The New Sudoku Players' Forum

[tarek]

The Ferz is an ancient chess piece and the ancestor of the modern Queen chess piece. It moves 1 square diagonally in any direction. It can't tour a regular chess board as it is confined to same coloured squares. It shares the same restriction as the: Bishop (x,x), Alfil (2,2) and Alibaba (0,2) + (2,2). For these pieces there has to be a toroidal board that has an odd number of squares in a line to allow a complete tour. I will present a few puzzles demonstrating these pieces before moving back to regular chess board puzzles.

7x7 Toroidal Closed Ferz tour Puzzle 01
Rating: Easy
Ferz on Square 1




7x7 Toroidal Closed Ferz tour Puzzle 02
Rating: Easy
Ferz on Square 1




7x7 Toroidal Closed Ferz tour Puzzle 03
Rating: Difficult
Ferz on Square 1



[EDIT: Changed images to show clear squares]

[tarek]

Toroidal Closed Alfil tour Puzzles

Alfil (The elephant) is an ancient chess piece and the predecessor of the modern Bishop chess piece. It Leaps (Jumps) 2 squares diagonally. It is restricted to the same colour squares oa regular chess board and therefore will not be able to tour it. A successful tour can be done on a toroidal board with an odd number of squares per line.

7x7 Toroidal Closed Alfil tour Puzzle 01
Rating: Easy
Alfil on Square 1




7x7 Toroidal Closed Alfil tour Puzzle 02
Rating: Easy
Alfil on Square 1




7x7 Toroidal Closed Alfil tour Puzzle 03
Rating: Easy
Alfil on Square 1



[EDIT: Changed images to show clear squares]

[tarek]

Toroidal Closed Alibaba tour Puzzles

Alibaba is a combination fairy chess piece. It Leaps (Jumps) 2 squares diagonally or Leaps (Jumps) 2 squares orthogonally. It is therefore a combination of Alfil and Dabbaba (this would explain the name). It also is restricted to the same colour squares on a regular chess board and therefore can't tour it. It can successfully tour a toroidal board that has an odd number of squares per line.

7x7 Toroidal Closed Alibaba tour Puzzle 01
Rating: Easy
Alibaba on Square 1




7x7 Toroidal Closed Alibaba tour Puzzle 02
Rating: Difficult
Alibaba on Square 1




7x7 Toroidal Closed Alibaba tour Puzzle 03
Rating: Difficult
Alibaba on Square 1



[EDIT: Changed images to show clear squares]

[tarek]

Closed Phoenix tour Puzzles

The Phoenix is a combination fairy chess piece. It Leaps (Jumps) 2 squares diagonally or Leaps (Jumps) 1 squares orthogonally. It is therefore a combination of Wazir and Alfil (this would explain the alternative names Wafil & Waffle). It is not restricted to the same colour squares on a regular chess board and therefore can tour it easily.

Returning to regular chess boards but sticking to the closed tours now! A closed tour with the chess piece on Sq 1 will give start/end which is an idea I'll try to stick to. I may return now to our roots here with the Wazir tour (which Numbrix is a modification of) & the King tour (which Hidato is a modification of).

I also may start introducing the difficulty as a number reflecting how many steps ahead are needed by the machine before starting guessing!!

8x8 Regular Closed Phoenix tour Puzzle 01
Rating: 0
Phoenix on Square 1




8x8 Regular Closed Phoenix tour Puzzle 02
Rating: 1
Phoenix on Square 1




8x8 Regular Closed Phoenix tour Puzzle 03
Rating: 1
Phoenix on Square 1




8x8 Regular Closed Phoenix tour Puzzle 04
Rating: 1
Phoenix on Square 1




8x8 Regular Closed Phoenix tour Puzzle 05
Rating: 3
Phoenix on Square 1




8x8 Regular Closed Phoenix tour Puzzle 06
Rating: 3
Phoenix on Square 1




8x8 Regular Closed Phoenix tour Puzzle 07
Rating: 3
Phoenix on Square 1




8x8 Regular Closed Phoenix tour Puzzle 08
Rating: 3
Phoenix on Square 1




8x8 Regular Closed Phoenix tour Puzzle 09
Rating: 3
Phoenix on Square 1




8x8 Regular Closed Phoenix tour Puzzle 10
Rating: 3
Phoenix on Square 1




8x8 Regular Closed Phoenix tour Puzzle 11
Rating: 3
Phoenix on Square 1




8x8 Regular Closed Phoenix tour Puzzle 12
Rating: 3
Phoenix on Square 1




8x8 Regular Closed Phoenix tour Puzzle 13
Rating: 3
Phoenix on Square 1

[tarek]

These come from frezcogames http://frezcogames.com/documents/ChessTour.pdf. The idea here is to find a solution, suggesting that the puzzle has more the one solution and the author provides a solution to each of the puzzles. These should be fun and should be easier to solve. I'll provide some other solutions but there are many more...

Code: Select all

8x8 Open rook tour with obstacles

..   ..   ..   08   ..   ..   ..   ..
..   ..   ..   24   ..   ..   ..   ..
..   ..   ..   40   ..   ..   ..   ..
..   ..   ..   56   ..   ..   ..   ..
..   ..   ..   64   ..   ..   ..   ..
..   ..   ..   48   ..   ..   ..   ..
..   ..   ..   32   ..   ..   ..   ..
01   ..   ..   16   ..   ..   ..   ..

Code: Select all

Other solutions:

02   03   04   08   09   07   06   05
11   23   25   24   10   18   19   20
12   22   26   40   41   39   27   21
13   29   57   56   55   54   28   14
45   62   63   64   44   53   35   34
47   61   60   48   49   52   51   50
46   31   59   32   43   38   37   33
01   30   58   16   42   17   36   15

02   03   04   08   09   07   06   05
11   23   25   24   10   18   19   20
12   22   26   40   41   39   27   21
13   55   57   56   54   38   37   14
34   51   63   64   53   52   36   35
49   50   62   48   47   46   29   30
33   60   61   32   43   45   44   31
01   59   58   16   42   17   28   15

02   03   04   08   09   07   06   05
11   23   25   24   10   18   19   20
12   22   26   40   41   39   27   21
52   58   57   56   55   54   53   30
51   62   63   64   50   38   37   36
46   61   47   48   49   45   34   35
13   60   14   32   43   44   33   31
01   59   15   16   42   17   28   29

Code: Select all

8x8 Open queen tour with obstacles

08   ..   ..   ..   ..   ..   ..   12
..   24   ..   ..   ..   ..   28   ..
..   ..   40   ..   01   44   ..   ..
..   ..   ..   56   60   ..   ..   ..
..   ..   ..   52   64   ..   ..   ..
..   ..   36   ..   ..   48   ..   ..
..   20   ..   ..   ..   ..   32   ..
04   ..   ..   ..   ..   ..   ..   16

Code: Select all

Other solutions:

08   07   02   10   11   13   14   12
18   24   22   27   29   30   28   15
25   23   40   39   01   44   31   34
09   26   41   56   60   49   45   42
51   53   57   52   64   50   46   43
54   55   36   63   61   48   38   37
05   20   21   35   62   19   32   33
04   06   03   47   59   58   17   16

08   07   02   10   11   13   14   12
18   24   23   22   43   27   28   15
25   19   40   53   01   44   58   29
09   41   54   56   60   59   57   30
39   42   55   52   64   45   31   34
38   37   36   51   63   48   47   35
05   20   50   21   62   46   32   33
04   06   03   49   61   26   17   16

08   07   02   10   11   13   14   12
18   24   23   27   29   30   28   15
25   41   40   51   01   44   31   46
09   54   53   56   60   57   45   47
39   42   55   52   64   61   58   43
37   38   36   26   63   48   59   49
05   20   22   62   21   19   32   50
04   06   03   34   35   33   17   16

[qiuyanzhe]

It is not so straightforward, but it holds for any square grids.
P.S. the chessboard coloring is sometimes misdirecting for manual solving..

[tarek]

It is not so straightforward, but it holds for any square grids.
P.S. the chessboard coloring is sometimes misdirecting for manual solving..

Thanks for the feedback. I can see that if the board is toroidal with an odd number of squares per line. It shouldn't be an issue with a regular board or a toroidal board with even squares per line.

The clear squares are better in those circumstaces and they actually look better on a toroid. I'll keep the chessboard theme with a lighter grey for the rest

[tarek]

Back to the Wazir and King tours. The following are rated 11 so it will be interesting to see how manual solvers handle these, The Wazir tour is similar to Numbrix while the King tour is similar to Hidato. Enjoy:

8x8 Regular Closed Wazir tour Puzzle 14
Rating: 11
Wazir on Square 1




8x8 Regular Closed Wazir tour Puzzle 15
Rating: 11
Wazir on Square 1




8x8 Regular Closed Wazir tour Puzzle 16
Rating: 11
Wazir on Square 1




8x8 Regular Closed Wazir tour Puzzle 17
Rating: 11
Wazir on Square 1




8x8 Regular Closed Wazir tour Puzzle 18
Rating: 11
Wazir on Square 1




8x8 Regular Closed Wazir tour Puzzle 19
Rating: 11
Wazir on Square 1




8x8 Regular Closed Wazir tour Puzzle 20
Rating: 11
Wazir on Square 1




8x8 Regular Closed Wazir tour Puzzle 21
Rating: 11
Wazir on Square 1

[tarek]

I will probably be adding this to the head post to explain some of the symbols / Pieces you may encounter in this thread

[tarek]

And now the King tours. The following are rated 5. The Wazir tour is similar to Numbrix while the King tour is similar to Hidato. Enjoy:

8x8 Regular Closed King Tour Puzzle 45
Rating: 5
King on Square 1




8x8 Regular Closed King Tour Puzzle 46
Rating: 5
King on Square 1




8x8 Regular Closed King Tour Puzzle 47
Rating: 5
King on Square 1




8x8 Regular Closed King Tour Puzzle 48
Rating: 5
King on Square 1




8x8 Regular Closed King Tour Puzzle 49
Rating: 5
King on Square 1




8x8 Regular Closed King Tour Puzzle 50
Rating: 5
King on Square 1




8x8 Regular Closed King Tour Puzzle 51
Rating: 5
King on Square 1




8x8 Regular Closed King Tour Puzzle 52
Rating: 5
King on Square 1




8x8 Regular Closed King Tour Puzzle 53
Rating: 5
King on Square 1




8x8 Regular Closed King Tour Puzzle 54
Rating: 5
King on Square 1

[tarek]

This is modified from http://christian.poisson.free.fr/problemesis/categories.html

Code: Select all

Leaper:
A (fairy) chess piece making a leap (jump) between its start square and its arrival square in an (m,n) vector. One of the coordinate of the vector 'start square - arrival square' must have an absolute value equal to m and the other one an absolute value equal to n

I've also had a play with the some freeware images & fonts since my last Alfil was a nearly a disaster. The Fonts from Nishiki-Teki http://hwm3.gyao.ne.jp/shiroi-niwatori/nishiki-teki.htm which are also based to a degree on Quivira http://www.quivira-font.com/impressum.php were most interesting to me. These include some Fairy chess Pieces and combined leapers

Here you can see the Dabbaba which is a (0,2) leaper (The names translates into War Machine) and some other presentations for the Phoenix (Wa-Fil or Waffle): here having a 1/2 wazir 1/2 Alfil & finally Alibaba: Here having the 1/2 Dabbaba 1/2 Alfil

[tarek]

And finally the open King tours. These are the closest you can get to Hidato. If you know Sq 1 & Sq 64 (the last sq) the it is a Hidato. Remember to look at the links section in the head post if you are interested in dyitto's Open King/Wazir/Knight tours Solver/Generator which should cover these following puzzles with ease as they are rated 5.

8x8 Regular Open King Tour Puzzle 55
Rating: 5
King on Square 1




8x8 Regular Open King Tour Puzzle 56
Rating: 5
King on Square 1




8x8 Regular Open King Tour Puzzle 57
Rating: 5
King on Square 1




8x8 Regular Open King Tour Puzzle 58
Rating: 5
King on Square 1



I will be posting in the next week some Dabbaba tour puzzle (which from testing are quite fun to do) then probably give everybody a well deserved rest

[tarek]

Toroidal Closed Dabbaba tour Puzzles

The "Dabbaba" is a fairy chess piece that can be found in ancient variations of chess. It Leaps (Jumps) 2 squares orthogonaly & therefore can be described as a (0,2) leaper. The name translates from old arabic meaning "War machine". It is restricted to the same colour squares on a regular chess board and therefore can't tour it (same fate as the Bishop, Ferz, Alfil & Alibaba). It can successfully tour a toroidal board that has an odd number of squares per line.

7x7 Toroidal Closed Dabbaba tour Puzzle 01
Rating: 5
Dabbaba on Square 1



7x7 Toroidal Closed Dabbaba tour Puzzle 02
Rating: 5
Dabbaba on Square 1



7x7 Toroidal Closed Dabbaba tour Puzzle 03
Rating: 5
Dabbaba on Square 1



7x7 Toroidal Closed Dabbaba tour Puzzle 04
Rating: 5
Dabbaba on Square 1



7x7 Toroidal Closed Dabbaba tour Puzzle 05
Rating: 5
Dabbaba on Square 1



7x7 Toroidal Closed Dabbaba tour Puzzle 06
Rating: 5
Dabbaba on Square 1



7x7 Toroidal Closed Dabbaba tour Puzzle 07
Rating: 5
Dabbaba on Square 1



7x7 Toroidal Closed Dabbaba tour Puzzle 08
Rating: 5
Dabbaba on Square 1



7x7 Toroidal Closed Dabbaba tour Puzzle 09
Rating: 5
Dabbaba on Square 1



7x7 Toroidal Closed Dabbaba tour Puzzle 10
Rating: 5
Dabbaba on Square 1



7x7 Toroidal Closed Dabbaba tour Puzzle 11
Rating: 5
Dabbaba on Square 1



7x7 Toroidal Closed Dabbaba tour Puzzle 12
Rating: 5
Dabbaba on Square 1

[tarek]

A few more terms which explain the movement of certain chess pieces on square or hexagonal chess boards. These have been mostly taken from https://www.chessvariants.com/

Stepper: A chess piece that moves without jumping to its destination one space at at time in a predefined fixed sequence.
It requires an unoccupied pass-through space between start and finish. the Mao is a known chess piece that moves similar to the knight.
It moves one step orthogonally followed by one step diagonally (in that sequence only)

Hopper: A chess piece that moves to destination only by jumping over an obstacle (Hopping) to the unoccupied space immediately after it.
If there are no obstacles in the possible path then the piece can't make that move.

Radial movement: Is a movement along the natural contours of the chessboard orthogonally or diagonally.
If you draw a line between the midpoint of the space a piece moves from and the midpoint of the space it moves to,
that line will pass through the midpoint of every space it crosses.
If it was an oblique move, the line will not pass through the midpoint of every space it crosses.

Orthogonally adjacent spaces share a side in common, and diagonally neighbouring spaces are connected at a corner and share no sides in common.

Diagonally neighbouring squares share a common corner. Diagonally neighbouring hexagons share no corners in common but are connected
by a line that touches a corner of each space

Colourbound piece: This means its movement is limited to spaces of only one colour on a suitably checkered regular chessboard.
The Ferz, Al-Fil and the Bishop are examples of colour bound chess pieces.

These terms will be added to the head post soon as I add more pieces and start introducing the hexagonal boards.

[tarek]

in this thread: http://forum.enjoysudoku.com/ali-baba-and-the-forty-thieves-t37980.html I introduced tour puzzles with predefined blocked spaces.

Using the AliBaba piece which leaps (0,2) or (2,2) I used it with jars representing the blocks to give the theme of Ali Baba and the forty thieves.

Four puzzles were posted V1 - V4.

There was at the end of thread a solution grid of a tour using a chess piece that leaps like a king or hops like AliBaba I called it King Ali Baba. I will update this post with those puzzles.