Fairy chess piece tour puzzles including Numbrix & Hidato

For fans of all other kinds of logic puzzles

Hexagonal Grids

Postby tarek » Wed Jun 17, 2020 1:34 pm

Hexagonal Grids:
I'll be producing Chess Tour puzzles on Hexagonal chess boards with hexagonal spaces arranged in a honeycomb pattern producing a larger hexagon.

The size of the board will be determined by the number of levels of hexagons around the central hexagon space. A board with 3 layers around the central hexagon will have 37 hexagonal spaces or cells. The longest straight line of hexagons would be 7. 4 layers has 61 spaces, 5 layers has 91 spaces and 6 layers has 127 spaces.

In the post above I mentioned how chess movement & terminology that has been used for rectangular chess boards has translated into the hexagonal board

The Wazir tour on such a board will be equivalent to Hidato played on hexagonal board.

The Kirin:
A Mythical creature popular in China, Korea and Japan under different names. This fairy chess piece will leap (jump) 2 spaces orthogonally or 1 space diagonally. You may think of it as a combination leaper combining the movements of the Ferz (1,1) and Dabbaba (0,2). I introduced it because on a hexagonal board it leaps into spaces 2 levels away. Here is a demonstration of the reach of such a chess piece on the hexagonal borad.

Image

With the introduction of chess boards that have pre-defined blocked spaces, I will also introduce another combination leaper which I'll mention next.

The Wazir leaper + Dabbaba hopper:
This fairy chess piece will have the ability to move like a Wazir which is 1 space orthogonally or hop (over an obstacle) similar to the Dabbaba 2 spaces orthogonally.
User avatar
tarek
 
Posts: 3646
Joined: 05 January 2006

Re: Open Kirin Tour Hexagon61

Postby tarek » Wed Jun 17, 2020 2:03 pm

Open Kirin Tour Hexagon61
Rating: 4 (Easy)
Image
User avatar
tarek
 
Posts: 3646
Joined: 05 January 2006

Wazir leap Dabbab hop combo tour puzzles

Postby tarek » Wed Jun 17, 2020 3:20 pm

I previously wrote:Hopper: A chess piece that moves to destination only by jumping over an obstacle (Hopping) to the unoccupied space immediately after it
Without an obstacle, a hopper can't hop … This has the advantage of working nicely with the blocked spaces boards. If the hopper move is based on a leaper or rider movement then I will usually use the same icon for the leaper piece but lying on its side.

The Wazir leaper + Dabbaba Hopper can tour the board using Wazir moves only. The Dabbaba hopper gives the chess piece more options and variety. There could be spaces in some boards that can only be accessed via a hop with this piece.

Open Wazir leaper + Dabbaba Hopper Hexagon61 puzzle:
Rating: 4 (Easy)

Image
User avatar
tarek
 
Posts: 3646
Joined: 05 January 2006

Introducing the Steppers: Mao and Sinbad

Postby tarek » Sun Jun 21, 2020 11:12 am

You need to think about Stepper chess pieces as Pieces that are unable to jump to clear obstacles.

They have a predefined movement path which that for some the movement is not reversible. They are suited for both Rectangular and Hexagonal Grids.

The Mao:
A known piece in some chess variants that translates into the word "Horse". It moves by stepping 1 space orthogonally followed by stepping 1 space diagonally. It therefore appears to have the same range as a Knight chess piece. Look at following on a hexagonal grid:

Image

The jars are blocked spaces. Xs are potential destinations. You can clearly see that if the orthogonal space is blocked then the Mao would not move. The Knight would have no problem jumping over that obstacle. The space 2 spaces away orthogonally is not part of the path so if that space is blocked, it wouldn't influence a successful move.

The movement is not reversible. If you look at the Green circles, The Mao can Move from the central hexagon into any of them, however, the Mao can't move back from them back to the center. This is because the move is blocked from the green circle to the center. This fact can be used in solving puzzles.


The Sinbad:
This one was created based on the suggestion of StrmCkr … So this piece is not found anywhere else :D
It moves in an arc; stepping 1 space diagonally then followed by another 1 space diagonally. The end result give the appearance of 2 orthogonal space movement on a rectangle and 3 spaces on a Hexagon. On a rectangular board this is similar to the Dabbaba movement range. As it doesn't jump, if any space in that arc is blocked then Sinbad has to choose an alternative path. The Sinbad has 2 paths to the potential destination. Both paths have to be blocked for the piece to fail in moving. With the pre-defined moves being symmetrical, The overall move is therefore reversible unlike the Mao.

With the movement of the Sinbad being on the diagonals, it is colourbound and can't tour a regular rectangular of hexagonal grids. The rectangular grid has to be toroidal with an odd number of spaces in length. Look at the following hexagonal grid:

Image

You can see that the Sinbad is a Ship. To complete the theme, I chose the blocked spaces to be occupied by an image of a rocky shore. Because the grids will be toroidal and with the Sinbad being able to get to destination by choosing 1 of two paths, it will be difficult to block the Sinbad's path.
Last edited by tarek on Sun Jun 21, 2020 12:57 pm, edited 1 time in total.
User avatar
tarek
 
Posts: 3646
Joined: 05 January 2006

Open Mao Hexagon37 puzzle:

Postby tarek » Sun Jun 21, 2020 11:58 am

Open Mao Hexagon37 puzzle 001:
Rating: Easy/Medium

Image
Last edited by tarek on Sun Jun 21, 2020 12:55 pm, edited 1 time in total.
User avatar
tarek
 
Posts: 3646
Joined: 05 January 2006

Open Toroidal Sinbad 7x7 puzzle 001

Postby tarek » Sun Jun 21, 2020 12:00 pm

Open Toroidal Sinbad 7x7 puzzle 001
Rating: Easy

Image
User avatar
tarek
 
Posts: 3646
Joined: 05 January 2006

Re: Fairy chess piece tour puzzles including Numbrix & Hidat

Postby StrmCkr » Mon Jun 22, 2020 3:19 am

Fantastic :D

SinBad version 1:
Code: Select all
. . . . . 5 . 27 . . x . . . . . . . x . . . . . . . . . 13 . x . x 1 . . . . 36 . . 34 . . 25 x . 11 .


1 solution
sinbad.PNG
sinbad.PNG (6.79 KiB) Viewed 20 times
Last edited by StrmCkr on Sun Jun 28, 2020 3:30 am, edited 1 time in total.
Some do, some teach, the rest look it up.
User avatar
StrmCkr
 
Posts: 1149
Joined: 05 September 2006

Solutions to puzzles June 17 -21

Postby tarek » Thu Jun 25, 2020 4:57 pm

Image

Image

Image

Image
User avatar
tarek
 
Posts: 3646
Joined: 05 January 2006

Hexagon61 Closed Wazir Tours 001 - 014

Postby tarek » Thu Jun 25, 2020 5:21 pm

On a hexagonal grid, The Wazir moves to an immediately adjacent space sharing an edge with the current one. The Wazir therefore can move into six adjacent spaces. The closed tour means that the chess piece returns to the starting space at the end of tour.
Hidato on a hexagonal board is actually no more than a Wazir tour on that same board.


Hexagon61 Closed Wazir tour Puzzle 01
Rating: Easy
Wazir on Space 1
Image


Hexagon61 Closed Wazir tour Puzzle 02
Rating: Easy
Wazir on Space 1
Image



Hexagon61 Closed Wazir tour Puzzle 03
Rating: Easy
Wazir on Space 1
Image



Hexagon61 Closed Wazir tour Puzzle 04
Rating: Easy
Wazir on Space 1
Image



Hexagon61 Closed Wazir tour Puzzle 05
Rating: Easy
Wazir on Space 1
Image



Hexagon61 Closed Wazir tour Puzzle 06
Rating: Easy
Wazir on Space 1
Image



Hexagon61 Closed Wazir tour Puzzle 07
Rating: Easy
Wazir on Space 1
Image



Hexagon61 Closed Wazir tour Puzzle 08
Rating: Easy
Wazir on Space 1
Image



Hexagon61 Closed Wazir tour Puzzle 09
Rating: Easy
Wazir on Space 1
Image



Hexagon61 Closed Wazir tour Puzzle 010
Rating: Easy
Wazir on Space 1
Image



Hexagon61 Closed Wazir tour Puzzle 11
Rating: Easy
Wazir on Space 1
Image



Hexagon61 Closed Wazir tour Puzzle 12
Rating: Easy
Wazir on Space 1
Image



Hexagon61 Closed Wazir tour Puzzle 13
Rating: Easy
Wazir on Space 1
Image



Hexagon61 Closed Wazir tour Puzzle 14
Rating: Easy
Wazir on Space 1
Image
User avatar
tarek
 
Posts: 3646
Joined: 05 January 2006

Previous

Return to Other logic puzzles