Mana Board

mana-board.scm

(define board
  '((2 2 3 1 2 2)
    (1 3 1 3 1 3)
    (3 1 2 2 3 1)
    (2 3 1 3 1 2)
    (2 1 3 1 3 2)
    (1 3 2 2 1 3)))

(define (invalid_range n)
  (cond ((> n 5) #t)
        ((negative? n) #t)
        (else #f)))

(define (row n b)
  (cond ((invalid_range n) (error "invalid range"))
        ((zero? n) (car b))
        (else (row (1- n) (cdr b)))))

(define (col n b)
  (cond ((invalid_range n) (error "invalid range"))
        ((zero? n) (map car b))
        (else (col (1- n) (map cdr b)))))

(define (transpose b)
  (if (nil? (car b))
      '()
       (cons (map car b) (transpose (map cdr b)))))

(define (sum-line line) (apply + line))

;; First symmetry found: all rows sum to 12
(map sum-line board)

;; First asymmetry found: not all rows equal to 12
(map sum-line (transpose board))

(define (average list)
  (/ (apply + list) (length list)))

;; Symmetry found: all rows average to 2
(map average board)

;; Asymmetry found: not all colums average to 2
(map average (transpose board))