According to legend, his gifts became apparent at the age of three when he corrected, in his head, an error his father had made on paper while calculating finances. Another story has it that in elementary school his teacher tried to occupy pupils by making them add up the integers from 1 to 100, but the young Gauss produced the correct answer within seconds, to the astonishment of all. Gauss had realized that pairwise addition of terms from opposite ends of the list yielded identical intermediate sums: 1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101, and so on, for a total sum of 50 × 101 = 5050. ...While the story is mostly true, the problem assigned by Gauss' teacher was actually a more difficult one. [1]

from Math Forum

Are mathematicians justified in bending historical truth in order to serve laudable aims, such as illustrating that mathematicians are real people or interesting students in mathematics? Another example of this tendency concerns the famous story of Gauss's discovery as a ten- year old boy of a simple method for summing an arithmetic series. (Multiply the number of terms by the average of the smallest and largest terms.) Most mathematicians who teach will assert that the problem given to Gauss by his tyrannical school teacher was to sum the integers from 1 to 1OO. In fact, Gauss was given a more difficult problem "of the following sort, 81297 + 81495 + 81693 +... + lOO899, where the step from one number to the next is the same all along (here 198), and a given number of terms (here 1OO) are to be added." (p. 221 of E.T. Bell's Men of Mathematics, 1937). With this particular example it's easy to maintain historical truth by telling students that Gauss was given a problem like summing the integers from 1 to 1OO.