Posts Tagged ‘project euler’

Problem 6 - What is the difference between the sum of the squares and the square of the sums?

// July 6th, 2009 // No Comments » // Project Euler

The sum of the squares of the first ten natural numbers is,

1^(2) + 2^(2) + … + 10^(2) = 385

The square of the sum of the first ten natural numbers is,

(1 + 2 + … + 10)^(2) = 55^(2) = 3025

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 - 385 = 2640.

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

Problem 5 - What is the smallest number divisible by each of the numbers 1 to 20?

// June 29th, 2009 // No Comments » // Project Euler

2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.

What is the smallest number that is evenly divisible by all of the numbers from 1 to 20?

Problem 4 - Find the largest palindrome made from the product of two 3-digit numbers

// June 22nd, 2009 // No Comments » // Project Euler

A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99.

Find the largest palindrome made from the product of two 3-digit numbers.

Problem 3 - Find the largest prime factor of a composite number

// June 15th, 2009 // 2 Comments » // Project Euler

The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number 600851475143 ?

Problem 2 - Find the sum of all the even-valued terms in the Fibonacci sequence which do not exceed four million

// June 9th, 2009 // 2 Comments » // Project Euler

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …

Find the sum of all the even-valued terms in the sequence which do not exceed four million.

About Project Euler

// May 22nd, 2009 // No Comments » // Project Euler

I found these challenges very useful to the development and assessment of my programming abilities. From now I I will post a question from the Project Euler website as a challenge to all readers who have an interest in programming. Ideally the solutions will be submitted in PHP, but other languages will be accepted. I will post a challenge every Monday to give you the week to work on it and from the order of the submitted solutions we will know who came up with the answer first.

What is Project Euler?

Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems.

The motivation for starting Project Euler, and its continuation, is to provide a platform for the inquiring mind to delve into unfamiliar areas and learn new concepts in a fun and recreational context.