# Project Euler – Problem 26 Solution

Yan Cui

I help clients go faster for less using serverless technologies.

#### Problem

A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:

1/2 = 0.5

1/3 = 0.(3)

1/4 = 0.25

1/5 = 0.2

1/6 = 0.1(6)

1/7 = 0.(142857)

1/8 = 0.125

1/9 = 0.(1)

1/10 = 0.1

Where 0.1(6) means 0.166666…, and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.

Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.

#### Solution

```let naturalNumbers = Seq.unfold (fun state -> Some(state, state+1)) 1

let rec cycleLength n =
if n % 2I = 0I then cycleLength (n/2I)
else
if n % 5I = 0I then cycleLength (n/5I)
else
naturalNumbers
|> Seq.filter (fun x -> ((pown 10I x) - 1I) % n = 0I)

let answer = [1I..999I] |> Seq.maxBy cycleLength
```

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### 1 thought on “Project Euler – Problem 26 Solution”

1. let p26 =
let getSeqLen i =
let rec loop rem remainders rlen =
match rem with
|x when List.exists (fun y -> y = x) remainders -> rlen
|x -> let r = ((rem*10)%i)
match r with
|0 -> rlen
|r -> loop r (x::remainders) (rlen+1)
loop 1 [] 0

let findMax =
let rec loop maxLen maxI i =
match i with
|i when i (maxLen, maxI)
|0 -> (maxLen, maxI)
|i -> let iLen = getSeqLen i
match iLen > maxLen with
|true -> loop iLen i (i-1)
|false -> loop maxLen maxI (i-1)
loop 0 0 1000

findMax