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; Problem 1:
; Find the sum of all the multiples of 3 or 5 below 1000.

(apply + (filter #(or (zero? (mod % 5))
		      (zero? (mod % 3)))
		 (range 1000)))

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; Problem 2:
; Find the sum of all the even-valued terms in the Fibonacci
; sequence which do not exceed four million.

(defn nextfib [[x y]]
  (cond (zero? x) [1 1]
	:else [y (+ x y)]))
(def fibs (map first (iterate nextfib [0 nil])))
(def even-fibs-lt-4mil 
	    (filter even? 

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; Problem 3
; The prime factors of 13195 are 5, 7, 13 and 29.
; What is the largest prime factor of the number 600851475143 ?

(defn prime? [x]
  (cond (< x 2) false
	(= x 2) true
	(even? x) false
	:else (let [boundary (inc (int (Math/sqrt x)))
		    candidates (range 3 boundary 2)]

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; Problem 4
; A palindromic number reads the same both ways. The largest
; palindrome made from the product of two 2-digit numbers
; is 9009 = 91  99.
;
; Find the largest palindrome made from the product of two 3-digit numbers.

(defn palindromic? [x]
  (let [strx (str x)]
    (= (seq strx) (reverse strx))))

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; Problem 5
; 2520 is the smallest number that can be divided by each of the
; numbers from 1 to 10 without any remainder.
;
; What is the smallest number that is evenly divisible by all of
; the numbers from 1 to 20?

(defn divisible-by? [x y]
  (zero? (mod y x)))

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; 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)))

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; Problem 7
;
; By listing the first six prime numbers: 2, 3, 5, 7, 11,
; and 13, we can see that the 6th prime is 13.
;
; What is the 10001st prime number?

(defn prime? [x]
  (cond (< x 2) false
	(= x 2) true

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; Problem 8
;
; Find the greatest product of five consecutive digits in the 1000-digit number.

(def digits
     (map #(Integer/parseInt %)
	  (rest (seq (.split 
		      (str
		       "73167176531330624919225119674426574742355349194934"
		       "96983520312774506326239578318016984801869478851843"

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; Problem 9
; A Pythagorean triplet is a set of three natural numbers, a < b < c,
; for which,
;
; a^2 + b^2 = c^2
; For example, 3^2 + 4^2 = 9 + 16 = 25 = 52.
;
; There exists exactly one Pythagorean triplet for which a + b + c = 1000.
; Find the product abc.

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; Problem 10
; 
; The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
; 
; Find the sum of all the primes below two million.

(defn prime? [x]
  (cond (< x 2) false
	(= x 2) true
	(even? x) false