### Champernowne's Constant - Project Euler Problem 40

Problem

An irrational decimal fraction is created by concatenating the positive integers:

0.12345678910

It can be seen that the 12th digit of the fractional part is 1.

If dn represents the nth digit of the fractional part, find the value of the following expression.

d1 x d10 x d100 x d1000 x d10000 x d100000 x d1000000

Original Problem Source

Solution

``````
//speed depends on using StringBuilder, non-idiomatic since it is mutable
let rec NumArray start max maxLength (numString:System.Text.StringBuilder) =
if start = max || numString.Length >= maxLength then
numString.Append(start.ToString())
else
let newString = numString.Append(start.ToString())
let nextNum = start + 1
NumArray nextNum max maxLength newString

//cast string to int
let convertStringToInt32 (value:string) =
let mutable result = 0
let found = System.Int32.TryParse(value, &result)
result

//test for conversion
//let test_conversion = convertStringToInt32("1")

//starts timer
let startChampernowne = System.DateTime.Now

//create string builder and initialize it
let numStringStart = new System.Text.StringBuilder()
let startString = numStringStart.Append(".")

//variety of tests
//let test_numArray = NumArray 1 100 100000 numStringStart
//let test_stringPosition1 = test_numArray.Chars(0)
//let test_stringPosition10 = test_numArray.Chars(9)
//let test_stringPosition100 = test_numArray.Chars(99)
//let test_stringPosition12 = test_numArray.Chars(11)

//Create Champernowne's constant nd convert to string
let GetNumArray = NumArray 1 1000000 1000000 startString
let NumArrayToString = GetNumArray.ToString()

//find solution
let ProdOfValues =
convertStringToInt32(NumArrayToString.Chars(1).ToString())
* convertStringToInt32(NumArrayToString.Chars(10).ToString())
* convertStringToInt32(NumArrayToString.Chars(100).ToString())
* convertStringToInt32(NumArrayToString.Chars(1000).ToString())
* convertStringToInt32(NumArrayToString.Chars(10000).ToString())
* convertStringToInt32(NumArrayToString.Chars(100000).ToString())
* convertStringToInt32(NumArrayToString.Chars(1000000).ToString())

//end times
printfn "%s" ((System.DateTime.Now - startChampernowne).ToString())

``````