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.
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.
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.
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.
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.
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.
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.
The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 600851475143?
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.
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?
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.
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?
Find the greatest product of five consecutive digits in the 1000-digit number.
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.
The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
Find the sum of all the primes below two million.