diff --git a/examples/benchmarks/lib/benchmarks/knights/chess_set.ak b/examples/benchmarks/lib/benchmarks/knights/chess_set.ak
index 4ff445e4..465758e7 100644
--- a/examples/benchmarks/lib/benchmarks/knights/chess_set.ak
+++ b/examples/benchmarks/lib/benchmarks/knights/chess_set.ak
@@ -26,14 +26,19 @@ pub fn first_piece(board: ChessSet) -> Tile {
 }
 
 pub fn delete_first(board: ChessSet) -> ChessSet {
-  let visited = board.visited
+  let ChessSet { move_number, visited, .. } = board
 
   expect Some(deleted_first) = list.init(visited)
 
-  ChessSet { ..board, start: second_last(visited), visited: deleted_first }
+  ChessSet {
+    ..board,
+    move_number: move_number - 1,
+    start: second_last(visited),
+    visited: deleted_first,
+  }
 }
 
-pub fn second_last(visited: List<a>) -> Option<a> {
+fn second_last(visited: List<a>) -> Option<a> {
   when visited is {
     [] -> None
     [_, ..rest] -> {
@@ -51,6 +56,14 @@ pub fn second_last(visited: List<a>) -> Option<a> {
     }
   }
 }
+
+pub fn is_square_free(board: ChessSet, tile: Tile) -> Bool {
+  not_in(board.visited, tile)
+}
+
+pub fn not_in(tiles: List<a>, tile: a) -> Bool {
+  !list.has(tiles, tile)
+}
 // {-# INLINABLE createBoard #-}
 // createBoard :: Integer -> Tile -> ChessSet
 // createBoard x t = Board x 1 (Just t) [t]
diff --git a/examples/benchmarks/lib/benchmarks/knights/heuristic.ak b/examples/benchmarks/lib/benchmarks/knights/heuristic.ak
index f736cd32..37d27f22 100644
--- a/examples/benchmarks/lib/benchmarks/knights/heuristic.ak
+++ b/examples/benchmarks/lib/benchmarks/knights/heuristic.ak
@@ -1,9 +1,37 @@
 use aiken/builtin
 use aiken/list
-use benchmarks/knights/chess_set.{add_piece, create_board, first_piece}
+use benchmarks/knights/chess_set.{
+  add_piece, create_board, delete_first, first_piece, is_square_free,
+}
 use benchmarks/knights/sort.{quick_sort}
 use benchmarks/knights/types.{ChessSet, Tile}
 
+type Direction {
+  UL
+  UR
+  DL
+  DR
+  LU
+  LD
+  RU
+  RD
+}
+
+fn move(direction: Direction, tile: Tile) -> Tile {
+  let (x, y) = tile
+
+  when direction is {
+    UL -> (x - 1, y - 2)
+    UR -> (x + 1, y - 2)
+    DL -> (x - 1, y + 2)
+    DR -> (x + 1, y + 2)
+    LU -> (x - 2, y - 1)
+    LD -> (x - 2, y + 1)
+    RU -> (x + 2, y - 1)
+    RD -> (x + 2, y + 1)
+  }
+}
+
 pub fn start_tour(st: Tile, size: Int) -> ChessSet {
   expect 0 = builtin.remainder_integer(size, 2)
 
@@ -20,7 +48,8 @@ pub fn descendants(board: ChessSet) -> List<ChessSet> {
   if and {
     can_jump_first(board),
     board
-      |> add_piece(first_piece(board))
+      |> first_piece
+      |> add_piece(board, _)
       |> dead_end,
   } {
     []
@@ -37,22 +66,62 @@ pub fn descendants(board: ChessSet) -> List<ChessSet> {
 }
 
 pub fn can_jump_first(board: ChessSet) -> Bool {
-  todo
+  can_move_to(delete_first(board), first_piece(board))
 }
 
 pub fn dead_end(board: ChessSet) -> Bool {
-  todo
+  board |> possible_moves |> builtin.null_list
 }
 
 pub fn single_descend(board: ChessSet) -> List<ChessSet> {
-  todo
+  let descendants_and_moves = desc_and_no(board)
+  list.filter_map(
+    descendants_and_moves,
+    fn(item) {
+      let (moves, board) = item
+      if moves == 1 {
+        Some(board)
+      } else {
+        None
+      }
+    },
+  )
 }
 
 pub fn desc_and_no(board: ChessSet) -> List<(Int, ChessSet)> {
-  todo
+  board
+    |> all_descend
+    |> list.map(
+         fn(item) {
+           (item |> delete_first |> possible_moves |> list.length, item)
+         },
+       )
 }
 
 pub fn can_move_to(board: ChessSet, tile: Tile) -> Bool {
+  let (x, y) = tile
+  let size = board.size
+
+  and {
+    x >= 1,
+    x <= size,
+    y >= 1,
+    y <= size,
+    is_square_free(board, tile),
+  }
+}
+
+pub fn all_descend(board: ChessSet) -> List<ChessSet> {
+  board
+    |> possible_moves
+    |> list.map(fn(direction) { move_knight(board, direction) })
+}
+
+fn move_knight(board: ChessSet, direction: Direction) -> ChessSet {
+  todo
+}
+
+fn possible_moves(board: ChessSet) -> List<Direction> {
   todo
 }
 // data Direction = UL | UR | DL |DR | LU | LD | RU | RD
diff --git a/examples/benchmarks/lib/benchmarks/knights/types.ak b/examples/benchmarks/lib/benchmarks/knights/types.ak
index 75449ffb..fc293456 100644
--- a/examples/benchmarks/lib/benchmarks/knights/types.ak
+++ b/examples/benchmarks/lib/benchmarks/knights/types.ak
@@ -2,9 +2,9 @@ pub type Tile =
   (Int, Int)
 
 pub type ChessSet {
+  size: Int,
   move_number: Int,
   visited: List<Tile>,
-  size: Int,
   start: Option<Tile>,
 }