Problem 6

The sum of the squares of the first ten natural numbers is,

1² + 2² + … + 10² = 385

The square of the sum of the first ten natural numbers is,

(1 + 2 + … + 10)² = 55² = 3025

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 385 = 2640.

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

Solution

(*

 The sum of the squares of

 the first ten natural numbers is,

 

 1^2 + 2^2 + … + 10^2 = 385

 The square of the sum of the

 first ten natural numbers is,

 

 (1 + 2 + … + 10)^2 = 55^2 = 3025

 Hence the difference between the sum

 of the squares of the first ten natural

 numbers and the square of the sum is

 3025 – 385 = 2640.

 

 Find the difference between the sum of

 the squares of the first one hundred natural

 numbers and the square of the sum.

*)

 

let sqr x = x*x

let numbers = [1..100]

 

let sumofsqrs x = x

                  |> List.map sqr

                  |> List.sum

 

let sqrofsum x = x

                 |> List.sum

                 |> sqr

 

let answer x = sqrofsum x – sumofsqrs x

 

printfn "%A" (answer numbers)

Discussion

The F# solution is rather elegant once again.  There is a common math ‘trick’, but for only 100 elements there is no reason to shy away from the brute force solution.  Later this week we’ll see the trick.

If you have questions, leave a comment or please find me on Twitter (@azzlsoft) or email (rich@azzlsoft.com).