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To: koan who wrote (13861)	6/19/2006 1:56:40 PM
From: E. Charters	Respond to of 78421

I tink me an dat Pascal guy are cousins of the same mother. Wunse on a test I figger out I can't do series of numbers like what is the next number of this groupo 1, 3, 4, 5, 9, 7, 16, 9, 25, 11, 36 etc... tils I figger, what can it be but if une takes the differunse atween the numbers and if that don't figger, you takes the differunces atween that list and so on until u sees what when the differunse don't matter. Then you goes down the far side of the differunses adding em up til you get the next differunse. Sor t of like a triangle of numbers. 1 1 -- final difference atween the 2's 2 2 2 -- diff atween the row below 3 5 7 9 -- diff atween the bott row 1 4 9 16 25 -- row that has you mystified. gets it you this: 1 1 1 -- add1 2 2 2 2 -- add 2 3 5 7 9 11 -- +2 makes 11 1 4 9 16 25 add 11 makes 36, the next number All you need to do is stop when the differating stops and then you got an adder, and it has to come out that if you add that it should give you the next number in the row below. Sometimez you gots to adds them if one row gives you negatives. I leave it to use to figger that out as to wen. Wyze it werk? well successive differunses show when the series "factors to make the differences" can be found to increase by some rule. Obviously the thing which generates the next number has to have a rule and that rule or generator must increase by some factor. You have to watch it when the differences between the differences are the same as the series as in a doubling series such as 1, 2, 4, 8, 16. Here the differences are the same as the series only moved over one. At any rate you can see when the series is predictable or as mathematicians say monotonous which really means increasing by set amount each time, i.e. 1,1,1, or 1, 2 etc.. Turns out Pascal got there first and I can't taike the kredut. EC:<-}