## Fairy chess piece tour puzzles including Numbrix & Hidato

For fans of all other kinds of logic puzzles

### Hexagonal Grids

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.

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.

tarek

Posts: 3762
Joined: 05 January 2006

### Re: Open Kirin Tour Hexagon61

Open Kirin Tour Hexagon61
Rating: 4 (Easy)

tarek

Posts: 3762
Joined: 05 January 2006

### Wazir leap Dabbab hop combo tour puzzles

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)

tarek

Posts: 3762
Joined: 05 January 2006

### Introducing the Steppers: Mao and Sinbad

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:

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.

This one was created based on the suggestion of StrmCkr … So this piece is not found anywhere else
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:

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.

tarek

Posts: 3762
Joined: 05 January 2006

### Open Mao Hexagon37 puzzle:

Open Mao Hexagon37 puzzle 001:
Rating: Easy/Medium

Last edited by tarek on Sun Jun 21, 2020 12:55 pm, edited 1 time in total.

tarek

Posts: 3762
Joined: 05 January 2006

### Open Toroidal Sinbad 7x7 puzzle 001

Open Toroidal Sinbad 7x7 puzzle 001
Rating: Easy

tarek

Posts: 3762
Joined: 05 January 2006

### Re: Fairy chess piece tour puzzles including Numbrix & Hidat

Fantastic

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

1 solution
sinbad.PNG (6.79 KiB) Viewed 4773 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.
stormdoku

StrmCkr

Posts: 1428
Joined: 05 September 2006

### Solutions to puzzles June 17 -21

tarek

Posts: 3762
Joined: 05 January 2006

### Hexagon61 Closed Wazir Tours 001 - 014

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

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

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

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

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

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

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

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

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

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

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

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

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

Hexagon61 Closed Wazir tour Puzzle 14
Rating: Easy
Wazir on Space 1

tarek

Posts: 3762
Joined: 05 January 2006

### Solutions to Hexagon61 Closed Wazir Tours 001 - 014

tarek

Posts: 3762
Joined: 05 January 2006

### Re: Fairy chess piece tour puzzles including Numbrix & Hidat

Some do, some teach, the rest look it up.
stormdoku

StrmCkr

Posts: 1428
Joined: 05 September 2006

### Re: Fairy chess piece tour puzzles including Numbrix & Hidat

Some do, some teach, the rest look it up.
stormdoku

StrmCkr

Posts: 1428
Joined: 05 September 2006

### Re: Fairy chess piece tour puzzles including Numbrix & Hidat

StrmCkr wrote:a New Sinbad to play
Great. I've been away for a while but will look at it when there is time ...

tarek

Posts: 3762
Joined: 05 January 2006

### Re: Fairy chess piece tour puzzles including Numbrix & Hidat

solution:
Hidden Text: Show
Code: Select all
`17 36 18 37 34 x 3524 3 23 x 5 25 416 x 11 38 10 39 921 30 22 29 x 26 3115 1 12 x x 40 820 x 19 28 33 27 3214 2 13 42 6 41 7 `
Some do, some teach, the rest look it up.
stormdoku

StrmCkr

Posts: 1428
Joined: 05 September 2006

### Re: Fairy chess piece tour puzzles including Numbrix & Hidat

New gaming piece for the sinbad

Island Fish

The island occupies a eri shape on the board

. X.
x x x
. X.

There is at least 2 locations on the board

Every turn the active location of the fish swaps to the next location.

While it's active the x's represents a blocked space for the specific turns.
Some do, some teach, the rest look it up.
stormdoku

StrmCkr

Posts: 1428
Joined: 05 September 2006

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