diff -r 92c31cbb1952 -r 863feeb5c760 testing2/knight3.scala
--- a/testing2/knight3.scala	Tue Nov 28 20:37:57 2017 +0000
+++ b/testing2/knight3.scala	Wed Nov 29 21:22:29 2017 +0000
@@ -1,96 +1,45 @@
-// Part 3 about finding a single tour using the Warnsdorf Rule
-//=============================================================
-
+import scala.annotation.tailrec
 object CW7c {
-
-type Pos = (Int, Int)
-type Path = List[Pos]
+type Pos = (Int, Int)    // a position on a chessboard 
+type Path = List[Pos]    // a path...a list of positions
 
-def print_board(dim: Int, path: Path): Unit = {
-  println
-  for (i <- 0 until dim) {
-    for (j <- 0 until dim) {
-      print(f"${path.reverse.indexOf((i, j))}%3.0f ")
-    }
-    println
-  } 
+def is_legal(dim: Int, path: Path)(x: Pos) : Boolean = {
+    if((x._1 >= 0) && (x._2 >= 0) && (x._1 < dim) && (x._2 < dim)){
+       !(path.contains(x))
+    } else false
+ }
+
+def legal_moves(dim: Int, path: Path, x: Pos) : List[Pos] = {
+  val lst = List( (1,2),(2,1),(2,-1),(1,-2), (-1,-2),(-2,-1),(-2,1),(-1,2) )
+  val mapping = lst.map(s => ( s._1 + x._1, s._2 + x._2) )   
+       for( i <- mapping if ( is_legal(dim,path)(i) )) yield i     
+  }
+
+def ordered_moves(dim: Int, path: Path, x: Pos) : List[Pos] = {
+legal_moves(dim,path,x).sortBy(legal_moves(dim,path,_).length  )
 }
 
-def add_pair(x: Pos)(y: Pos): Pos = 
-  (x._1 + y._1, x._2 + y._2)
-
-def is_legal(dim: Int, path: Path)(x: Pos): Boolean = 
-  0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)
-
-def moves(x: Pos): List[Pos] = 
-  List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),
-       (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair(x))
-
-def legal_moves(dim: Int, path: Path, x: Pos): List[Pos] = 
-  moves(x).filter(is_legal(dim, path))
+def first(xs: List[Pos], f: Pos => Option[Path]) : Option[Path] ={
+  if(xs.isEmpty)
+  None 
+  else {
+            val b = f(xs.head)
+            if (b!=None)
+            b
+          else
+             first(xs.tail,f)
+       }
+  }
 
-def ordered_moves(dim: Int, path: Path, x: Pos): List[Pos] = 
-  legal_moves(dim, path, x).sortBy((x) => legal_moves(dim, path, x).length)
-
-
-import scala.annotation.tailrec
-
-@tailrec
-def first(xs: List[Pos], f: Pos => Option[Path]): Option[Path] = xs match {
-  case Nil => None
-  case x::xs => {
-    val result = f(x)
-    if (result.isDefined) result else first(xs, f)
+def first_closed_tour_heuristic(dim: Int, path: Path) : Option[Path] = {
+  if (dim < 5) None 
+    else 
+        if(path.length==dim*dim) Some(path)
+       else 
+      first(ordered_moves(dim,path,path.head),y => first_closed_tour_heuristic(dim, y::path))
   }
+  
 }
 
 
-def first_closed_tour_heuristic(dim: Int, path: Path): Option[Path] = {
-  if (path.length == dim * dim && moves(path.head).contains(path.last)) Some(path)
-  else
-    first(ordered_moves(dim, path, path.head), (x: Pos) => first_closed_tour_heuristic(dim, x::path))
-}
-
-/*
-for (dim <- 1 to 6) {
-  val t = first_closed_tour_heuristic(dim, List((dim / 2, dim / 2)))
-  println(s"${dim} x ${dim} closed: " + (if (t == None) "" else { print_board(dim, t.get) ; "" }))
-}*/
-
-
-def first_tour_heuristic(dim: Int, path: Path): Option[Path] = {
-
-  @tailrec
-  def aux(dim: Int, path: Path, moves: List[Pos]): Option[Path] =  
-  if (path.length == dim * dim) Some(path)
-  else
-    moves match {
-      case Nil => None
-      case x::xs => {
-        val r = first_tour_heuristic(dim, x::path)
-        if (r.isDefined) r else aux(dim, path, xs)
-    }
-  }    
- 
-  aux(dim, path, ordered_moves(dim, path, path.head)) 
-}
-
-/*
-def first_tour_heuristic(dim: Int, path: Path): Option[Path] = {
-  if (path.length == dim * dim) Some(path)
-  else
-    first(ordered_moves(dim, path, path.head), (x: Pos) => first_tour_heuristic(dim, x::path))
-}
-*/
-
-/*
-for (dim <- 1 to 50) {
-  val t = first_tour_heuristic(dim, List((dim / 2, dim / 2)))
-  println(s"${dim} x ${dim}: " + (if (t == None) "" else { print_board(dim, t.get) ; "" }))
-}
-*/
-
-}
-
-
-//CW7c.first_tour_heuristic(50, List((0,0))).get
+first_closed_tour_heuristic(6, List((3, 3)))