euler006.clj

; Problem 6
; The sum of the squares of the first ten natural numbers is,
;
; 1^2 + 2^2 + ... + 10^2 = 385

(def natural-numbers (iterate inc 1))
(def squares (map #(* % %) natural-numbers))
(def sum-of-squares
     (reduce + (take 10 squares)))

; The square of the sum of the first ten natural numbers is,
;
; (1 + 2 + ... + 10)^2 = 55^2 = 3025

(def square-of-sum
     (let [sum (reduce + (take 10 natural-numbers))]
       (* sum sum)))

; 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.

(- square-of-sum sum-of-squares)

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

(defn sum-of-squares* [n]
  (reduce + (take n squares)))

(defn square-of-sum* [n]
  (let [sum (reduce + (take n natural-numbers))]
    (* sum sum)))

(defn diff [n]
  (- (square-of-sum* n) (sum-of-squares* n)))