Project Euler (named after Leonhard Euler) is a website dedicated to a series of computational problems intended to be solved with computer programs.
[1][2] The project attracts graduates and students interested in mathematics and computer programming.
Since its creation in 2001 by Colin Hughes, Project Euler has gained notability and popularity worldwide.
[3] It includes 923 problems as of December 22 2024,[4] with a new one added approximately every week.
[5] Problems are of varying difficulty, but each is solvable in less than a minute of CPU time using an efficient algorithm on a modestly powered computer.
[6] Problems can be sorted on ID, number solved and difficulty.
Participants can track their progress through achievement levels based on the number of problems solved.
A new level is reached for every 25 problems solved.
For instance, there is an award for solving fifty prime numbered problems.
A special "Eulerians" level exists to track achievement based on the fastest fifty solvers of recent problems so that newer members can compete without solving older problems.
It is a 5% rated problem, indicating it is one of the easiest on the site.
The initial approach a beginner can come up with is a bruteforce attempt.
Given the upper bound of 1000 in this case, a bruteforce is easily achievable for most current home computers.
A user could keep refining their solution for any given problem further.
In this case, there exists a constant time solution for the problem.
The inclusion-exclusion principle claims that if there are two finite sets
This is a pretty popular combinatorics result.
One can extend this result and express a relation for the sum of their elements, namely
Later problems progress (non-linearly) in difficulty, requiring more creative methodology and higher understanding of the mathematical principles behind the problems.