Project Euler for F#un

Alright, we completed through problem 50! First, I thought it was about time I implemented a decent prime sequence generator instead of co...

This was a tough problem. Even after dreaming up an algorithm which would perform well enough, it went through several tweaks until I was sa...

Again, easy problem using functional composition, the “hard” work was done in our previous implementation of the Digits module. The answer ...

Not the best performing solution (perhaps inherently so, though), but a shining example of the power of functional composition (the hard wor...

The difficult part of this problem was working around F#'s lack of break, continue, and return in for loops. hasForm would be most easi...

Here we reused the technique from Problem 44 for quickly asserting that a number is in the range of a function by verifying that n = f (f-1(...

This problem was a big disappointment.  It turns out that the first pair you find for which their sum and difference is pentagonal is the so...

Combining our Digits and permutations implementations with F#’s built-in Seq functions, we really see how functional programming shines i...

This problem is designed to make use of several tools. let problem42a = let triangle n = let n' = n |> float in (0.5)*(n')*...

My first approach was to try and find the first odd number descending from 987654321 which was both prime and pandigital, but despite attemp...

An imperative solution seems appropriate. let problem40a = let sb = System.Text.StringBuilder() let mutable n = 1 while sb.Len...

Brute force algorithm with no real optimizations. let problem39c = let countTriplets p = let mutable count = 0 for a ...

Wow, interesting - tough!  And I finally found Seq.choose (I was looking for Seq.pickAll). let problem38a = let isPosPd (nstr:string)...

Kind of a variation on Problem 35.  I was surprised by how fast it ran! let problem37a = let isTruncatablePrime n = if n |>...

Reusing isPalindrome from Problem 4 and leveraging System.Convert for obtaining the binary representation of a given decimal number, this pr...

Now we get to use our Digits module.  The most interesting part of this algorithm is performing digit rotations (the assignment of r ), whic...

We’ve had a lot of problems involving digit manipulation and so far have implemented ad-hoc string parsing solutions.  But this approach is ...

The upper bound is 2540160, since (factorial 9)*7 = 2540160 and (factorial 9)^x grows faster than 10^x for x >= 7. let problem34b = ...

With F#, there are two ways to solve this: the easy way, and the slightly easier way.  The first way, we’ll work entirely with integers, inc...

While having lots of pieces, this problem is mostly straightforward.  The only part that required any analysis is determining sufficient low...

More fun with recursive sequence expressions! In this solution, we generate all of the combinations instead of only counting them. let pro...

We must find an upper limit for numbers to search.  As the length of a number increases, 9**5 is the greatest additional contribution a di...

Too easy. let problem29a = seq { for a in 2I..100I do for b in 2..100 do yield bigint.Pow(a,b)} |> Seq.distinct |> Seq....

Another pleasant one where by writing down the first few terms of the sequence (by dimension) of sequences (corners in a dimension), it was ...

This one was straight forward, just had to follow instructions (I didn’t apply any mathematical optimizations, because it looked like if onc...

After taking a break for a few days, having spent 3 consecutive weeks solving problems 1-25 every free hour and deep into the night, this tu...

The past couple of days I've been interested in exploring PLINQ with F#.  But Since I’m using F# 2.0 for Visual Studio 2008 (i.e. .NET 2...

The key to this one, unlike the traditional non-tail-recursive definition of the Fibonacci sequence, is to generate the next element in the ...

Completing this one marks my advance to “level 1”, having completed 25 problems (I completed Problem 67 when I completed Problem 18), and pl...

Since we’ll be reusing the sigma-divisor function again, we’ll generalize it and move it to Calc.Generalize.  Along with that I have added a...

Due to the nature of this problem, we don’t shy away from mutation for performance gains.  For example, sorting the names array in place.  T...

First, using our fast factorize function, we implement the well-known sigma-divisor function and it’s proper companion. let sigma n = ...

Over the past few days I’ve been exploring ways to organize and reuse common functions which repeat across Euler problems.  Something I’ve b...

Reusing the fact function we slipped into Problem 15, this is essentially the same as Problem 16. let problem20a = fact 100I |> st...

Relieved .NET DateTime was sufficient for this. let problem19a = let mutable cur = new System.DateTime(1901, 1, 1); let last = ne...

Wow.  The algorithm just took a little bit of pacing to realize, but I’ve gone through several refinements and variations of the implementat...

After simplifying, and taking care to spell “forty” correctly. let problem17d = "OneThousand" .Length + "OneHu...

Easy. let problem16a = bigint.Pow(2I, 1000) |> string |> Seq.sumBy ( fun c -> c |> string |> int)

OK.  I am incredibly pleased with myself for solving this one almost entirely through mathematical proof.  Indeed, I’ve solved it generally ...

I coded  this solution in just a couple of minutes, but ran into trouble with F#’s unchecked Int32 operations.  We can do checked operations...

With F#’s bigint, this is trivial. let problem13a = [37107287533902102798797998220837590246510135740250I; 46376937677490009712...

This has been the most sophisticated problem yet. My first solution took 2 minutes to write, but I gave up on it after 5 minutes of runnin...

Not too hard, but it offered some frustration.  First, I couldn’t get the compiler to parse my multi-line list of lists for the grid.  Secon...

This problem is a variation on Problem 7 allowing us to reuse isPrime and modify nthPrime to build a list of primes up to a max. //problem...

Here we generate a sequence of all possible triplets meeting the conditions, and find the first which is Pythagorean.  It took a while to ge...