When Carl Gauss was in elementary school, his teacher assigned his class the task of summing the integers from 1 to 100. The
teacher was probably expecting some minutes of quiet, but Gauss produced the answer of 5,050 in seconds.
But here is what really happened, or as Paul Harvey would say, "Now, for the rest of the story ..."
School Master: Class, I want each of you to spend the next quarter-hour summing the numbers from 1 to 100.
This is difficult and I'm not sure of what
your chances are for success.
Gauss: Fifty-fifty?
School Master: Incredible! You calculated the correct sum immediately! You're a genius!