### The Problem

The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832.

73167176531330624919225119674426574742355349194934 96983520312774506326239578318016984801869478851843 85861560789112949495459501737958331952853208805511 12540698747158523863050715693290963295227443043557 66896648950445244523161731856403098711121722383113 62229893423380308135336276614282806444486645238749 30358907296290491560440772390713810515859307960866 70172427121883998797908792274921901699720888093776 65727333001053367881220235421809751254540594752243 52584907711670556013604839586446706324415722155397 53697817977846174064955149290862569321978468622482 83972241375657056057490261407972968652414535100474 82166370484403199890008895243450658541227588666881 16427171479924442928230863465674813919123162824586 17866458359124566529476545682848912883142607690042 24219022671055626321111109370544217506941658960408 07198403850962455444362981230987879927244284909188 84580156166097919133875499200524063689912560717606 05886116467109405077541002256983155200055935729725 71636269561882670428252483600823257530420752963450

Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?

### F# Solution

I had a lot of fun solving this one. The solution I came up with is a great example of using the pipeline operator `|>` to break a solution into a series of steps that eventually yield the answer. First, let’s define the input:

``````let inputs = [|
"73167176531330624919225119674426574742355349194934"
"96983520312774506326239578318016984801869478851843"
"85861560789112949495459501737958331952853208805511"
"12540698747158523863050715693290963295227443043557"
"66896648950445244523161731856403098711121722383113"
"62229893423380308135336276614282806444486645238749"
"30358907296290491560440772390713810515859307960866"
"70172427121883998797908792274921901699720888093776"
"65727333001053367881220235421809751254540594752243"
"52584907711670556013604839586446706324415722155397"
"53697817977846174064955149290862569321978468622482"
"83972241375657056057490261407972968652414535100474"
"82166370484403199890008895243450658541227588666881"
"16427171479924442928230863465674813919123162824586"
"17866458359124566529476545682848912883142607690042"
"24219022671055626321111109370544217506941658960408"
"07198403850962455444362981230987879927244284909188"
"84580156166097919133875499200524063689912560717606"
"05886116467109405077541002256983155200055935729725"
"71636269561882670428252483600823257530420752963450"
|]
``````

I copied and pasted most of that right out of the problem definition, adding `"` at each end, which is super easy to do if you use column selection in Visual Studio.

Next, we’re going to need a function that computes the product of the elements in a sequence. So, for example, `product [1I..4I]` returns 24.

``````let product nums =
nums
|> Seq.reduce (fun acc elem -> acc*elem)
``````

The `product` function above uses `Seq.reduce` to multiple each element in the sequence by the previous one and then return the result.

Finally, we build our pipeline to get the result:

``````inputs
|> Seq.concat
|> Seq.map (fun c -> bigint(int(string c)))
|> Seq.windowed 13
|> Seq.map (fun s -> s,product s)
|> Seq.maxBy snd
``````

The above:

• Concatenates all the inputs into a long sequence of characters
• Converts each character to a `bigint`
• Breaks it up into sliding windows of 13 numbers each
• Converts each sequence of 13 numbers to its product
• Finds the maximum product (the answer)
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