Introdcution
Recall that story of Little Gauss who was asked by his teacher to add all the digits up to 100. Contrary to the teacher's expectation of enjoying a short respite from nagging of her students who would be busily using their fingers and toes to add up the numbers, Little Gauss came up with the correct answer in matter of seconds. He had found a simple formula for adding the sum of digits up to n. Better yet, his formula could add up all the digits up to 100, 1000, or even 12123897129371927391287 in matter of seconds- it had a constant run time no matter the input n.
Euler project presents problems of these types. It is not the solutions that is being sought; it is the most graceful one that is coveted. We want to approach each problems like our Little Gauss, always looking for more graceful, elegant, and compact solutions.
I divide my solutions to each problems from the Euler project in two sections, if possible: "The Naive" and "Little Gauss". The reason is two-folds; The Naive usually represents a brute-force type approach to the problems, and the Little Gauss explains solutions to the problems. Little Gauss solutions are usually what I have discovered from other users who posted their thoughts on the Project Euler forums and from the solution packet that is distributed once a correct answer is submitted by the player. On rare occasions, I hope to write of my original approach that I believe would rival the current proposed solution made by Project Euler groups.
Have fun with Euler Project.
