## Project Euler

Recently I decided that I wanted to learn F#.  After perusing a few “tutorials” I felt that the language was going to be difficult to grasp without some real problems to solve.  That’s when I stumbled across Project Euler.  Here is the description from their website:

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.

This is the perfect avenue to explore a language like F#.  After I solved a few problems I decided that I could use this to keep mentally fit. in several languages.  I chose five different languages so I could solve one problem per week and post solutions each week day.  Without further adieu, here are the languages I chose and why.

My Languages

F#

I have been intrigued by this language for some time.  I don’t know enough about it yet to say what it is or even if I like it.  I have heard that if I understand F#, it will make me a better C# programmer.  I guess we’ll find out.

C#

Because I use C# everyday, sometimes I prototype the Euler solutions in it before trying the other languages.  After I’ve worked out a solution, I will often try to figure out the “F# way” to solve the problem.  This takes quite a while for me.

IronRuby

I wanted to throw in a dynamic language and narrowed it down to Python or Ruby.  I have done some Python programming in the past so I thought why not try something new.  IronRuby, for those that don’t know, is a .NET implementation of Ruby so it works well for me in Visual Studio.

Transact-SQL

With most of these problems there is a clever trick you have to figure out and once know that, the problem is usually simple to code.  For my SQL solutions, however, I want to take a different approach by assuming the database is filled with lots of number information and then I just need to write the query.

JavaScript

I’m not real excited about JavaScript but it’s just too damned popular to ignore.

Problems

001

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.

002

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, …

By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.

003

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

What is the largest prime factor of the number 600851475143?

004

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.

005

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 by all of the numbers from 1 to 20?

006

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.

007

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?

008

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

009

A Pythagorean triplet is a set of three natural numbers, a b c, for which,

a2 + b2 = c2

For example, 32 + 42 = 9 + 16 = 25 = 52.

There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.

F#C#IronRuby TSQL JavaScript

010

The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.

Find the sum of all the primes below two million.

F# – C# – IronRuby – TSQL – JavaScript