3 * 3 magic square

magic_square.clj

(use '[clojure.contrib.combinatorics :only (permutations)])

(for [pattern (permutations [1 2 3 4 5 6 7 8 9])      
      :when
      (let [a1 (nth pattern 0)
	    a2 (nth pattern 1)
	    a3 (nth pattern 2)
	    b1 (nth pattern 3)
	    b2 (nth pattern 4)
	    b3 (nth pattern 5)
	    c1 (nth pattern 6)
	    c2 (nth pattern 7)
	    c3 (nth pattern 8)]
	(= (+ a1 a2 a3)
	   (+ b1 b2 b3)
	   (+ c1 c2 c3)
	   (+ a1 b1 c1)
	   (+ a2 b2 c2)
	   (+ a3 b3 c3)
	   (+ a1 b2 c3)
	   (+ a3 b2 c1)))]
  pattern)

(comment
  ((2 7 6 9 5 1 4 3 8)
   (2 9 4 7 5 3 6 1 8)
   (4 3 8 9 5 1 2 7 6)
   (4 9 2 3 5 7 8 1 6)
   (6 1 8 7 5 3 2 9 4)
   (6 7 2 1 5 9 8 3 4)
   (8 1 6 3 5 7 4 9 2)
   (8 3 4 1 5 9 6 7 2)))