WARNING! This post contains a spoiler for Problem #1 listed at Project Euler. Do not read the rest of this post if you’re planning to attempt to solve the problem yourself.

I decided to work my way through these problems using Haskell, as I felt it’d be a great way to learn the language (or at least start to get familiar with it).

Problem #1 in the series is a nice “starter” question. It’s a simple one to get you going, which for me was great since I am a bit of a Haskell beginner:

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.

Here is my Haskell source that generates the required answer:

1

sum [ n | n <- [1..999], ((mod n 3) == 0) || ((mod n 5) == 0) ]

Don’t you just love how concise the answer is? If you’re like me and are new to Haskell, let me explain it a little.

1. [1..999] - this generates a list of values from 1 to 999 inclusive.
2. [ value | item <- source list, condition ] - this is the basic list comprehension syntax in Haskell (basically this is how you generate lists from other lists). Here is the breakdown.
   1. source list is a reference to a list which is used as the source to generate the new list.
   2. item is the variable that is an alias for each item in the source list. This is usually referenced in the value expression.
   3. condition is a boolean condition that indicates whether or not a value should be included in the list.
   4. value is the final expression that gets evaluated and stored in the list. The expression is only evaluated and added to the list if the condition is true
3. mod n 3 - this evaluates “n modulo 3”, and hence gives the remainder when n is divided by 3.
4. ((mod n 3) == 0) || ((mod n 5) == 0) - this is a condition that evaluates to true if n is evenly divisible by 3 or 5.
5. [ n | n <- [1..999], ((mod n 3) == 0) || ((mod n 5) == 0) ] - for each item n in the list of numbers 1 through 999, if the number is evenly divisible by 3 or 5, then include it in the list.
6. sum - this function simply produces the sum of all the numbers in the given list.

Pretty simple really isn’t it :) Enjoy.