--- a/progs/knight2_sol.scala	Thu Dec 08 12:50:54 2016 +0000
+++ b/progs/knight2_sol.scala	Tue Dec 13 13:02:52 2016 +0000
@@ -36,6 +36,10 @@
   }
 }
 
+first(List((1, 0),(2, 0),(3, 0),(4, 0)), (x => if (x._1 > 3) Some(List(x)) else None))
+first(List((1, 0),(2, 0),(3, 0)), (x => if (x._1 > 3) Some(List(x)) else None))
+
+
 
 def first_tour(dim: Int, path: Path): Option[Path] = {
   if (path.length == dim * dim) Some(path)
@@ -49,7 +53,36 @@
   println(s"${dim} x ${dim} " + (if (t == None) "" else { print_board(dim, t.get) ; "" }))
 }
 */
+
+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 ts1 = first_tour(8, List((0, 0))).get
+  assert(correct_urban(8)(ts1) == true)
+
+val ts2 = first_tour(4, List((0, 0)))
+assert(ts2 == None)  
+
 print_board(8, first_tour(8, List((0, 0))).get)