Template

(define (neighbours state)
  (local
    ;; Generates all the possible rectangles starting at the first unused square
    [(define (all-rectangles grid)
       'NOT_IMPLEMENTED)

     ;; Takes a rectangle and returns true if the rectangle is valid in the grid
     ;; 1. Every cell is unused
     ;; 2. There is only one number
     ;; 3. That number is the area of the rectangle
     (define (rectangle-valid? _rect grid)
       'NOT_IMPLEMENTED)

     ;; Does all the work to "add" a rectangle
     ;; 1. Set everything to used
     ;; 2. Add the rectangle to the rectangle list
     (define (add-rectangle state _rect)
       'NOT_IMPLEMENTED)]

    ;; If its solved, just return an empty list
    (if (solved? state) empty
        ;; Otherwise, generate all possible rectangles, filter out the valid ones,
        ;;     and then map over and add each rectangle to the state
        (map (lambda (x) (add-rectangle state x))
             (filter (lambda (x) (rectangle-valid? x (state-grid state)))
                     (all-rectangles (state-grid state)))))))