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Posted 10 Aug 2011

# Project Euler Problem #1

, 10 Aug 2011
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Project Euler Problem #1

Alright, here we go on Project Euler. Time for the first problem:

```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.```

That doesn't sound quite that hard. Right? The first problem couldn't possibly be hard.

Well, let's break it down. All the numbers that are multiples of 3 or 5 under 10 are 3, 5, 6 and 9. Or in other words, 3, 5, 6 and 9 are the only numbers (under 10) that are divisible by 3 or 5 and leave no remainder behind.

So now we have to find all the numbers under 1000 that satisfy the same requirement. And then sum those numbers.

At first thought, I suppose it would be easy enough to create a loop that goes through each possibility and adds the number to a list if it passes the divisible test.

Something like this:

```List<int> multiples = new List<int>();

for (int i = 1; i < 1000; i++)
{
if ((i % 3 == 0) || (i % 5 == 0))
{
}
}

return multiples.Sum();
```

Simple enough right? Well yes, and for this simple type of problem, it won't really have any effect on performance. However, I wanted the least amount of lines as possible. I had recently discovered the wonderful world of lambda expressions and I feel that I should use them as often as I can (for better or for worse).

So here is my solution:

```return Enumerable.Range(1, 999).Where(i => (i % 3).Equals(0) || (i % 5).Equals(0)).Sum();
```

Ah. Enumerables. By using the '`Range`' extension, I can retrieve an enumerable list of `int`s to select from. The '`Where`' extension method will ensure that I only retrieve the numbers that are multiples of 3 or 5. And finally, the '`Sum`' extension will return the sum of all the numbers left.

Or if we want to get really fancy, we could create a lambda function delegate to make things a bit more readable:

```Func<int, int, bool> IsMultiple = (int i, int j) => (i % j).Equals(0);
return Enumerable.Range(1, 999).Where(i => IsMultiple(i, 3) || IsMultiple(i, 5)).Sum();
```

However, the previous solution will do in this case.

Simple and concise. KISS principle in action.

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 Lazy not simple Zebedee Mason15-Aug-11 21:35 Zebedee Mason 15-Aug-11 21:35
 Try ```def Euler(n): return n * (n+1) / 2   def Summation(n): return 3 * Euler(n/3) + 5 * Euler(n/5) - 15 * Euler(n/15)``` instead and notice the speed difference between constant time and linear time.
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