# August, 2009

Posts
• #### Project Euler Problem #7

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Find the 10001st prime let naturals = Seq.unfold ( fun i -> Some(i, i + 1 )) let primes = naturals 2 |> Seq.filter ( fun n -> seq { 2.. int (sqrt (float n)) } |> Seq.forall ( fun x -> n % x <> 0 )) Seq.nth 10000 primes
• #### Project Euler Problem #6

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Difference between sum of the squares and the square of the sum of 1 - 100 : ( fun ns -> let sqr x = x * x (sqr (List.sum ns)) - (List.map sqr ns |> List.sum) ) [1..100]
• #### Project Euler Problem #5

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Smallest number divisible by each of 1 to 20 : First cut (takes almost an hour to execute!): let isFactor n d = n % d = 0 {1..Int32.MaxValue} |> Seq.find ( fun n -> [1..20] |> List.forall (isFactor n)) Second cut (takes a...
• #### Project Euler Problem #4

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Largest palindrome from product of two 3-digit numbers : let isPalendrome n = let s = n.ToString() |> List.of_seq s = List.rev s seq { for a in 100..999 do for b in a..999 -> a * b } |> Seq.filter isPalendrome |> Seq.max
• #### Project Euler Problem #3

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Largest prime factor of 600851475143 : let primeFactors n = let isFactor n d = n % d = 0L let nextFactor n d = seq {d..n} |> Seq.find (isFactor n) (n, 2L, []) |> Seq.unfold ( fun (n, d, a) -> if isFactor n d then Some(d, ((n...
• #### Project Euler Problem #2

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Sum of even terms in Fibonacci sequence which are < four-million : (1, 1) |> Seq.unfold ( fun (a, b) -> Some(a, (b, a + b))) // fibs |> Seq.takeWhile ( fun x -> x <= 4000000) |> Seq.filter ( fun x -> x % 2 = 0) ...
• #### Project Euler Problem #1

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Project Euler is pretty darn cool. It’s a bunch of mathematical problems that require programming to solve. I’m having fun doing them in F#. They start very simple but quickly become more difficult. Problem 1 is to find the sum of all the multiples...
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