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Today's challenge is provided by Jeroen Landheer.

Write a program that lets a knight hop over a chessboard so it touches all squares, but that knight may never use the same spot twice. Starting position should be given by the user (or provided as a random location if you don't feel like accepting user input), and the program must compute and output the solution in a list of coordinates.

Example:

Start at: A1
Solution: A1 – B3 – C5 etc

Last week
Special mention to ProgramFOX for his polyglot solution. Awesome. For the winner it was neck and neck between Jörgen Andersson and Graeme but I'm going to give it to Jörgen in the hope of inspiring Graeme to even higher feats of insanity.
Posted
Updated 22-Feb-23 23:04pm
Graeme_Grant 10-Mar-17 7:35am
So performance & reliability when a word not found was not important? In-memory SQLite was just as fast as my optimized Dictionary solution... Much faster & more reliable than Jörgen's... Hmmm... The table is stacked against me. :/

I must admit that Jörgen gave it a good shot... well done mate.
Chris Maunder 12-Mar-17 23:30pm
If this becomes something where I have to sit down and fully test each solution, time them, verify their correctness, check for plagiarism and provide a point-by point independently verified set of judging criteria then I'm afraid I'll have to leave it to you guys to come up with the challenges and announce a "winner".

It's for fun. The judging is deliberately random and sometimes wildly biased.

How about we just leave this as a challenge and I forgo any attempt at declaring a winner. I want this to be fun, not something where it could potentially upset participants.
Graeme_Grant 13-Mar-17 11:53am
Noted and I will be more mindful in future.
PIEBALDconsult 10-Mar-17 23:40pm
... and the world's your oyster.
Graeme_Grant 11-Mar-17 2:01am

## Solution 1

Here is a solution using an interpretation of Warnsdorff’s Algorithm: Knight's tour - Wikipedia[^]

Update: the code was refactored without sacrificing performance.

### Objective

Flexible core with the following goals:

1. Reuse in other board-orientated puzzles like: Eight queens puzzle - Wikipedia[^], Rook polynomial - Wikipedia[^], and No-three-in-line problem - Wikipedia[^].

2. Plus other "bonus" tasks like:
2a. Determine all solvable tours for a given board size
2b. Determine the smallest board size with a valid solution
2c. Duelling Knights - solvable solutions with one or more knights on the board.
2d. The user can visually navigate forwards and backwards through the tour and see the how the decision making process works, not just the moves being made.
2e. Performance - not sacrifice flexibility over performance

To meet all of the above objectives, I chose to work with the Stack(T) Class (System.Collections.Generic)[^].

### Core Code

The code is self-contained in a PCL (portable class library).

To meet the performance goal, when the `Knight` class is initialized, it will reset the board and pre-calculate moves for every position.

1. `Location` class:
C#
```public class Location // a Knight's move
{
public Location(int cols, int rows, int index)
{
this.cols = cols;
this.rows = rows;
this.index = index;
}

public Location(int cols, int rows, int index, int moveNum)
: this(cols, rows, index)
{
this.moveNum = moveNum;
}

int cols, rows, iRow, col, row, index, moveNum;

public int MoveNum => moveNum;

public int Index => index;

public int Col
{
get
{
if (col == 0) calcCoords();
return col;
}
}

public int Row
{
get
{
if (row == 0) calcCoords();
return row;
}
}

private void calcCoords()
{
col = index % cols;
row = index / cols;
iRow = rows - row;
}

public override string ToString()
{
if (col == 0) calcCoords();
if (col < 26) return \$"{(char)(col % 26 + 'A')}-{iRow}";
if (col < 52) return \$"{new string('A', col / 26) + (char)(col % 26 + 'A')}-{iRow}";
return \$"{"AZ" + (col - 52).ToString()}-{iRow}";
}
}```
2. `Board` class & interface:
C#
```using System.Collections.Generic;

public interface IBoard
{
int Columns { get; }
List<List<int>> Locations { get; }
IEnumerable<int> Missed { get; }
int Rows { get; }
IRule Rules { set; }
bool[] Visited { get; }

Location Init(int? cellId = default(int?));
void ResetVisits();
void UndoVisit(int index);
}

public class Board : IBoard
{
public Board(int columns, int rows)
{
Columns = columns;
Rows = rows;
Size = columns * rows;
}

public int Size { get; }

public int Rows { get; } = 8;

public int Columns { get; } = 8;

public List<List<int>> Locations { get; private set; }
= new List<List<int>>();

public IEnumerable<int> Missed
=> Locations.Where((x, i) => !Visited[i]).Select((x, i) => i);

private static bool[] visited;
public bool[] Visited => visited;

public IRule Rules { private get; set; }

public Location Init(int? locationId = null)
{
totalLocations = Columns * Rows;
BuildMovesTable();
return new Location(Columns, Rows,
locationId.HasValue && locationId.Value > -1
? locationId.Value : r.Next(0, totalLocations), 0);
}

public void ResetVisits()
{
visited = new bool[totalLocations];
}

public void UndoVisit(int index)
{
Visited[index] = false;
}

private int totalLocations;
private Random r = new Random();

private void BuildMovesTable()
{
ResetVisits();
RebuildTable();
}

private void RebuildTable()
{
Locations = Enumerable.Range(0, totalLocations)
.Select(x => Rules.BuildLocation(x))
.ToList();
}
}```
3. `Knight` class & `IRule` interface:
C#
```using System.Collections.Generic;

public interface IRule
{
List<int> BuildLocation(int index);
}

public class Knight : IRule
{
public Knight(IBoard board, int? startLocation = null)
{
Board = board;
board.Rules = this;
Init(startLocation);
}

public void Init(int? startLocation)
{
Board.ResetVisits();
Moves = new Stack<Location>();
Moves.Push(Board.Init(startLocation));
CanMoveNext = true;
}

public IBoard Board { get; }

public Location Start => Moves?.Last();

public Location Current => Moves?.Peek();

public Stack<Location> Moves { get; private set; }

public bool CanMoveNext { get; private set; }

public void ExecuteMoves()
{
while (true) { if (MoveNext() == null) break; }
}

public Location MovePrevious()
{
if (Moves.Count > 0) Board.Visited[Moves.Pop().Index] = false;
CanMoveNext = true;
return Moves.Count > 0 ? Moves.Peek() : null;
}

public Location MoveNext()
{
var index = Moves.Peek().Index;
var c1 = Board.Locations[index];
int ndx = 0, score = int.MaxValue;

for (int i = 0; i < c1.Count; i++)
if (!Board.Visited[c1[i]] && c1[i] != index)
{
var tscore = 0;
var c2 = Board.Locations[c1[i]];
for (int j = 0; j < c2.Count; j++)
if (!Board.Visited[c2[j]] && c2[j] != i) tscore++;

if (tscore < score)
{
ndx = c1[i];
score = tscore;
}
}

Board.Visited[index] = true;

CanMoveNext = score != int.MaxValue;
if (CanMoveNext)
{
var newLoc = new Location(Board.Columns, Board.Rows, ndx, Moves.Count);
Moves.Push(newLoc);
return newLoc;
}
return null;
}

List<int> IRule.BuildLocation(int index)
{
var loc = new List<int>();
int pc = index % Board.Columns, pr = index / Board.Columns;
for (int k = 0; k < rules.GetLength(0); k++)
{
int nc = pc + rules[k, 0], nr = pr + rules[k, 1];
if (nc < Board.Columns && nc > -1 && nr < Board.Rows && nr > -1)
}
return loc;
}

private readonly int[,] rules = new int[,]
{
{ -1, -2 }, {  1, -2 }, {  2, -1 }, {  2,  1 },
{  1,  2 }, { -1,  2 }, { -2,  1 }, { -2, -1 }
};
}```

### Challenge Proof

This project tests the Core Code against a number of different board sizes and dimensions for a). completing the challenge; b). performance.
C#
```using System;
using System.Linq;
using System.Diagnostics;
using System.Collections.Generic;
using KnightsTour.Core;

static class Program
{
static void Main()
{
ResetWindow();
Console.WriteLine("Weekly Challenge: Knight's Tour");
Console.WriteLine("===============================\n");

var styles = new List<IReportStyle>
{
new ChessStyle(),
new IndexedStyle(),
new LocationStyle()
};

foreach (var tour in new List<Tour>
{
new Tour("Standard Chess Board (8 x 8)", () => Activity(8, 8, null)),
new Tour("Smallest Viable Rectangle (4 x 3)", () => Activity(4, 3, 0)),
new Tour("2nd Smallest Viable Rectangle (7 x 3)", () => Activity(7, 3, 0)),
new Tour("Smallest Viable Square (5 x 5)", () => Activity(5, 5, 0)),
new Tour("Large Square Board", () => Activity(20, 20, null)),
new Tour("Very Large Square Board", () => Activity(300, 300, 89700)),
})
// choose a reporting style format...
Report(tour.Activity(), styles[(int)ReportStyle.Chess]);

Console.WriteLine("\n-- press any key to exit --");
Console.CursorVisible = true;
}

private static Tuple<TimeSpan, Knight>
Activity(int cols, int rows, int? startLocation)
{
TimeSpan elapsed;
var sw = new Stopwatch();

var knight = new Knight(new Board(cols, rows), startLocation);

//Prime to ensure correct timings...
knight.ExecuteMoves();
knight.Init(startLocation);

sw.Start();
knight.ExecuteMoves();
elapsed = sw.Elapsed;
sw.Stop();

return new Tuple<TimeSpan, Knight>(elapsed, knight);
}

private static void Report(Tuple<TimeSpan, Knight> result,
IReportStyle styleWriter)
{
var elapsed = result.Item1;
var knight = result.Item2;

Console.WriteLine(\$"Board Size   : {knight.Board.Columns}, {knight.Board.Rows}");
Console.WriteLine(\$"\nStarted at   : {knight.Start}");
Console.WriteLine(\$"Final Loc'n  : {knight.Current}");
Console.WriteLine(\$"Total moves  : {knight.Moves.Count - 1:N0}");
Console.WriteLine(\$"Time taken   : {elapsed.TotalMilliseconds:N6} ms");

if (knight.Moves.Count < 500)
{
Console.WriteLine("\nMoves used   :");
Console.WriteLine(styleWriter.Format
(knight.Moves.OrderBy(x => x.MoveNum)));
}

if (knight.Board.Missed.Any())
{
var missedLocations
= knight.Board.Missed.Select
(x => new Location(knight.Board.Columns, knight.Board.Rows, x));
Console.WriteLine(\$"\nCells skipped : {missedLocations.Count()}");
if (knight.Moves.Count < 500)
Console.WriteLine(styleWriter.Format(missedLocations));
}
else
{
Console.WriteLine("\nCompleted the board!");
}

Console.WriteLine(\$"\n{new string('-', 80)}\n");
}

private static void ResetWindow()
{
Console.Title = "CODE PROJECT | WEEKLY CODE CHALENGE";
Console.CursorVisible = false;
Console.SetWindowSize(80, Console.WindowHeight);
Console.Clear();
}
}

class Tour : Job<Knight>
{
public Tour(string title, Func<Tuple<TimeSpan, Knight>> func)
: base(title, func) { }
}

class Job<T>
{
public Job(string title, Func<Tuple<TimeSpan, T>> func)
{
Title = title;
this.func = func;
}

public string Title { get; }

public Tuple<TimeSpan, T> Activity()
{
Console.WriteLine(Title);
Console.WriteLine(new string('-', Title.Length));
Console.WriteLine();

return func.Invoke();
}
}

enum ReportStyle
{
Chess,
Indexed,
Location
}

interface IReportStyle
{
string Format(IEnumerable<Location> moves);
}

class ChessStyle : IReportStyle
{
public string Format(IEnumerable<Location> moves)
=> string.Join(", ", moves);
}

class IndexedStyle : IReportStyle
{
public string Format(IEnumerable<Location> moves)
{
var m = moves.ToList();
return string.Join("\n",
Enumerable.Range(0, m.Count - 1)
.Select(i => \$"{i,-3}: {m[i].Index + 1}"));
}
}

class LocationStyle : IReportStyle
{
public string Format(IEnumerable<Location> moves)
{
var m = moves.ToList();
return string.Join(", ",
Enumerable.Range(0, m.Count - 1)
.Select(i => \$"{{{m[i].Row}, {m[i].Col}}}")); ;
}
}```
And the output:
```Weekly Challenge: Knight's Tour
===============================

Standard Chess Board (8 x 8)
----------------------------

Board Size   : 8, 8

Started at   : E-2
Final Loc'n  : B-2
Total moves  : 63
Time taken   : 0.049700 ms

Moves used   :
E-2, G-1, H-3, G-5, H-7, F-8, G-6, H-8, F-7, H-6, G-8, E-7, C-8, A-7, C-6, B-8, A-6, B-4, A-2, C-1, B-3, A-1, C-2, E-1, G-2, H-4, F-3, H-2, F-1, D-2, B-1, A-3, B-5, D-4, F-5, G-7, H-5, G-3, H-1, F-2, G-4, E-3, D-1, C-3, E-4, D-6, E-8, F-6, D-5, C-7, A-8, B-6, D-7, E-5, C-4, A-5, B-7, D-8, E-6, F-4, D-3, C-5, A-4, B-2

Completed the board!

--------------------------------------------------------------------------------

Smallest Viable Rectangle (4 x 3)
---------------------------------

Board Size   : 4, 3

Started at   : A-3
Final Loc'n  : D-1
Total moves  : 5
Time taken   : 0.017400 ms

Moves used   :
A-3, C-2, A-1, B-3, D-2, B-1, C-3, A-2, C-1, D-3, B-2, D-1

Completed the board!

--------------------------------------------------------------------------------

2nd Smallest Viable Rectangle (7 x 3)
-------------------------------------

Board Size   : 7, 3

Started at   : A-3
Final Loc'n  : F-2
Total moves  : 20
Time taken   : 0.006800 ms

Moves used   :
A-3, C-2, A-1, B-3, C-1, A-2, C-3, B-1, D-2, F-3, G-1, E-2, G-3, F-1, E-3, G-2, E-1, D-3, B-2, D-1, F-2

Completed the board!

--------------------------------------------------------------------------------

Smallest Viable Square (5 x 5)
------------------------------

Board Size   : 5, 5

Started at   : A-5
Final Loc'n  : B-2
Total moves  : 24
Time taken   : 0.009800 ms

Moves used   :
A-5, C-4, E-5, D-3, E-1, C-2, A-1, B-3, C-5, E-4, D-2, B-1, A-3, B-5, D-4, E-2, C-1, A-2, B-4, D-5, E-3, D-1, C-3, A-4, B-2

Completed the board!

--------------------------------------------------------------------------------

Large Square Board
------------------

Board Size   : 20, 20

Started at   : J-15
Final Loc'n  : C-5
Total moves  : 399
Time taken   : 0.341300 ms

Moves used   :
J-15, I-17, H-19, J-20, L-19, N-20, P-19, R-20, T-19, S-17, T-15, S-13, T-11, S-9, T-7, S-5, T-3, S-1, Q-2, O-1, M-2, K-1, I-2, G-1, E-2, C-1, A-2, B-4, A-6, B-8, A-10, B-12, A-14, B-16, A-18, B-20, D-19, F-20, G-18, H-20, J-19, L-20, N-19, P-20, R-19, T-20, S-18, T-16, S-14, T-12, S-10, T-8, S-6, T-4, S-2, Q-1, R-3, T-2, R-1, S-3, T-1, R-2, P-1, O-3, N-1, P-2, Q-4, R-6, T-5, R-4, P-3, N-2, L-1, K-3, J-1, L-2, M-4, O-5, N-3, M-1, O-2, P-4, Q-6, R-8, T-9, S-7, R-5, T-6, S-4, Q-3, P-5, N-4, L-3, J-2, H-1, G-3, F-1, H-2, I-4, K-5, J-3, I-1, K-2, L-4, M-6, O-7, Q-8, R-10, S-8, T-10, S-12, T-14, R-15, Q-17, S-16, T-18, S-20, R-18, Q-20, S-19, T-17, R-16, Q-18, O-19, M-20, N-18, O-20, Q-19, P-17, Q-15, R-17, P-18, O-16, M-17, O-18, P-16, Q-14, S-15, T-13, R-12, Q-10, S-11, R-13, Q-11, R-9, Q-7, P-9, O-11, P-13, R-14, Q-16, P-14, Q-12, P-10, R-11, Q-13, P-15, O-17, N-15, O-13, P-11, Q-9, R-7, Q-5, P-7, O-9, N-11, P-12, O-14, N-16, M-18, K-17, M-16, O-15, N-17, M-19, K-18, L-16, M-14, N-12, O-10, P-8, O-6, N-8, M-10, L-12, N-13, M-15, L-17, K-19, I-20, J-18, K-20, L-18, K-16, L-14, M-12, N-14, O-12, N-10, O-8, P-6, O-4, N-6, M-8, L-10, N-9, M-11, L-13, K-15, J-17, I-19, G-20, H-18, I-16, J-14, L-15, M-13, K-12, I-13, K-14, J-16, I-18, H-16, I-14, K-13, L-11, M-9, N-7, M-5, L-7, K-9, J-11, H-12, J-13, I-15, H-17, G-19, E-20, F-18, G-16, H-14, I-12, K-11, L-9, M-7, N-5, M-3, L-5, K-7, J-9, L-8, K-10, J-12, I-10, J-8, K-6, J-4, I-6, H-8, J-7, L-6, K-4, J-6, K-8, J-10, I-8, H-10, G-12, I-11, H-13, G-15, F-17, E-19, C-20, A-19, C-18, D-20, B-19, A-17, B-15, A-13, C-14, A-15, B-17, C-19, A-20, B-18, D-17, E-15, G-14, F-16, E-18, D-16, F-15, E-17, F-19, G-17, H-15, G-13, H-11, I-9, G-10, F-12, E-14, C-15, A-16, C-17, E-16, D-18, C-16, D-14, F-13, G-11, H-9, I-7, J-5, I-3, H-5, G-7, F-9, E-11, D-13, F-14, D-15, B-14, A-12, C-13, E-12, F-10, G-8, H-6, G-4, I-5, H-3, F-2, D-1, B-2, A-4, C-3, B-1, A-3, B-5, A-7, B-9, A-11, B-13, C-11, D-9, C-7, A-8, B-10, C-12, E-13, D-11, E-9, F-11, D-10, B-11, D-12, C-10, A-9, C-8, B-6, D-5, E-7, G-6, H-4, G-2, F-4, D-3, E-1, C-2, A-1, B-3, A-5, C-6, D-4, F-5, E-3, C-4, D-2, F-3, E-5, D-7, C-9, E-10, F-8, H-7, G-9, E-8, F-6, E-4, D-6, F-7, G-5, E-6, D-8, B-7, C-5

Completed the board!

--------------------------------------------------------------------------------

Very Large Square Board
-----------------------

Board Size   : 300, 300

Started at   : A-1
Final Loc'n  : L-21
Total moves  : 89,999
Time taken   : 124.877700 ms

Completed the board!

--------------------------------------------------------------------------------

-- press any key to exit --```

### Bonus Task 1 - Number of Possible Tours

Given a board size, find all the possible solvable paths available.
C#
```using KnightsTour.Core;
using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;

class Program
{
static List<Tuple<TimeSpan, Knight>> Tours = new List<Tuple<TimeSpan, Knight>>();

static void Main()
{
ResetWindow();
Console.WriteLine("Weekly Challenge: Knight's Tour");
Console.WriteLine("===============================\n");

Console.WriteLine("Bonus Challenge: Find All Solutions for a given Board Size\n");

var styles = new List<IReportStyle>
{
new ChessStyle(),
new IndexedStyle(),
new LocationStyle()
};

TripPlanner(3, 7);
ReportResults(styles[(int)ReportStyle.Chess]);

Console.WriteLine("\n-- press any key to exit --");
Console.CursorVisible = true;
}

private static void TripPlanner(int rows, int cols)
{
int size = rows * cols;

// try each location for a valid solution
for (int start = 0; start < size; start++)
TryTour(rows, cols, start);

}

private static void TryTour(int rows, int cols, int startLocation)
{
TimeSpan elapsed;
var sw = new Stopwatch();

var knight = new Knight(new Board(cols, rows), startLocation);

//Prime to ensure correct timings...
knight.ExecuteMoves();
knight.Init(startLocation);

sw.Start();
knight.ExecuteMoves();
elapsed = sw.Elapsed;
sw.Stop();

var success = !knight.Board.Missed.Any();

if (success)
}

private static void ReportResults(IReportStyle styleWriter)
{
var board = Tours[0].Item2.Board;
Console.WriteLine(\$"Board Size   : {board.Columns}, {board.Rows}");
Console.WriteLine(\$"Task Outcome : {(Tours.Any() ? "Completed!"
: "Failed!")}");
Console.WriteLine(\$"Total Tours  : {Tours.Count} possible");

foreach (var tour in Tours)
{
var elapsed = tour.Item1;
var knight = tour.Item2;
Console.WriteLine(\$"\nStarted at   : {knight.Start}");
Console.WriteLine(\$"Final Loc'n  : {knight.Current}");
Console.WriteLine(\$"Time taken   : {elapsed.TotalMilliseconds:N6} ms");
if (knight.Moves.Count < 500)
{
Console.WriteLine("Moves used   :\n");
Console.WriteLine(styleWriter.Format
(knight.Moves.OrderBy(x => x.MoveNum)));
}
}
}

private static void ResetWindow()
{
Console.Title = "CODE PROJECT | WEEKLY CODE CHALENGE";
Console.CursorVisible = false;
Console.SetWindowSize(80, Console.WindowHeight);
Console.Clear();
}
}```

And the output:
```Weekly Challenge: Knight's Tour
===============================

Bonus Challenge: Find All Solutions for a given Board Size

Board Size   : 7, 3
Total Tours  : 5 possible

Started at   : A-3
Final Loc'n  : F-2
Time taken   : 0.006800 ms
Moves used   :

A-3, C-2, A-1, B-3, C-1, A-2, C-3, B-1, D-2, F-3, G-1, E-2, G-3, F-1, E-3, G-2, E-1, D-3, B-2, D-1, F-2

Started at   : E-3
Final Loc'n  : F-2
Time taken   : 0.033800 ms
Moves used   :

E-3, G-2, E-1, F-3, G-1, E-2, G-3, F-1, D-2, B-1, A-3, C-2, A-1, B-3, C-1, A-2, C-3, D-1, B-2, D-3, F-2

Started at   : F-2
Final Loc'n  : C-3
Time taken   : 0.013300 ms
Moves used   :

F-2, D-1, B-2, D-3, E-1, G-2, E-3, F-1, G-3, E-2, G-1, F-3, D-2, B-1, A-3, C-2, A-1, B-3, C-1, A-2, C-3

Started at   : C-1
Final Loc'n  : F-2
Time taken   : 0.00600 ms
Moves used   :

C-1, A-2, C-3, B-1, A-3, C-2, A-1, B-3, D-2, F-3, G-1, E-2, G-3, F-1, E-3, G-2, E-1, D-3, B-2, D-1, F-2

Started at   : E-1
Final Loc'n  : F-2
Time taken   : 0.007200 ms
Moves used   :

E-1, G-2, E-3, F-1, G-3, E-2, G-1, F-3, D-2, B-1, A-3, C-2, A-1, B-3, C-1, A-2, C-3, D-1, B-2, D-3, F-2

-- press any key to exit --```

### Bonus Task 2 - Smallest Square and Rectangular Board Sizes

This task uses the concept from Bonus 1 and looks from a standard-size chess board grid of 8 x 8 and looks for smaller Square and rectangular board sizes that are solvable. The code to perform this task is quite compact.
C#
```using KnightsTour.Core;
using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;

class Program
{
static List<Tuple<TimeSpan, Knight>> Tours = new List<Tuple<TimeSpan, Knight>>();

static void Main()
{
ResetWindow();
Console.WriteLine("Weekly Challenge: Knight's Tour");
Console.WriteLine("===============================\n");

Console.WriteLine("Bonus Challenge: Find the smallest Solvable Board Sizes\n");

Console.WriteLine("Starting at the size of a Chess board size (8 x 8 = 64), determine (up to 10)\ndimensions of the smallest solvable solution for both square and rectangular\nboards.\n");

// down to 4 x 4 = 20 which is invalid & test each location as a start point

for (int size = 64 - 1; size >= 9; size--)
TryTour(size);

// smallest grid to largest
var orderedTours = Tours.OrderBy(x => x.Item2.Moves.Count);

// group square boards by dimensions
var bestBox = orderedTours
.Where(x => x.Item2.Board.Columns.Equals(x.Item2.Board.Rows))
.GroupBy(x => \$"{x.Item2.Board.Columns} x {x.Item2.Board.Rows}")
.Take(10);

// group rectangular boards by dimensions
var bestRects = orderedTours
.Where(x => !x.Item2.Board.Columns.Equals(x.Item2.Board.Rows))
.GroupBy(x => \$"{x.Item2.Board.Columns} x {x.Item2.Board.Rows}")
.Take(10);

// false = sized grid summary only,
// true  = every solution by grid size
var detailedReporting = false;

Console.WriteLine("Smallest Boxes");
ReportSolutions(bestBox, detailedReporting);

Console.WriteLine("\nSmallest Rectangles");
ReportSolutions(bestRects, detailedReporting);

Console.WriteLine("\n-- press any key to exit --");
Console.CursorVisible = true;
}

private static void TryTour(int size)
{
// break the size into boxes
var factors = getFactors(size).ToArray();

if (factors.Length == 1)
// square
TryTour(new int[,] { { factors[0], factors[0] } }, size);
else
//rectangle
for (int factor = 0; factor < factors.Length / 2; factor++)
{
var index = factor * 2;
TryTour(new int[,] { { factors[index], factors[index + 1] } }, size);
}
}

private static void TryTour(int[,] gridSize, int size)
{
// try each location for a valid solution
for (int start = 0; start < size; start++)
{
// try the normal grid
TryTour(gridSize[0, 0], gridSize[0, 1], start);

//try the inverted grid if failed
if (!gridSize[0, 0].Equals(gridSize[0, 1]))
TryTour(gridSize[0, 1], gridSize[0, 0], start);
}
}

private static bool TryTour(int rows, int cols, int startLocation)
{
TimeSpan elapsed;
var sw = new Stopwatch();

var knight = new Knight(new Board(cols, rows), startLocation);

//Prime to ensure correct timings...
knight.ExecuteMoves();
knight.Init(startLocation);

sw.Start();
knight.ExecuteMoves();
elapsed = sw.Elapsed;
sw.Stop();

var success = !knight.Board.Missed.Any();

if (success)

return success;
}

public static IEnumerable<int> getFactors(int x)
{
for (int i = 2; i * i <= x; i++)
if (0 == (x % i))
{
yield return i;
if (i != (x / i)) yield return x / i;
}
}

private static void ReportSolutions
(IEnumerable<IGrouping<string, Tuple<TimeSpan, Knight>>> bestBox,
bool isDetailed = false)
{
foreach (var item in bestBox)
{
var loc = \$"{{{item.First().Item2.Board.Rows},{ item.First().Item2.Board.Columns}}}";
var count = item.Count();
var moves = item.First().Item2.Moves.Count - 1;
Console.WriteLine(\$"{loc} has {count} solutions in {moves} moves");

if (isDetailed)
foreach (var result in item)
{
var start = result.Item2.Moves.First();
var end = result.Item2.Moves.Last();
var ms = result.Item1.TotalMilliseconds;
Console.WriteLine(\$" - From: {start} To: {end} in {ms:N6} ms");
}
}
}

private static void ResetWindow()
{
Console.Title = "CODE PROJECT | WEEKLY CODE CHALENGE";
Console.CursorVisible = false;
Console.SetWindowSize(80, Console.WindowHeight);
Console.Clear();
}
}```
And the output:
```Weekly Challenge: Knight's Tour
===============================

Bonus Challenge: Find the smallest Solvable Board Sizes

Starting at the size of a Chess board size (8 x 8 = 64), determine (up to 10)
dimensions of the smallest solvable solution for both square and rectangular
boards.

Smallest Boxes
{5,5} has 5 solutions in 24 moves
{7,7} has 19 solutions in 48 moves

Smallest Rectangles
{3,4} has 6 solutions in 11 moves
{4,3} has 5 solutions in 11 moves
{4,5} has 5 solutions in 19 moves
{5,4} has 10 solutions in 19 moves
{3,7} has 5 solutions in 20 moves
{7,3} has 5 solutions in 20 moves
{3,8} has 11 solutions in 23 moves
{8,3} has 10 solutions in 23 moves
{4,6} has 10 solutions in 23 moves
{6,4} has 4 solutions in 23 moves

-- press any key to exit --```

### Bonus Task 3 - Duelling Knights

With this task, I am using a 8 x 8 board with 4 Knights, and a 20 x 20 board with 8 Knights, each with Knights independently doing their tours attempting to complete the tasks.
C#
```using System;
using System.Linq;
using System.Diagnostics;
using System.Collections.Generic;
using KnightsTour.Core;

static class Program
{
static void Main()
{
ResetWindow();
Console.WriteLine("Weekly Challenge: Knight's Tour");
Console.WriteLine("===============================\n");

Console.WriteLine("Bonus Challenge: Dueling Knights\n");

var styles = new List<IReportStyle>
{
new ChessStyle(),
new IndexedStyle(),
new LocationStyle()
};

foreach (var tour in new List<Tour>
{
new Tour("Standard Chess Board (8 x 8)",
() => Test(8, 8, new List<int?>
{ null, null, null, null })),

new Tour("Large Board (20 x 20)",
() => Test(20, 20, new List<int?>
{ 0, 19, 126, 133, 266, 273, 380, 399 }))
})
// choose a reporting style format...
ReportResults(tour.Activity(), styles[(int)ReportStyle.Chess]);

Console.WriteLine("\n-- press any key to exit --");
Console.CursorVisible = true;
}

private static Tuple<TimeSpan, List<Knight>>
Test(int cols, int rows, List<int?> startLocations)
{
TimeSpan elapsed;
var sw = new Stopwatch();

bool canMove;
var board = new Board(cols, rows);
var knights = new List<Knight>();

foreach (var loc in startLocations)
{
var knight = new Knight(new Board(cols, rows), loc);

//Prime to ensure correct timings...
knight.ExecuteMoves();
knight.Init(loc);

}

int tl = knights.Count;

sw.Start();
do
{
canMove = false;
for (int i = 0; i < tl; i++)
{
knights[i].MoveNext();
if (knights[i].CanMoveNext) canMove = true;
}
if (!canMove)
{
elapsed = sw.Elapsed;
break;
}
} while (true);
sw.Stop();

return new Tuple<TimeSpan, List<Knight>>(elapsed, knights);
}

private static void ReportResults(Tuple<TimeSpan, List<Knight>> result,
IReportStyle styleWriter)
{
var elapsed = result.Item1;
var knights = result.Item2;
var board = knights[0].Board;

Console.WriteLine(\$"Board Size   : {board.Columns}, {board.Rows}");
Console.WriteLine(\$"Time taken   : {elapsed.TotalMilliseconds:N6} ms");
? "Failed!" : "Completed!")}");

for (int i = 0; i < knights.Count; i++)
{
var knight = knights[i];
Console.WriteLine(\$"\nStarted at   : {knight.Start}");
Console.WriteLine(\$"Final Loc'n  : {knight.Current}");
Console.WriteLine(\$"Total moves  : {knight.Moves.Count - 1:N0}");

if (knight.Moves.Count < 500)
{
Console.WriteLine("Moves used   :\n");
Console.WriteLine(styleWriter.Format
(knight.Moves.OrderBy(x => x.MoveNum)));
}
}

Console.WriteLine(\$"\n{new string('-', 80)}\n");
}

private static void ResetWindow()
{
Console.Title = "CODE PROJECT | WEEKLY CODE CHALENGE";
Console.CursorVisible = false;
Console.SetWindowSize(80, Console.WindowHeight);
Console.Clear();
}
}```
And the output:
```Weekly Challenge: Knight's Tour
===============================

Bonus Challenge: Duelling Knights

Standard Chess Board (8 x 8)
----------------------------

Board Size   : 8, 8
Time taken   : 0.085500 ms

Started at   : F-6
Final Loc'n  : D-3
Total moves  : 23
Moves used   :

F-6, G-8, H-6, G-4, F-2, H-3, G-1, E-2, C-3, B-1, A-3, B-5, A-7, C-8, D-6, F-5, D-4, E-6, C-5, B-3, A-1, C-2, E-1, D-3

Started at   : C-1
Final Loc'n  : D-3
Total moves  : 23
Moves used   :

C-1, A-2, B-4, A-6, B-8, D-7, F-8, H-7, G-5, E-4, D-2, C-4, E-3, G-2, H-4, F-5, D-4, E-6, C-5, B-3, A-1, C-2, E-1, D-3

Started at   : D-1
Final Loc'n  : F-3
Total moves  : 22
Moves used   :

D-1, B-2, A-4, B-6, A-8, C-7, E-8, G-7, H-5, F-4, D-5, E-7, C-8, D-6, F-5, D-4, E-6, D-8, F-7, H-8, G-6, E-5, F-3

Started at   : H-2
Final Loc'n  : D-3
Total moves  : 23
Moves used   :

H-2, F-1, G-3, H-1, F-2, H-3, G-1, E-2, C-3, B-1, A-3, B-5, A-7, C-6, A-5, B-7, D-8, F-7, H-8, G-6, E-5, F-3, E-1, D-3

--------------------------------------------------------------------------------

Large Board (20 x 20)
---------------------

Board Size   : 20, 20
Time taken   : 0.958200 ms

Started at   : L-18
Final Loc'n  : D-7
Total moves  : 131
Moves used   :

L-18, K-20, M-19, O-20, Q-19, S-20, T-18, R-19, P-20, Q-18, R-16, S-14, T-12, S-10, T-8, S-6, T-4, S-2, R-4, Q-6, R-8, Q-10, R-12, Q-14, O-15, Q-16, R-14, P-13, O-11, Q-12, R-10, P-9, Q-7, R-5, P-4, R-3, T-2, R-1, P-2, N-1, O-3, P-1, R-2, Q-4, P-6, O-8, N-10, M-12, L-14, K-16, J-18, I-16, J-14, K-12, L-10, N-9, O-7, N-5, M-3, O-2, Q-1, P-3, N-4, L-3, M-1, K-2, I-1, J-3, L-4, M-6, K-5, J-7, K-9, J-11, I-13, H-15, I-17, H-19, G-17, E-16, G-15, I-14, J-12, H-13, F-12, H-11, I-9, K-10, L-8, J-9, I-11, G-10, H-8, I-10, G-11, E-12, C-11, E-10, G-9, E-8, F-10, H-9, J-8, K-6, J-4, H-5, I-3, K-4, J-2, H-1, G-3, F-5, E-7, D-9, C-7, B-5, D-6, F-7, D-8, C-6, D-4, F-3, G-5, H-7, I-5, H-3, F-2, E-4, F-6, G-4, E-5, D-7

Started at   : T-20
Final Loc'n  : D-7
Total moves  : 131
Moves used   :

T-20, S-18, R-20, T-19, S-17, T-15, S-13, T-11, S-9, T-7, S-5, T-3, S-1, Q-2, O-1, M-2, K-1, I-2, G-1, E-2, C-1, A-2, B-4, A-6, B-8, A-10, C-9, A-8, B-10, A-12, B-14, C-16, E-15, F-17, D-18, E-20, G-19, I-20, K-19, L-17, M-15, N-13, M-11, L-13, K-15, M-14, L-16, N-15, M-13, N-11, P-10, Q-8, R-6, S-4, Q-3, P-5, O-7, N-5, M-3, O-2, Q-1, P-3, N-4, L-3, M-1, K-2, I-1, J-3, L-4, M-6, K-5, J-7, K-9, J-11, I-13, H-15, I-17, H-19, G-17, E-16, G-15, I-14, J-12, H-13, F-12, H-11, I-9, K-10, L-8, J-9, I-11, G-10, H-8, I-10, G-11, E-12, C-11, E-10, G-9, E-8, F-10, H-9, J-8, K-6, J-4, H-5, I-3, K-4, J-2, H-1, G-3, F-5, E-7, D-9, C-7, B-5, D-6, F-7, D-8, C-6, D-4, F-3, G-5, H-7, I-5, H-3, F-2, E-4, F-6, G-4, E-5, D-7

Started at   : G-14
Final Loc'n  : D-3
Total moves  : 130
Moves used   :

G-14, F-16, E-18, D-20, B-19, A-17, C-18, B-20, A-18, C-19, A-20, B-18, C-20, A-19, B-17, A-15, C-14, D-16, E-14, C-15, D-17, E-19, G-20, I-19, K-18, J-20, L-19, M-17, O-16, Q-17, R-15, P-14, O-12, Q-13, P-15, O-17, M-18, N-16, O-14, P-12, R-11, Q-9, O-10, N-12, P-11, O-13, N-15, M-13, N-11, P-10, Q-8, R-6, S-4, Q-3, P-5, O-7, N-5, M-7, O-6, Q-5, O-4, N-2, L-1, K-3, J-1, L-2, M-4, N-6, M-8, L-6, K-8, J-6, L-5, K-7, I-8, H-10, G-12, F-14, G-16, E-17, D-15, C-13, D-11, E-13, F-15, G-13, F-11, H-12, F-13, D-12, C-10, A-11, B-13, D-14, C-12, D-10, B-9, A-7, C-8, E-9, G-8, I-7, K-6, J-4, I-6, H-4, J-5, H-6, I-4, H-2, F-1, D-2, B-1, A-3, C-2, E-1, G-2, E-3, D-1, C-3, D-5, B-6, C-4, B-2, A-4, C-5, E-6, F-8, G-6, F-4, D-3

Started at   : N-14
Final Loc'n  : D-7
Total moves  : 131
Moves used   :

N-14, M-16, N-18, M-20, O-19, Q-20, S-19, T-17, S-15, R-17, T-16, S-14, T-12, S-10, T-8, S-6, T-4, S-2, R-4, Q-6, R-8, Q-10, R-12, Q-14, O-15, Q-16, R-14, P-13, O-11, Q-12, R-10, P-9, Q-7, R-5, P-4, R-3, T-2, R-1, P-2, N-1, O-3, P-1, R-2, Q-4, P-6, O-8, N-10, M-12, L-14, K-16, J-18, I-16, J-14, K-12, L-10, N-9, M-7, O-6, Q-5, O-4, N-2, P-3, N-4, L-3, M-1, K-2, I-1, J-3, L-4, M-6, K-5, J-7, K-9, J-11, I-13, H-15, I-17, H-19, G-17, E-16, G-15, I-14, J-12, H-13, F-12, H-11, I-9, K-10, L-8, J-9, I-11, G-10, H-8, I-10, G-11, E-12, C-11, E-10, G-9, E-8, F-10, H-9, J-8, I-6, H-4, J-5, I-3, K-4, J-2, H-1, G-3, F-5, E-7, D-9, C-7, B-5, D-6, F-7, D-8, C-6, D-4, F-3, G-5, H-7, I-5, H-3, F-2, E-4, F-6, G-4, E-5, D-7

Started at   : G-7
Final Loc'n  : D-7
Total moves  : 131
Moves used   :

G-7, F-9, E-11, D-13, B-12, A-14, B-16, A-18, C-19, A-20, B-18, C-20, A-19, B-17, A-15, C-14, D-16, E-14, C-15, D-17, E-19, G-20, I-19, K-18, J-20, L-19, M-17, O-16, Q-17, R-15, P-14, O-12, Q-13, P-15, O-17, M-18, N-16, O-14, P-12, R-11, Q-9, O-10, N-12, P-11, O-13, M-14, L-16, J-17, H-18, F-19, H-20, I-18, J-16, H-17, I-15, K-14, L-12, J-13, K-11, M-10, O-9, P-7, O-5, N-3, M-1, K-2, I-1, J-3, L-4, M-6, K-5, J-7, K-9, J-11, I-13, H-15, I-17, H-19, G-17, E-16, G-15, I-14, J-12, H-13, F-12, H-11, I-9, K-10, L-8, J-9, I-11, G-10, H-8, I-10, G-11, E-12, C-11, E-10, G-9, E-8, F-10, H-9, J-8, I-6, H-4, J-5, I-3, K-4, J-2, H-1, G-3, F-5, E-7, D-9, C-7, B-5, D-6, F-7, D-8, C-6, D-4, F-3, G-5, H-7, I-5, H-3, F-2, E-4, F-6, G-4, E-5, D-7

Started at   : N-7
Final Loc'n  : D-3
Total moves  : 130
Moves used   :

N-7, M-9, L-11, K-13, L-15, K-17, J-19, L-20, N-19, P-18, N-17, P-16, O-18, N-20, P-19, R-18, P-17, Q-15, S-16, T-14, R-13, Q-11, S-12, T-10, R-9, P-8, R-7, T-6, S-8, R-10, P-9, Q-7, R-5, P-4, R-3, T-2, R-1, P-2, N-1, O-3, P-1, R-2, Q-4, P-6, O-8, N-10, M-12, L-14, K-16, J-18, I-16, J-14, K-12, L-10, N-9, O-7, N-5, M-3, O-2, Q-1, P-3, N-4, L-3, M-1, K-2, I-1, J-3, L-4, M-6, K-5, J-7, K-9, J-11, I-13, H-15, I-17, H-19, G-17, E-16, G-15, I-14, J-12, H-13, F-12, H-11, G-13, F-11, H-12, F-13, D-12, C-10, A-11, B-13, D-14, C-12, D-10, B-9, A-7, C-8, E-9, G-8, I-7, K-6, J-4, H-5, I-3, K-4, J-2, H-1, G-3, F-1, D-2, B-1, A-3, C-2, E-1, G-2, E-3, D-1, C-3, D-5, B-6, C-4, B-2, A-4, C-5, E-6, F-8, G-6, F-4, D-3

Started at   : A-1
Final Loc'n  : D-7
Total moves  : 131
Moves used   :

A-1, B-3, A-5, B-7, A-9, B-11, A-13, B-15, C-17, A-16, B-18, C-20, A-19, B-17, A-15, C-14, D-16, E-14, C-15, D-17, E-19, G-20, I-19, K-18, J-20, L-19, M-17, O-16, Q-17, R-15, P-14, O-12, Q-13, P-15, O-17, M-18, N-16, O-14, P-12, R-11, Q-9, O-10, N-12, P-11, O-13, M-14, L-16, J-17, H-18, F-19, H-20, I-18, J-16, H-17, I-15, K-14, L-12, J-13, K-11, M-10, O-9, P-7, O-5, N-3, M-5, L-7, N-8, L-9, J-10, I-12, H-14, J-15, H-16, G-18, F-20, D-19, F-18, G-16, E-17, D-15, C-13, D-11, E-13, F-15, G-13, F-11, H-12, F-13, D-12, C-10, A-11, B-13, D-14, C-12, D-10, E-12, C-11, E-10, G-9, E-8, F-10, H-9, J-8, I-6, H-4, J-5, H-6, I-4, H-2, F-1, D-2, B-1, A-3, C-2, E-1, G-2, E-3, D-1, C-3, D-5, B-6, C-4, B-2, A-4, C-5, E-6, F-8, G-6, F-4, D-3, E-5, D-7

Started at   : T-1
Final Loc'n  : D-7
Total moves  : 130
Moves used   :

T-1, S-3, T-5, S-7, T-9, S-11, T-13, S-15, R-17, T-16, S-14, T-12, S-10, T-8, S-6, T-4, S-2, R-4, Q-6, R-8, Q-10, R-12, Q-14, O-15, Q-16, R-14, P-13, O-11, Q-12, R-10, P-9, Q-7, R-5, P-4, R-3, T-2, R-1, P-2, N-1, O-3, P-1, R-2, Q-4, P-6, O-8, N-10, M-12, L-14, K-16, J-18, I-16, J-14, K-12, L-10, N-9, O-7, N-5, M-3, O-2, Q-1, P-3, N-4, L-3, M-1, K-2, I-1, J-3, L-4, M-6, K-5, J-7, K-9, J-11, I-13, H-15, I-17, H-19, G-17, E-16, G-15, I-14, J-12, H-13, F-12, H-11, I-9, K-10, L-8, J-9, I-11, G-10, H-8, I-10, G-11, E-12, C-11, E-10, G-9, E-8, F-10, H-9, J-8, K-6, J-4, H-5, I-3, K-4, J-2, H-1, G-3, F-5, E-7, D-9, C-7, B-5, D-6, F-7, D-8, C-6, D-4, F-3, G-5, H-7, I-5, H-3, F-2, E-4, F-6, G-4, E-5, D-7

--------------------------------------------------------------------------------

-- press any key to exit --```

NOTE: The first tour is an 8 x 8 chess board with 4 knights randomly placed. It is possible that not all 4-Knight-Tours will complete based on where they start. However, it is possible this puzzle to be solved. Experiment and have fun with it.

This task is quite a simple one as the title indicates - move forwards and backwards and watch the board get solved. This does quite a bit more than just that. Rather than trying to describe it in words, a picture tells it much better... Screenshot[^]

There are a few hundred lines of code in this project, so rather than post it all here, I have provided a downloadable link below so you can try it out and see visually exactly how the algorithm works, not just the moves that the Knight makes on its tour of the board. ;)

Here an extract of the core navigation code that allows the user to move forwards & backwards. Navigation is only a single line per direction and a check if we are at the end of the tour or not.
C#
```private static void TourGuide(int cols, int rows)
{
InitWorkArea(cols, rows);
knight = new Knight(new Board(cols, rows));
UpdateLocation(knight.Moves.Peek());

bool Active = true;

while (Active)
{
{
case ConsoleKey.P:

isPreview = !isPreview; // show/hide
break;

case ConsoleKey.PageUp:
case ConsoleKey.LeftArrow:
case ConsoleKey.UpArrow:    // back

if (knight.Moves.Count > 1)
{
ClearLocation(knight.Moves.Peek());
UpdateLocation(knight.MovePrevious());
}
break;

case ConsoleKey.Spacebar:
case ConsoleKey.RightArrow:
case ConsoleKey.PageDown:
case ConsoleKey.DownArrow:  // forward

if (knight.CanMoveNext)
UpdateLocation(knight.MoveNext());
break;

case ConsoleKey.Escape: // exit

Active = false;
break;
}
}
}```
Output:
```Weekly Challenge: Knight's Tour
===============================

Bonus Challenge: Visually let a user move through the moves of a tour

Hot Keys:
Forward:  Down arrow / PgDn / Right arrow / SpaceBar
Backward: Up arrow / PgUp / Left arrow
Preview:  P - toggles preview decisions before move
Exit:     ESC to quit

-- press any key to begin --```

And a Screenshot[^] of the visual output.

The Download includes the Core PCL + all the sample apps for each of the Tours above. Bonus: I have included the original prototype for this challenge. ;)

A detailed article coming soon (time permitting)...

Enjoy!

v16
Maciej Los 13-Mar-17 17:41pm
Well, what to say to version 13? WOW!
5ed!
Graeme_Grant 13-Mar-17 19:35pm
Thanks! Chris did ask for "even higher feats of insanity"... :)

## Solution 3

That was fun! My code and answer were growing really big, here's an article instead:
Knight's tour on a square chess board: coding challenge[^]
As a bonus, it can also draw a picture or animated GIF of the knight path :)

v2
Maciej Los 12-Mar-17 15:44pm
Great!
Thomas Daniels 12-Mar-17 16:28pm
Thank you!

## Solution 2

Here's my solution based on shortest path algorithm:

C#
```using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace KnightChess
{
class KnightMove
{
public bool ChessToIndex(string sMove, ref int Row, ref int Col)
{
if ((sMove[0] >= 'A' && sMove[0] <= 'H') &&
(sMove[1] >= '1' && sMove[1] <= '8'))
{
Col = System.Convert.ToInt32(sMove[0]) - 0x41;
Row = System.Convert.ToInt32(sMove[1].ToString()) - 1;

return true;
}

return false;
}

public bool IndexToChess(ref string sMove, int Row, int Col)
{
sMove += Convert.ToChar(Col + 0x41);
sMove += Convert.ToString(Row + 1);

return true;
}
public KnightMove(int Row, int Col)
{
this.Row = Row; this.Col = Col;
}
public KnightMove(string sMove)
{
int Row = -1, Col = -1;
if (this.ChessToIndex(sMove, ref Row, ref Col) != false)
this.Row = Row; this.Col = Col;
}

public int Row
{
get { return m_Row; }
set { m_Row = value; }
}
public int Col
{
get { return m_Col; }
set { m_Col = value; }
}

private int m_Row = -1;
private int m_Col = -1;
}

class Corner
{
public Corner(KnightMove mv1, KnightMove mv2)
{
this.Move1 = mv1; this.m_Move2 = mv2;
}

public KnightMove Move1
{
get { return m_Move1; }
set { m_Move1 = value; }
}
public KnightMove Move2
{
get { return m_Move2; }
set { m_Move2 = value; }
}

private KnightMove m_Move1;
private KnightMove m_Move2;
}

class KnightMoves : ICloneable
{
public KnightMoves() { }
public KnightMoves(List<KnightMove> Path, int Length)
{
this.Path = Path; this.Length = Length;
}

public List<KnightMove> Path
{
get { return m_Path; }
set { m_Path = value; }
}

public int Length
{
get { return m_Length; }
set { m_Length = value; }
}

private int m_Length = -1;
private List<KnightMove> m_Path = null;

public object Clone()
{
KnightMoves Target_Moves = new KnightMoves();
Target_Moves.m_Length = Length;
Target_Moves.Path = new List<KnightMove>();
foreach (KnightMove km in this.Path)
return Target_Moves;
}
}

class KnightPaths : IEnumerable<KnightMoves>
{
private List<KnightMoves> m_PathList = null;
public KnightPaths()
{
if (m_PathList == null)
m_PathList = new List<KnightMoves>();
}

public KnightPaths(KnightPaths Knight_Path)
{
m_PathList = new List<KnightMoves>();
foreach (KnightMoves km in Knight_Path)
}

{
}
public KnightMoves this[int iIndex]
{
get { return m_PathList[iIndex]; }
set { m_PathList[iIndex] = value; }
}
public int Count() { return m_PathList.Count(); }
public void Clear() { m_PathList.Clear(); }

public IEnumerator GetEnumerator()
{
return m_PathList.GetEnumerator();
}
IEnumerator<KnightMoves> IEnumerable<KnightMoves>.GetEnumerator()
{
return (IEnumerator<KnightMoves>)this.GetEnumerator();
}
}
class Program
{
static bool IsValidMove(int value1, int value2, int PathID)
{
if ((value1 > value2) && (PathID == 0 || PathID == 1) ||
(value1 < value2) && (PathID == 2 || PathID == 3)) return true;

return false;
}
static bool IsValidPath(int Row1, int Col1, int Row2, int Col2, int PathID)
{
if (((((Row1 == 0 && Col1 == 5) &&
(Row2 == 1 && Col2 == 7)) ||
((Row1 == 0 && Col1 == 6) &&
(Row2 == 2 && Col2 == 7))) && (PathID == 0)) ||

((((Row1 == 5 && Col1 == 7) &&
(Row2 == 7 && Col2 == 6)) ||
((Row1 == 6 && Col1 == 7) &&
(Row2 == 7 && Col2 == 5))) && (PathID == 1)) ||

((((Row1 == 7 && Col1 == 2) &&
(Row2 == 6 && Col2 == 0)) ||
((Row1 == 7 && Col1 == 1) &&
(Row2 == 5 && Col2 == 0))) && (PathID == 2)) ||

((((Row1 == 2 && Col1 == 0) &&
(Row2 == 0 && Col2 == 1)) ||
((Row1 == 1 && Col1 == 0) &&
(Row2 == 0 && Col2 == 2))) && (PathID == 3))) return true;

return false;
}
static void Main(string[] args)
{
string _StartMove = "";
Console.Write("Start At: ");

Console.WriteLine();

KnightPaths Knight_Paths = new KnightPaths();
KnightMoves Knight_Moves = new KnightMoves();

Knight_Moves.Path = new List<KnightMove>();

Knight_Moves.Length = 1;

KnightPaths Knight_Paths2 = new KnightPaths();

List<Corner> Corners = new List<Corner>();
Corners.Add(new Corner(new KnightMove(0, 5), new KnightMove(1, 7)));
Corners.Add(new Corner(new KnightMove(0, 6), new KnightMove(2, 7)));

Corners.Add(new Corner(new KnightMove(5, 7), new KnightMove(7, 6)));
Corners.Add(new Corner(new KnightMove(6, 7), new KnightMove(7, 5)));

Corners.Add(new Corner(new KnightMove(7, 2), new KnightMove(6, 0)));
Corners.Add(new Corner(new KnightMove(7, 1), new KnightMove(5, 0)));

Corners.Add(new Corner(new KnightMove(2, 0), new KnightMove(0, 1)));
Corners.Add(new Corner(new KnightMove(1, 0), new KnightMove(0, 2)));

var watch = new System.Diagnostics.Stopwatch();
watch.Start();

for (int PathID = 0; PathID < 4; PathID++)
{
for (int Route = 0; Route < Knight_Paths.Count(); Route++)
{
KnightMoves CurrPath = Knight_Paths[Route];

if (Knight_Paths[Route].Path.Count() > 1)
{
if (IsValidPath(CurrPath.Path[Knight_Paths[Route].Path.Count() - 2].Row,
CurrPath.Path[Knight_Paths[Route].Path.Count() - 2].Col,
CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row,
CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col, PathID))
{
}
}

if (((CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row + 1) < 8) &&
((CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col + 2) < 8))
{
bool Exists = false;
for (int Index = 0; Index < CurrPath.Path.Count() && !Exists; Index++)
if (CurrPath.Path[Index].Row == CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row + 1 &&
CurrPath.Path[Index].Col == CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col + 2)
Exists = true;

int value1 = 0, value2 = 0;
if (PathID == 0 || PathID == 2)
{
value1 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col + 2;
value2 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col;
}

if (PathID == 1 || PathID == 3)
{
value1 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row + 1;
value2 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row;
}

if (Exists == false && IsValidMove(value1, value2, PathID))
{
KnightMoves NewPath = (KnightMoves)CurrPath.Clone();
NewPath.Length = Knight_Paths[Route].Length + 1;
NewPath.Path.Add(new KnightMove(CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row + 1,
CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col + 2));

}
}

if (((CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row - 1) >= 0) &&
((CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col + 2) < 8))
{
bool Exists = false;
for (int Index = 0; Index < CurrPath.Path.Count() && !Exists; Index++)
if (CurrPath.Path[Index].Row == CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row - 1 &&
CurrPath.Path[Index].Col == CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col + 2)
Exists = true;

int value1 = 0, value2 = 0;
if (PathID == 0 || PathID == 2)
{
value1 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col + 2;
value2 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col;
}

if (PathID == 1 || PathID == 3)
{
value1 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row - 1;
value2 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row;
}

if (Exists == false && IsValidMove(value1, value2, PathID))
{
KnightMoves NewPath = (KnightMoves)CurrPath.Clone();
NewPath.Length = Knight_Paths[Route].Length + 1;
NewPath.Path.Add(new KnightMove(CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row - 1,
CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col + 2));

}
}

if (((CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row + 1) < 8) &&
((CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col - 2) >= 0))
{
bool Exists = false;
for (int Index = 0; Index < CurrPath.Path.Count() && !Exists; Index++)
if (CurrPath.Path[Index].Row == CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row + 1 &&
CurrPath.Path[Index].Col == CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col - 2)
Exists = true;

int value1 = 0, value2 = 0;
if (PathID == 0 || PathID == 2)
{
value1 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col - 2;
value2 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col;
}

if (PathID == 1 || PathID == 3)
{
value1 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row + 1;
value2 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row;
}

if (Exists == false && IsValidMove(value1, value2, PathID))
{
KnightMoves NewPath = (KnightMoves)CurrPath.Clone();
NewPath.Length = Knight_Paths[Route].Length + 1;
NewPath.Path.Add(new KnightMove(CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row + 1,
CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col - 2));

}
}

if (((CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row - 1) >= 0) &&
((CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col - 2) >= 0))
{
bool Exists = false;
for (int Index = 0; Index < CurrPath.Path.Count() && !Exists; Index++)
if (CurrPath.Path[Index].Row == CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row - 1 &&
CurrPath.Path[Index].Col == CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col - 2)
Exists = true;

int value1 = 0, value2 = 0;

if (PathID == 0 || PathID == 2)
{
value1 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col - 2;
value2 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col;
}

if (PathID == 1 || PathID == 3)
{
value1 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row - 1;
value2 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row;
}

if (Exists == false && IsValidMove(value1, value2, PathID))
{
KnightMoves NewPath = (KnightMoves)CurrPath.Clone();
NewPath.Length = Knight_Paths[Route].Length + 1;
NewPath.Path.Add(new KnightMove(CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row - 1,
CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col - 2));

}
}

if (((CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row - 2) >= 0) &&
((CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col + 1) < 8))
{
bool Exists = false;
for (int Index = 0; Index < CurrPath.Path.Count() && !Exists; Index++)
if (CurrPath.Path[Index].Row == CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row - 2 &&
CurrPath.Path[Index].Col == CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col + 1)
Exists = true;

int value1 = 0, value2 = 0;

if (PathID == 0 || PathID == 2)
{
value1 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col + 1;
value2 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col;
}

if (PathID == 1 || PathID == 3)
{
value1 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row - 2;
value2 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row;
}

if (Exists == false && IsValidMove(value1, value2, PathID))
{
KnightMoves NewPath = (KnightMoves)CurrPath.Clone();
NewPath.Length = Knight_Paths[Route].Length + 1;
NewPath.Path.Add(new KnightMove(CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row - 2,
CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col + 1));

}
}

if (((CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row - 2) >= 0) &&
((CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col - 1) >= 0))
{
bool Exists = false;
for (int Index = 0; Index < CurrPath.Path.Count() && !Exists; Index++)
if (CurrPath.Path[Index].Row == CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row - 2 &&
CurrPath.Path[Index].Col == CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col - 1)
Exists = true;

int value1 = 0, value2 = 0;

if (PathID == 0 || PathID == 2)
{
value1 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col - 2;
value2 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col;
}

if (PathID == 1 || PathID == 3)
{
value1 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row - 2;
value2 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row;
}

if (Exists == false && IsValidMove(value1, value2, PathID))
{
KnightMoves NewPath = (KnightMoves)CurrPath.Clone();
NewPath.Length = Knight_Paths[Route].Length + 1;
NewPath.Path.Add(new KnightMove(CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row - 2,
CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col - 1));

}
}

if (((CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row + 2) < 8) &&
((CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col - 1) >= 0))
{
bool Exists = false;
for (int Index = 0; Index < CurrPath.Path.Count() && !Exists; Index++)
if (CurrPath.Path[Index].Row == CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row + 2 &&
CurrPath.Path[Index].Col == CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col - 1)
Exists = true;

int value1 = 0, value2 = 0;

if (PathID == 0 || PathID == 2)
{
value1 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col - 1;
value2 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col;
}

if (PathID == 1 || PathID == 3)
{
value1 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row + 2;
value2 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row;
}

if (Exists == false && IsValidMove(value1, value2, PathID))
{
KnightMoves NewPath = (KnightMoves)CurrPath.Clone();
NewPath.Length = Knight_Paths[Route].Length + 1;
NewPath.Path.Add(new KnightMove(CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row + 2,
CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col - 1));

}
}

if (((CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row + 2) < 8) &&
((CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col + 1) < 8))
{
bool Exists = false;
for (int Index = 0; Index < CurrPath.Path.Count() && !Exists; Index++)
if (CurrPath.Path[Index].Row == CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row + 2 &&
CurrPath.Path[Index].Col == CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col + 1)
Exists = true;

int value1 = 0, value2 = 0;

if (PathID == 0 || PathID == 2)
{
value1 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col + 1;
value2 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col;
}

if (PathID == 1 || PathID == 3)
{
value1 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row + 2;
value2 = CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row;
}

if (Exists == false && IsValidMove(value1, value2, PathID))
{
KnightMoves NewPath = (KnightMoves)CurrPath.Clone();
NewPath.Length = Knight_Paths[Route].Length + 1;
NewPath.Path.Add(new KnightMove(CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Row + 2,
CurrPath.Path[Knight_Paths[Route].Path.Count() - 1].Col + 1));

}
}
}

if (Knight_Paths2.Count() > 0)
{
Knight_Paths = new KnightPaths(Knight_Paths2);
Knight_Paths2.Clear();
}
}

var elapsed = watch.Elapsed;
watch.Stop();

int nCount = 0;
for (int Index = 0; Index < Knight_Paths.Count(); Index++)
{
int Count = 0;
KnightMoves CurrPath = Knight_Paths[Index];
for (int Move = 0; Move < CurrPath.Path.Count() - 1; Move++)
{
for (int nIndex = 0; nIndex < Corners.Count(); nIndex++)
Count = (Corners[nIndex].Move1.Row == CurrPath.Path[Move].Row &&
Corners[nIndex].Move1.Col == CurrPath.Path[Move].Col &&
Corners[nIndex].Move2.Row == CurrPath.Path[Move + 1].Row &&
Corners[nIndex].Move2.Col == CurrPath.Path[Move + 1].Col) ? Count + 1 : Count;
}

if (Count == 4)
{
Console.Write("{0}. ", nCount);

for (int Move = 0; Move < CurrPath.Path.Count(); Move++)
{
string sMove = "";
CurrPath.Path[Move].IndexToChess(ref sMove,
CurrPath.Path[Move].Row, CurrPath.Path[Move].Col);

Console.Write("({0};{1})", sMove[0], sMove[1]);
}

Console.WriteLine(" Moves = {0}", CurrPath.Path.Count());

nCount++;
}
}

Console.WriteLine("Total = {0}", nCount);
Console.WriteLine("Execution Time: {0:N6} msecs", elapsed.TotalMilliseconds);

}
}
}```

Output: (the following code provides the variety of different paths across a chess board touching all board's squares)
```Start At: A1

0. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(H;6)(G;8)(E;7)(C;8)(A;7)(B;5)(A;3)(B;1) Moves = 14
1. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(H;6)(G;8)(E;7)(C;8)(A;7)(B;5)(A;3)(B;1) Moves = 14
2. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 15
3. (A;1)(C;2)(D;4)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 15
4. (A;1)(C;2)(D;4)(E;2)(G;1)(H;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 15
5. (A;1)(B;3)(D;4)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 15
6. (A;1)(B;3)(D;4)(E;2)(G;1)(H;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 15
7. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 15
8. (A;1)(B;3)(C;5)(D;3)(E;1)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
9. (A;1)(B;3)(C;5)(D;3)(E;5)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
10. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 15
11. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 15
12. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 15
13. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 15
14. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(E;7)(C;8)(A;7)(B;5)(A;3)(B;1) Moves = 16
15. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(E;7)(C;8)(A;7)(B;5)(A;3)(B;1) Moves = 16
16. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(E;7)(C;8)(A;7)(B;5)(A;3)(B;1) Moves = 16
17. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(E;7)(C;8)(A;7)(B;5)(A;3)(B;1) Moves = 16
18. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
19. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
20. (A;1)(C;2)(D;4)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
21. (A;1)(C;2)(D;4)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
22. (A;1)(C;2)(D;4)(E;2)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
23. (A;1)(C;2)(D;4)(E;2)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
24. (A;1)(B;3)(D;4)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
25. (A;1)(B;3)(D;4)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
26. (A;1)(B;3)(D;4)(E;2)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
27. (A;1)(B;3)(D;4)(E;2)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
28. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
29. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
30. (A;1)(B;3)(C;5)(D;3)(E;1)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
31. (A;1)(B;3)(C;5)(D;3)(E;1)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
32. (A;1)(B;3)(C;5)(D;3)(E;5)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
33. (A;1)(B;3)(C;5)(D;3)(E;5)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
34. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(H;6)(G;8)(E;7)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 15
35. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 15
36. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(H;6)(G;8)(E;7)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 15
37. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 15
38. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(E;7)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
39. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
40. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(E;7)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
41. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
42. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(E;7)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
43. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
44. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(E;7)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
45. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(D;7)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
46. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(B;5)(A;3)(B;1) Moves = 16
47. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(B;5)(A;3)(B;1) Moves = 16
48. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(B;5)(A;3)(B;1) Moves = 16
49. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(B;5)(A;3)(B;1) Moves = 16
50. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
51. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
52. (A;1)(C;2)(D;4)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
53. (A;1)(C;2)(D;4)(E;2)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
54. (A;1)(B;3)(D;4)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
55. (A;1)(B;3)(D;4)(E;2)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
56. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
57. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
58. (A;1)(B;3)(C;5)(D;3)(E;1)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
59. (A;1)(B;3)(C;5)(D;3)(E;1)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
60. (A;1)(B;3)(C;5)(D;3)(E;5)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
61. (A;1)(B;3)(C;5)(D;3)(E;5)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
62. (A;1)(B;3)(C;5)(D;7)(E;5)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
63. (A;1)(B;3)(C;5)(D;7)(E;5)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
64. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(G;5)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
65. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
66. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(F;6)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
67. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
68. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(G;5)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
69. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
70. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(F;6)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
71. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 17
72. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(B;5)(A;3)(B;1) Moves = 18
73. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(B;5)(A;3)(B;1) Moves = 18
74. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(B;5)(A;3)(B;1) Moves = 18
75. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(B;5)(A;3)(B;1) Moves = 18
76. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(B;5)(A;3)(B;1) Moves = 18
77. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(B;5)(A;3)(B;1) Moves = 18
78. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(B;5)(A;3)(B;1) Moves = 18
79. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(B;5)(A;3)(B;1) Moves = 18
80. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
81. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
82. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
83. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
84. (A;1)(C;2)(D;4)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
85. (A;1)(C;2)(D;4)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
86. (A;1)(C;2)(D;4)(E;2)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
87. (A;1)(C;2)(D;4)(E;2)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
88. (A;1)(B;3)(D;4)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
89. (A;1)(B;3)(D;4)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
90. (A;1)(B;3)(D;4)(E;2)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
91. (A;1)(B;3)(D;4)(E;2)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
92. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
93. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
94. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
95. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 19
96. (A;1)(B;3)(C;5)(D;3)(E;1)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 21
97. (A;1)(B;3)(C;5)(D;3)(E;1)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 21
98. (A;1)(B;3)(C;5)(D;3)(E;1)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 21
99. (A;1)(B;3)(C;5)(D;3)(E;1)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 21
100. (A;1)(B;3)(C;5)(D;3)(E;5)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 21
101. (A;1)(B;3)(C;5)(D;3)(E;5)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 21
102. (A;1)(B;3)(C;5)(D;3)(E;5)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 21
103. (A;1)(B;3)(C;5)(D;3)(E;5)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 21
104. (A;1)(B;3)(C;5)(D;7)(E;5)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 21
105. (A;1)(B;3)(C;5)(D;7)(E;5)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 21
106. (A;1)(B;3)(C;5)(D;7)(E;5)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 21
107. (A;1)(B;3)(C;5)(D;7)(E;5)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(B;4)(A;2)(C;1) Moves = 21
108. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(H;6)(G;8)(E;7)(C;8)(A;7)(C;6)(B;4)(A;2)(C;1) Moves = 15
109. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(H;6)(G;8)(E;7)(C;8)(A;7)(B;5)(C;3)(A;2)(C;1) Moves = 15
110. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(H;6)(G;8)(E;7)(C;8)(A;7)(C;6)(B;4)(A;2)(C;1) Moves = 15
111. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(H;6)(G;8)(E;7)(C;8)(A;7)(B;5)(C;3)(A;2)(C;1) Moves = 15
112. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(E;7)(C;8)(A;7)(C;6)(B;4)(A;2)(C;1) Moves = 17
113. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(E;7)(C;8)(A;7)(B;5)(C;3)(A;2)(C;1) Moves = 17
114. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(E;7)(C;8)(A;7)(C;6)(B;4)(A;2)(C;1) Moves = 17
115. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(E;7)(C;8)(A;7)(B;5)(C;3)(A;2)(C;1) Moves = 17
116. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(E;7)(C;8)(A;7)(C;6)(B;4)(A;2)(C;1) Moves = 17
117. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(E;7)(C;8)(A;7)(B;5)(C;3)(A;2)(C;1) Moves = 17
118. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(E;7)(C;8)(A;7)(C;6)(B;4)(A;2)(C;1) Moves = 17
119. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(E;7)(C;8)(A;7)(B;5)(C;3)(A;2)(C;1) Moves = 17
120. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(C;6)(B;4)(A;2)(C;1) Moves = 17
121. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(B;5)(C;3)(A;2)(C;1) Moves = 17
122. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(C;6)(B;4)(A;2)(C;1) Moves = 17
123. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(B;5)(C;3)(A;2)(C;1) Moves = 17
124. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(C;6)(B;4)(A;2)(C;1) Moves = 17
125. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(B;5)(C;3)(A;2)(C;1) Moves = 17
126. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(C;6)(B;4)(A;2)(C;1) Moves = 17
127. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(B;5)(C;3)(A;2)(C;1) Moves = 17
128. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(C;6)(B;4)(A;2)(C;1) Moves = 19
129. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(B;5)(C;3)(A;2)(C;1) Moves = 19
130. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(C;6)(B;4)(A;2)(C;1) Moves = 19
131. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(B;5)(C;3)(A;2)(C;1) Moves = 19
132. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(C;6)(B;4)(A;2)(C;1) Moves = 19
133. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(B;5)(C;3)(A;2)(C;1) Moves = 19
134. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(C;6)(B;4)(A;2)(C;1) Moves = 19
135. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(B;5)(C;3)(A;2)(C;1) Moves = 19
136. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(C;6)(B;4)(A;2)(C;1) Moves = 19
137. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(B;5)(C;3)(A;2)(C;1) Moves = 19
138. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(C;6)(B;4)(A;2)(C;1) Moves = 19
139. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(B;5)(C;3)(A;2)(C;1) Moves = 19
140. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(C;6)(B;4)(A;2)(C;1) Moves = 19
141. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(B;5)(C;3)(A;2)(C;1) Moves = 19
142. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(C;6)(B;4)(A;2)(C;1) Moves = 19
143. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(B;5)(C;3)(A;2)(C;1) Moves = 19
144. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(H;6)(G;8)(E;7)(C;8)(A;7)(C;6)(E;5)(C;4)(A;3)(B;1) Moves = 16
145. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(H;6)(G;8)(E;7)(C;8)(A;7)(C;6)(A;5)(C;4)(A;3)(B;1) Moves = 16
146. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(H;6)(G;8)(E;7)(C;8)(A;7)(C;6)(E;5)(C;4)(A;3)(B;1) Moves = 16
147. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(H;6)(G;8)(E;7)(C;8)(A;7)(C;6)(A;5)(C;4)(A;3)(B;1) Moves = 16
148. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 17
149. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 17
150. (A;1)(C;2)(D;4)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 17
151. (A;1)(C;2)(D;4)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 17
152. (A;1)(C;2)(D;4)(E;2)(G;1)(H;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 17
153. (A;1)(C;2)(D;4)(E;2)(G;1)(H;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 17
154. (A;1)(B;3)(D;4)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 17
155. (A;1)(B;3)(D;4)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 17
156. (A;1)(B;3)(D;4)(E;2)(G;1)(H;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 17
157. (A;1)(B;3)(D;4)(E;2)(G;1)(H;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 17
158. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 17
159. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 17
160. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 17
161. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 17
162. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 17
163. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 17
164. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 17
165. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(G;5)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 17
166. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 17
167. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 17
168. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(E;7)(C;8)(A;7)(C;6)(E;5)(C;4)(A;3)(B;1) Moves = 18
169. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(E;7)(C;8)(A;7)(C;6)(A;5)(C;4)(A;3)(B;1) Moves = 18
170. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(E;7)(C;8)(A;7)(C;6)(E;5)(C;4)(A;3)(B;1) Moves = 18
171. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(E;7)(C;8)(A;7)(C;6)(A;5)(C;4)(A;3)(B;1) Moves = 18
172. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(E;7)(C;8)(A;7)(C;6)(E;5)(C;4)(A;3)(B;1) Moves = 18
173. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(E;7)(C;8)(A;7)(C;6)(A;5)(C;4)(A;3)(B;1) Moves = 18
174. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(E;7)(C;8)(A;7)(C;6)(E;5)(C;4)(A;3)(B;1) Moves = 18
175. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(E;7)(C;8)(A;7)(C;6)(A;5)(C;4)(A;3)(B;1) Moves = 18
176. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
177. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
178. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
179. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
180. (A;1)(C;2)(D;4)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
181. (A;1)(C;2)(D;4)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
182. (A;1)(C;2)(D;4)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
183. (A;1)(C;2)(D;4)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
184. (A;1)(C;2)(D;4)(E;2)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
185. (A;1)(C;2)(D;4)(E;2)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
186. (A;1)(C;2)(D;4)(E;2)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
187. (A;1)(C;2)(D;4)(E;2)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
188. (A;1)(B;3)(D;4)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
189. (A;1)(B;3)(D;4)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
190. (A;1)(B;3)(D;4)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
191. (A;1)(B;3)(D;4)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
192. (A;1)(B;3)(D;4)(E;2)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
193. (A;1)(B;3)(D;4)(E;2)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
194. (A;1)(B;3)(D;4)(E;2)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
195. (A;1)(B;3)(D;4)(E;2)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
196. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
197. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
198. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
199. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
200. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(H;6)(G;8)(E;7)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 17
201. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(H;6)(G;8)(E;7)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 17
202. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 17
203. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 17
204. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(H;6)(G;8)(E;7)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 17
205. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(H;6)(G;8)(E;7)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 17
206. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 17
207. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 17
208. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(E;7)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
209. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(E;7)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
210. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
211. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
212. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(E;7)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
213. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(E;7)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
214. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
215. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
216. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(E;7)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
217. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(E;7)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
218. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
219. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
220. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(E;7)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
221. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(E;7)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
222. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(D;7)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
223. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(D;7)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
224. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(C;6)(E;5)(C;4)(A;3)(B;1) Moves = 18
225. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(C;6)(A;5)(C;4)(A;3)(B;1) Moves = 18
226. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(C;6)(E;5)(C;4)(A;3)(B;1) Moves = 18
227. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(C;6)(A;5)(C;4)(A;3)(B;1) Moves = 18
228. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(C;6)(E;5)(C;4)(A;3)(B;1) Moves = 18
229. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(C;6)(A;5)(C;4)(A;3)(B;1) Moves = 18
230. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(C;6)(E;5)(C;4)(A;3)(B;1) Moves = 18
231. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(C;6)(A;5)(C;4)(A;3)(B;1) Moves = 18
232. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
233. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
234. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
235. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
236. (A;1)(C;2)(D;4)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
237. (A;1)(C;2)(D;4)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
238. (A;1)(C;2)(D;4)(E;2)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
239. (A;1)(C;2)(D;4)(E;2)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
240. (A;1)(B;3)(D;4)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
241. (A;1)(B;3)(D;4)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
242. (A;1)(B;3)(D;4)(E;2)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
243. (A;1)(B;3)(D;4)(E;2)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
244. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
245. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
246. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
247. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
248. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(G;5)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
249. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(G;5)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
250. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
251. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
252. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(F;6)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
253. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(F;6)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
254. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
255. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
256. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(G;5)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
257. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(G;5)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
258. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
259. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(G;5)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
260. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(F;6)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
261. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(F;6)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
262. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 19
263. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 19
264. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(C;6)(E;5)(C;4)(A;3)(B;1) Moves = 20
265. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(C;6)(A;5)(C;4)(A;3)(B;1) Moves = 20
266. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(C;6)(E;5)(C;4)(A;3)(B;1) Moves = 20
267. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(C;6)(A;5)(C;4)(A;3)(B;1) Moves = 20
268. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(C;6)(E;5)(C;4)(A;3)(B;1) Moves = 20
269. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(C;6)(A;5)(C;4)(A;3)(B;1) Moves = 20
270. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(C;6)(E;5)(C;4)(A;3)(B;1) Moves = 20
271. (A;1)(C;2)(E;3)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(C;6)(A;5)(C;4)(A;3)(B;1) Moves = 20
272. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(C;6)(E;5)(C;4)(A;3)(B;1) Moves = 20
273. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(C;6)(A;5)(C;4)(A;3)(B;1) Moves = 20
274. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(C;6)(E;5)(C;4)(A;3)(B;1) Moves = 20
275. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(H;4)(F;5)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(C;6)(A;5)(C;4)(A;3)(B;1) Moves = 20
276. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(C;6)(E;5)(C;4)(A;3)(B;1) Moves = 20
277. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(E;4)(D;6)(C;8)(A;7)(C;6)(A;5)(C;4)(A;3)(B;1) Moves = 20
278. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(C;6)(E;5)(C;4)(A;3)(B;1) Moves = 20
279. (A;1)(B;3)(D;2)(F;1)(H;2)(F;3)(D;4)(F;5)(H;6)(G;8)(F;6)(E;8)(D;6)(C;8)(A;7)(C;6)(A;5)(C;4)(A;3)(B;1) Moves = 20
280. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 21
281. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 21
282. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 21
283. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 21
284. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 21
285. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 21
286. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 21
287. (A;1)(C;2)(E;1)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 21
288. (A;1)(C;2)(D;4)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 21
289. (A;1)(C;2)(D;4)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 21
290. (A;1)(C;2)(D;4)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 21
291. (A;1)(C;2)(D;4)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 21
292. (A;1)(C;2)(D;4)(E;2)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 21
293. (A;1)(C;2)(D;4)(E;2)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 21
294. (A;1)(C;2)(D;4)(E;2)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 21
295. (A;1)(C;2)(D;4)(E;2)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 21
296. (A;1)(B;3)(D;4)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 21
297. (A;1)(B;3)(D;4)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 21
298. (A;1)(B;3)(D;4)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 21
299. (A;1)(B;3)(D;4)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 21
300. (A;1)(B;3)(D;4)(E;2)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 21
301. (A;1)(B;3)(D;4)(E;2)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 21
302. (A;1)(B;3)(D;4)(E;2)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 21
303. (A;1)(B;3)(D;4)(E;2)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 21
304. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 21
305. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 21
306. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 21
307. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(F;4)(H;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 21
308. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 21
309. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;4)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 21
310. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(E;4)(C;3)(A;2)(C;1) Moves = 21
311. (A;1)(B;3)(D;2)(F;3)(G;1)(H;3)(F;4)(D;5)(F;6)(H;7)(F;8)(E;6)(D;8)(C;6)(B;8)(A;6)(C;5)(A;4)(C;3)(A;2)(C;1) Moves = 21
Total = 312
Execution Time: 99,043500 msecs```

v2
Thomas Daniels 11-Mar-17 7:55am
"Moves = 14" is impossible for an 8x8 board if you want to visit all squares. Am I missing something?
Arthur V. Ratz 11-Mar-17 8:04am
ProgramFox, all these two paths:

0. (A;1)(C;2)(E;3)(F;1)(H;2)(G;4)(H;6)(G;8)(E;7)(C;8)(A;7)(B;5)(A;3)(B;1) Moves = 14
1. (A;1)(B;3)(D;2)(F;1)(H;2)(G;4)(H;6)(G;8)(E;7)(C;8)(A;7)(B;5)(A;3)(B;1) Moves = 14

*ARE* *VALID*. The first and second paths really touch all squares:

(F;1), (H;2) - 1st corner
(H;6), (G;8) - 2nd corner
(C;8), (A;7) - 3rd corner
(A;3), (B;1) - 4th corner

That's all. If you've got any more comments or questions, just post your message.
Thomas Daniels 11-Mar-17 8:19am
I don't understand it. Touching all squares on a 3x3 board means that you have 63 moves, right? Just 'moving over a square with the knight' does not count as 'touching', if that's what you did here.
Arthur V. Ratz 11-Mar-17 8:43am
if it's not, what does it mean "to touch a square" unless otherwise ??
Thomas Daniels 11-Mar-17 8:54am
Touching a square means that the square is used as the begin-point and end-point of a new knight hop. See the GIFs on this Wikipedia page to see what I mean: https://en.wikipedia.org/wiki/Knight's_tour

## Solution 5

Well, ummm, my solution is not complete. The problem isn't really interesting to me, but I have a brute-force exhaustive backtracking implementation that, in theory, can find all tours. Given a 6x6 board, it found what it says are all the tours from square (0,0) in about an hour. But, given a chess board (8x8), it has been running for two days and has not reported any results yet.

All I'm really prepared to say at this time is that I use a Graph (Network) of Nodes, not a two-dimensional representation of the board. No recursion either.

I'm not interested in finding a tour or any tour, I'm looking for a closed tour and I'm too lazy to transcribe one from the Net; I want to find one myself.

A Closed Knight's Tour from any square is a Closed Knight's Tour from every square.

Anyway, my plan for a solution to the Challenge is:
Given (well, not given, as stated above) a Closed Knight's Tour of a Chess Board...
Hard code that tour and simply use it every time.
Whatever square is specified as the starting place, start there on the hard-coded tour, and tour.
Done
(I'll try to keep you updated on that.)

Having said that, and having a Graph traversing implementation, I am now considering generalizing my code to address more general questions of traversing Graphs. In fact, there is a puzzle from the mid-80s that I completely failed to solve, which comes to mind occasionally (like a white whale), and I think I might be able to apply this technique to it.

Update: After running for a full week -- using 100% of one virtual CPU -- my code found no tours at all. Time to kill it and find the problem...

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