Project Euler

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Project Euler
Type of site
Problem Solving Website
Created by Colin Hughes
Alexa rank Positive decrease 31,756 (Jul 2017)[1]
Commercial No
Registration Free
Launched October 5, 2001

Project Euler (named after Leonhard Euler) is a website dedicated to a series of computational problems intended to be solved with computer programs. The project attracts adults and students interested in mathematics and computer programming. Since its creation in 2001 by Colin Hughes, Project Euler has gained notability and popularity worldwide.[2] It includes over 600 problems,[3] with a new one added every weekend (except during the summer). Problems are of varying difficulty but each is solvable in less than a minute using an efficient algorithm on a modestly powered computer. Problems can be sorted on difficulty. A forum specific to each question may be viewed after the user has correctly answered the given question.[4] As of August 2017 Project Euler has about 720,000[5] users, from all over the world, who have solved at least one problem.[6]

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. Special awards exist for solving special combinations of problems, 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.[7]

There are 111 sequences[8] in the On-Line Encyclopedia of Integer Sequences (OEIS) referencing Project Euler problems.

Example problem and solutions[edit]

The first Project Euler problem is

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000.[note 1]

Though this problem is much simpler than the typical problem, it serves to illustrate the potential difference that an efficient algorithm makes. The brute-force algorithm examines every natural number less than 1000 and keeps a running sum of those meeting the criteria. This method is simple to implement, as shown by the following pseudocode:

Set TOTAL to 0;
for NUM from 1 through 999 do
  if NUM mod 3 = 0 or if NUM mod 5 = 0 then
    add NUM to TOTAL;
output TOTAL

For harder problems, it becomes increasingly important to find an efficient algorithm. For this problem, we can reduce 1000 operations to a handful by using the inclusion–exclusion principle and a closed-form summation formula.

Here, denotes the sum of multiples of below . In big O notation, the brute-force algorithm is O(n) and the efficient algorithm is O(1) (assuming constant time arithmetic operations).


  1. ^ This is the inclusive OR, not the exclusive OR

See also[edit]


  1. ^ " Site Overview". Alexa Internet. Retrieved 16 July 2017. 
  2. ^ James Somers (June 2011). "How I Failed, Failed, and Finally Succeeded at Learning How to Code - Technology". The Atlantic. Retrieved 2013-12-14. 
  3. ^ "Project Euler (list of problems)". Retrieved 2016-11-02. 
  4. ^ "Project Euler - About". Retrieved 2008-04-04. 
  5. ^ Hughes, Colin. "About - Project Euler". Retrieved 2016-07-06. 
  6. ^ "Project Euler (Statistics) - not accessible for anonymous users". Retrieved 2016-05-24. 
  7. ^ "Project Euler (News Archives)". Retrieved 2015-03-31. 
  8. ^ "OEIS sequences referencing Project Euler problems". Retrieved 2016-05-30. 

External links[edit]