n-1) moves you can make if your first step is 1, and another S(n-2) moves you can make if your first step is 2.

Re: 2015 permutation X2 marathon Let S(n) be the number of ways of climbing n steps. The first move is either 1 step or 2 steps. If it is 1 step, there are S(n-1) ways of climbing the remaining n-1 steps. If it is 2 steps, there are S(n-2) ways of climbing the remaining n-2 steps. So...

Re: 2015 permutation X2 marathon 13th

Re: 2015 permutation X2 marathon So no-one can see the connection to Fibonacci numbers?

In Ext 2 last year, only 1st place scored 100 (at least I'm assuming he got 100).