Is Gauss's story real?

You've probably remembered the story of Gauss in High School the genius 6-year-old  prodigy who found a genius method to calculate an arithmetic sequence, but is it true? For those who aren't familiar with the story here's how it goes

Once Upon a time in the math class, Gauss's teacher gives the class a fairly unusual question. he asks the class to sum all the numbers between one and 100 while the rest of the class is churning through the numbers, Gauss thinks for a minute then, eureka! He finds an ingenious way to solve the problem instead of  calculating all the numbers manually he rearranges the equation like this

                

                                                        1+2+3+...+98+99+100

                                                       =100+1+99+98+3...+51+50

                                                        =101+101+101+...

                                                        =50(101)

                                                        =5500

he hands his paper to his teacher, thinking gauss was slacking off Gauss's teacher gets his cane out, and checks his answer, but to his astonishment Gauss was correct! The teacher sat there dumbfounded and Gauss got the rest of the 55 minutes of class for silent reading (lucky him!)

So Where Did this story originate from

Sartorius, one of Gauss's best friends claimed that when ol' Gauss grew up, he enjoyed repeating the story himself. He does specifically note that the problem at hand included "the summation of an arithmetic series," although he does not say which series.

According to a post on stack overflow online, the 1-100 sum written down first appears in this anecdote in a 1938 biography of Gauss by Ludwig Bieber Bach, which also tells the story of Gauss' rearrangement method for adding the numbers.

                                   

In conclusion, this might be true although the story has been altered a lot as the gap between Sartorius and Bieber Bach is over 100 years old, in fact, there are over 132 different variants of his story! So it could be that Gauss was just pulling our leg, or maybe he was telling the truth.