This Chess piece is one I created suggestions seen herein Fairy chess tour puzzles
This piece is not found anywhere else
Sinbad 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:
https://i.imgur.com/8gyiNvU.png
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.
A starting Grid to play
https://i.imgur.com/ODt16pe.png
A harder Grid
https://imgur.com/i5YHZRc
​

Description

From wikipedia

Hidato (Hebrew: חידאתו‎‎, originating from the Hebrew word Hida = Riddle) is a logic puzzle game invented by Dr. Gyora M. Benedek, an Israeli mathematician. The goal of Hidato is to fill the grid with consecutive numbers that connect horizontally, vertically, or diagonally. Numbrix puzzles, created by Marilyn vos Savant, are similar to Hidato except that diagonal moves are not allowed. Jadium puzzles (formerly Snakepit puzzles), created by Jeff Marchant, are a more difficult version of Numbrix with fewer given numbers and have appeared on the Parade magazine web site regularly since 2014. The name Hidato is a registered trademark of Doo-Bee Toys and Games LTD, a company co-founded by Benebek himself. Some publishers use different names for this puzzle such as Number Snake.

Further info:

In Hidato, a grid of cells is given. It is usually square-shaped, like Sudoku or Kakuro, but it can also include irregular shaped grids like hearts, skulls, and so forth. It can have inner holes (like a disc), but it has to be made of only one piece. The goal is to fill the grid with a series of consecutive numbers adjacent to each other vertically, horizontally, or diagonally. In every Hidato puzzle the smallest and the highest numbers are given on the grid. There are also other given numbers on the grid (with values between the smallest and the highest) to help direct the player how to start the solution and to ensure that Hidato has a single solution. Note: the above condition on the smallest or highest numbers are sometimes relaxed: only their values can be given, without their positions on the grid (of course, the difference between these values must be equal to the number of cells in the grid minus one). This may lead to harder puzzles. Every well-formed Hidato puzzle is supposed to have a unique solution. Moreover, a Hidato puzzle intended for human solvers should have a solution that can be found by (more or less) simple logic. However, there exist very hard Hidato puzzles, even of small size. Hidato puzzles are published in newspapers such as the Daily Mail and Detroit Free Press.

So basically:
You'll recieve a grid with numbers, empty spaces and blocked spaces.
You need to fill in all empty spaces with numbers. These numbers must be consecutive that connect in any direction.

Formal Inputs & Outputs

Input description

A Hidato puzzle to solve.

Input 1

. 33 35 . . x x x . . 24 22 . x x x . . . 21 . . x x . 26 . 13 40 11 x x 27 . . . 9 . 1 x x x . . 18 . . x x x x x . 7 . . x x x x x x 5 . 

Input 2

. . 3 . . . . . x x x x x x x . . . . . . . . . . x x x x x x x . . . . . . . . x x x x x x x . . . . . . . . . . x x x x x x x . . . . . . . . 

Input 3

1 . 

Input 4

1 . x . 5 . 

Input 5

. 4 5 16 8 6 . . . 12 . 14 10 . 13 1 

Input 6

1 . . 23 . . 11 . 3 . . 18 . 13 . . . . . . . . 26 . 8 . . 15 . 30 . . 36 . . 31 

Output description

A solved Hidato

Output 1

32 33 35 36 37 x x x 31 34 24 22 38 x x x 30 25 23 21 12 39 x x 29 26 20 13 40 11 x x 27 28 14 19 9 10 1 x x x 15 16 18 8 2 x x x x x 17 7 6 3 x x x x x x 5 4 

Output 2

1 2 3 4 5 6 7 8 x x x x x x x 9 17 16 15 14 13 12 11 10 18 x x x x x x x 19 20 21 22 23 24 25 26 x x x x x x x 27 35 34 33 32 31 30 29 28 36 x x x x x x x 37 38 39 40 41 42 43 44 

Output 3

1 2 

Output 4

1 2 x 3 5 4 

Output 5

7 4 5 16 8 6 3 15 9 12 2 14 10 11 13 1 

Output 6

1 2 22 23 20 19 11 12 3 21 24 18 10 13 4 25 17 27 9 5 14 16 26 28 8 6 34 15 29 30 7 35 36 33 32 31 

Notes/Hints

Also from wikipedia

As in many logic puzzles, the basic resolution technique consists of analyzing the possibilities for each number of being present in each cell. When a cell can contain only one number (Naked Single) or when a number has only one possible place (Hidden Single), it can be asserted as belonging to the solution. One key to the solution is, it does not have to be built in ascending (or descending) order; it can be built piecewise, with pieces starting from different givens. As in the Sudoku case, the resolution of harder Hidato or Numbrix puzzles requires the use of more complex techniques - in particular of various types of chain patterns.

Finally

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