135 versions of the Gauss Schoolroom Anecdote

http://bit-player.org/wp-content/extras/gaussfiles/gauss-snippets.html

The great mathematicians feel mathematics in a way the rest of us do not. And their genius for mathematics is immediately recognizable. When Gauss was eight years old, he and his classmates were asked by their teacher to find the sum of the integers from 1 to 100. The children began laboriously to calculate on their slates. All of them (except Gauss) began 1+2=3, 3+3=6, 6+4=10.... Gauss noticed that the integers 1, 2, 3,..., 99, 100 can be placed in pairs as follows: (1, 100), (2, 99), (3, 98), ..., (50, 51). There are exactly 50 such pairs and the sum of the integers in each pair is 101. Hence, the desired sum is the same as 50 times 101, which is 5050. Gauss wrote this number on his slate and handed it to the teacher. The whole process took him only seconds.