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.*

**F#**** –** **C#** - **IronRuby** - **TSQL** - **JavaScript**

**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.*

**F#** – **C#** – **IronRuby** – **TSQL** – **JavaScript**

**003**

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

*What is the largest prime factor of the number 600851475143?*

**F#*** –* **C#*** –* **IronRuby** *–* **TSQL** *–* **JavaScript**

**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.*

**F#*** – ***C#*** – ***IronRuby*** –* **TSQL** *–* **JavaScript**

**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?*

**F#*** –* **C#*** –* **IronRuby** *–* **TSQL** *–* **JavaScript**

**006**

*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.*

**F#*** –* **C#*** –* **IronRuby** *–* **TSQL** *– ***JavaScript**

**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? *

**F#*** – ***C#*** – ***IronRuby*** –* **TSQL** *–* **JavaScript**

**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*

**F#*** – ***C#*** – ***IronRuby*** –* **TSQL** *–* **JavaScript**

**009**

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

`a`^{2} + `b`^{2} = `c`^{2}

*For example, 3 ^{2} + 4^{2} = 9 + 16 = 25 = 5^{2}.*

*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*

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