--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/marking3/knight1_test3b.scala	Sun Dec 09 01:36:49 2018 +0000
@@ -0,0 +1,33 @@
+
+type Pos = (Int, Int)    // a position on a chessboard 
+type Path = List[Pos]    // a path...a list of positions
+
+def count_all_tours_urban(dim: Int) = {
+  for (i <- (0 until dim).toList; 
+       j <- (0 until dim).toList) yield count_tours(dim, List((i, j)))
+}
+
+def add_pair_urban(x: Pos)(y: Pos): Pos = 
+  (x._1 + y._1, x._2 + y._2)
+
+def is_legal_urban(dim: Int, path: Path)(x: Pos): Boolean = 
+  0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)
+
+def moves_urban(x: Pos): List[Pos] = 
+  List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),
+       (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair_urban(x))
+
+def legal_moves_urban(dim: Int, path: Path, x: Pos): List[Pos] = 
+  moves_urban(x).filter(is_legal_urban(dim, path))
+
+def correct_urban(dim: Int)(p: Path): Boolean = p match {
+  case Nil => true
+  case x::Nil => true
+  case x::y::p => if (legal_moves_urban(dim, p, y).contains(x)) correct_urban(dim)(y::p) else false
+}
+
+
+
+val ts_urban = enum_tours(5, List((0, 2)))
+assert(ts_urban.map(correct_urban(5)).forall(_ == true) == true)
+assert(ts_urban.length == 56)