Project Euler

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Project Euler
Type of site
Problem Solving Website for Computational Mathematics
Created byColin Hughes
Launched5 October 2001

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 800 problems as of 30 May 2022,[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] As of 27 April 2021, Project Euler has more than 1,000,000 users who have solved at least one problem, in over 100 different programming languages.[7]

Features of the site[edit]

A forum specific to each question may be viewed after the user has correctly answered the given question.[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. 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.[8]

Example problem and solutions[edit]

The first Project Euler problem is Multiples of 3 and 5

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.

Although 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:

total := 0
for NUM from 1 through 999 do
    if NUM mod 3 = 0 or NUM mod 5 = 0 then
        total := total + NUM
return total

For harder problems, it becomes increasingly important to find an efficient algorithm. For this problem, we can reduce 1000 operations to a few 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 and the efficient algorithm is (assuming constant time arithmetic operations).

See also[edit]


  1. ^ Suri, Manil (12 October 2015). "The importance of recreational math". The New York Times. Retrieved 5 June 2018.
  2. ^ Foote, Steven (2014). Learning to Program. Addison-Wesley learning series. Pearson Education. p. 249. ISBN 9780789753397.
  3. ^ James Somers (June 2011). "How I Failed, Failed, and Finally Succeeded at Learning How to Code - Technology". The Atlantic. Retrieved 14 December 2013.
  4. ^ "Project Euler (list of problems)". Retrieved 14 March 2022.{{cite web}}: CS1 maint: url-status (link)
  5. ^ "News - Project Euler". Retrieved 27 April 2021.
  6. ^ a b "Project Euler - About". Retrieved 4 April 2008.
  7. ^ "Project Euler (Statistics)". Retrieved 27 April 2021.{{cite web}}: CS1 maint: url-status (link)
  8. ^ "Project Euler (News Archives)". Retrieved 31 March 2015.

External links[edit]