# Project Euler – Problem 17 Solution

Yan Cui

I help clients go faster for less using serverless technologies.

#### Problem

If the numbers 1 to 5 are written out in words: one, two, three, four, five, then there are 3 + 3 + 5 + 4 + 4 = 19 letters used in total.

If all the numbers from 1 to 1000 (one thousand) inclusive were written out in words, how many letters would be used?

NOTE: Do not count spaces or hyphens. For example, 342 (three hundred and forty-two) contains 23 letters and 115 (one hundred and fifteen) contains 20 letters. The use of “and” when writing out numbers is in compliance with British usage.

#### Solution

```
let onesToWord prefix n postfix =
match n with
| 1 -> prefix + "one" + postfix
| 2 -> prefix + "two" + postfix
| 3 -> prefix + "three" + postfix
| 4 -> prefix + "four" + postfix
| 5 -> prefix + "five" + postfix
| 6 -> prefix + "six" + postfix
| 7 -> prefix + "seven" + postfix
| 8 -> prefix + "eight" + postfix
| 9 -> prefix + "nine" + postfix
| _ -> ""

let tensToWord prefix tens ones =
match tens with
| 0 ->  onesToWord prefix ones ""
| 1 -> match ones with
| 0 -> prefix + "ten"
| 1 -> prefix + "eleven"
| 2 -> prefix + "twelve"
| 3 -> prefix + "thirteen"
| 4 -> prefix + "fourteen"
| 5 -> prefix + "fifteen"
| 6 -> prefix + "sixteen"
| 7 -> prefix + "seventeen"
| 8 -> prefix + "eighteen"
| 9 -> prefix + "nineteen"
| _ -> ""
| 2 -> prefix + "twenty" + (onesToWord "" ones "")
| 3 -> prefix + "thirty" + (onesToWord "" ones "")
| 4 -> prefix + "forty" + (onesToWord "" ones "")
| 5 -> prefix + "fifty" + (onesToWord "" ones "")
| 6 -> prefix + "sixty" + (onesToWord "" ones "")
| 7 -> prefix + "seventy" + (onesToWord "" ones "")
| 8 -> prefix + "eighty" + (onesToWord "" ones "")
| 9 -> prefix + "ninety" + (onesToWord "" ones "")
| _ -> ""

let toWord n =
let thousands = n / 1000
let hundreds = (n - 1000 * thousands) / 100
let tens = (n - 1000 * thousands - 100 * hundreds) / 10
let ones = n % 10

let thousandsWord = onesToWord "" thousands "thousand"
let hundredsWord = onesToWord "" hundreds "hundred"
let tensPrefix = if (thousands > 0 || hundreds > 0) && (tens > 0 || ones > 0)
then "and"
else ""
let tensWord = tensToWord tensPrefix tens ones

thousandsWord + hundredsWord + tensWord
let answer = [1 .. 1000] |> List.map toWord |> List.sumBy (fun s -> s.Length)
```

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### 2 thoughts on “Project Euler – Problem 17 Solution”

1. I actually did this problem when I was in school (at last bench, literature class, was bored), did it up to a million after some years I needed at work and did it up to infinite, you just had to have an array of [“millions”,”billion”,”trillion”, …]

let p17 =
let rec toWords x =
let words = [“”;”one”;”two”;”three”;”four”;”five”;”six”;”seven”;”eight”;”nine”;”ten”;”eleven”;”twelve”;”thirteen”;
“fourteen”;”fifteen”;”sixteen”;”seventeen”;”eighteen”;”nineteen”]
let wordsTy = [ “”;””;”twenty”;”thirty”;”forty”;”fifty”;”sixty”;”seventy”;”eighty”;”ninety”]

match x with
|n when n words.[n]
|n when n wordsTy.[n / 10] + words.[n % 10];
|1000 -> “onethousand”;
|n when (n % 100) > 0 -> words.[n / 100] + “hundredand” + toWords (n%100)
|n -> words.[n / 100] + “hundred”
[1..1000]|> List.map (toWords >> String.length) |> List.sum