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We all have heard the story of the young Guass, summing 1 to 100 by writing the sum backward below the original one.

In this article, just two books are referred for the trick. I looked at both of them but the story was just mentioned briefly without any firsthand reference.

Is this story true and reliable? Is there any good reference proving this?


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Formulas for the sum were known for a very long time before Gauss was born. Are you asking if the story of school-child Gauss is true as a biographical fact about him? – zyx Nov 8 '13 at 22:22
no idea how to find out with any reliability. I believed a story about young Milnor for decades. Somebody finally asked him, it turns out it happened to Dantzig some decades earlier; and that is relativley recent. – Will Jagy Nov 8 '13 at 22:23
There is a part of the story that is usually not told, partly because I made it up. When Gauss showed the teacher the answer, the teacher, irritated at having his rest interrupted, took a very large ruler and $\dots$. – André Nicolas Nov 8 '13 at 22:23
@zyx Yes, that's what I'm asking for. – Behzad Nov 8 '13 at 22:26
I only remember what I wrote. If I had more details I would have provided them. – zyx Nov 8 '13 at 23:08
up vote 4 down vote accepted

Brian Hayes, who does the "Computing Science" column for American Scientist, wrote about the Gauss legend in one of his columns in 2006. Brian was particularly interested in variations on the story. A pdf reprint of the column is available here, and additional material, which he's gathered at his blog, is available here and here.

It's worth noting that there is no universal agreement as to exactly what problem Gauss is said to have solved, nor the precise means by which he solved it.

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Really? I've never heard any version of the story other than 'summing the numbers 1 to 100' with the 1+100, 2+99, etc. 'trick'. – Steven Stadnicki Nov 8 '13 at 22:58

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