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Trios and Extensions of Trios Aim: My aim is to study the topic of trios and work on from that, to discover patterns and links. I will study trios using permutations as I believe these to have the most regularity and a much easier sequence to work with. I am going to investigate how many trios there are for the number 5. Once I have worked this out, I will work out how many trios there are for the number 6; then for the number 7 and so on. I will then try to make a connection between the above numbers and come up with a formula which can be used to work out a trio. I will then explore further into this question, by investigating 'quartets', 'quintets', 'sextet' etc. What is a trio? A trio is a set of 3 numbers greater than zero, that when added together make another number. For...

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