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Adding sequential numbersRead the article this discussion is about
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» Dan_Ellsworth - Nice! I've subscribed for some time but quietly. It's time to give you a moment of support -- overdue support -- for a good topic.This title captured my interest, and you have explained clearly the exploit of the young Gauss. I like to detect the patterns in numbers, and I like to use use the patterns and order of numbers in calculation. The method you outline can even be used if the sequence does not start at one. For the Michigan Mathematics Prize competition several years ago, the problem was to find the number of logs in a pile, with 41 (I think it was) on the bottom row, 40 on the next, and so on for seven rows. My approach was a minor variation of yours. Top row plus bottom row, 41+35 = 76. Average logs per row, 38. Next to top row plus next to bottom row, 40+36, total 76, average 38. Third plus fifth row ... average 38. Fourth row, 38. Average per row, 38. 7 rows. 38 x 7 = 266. If it had been 25 rows, the principles would be the same. Shortcuts are fun. I've made up a saying (I *think* it's mine.): Laziness is the father of invention. It's not total laziness, though; I'd rather work hard at finding a shortcut than work hard without a shortcut. My compliments on this article and your topic. -- posted by Dan_Ellsworth » VidyaNarayan - Re: Nice! In response to message posted by Dan_Ellsworth:Thanks Dan Ellsworth, for nice words. Your way of calculations is the same. Instead of finding out total of all pairs first and then dividing the sum by two, divide the total of each pair by two, first and then multiply the sum by number of pairs! However, if Gauss would have divided the total for each pair by two, he would have got the answer 50.5(101 divide by 2) and then he would have solved 50.5 * 100 getting 5050! In the example you have given, dividing the sum for the pairs you get a smaller number which makes the further multiplication easier. Therefore, following division before multiplication is really an effective approach for the example you have chosen! Thanks once again for your encouraging words! -- posted by VidyaNarayan
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