User talk:Tuwalithi

Dear Tuwalithi: Thank you, so very much, for your incredibly helpful contributions to Wikipedia's article (at the following URL: http://en.wikipedia.org/wiki/Divisibility_rule) about the various rules for determining whether or not given numbers are evenly divisibile by different whole-numbers. I do have a question, however, about one of your quite-useful rules. Specifically, in the section entitled "2 through 20"... a chart lists various divisibility rules (for these 19 whole-numbers-- from 2 through 20)... I have been able to understand (& gratefully utilize) all of these rules... all, EXCEPT FOR ONE-- that one being: the second rule listed for the number 17. The description of the "Divisibility Condition"... does NOT seem to match the given "Example". The named "Divisibility Condition" is described (with ambiguous wording) as follows (below): "Alternatively subtract and add blocks of two digits from the end, doubling the last block and halving the result of the operation, rounding any decimal end result as necessary." Does this mean "doubling the last block" of those 2-digit blocks-of-digits which a person (in reverse order) does "[a]lternatively subtract and add"... or does this mean "doubling the last block" of the original number? Oddly, in the given "Example", though, every "block of two digits" EXCEPT FOR "the last block" of the original number... are ones which the article's readers can witness the said "Example" to be "doubling". Perhaps, you had intended to say "doubling each 2-digit block-of-digits OTHER THAN the last block". The reader is left to guess. Another wording leaves uncertainty, as well. Specifically, when does "halving the result of the operation" occur? To do so, immediately after doubling any 2-digit block-of-digits... would leave the same 2-digit block-of-digits which had existed prior to the original doubling (making that doubling-- be a pointless waste-of-time). If, instead, the doubling should occur AFTER a doubled 2-digit block-of-digits has been subtracted from, or added to, another 2-digit block-of-digits... then, should that "halving" occur after EACH subtraction, or addition, of a (possibly, doubled) 2-digit block-of-digits... ONLY after the FIRST subtraction of a (possibly, doubled) 2-digit block-of-digits... or ONLY after ALL of the (possibly, doubled) 2-digit blocks-of-digits have been subtracted, or added? Looking (for insight into these matters) to the provided "Example"... provides no clear answers... and, instead, only creates more questions. The "Example" (for 209,865-- which commas divide... into each, said block of 2 digits-- as "20,98,65"), however, does not double the last block (i.e., of 65); but rather, that said "Example" doubles both the middle block (of 98... which becomes "(98x2)")... as well as the first block (i.e., of 20... becoming "40"). Plus, the "Example" does NOT remove the resulting decimal... by "rounding" (but rather, through multiplication by 10). The said "Example" (which appears as: "20,98,65: (65 - (98x2)) : 2 + 40 = - 25.5 = 255 = 15x17")... CAN work, however, when expressed as follows: "209,865: ( [65 - (98•2) ] / 2) + (2•20) = [ (65 - 196) / 2] + 40 = (-131 / 2) + 40 = -65.5 + 40 = -25.5"... and "∣-25.5•10∣ = 255 = 15•17". Despite my best efforts, though, NONE of my attempts to apply this divisibility rule to larger multiples of 17 (ones with more digits than the given "Example") have ever been successful. Please, help me to understand this Divisibility Rule... so that I'll learn how to apply the Divisibility Condition to this sizable multiple of 17: 9,349,990,820,016,829,983 (a whole-number which is the product of the following prime factors: 3 • 3 • 3 • 3 • 7 • 11 • 13 • 13 • 13 • 17 • 37 • 43 • 557 • 45,293). Thanking you, in advance, for your prompt reply, Danny ooiyq2@yahoo.com