# Project Euler

My solutions for Project Euler, most of them are written in C#. I have two aims for the solution – speed and readability.

Whenever possible, I exploit the math behind the problem to obtain a much faster solution than what can be done through bruteforcing the problem.

## Solution to Problem 8 of Project Euler

We have now treated a couple of problems where a really clever solution could be derived from different branches of number theory. Problem 8 of Project Euler is inherently different.  The problem goes

Find the greatest product of five consecutive digits in the 1000-digit number.

73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450

Posted by Kristian in Project Euler, 28 comments

## Project Euler – Problem 7

Now we reached Problem 7 of Project Euler which is about prime numbers. The problem reads

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.

What is the 10001st prime number?

We could solve this by brute force checking all the numbers, or we could reuse part of the solution to problem 5, where we generated a list of primes using trial division with already found prime numbers. I haven’t found a way to solve this without finding the 10000 primes before finding the answer.

Wikipedia comes with a great article about prime numbers, which also refers to several methods for checking if a number is a prime. We will take a bit of simpler approach though. But dive into the article, it is pretty interesting.

Posted by Kristian in Project Euler, 9 comments

## Project Euler – Problem 6

This exercise has a longer problem description than the previous, so lets jump right into it.

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

12 + 22 + … + 102 = 385
The square of the sum of the first ten natural numbers is,

(1 + 2 + … + 10)2 = 552 = 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.

Posted by Kristian in Project Euler, 9 comments

## Project Euler – Problem 5

Lets jump right into solving Problem 5 of Project Euler and let me try to give you an answer on how to solve it. The problem formulation is :

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 positive number that is evenly divisible (divisible with no remainder) by all of the numbers from 1 to 20?

Once again I will provide you with two different solutions and some tips and tricks on how to speed them up a bit.

Posted by Kristian in Project Euler, 40 comments

## Project Euler – Problem 4

Today it is time to look at the solution to Problem 4 of Project Euler. It differs a bit in the nature of the problem from the first 3 we have looked at so far. However, it is still mathematics and a solution can still be coded, and most important it is still fun.

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.

I think it is a nice recreational little exercise.

Posted by Kristian in Project Euler, 29 comments

## Project Euler – Problem 3

I am sorry, I haven’t posted anything for a while. I have been busy moving, and is currently without an Internet connection. However I couldn’t keep away any more.

Problem 3 in Project Euler reads:

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

What is the largest prime factor of the number 600851475143 ?

I used two different approaches for this, and lets get right to them. Continue reading →

Posted by Kristian in Project Euler, 27 comments

## Project Euler – Problem 2

The problem description of Problem 2 of Project Euler reads

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.

Before heading on with a solution, I will make a small comment on the problem formulation. Usually the first two numbers in the Fibonacci sequence is defined as F1 = F2 = 1. But that is just nitpicking and wont change anything in the solution.

Posted by Kristian in Project Euler, 31 comments

## Project Euler – Problem 1

Now that the fluff around the coding is covered, we are ready to solve the first problem.

The description of problem 1 on Project Euler reads

Find the sum of all the multiples of 3 or 5 below 1000.

There are multiple methods for finding the solution for this problem…

Posted by Kristian in Project Euler, 54 comments

## Project Euler – Prolog

Recently I found a website called Project Euler. It is a website, which has a series of problems which can be solved using a mix of math and programming. I like both math and programming, so I really do enjoys the problems. I have only solved a fraction of the problems, but I have already touched many branches of mathematics I usually don’t dabble much in.

It is stated that the problems should be solvable in under one minute once a program has been written. Writing the programs might takes several hours though, and this is the fun challenge is.

In this series of posts, I will gives a run through, and a solution methodology for solving some of the problems (the ones I have solved…), but I will in each case elaborate a bit more on it, than just finding a solution.

The code for these problems will be written in C#, and I wont provide the full code, only the useful snippets. I will use this first blog post on the subject to give you a bit of the structure around the interesting code.

Posted by Kristian in Project Euler, 0 comments