## Sudothello

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Sudothello

A given sudoku cell can "see" across a row, column, and one of 9 nine-cell boxes.
Reversi/Othello does its tile-flipping along row, column and diagonal. Let's call these "rays".
Let's merge these two boards.
Imagine two players, Black and White. A third referee/arbitrator/computer who knows the unique solution to a standard sudoku board.
Let's say a resolved or known cell is now a "tile"
The board starts with a certain number of resolved cells/tiles as normal.
These are neutral in color/affiliation.
Let's say it's White's turn. He declares R5C3=7.
Computer says wrong, R5C3 is Not 7.
Move is noted in list of moves for players to review, and no action is taken.
White in effect loses a turn.

Black declares a move, say R2C8=2 and computer says that's correct.
That cell is now a Black tile and any white and/or neutral tiles now bookended along any ray by this black move are toggled to Black.

And so on...

When board is fully resolved, number of affiliated tiles determines winner.
Plattso.ver2.0

Posts: 18
Joined: 21 January 2013

### Re: Sudothello

Or we could call it Reverdoku.
Let's also say that the neutral and/or opponent tiles must be contiguous along a ray
with no unresolved cells between the bookend tiles formed by a player's new move,
or the tiles do not toggle.
Plattso.ver2.0

Posts: 18
Joined: 21 January 2013

### Re: Sudothello

I've taken a look here, so now checking my understanding:
If the starting position was like this:
Code: Select all
`.6.|.2.|.3....|.1.|64.7..|...|...---+---+---...|4.3|.87..4|.91|....7.|...|...---+---+---618|...|...5..|...|.684..|2..|1..`

(valid regular sudoku, with one unique solution)

and the computer knew the solution was like this:
Code: Select all
`965|824|731283|917|645741|536|892---+---+---126|453|987854|791|326379|682|514---+---+---618|345|279532|179|468497|268|153`

then white's move R3C6=6:
Code: Select all
`.6.|.2.|.3....|.1.|64.7..|..6|...---+---+---...|4.3|.87..4|.91|....7.|...|...---+---+---618|...|...5..|...|.684..|2..|1..`

black's move R6C6=2:
Code: Select all
`.6.|.2.|.3....|.1.|64.7..|..6|...---+---+---...|4.3|.87..4|.91|....7.|..2|...---+---+---618|...|...5..|...|.684..|2..|1..`

white's move R7C6=5:
Code: Select all
`.6.|.2.|.3....|.1.|64.7..|..6|...---+---+---...|4.3|.87..4|.91|....7.|..2|...---+---+---618|..5|...5..|...|.684..|2..|1..`

and white has won R4-6C6.

- Is my understanding correct?
- Would white win R8C8-9 after move R8C7=4?
- Is the starting position always a valid sudoku with one unique solution?
evert

Posts: 186
Joined: 26 August 2005

### Re: Sudothello

Thank you so much.
Yes tiles R4-6C6 toggle to white in this case, looks like.
So that understanding is correct.
No, I don't see any toggling after R8C7=4, other than R8C7 to white.
Since there has been no "bookending" in that case.
Yes, starting position is always a "valid" sudoku with one solution.
Plattso.ver2.0

Posts: 18
Joined: 21 January 2013

### Re: Sudothello

Very nice!

I wouldn't allow much thinking time, or each player could then work out the entire solution on another piece of paper and it would start looking very much like regular Reversi.
evert

Posts: 186
Joined: 26 August 2005

### Re: Sudothello

Uh-Oh. Now you're making my wheels turn.
For one thing, can this BBCode business show us our white and black tiles (digits with ANSI-like color)?
And maybe we can make the tiles interact in some additional ways.
Or maybe a player gets points according to the toggled tile values as numbers.
You know, toggling a "9" gets you nine points....
And I suppose the corners would be prized here as in reversi.
Plattso.ver2.0

Posts: 18
Joined: 21 January 2013

### Re: Sudothello

You might want to use a color other than white, which is difficult to read on this background color.
White text Green text
Code: Select all
`[color=white]White text[/color] [color=green]Green text[/color]`

JasonLion
2017 Supporter

Posts: 640
Joined: 25 October 2007
Location: Silver Spring, MD, USA

### Re: Sudothello

Yeah, maybe green and red. That would be real Christmas-y.
Plattso.ver2.0

Posts: 18
Joined: 21 January 2013

### Re: Sudothello

Say there's one player. He's talking to Mr. Computer who has a known completely resolved sudoku grid.
Player has a blank grid. He guesses some quasi random cell is a particular digit.
He's right or wrong. And makes more moves/guesses. He reviews his list of moves or takes notes or something or has a superb memory.
Eventually, he gets enough cells resolved that he can figure the rest of it out logically without error.
A sort of tipping point.
This might not be such a fun game, but it is a theoretically possible one.
But then aren't there some grids that are not logically solvable right on up to the last couple resolved cells? Beats me.

But there is a universe of possible grids. An extremely large but finite group.
As player resolves more cells, the group of which player's working grid is a member gets smaller.

Say there's two players. Mr Computer's job is simply to confirm each player's move is allowable according to the 0-9 digits and the rows, columns, boxes, blah blah.
They start with a blank grid. Alternating moves by placing digits as they see fit anywhere on the grid.
Let's say Mr Computer is a simple solver. At each move, he attempts to solve the puzzle by iterative simple singles.
When he can, he rings a bell. I don't know why, but it seems gratifying that he should ring a bell.
The player who made that last move, will be either happy or sad depending on the interpretation of the bell ringing.
Well, they've created a sudoku grid. Might not be a quality one. But then, the solver could be more sophisticated, too.

In this "Sudothello" we are designing, should the starting grid be one with a unique solution? Maybe not.
Maybe it should have a plethora of those Uniqueness Rectangle thingies, and Mr Computer's "correct" grid is simply One Of the many possible solutions.
This might keep Red and Green players sweating it out for a while guessing and maneuvering.
Of course, even if both players have scribbled out the solution, there's still the order in which they play the moves that determine the affiliation of tiles.

"Contiguous" toggling is more Reversi-like. But let's say when Red player resolves a cell to Red tile, the process goes like:
Look outward along every Ray until either another Red tile is seen, or you hit the end of the board.
If another Red tile is seen, any Green or Neutral tiles between those two, regardless of unresolved cells appearing as well, toggle to Red.
Plattso.ver2.0

Posts: 18
Joined: 21 January 2013

### Re: Sudothello

I like the idea of starting with an empty board. The additional flexibility allows more use of knowledge about the best way to play Reversi.

JasonLion
2017 Supporter

Posts: 640
Joined: 25 October 2007
Location: Silver Spring, MD, USA

### Re: Sudothello

Yeah. I like it. Empty board. We don't start with a known puzzle.
Red and Green make their alternating moves placing digits whereever they please, with an eye toward
bookending and toggling the opponent's tiles. Each move is checked for validity by mr computer .
You know, no two of same digit may sudoku-see each other, etc.

Optionally, mr computer may be set for various "hardcore" levels. Each move is checked for validity plus whether it results in a grid that is completely solveable by iterative simple singles or that plus any set of special techniques such as naked pairs or xwings or whatever. If so, that move is denied. Player loses turn. Maybe three in a row denies-by-solveability and game is called. Tiles are tallied. Or maybe that solved grid is now shown to both players who may choose their subsequent moves from it.
Plattso.ver2.0

Posts: 18
Joined: 21 January 2013

### Re: Sudothello

Right, and the bookending is not necessarily contiguous. You may, but you don't have to, play right next to opponent's tile. This makes the play more sudoku-like.
Plattso.ver2.0

Posts: 18
Joined: 21 January 2013

### Re: Sudothello

You know, it just hit me. Regardless of tile flipping, we're talking about two players making alternate moves, laying digits down on a sudoku grid. And after each move a solver checking to see if one of a set of techniques has been created. That's really something. So Player Red lays down a digit, and solver finds that an XY wing has been created that then leads to a completely solved board by simple singles. Well, that was a pretty cool move from Red, wasn't it? He should get something for that. That's like a checkmate or something. You could try playing this game with different techniques "turned on" and learn to make these structures from the other side, so to speak.
Plattso.ver2.0

Posts: 18
Joined: 21 January 2013

### Re: Sudothello

After each turn, Mr. Computer figures out whether, starting with the position now on the board, the number of solutions is Multiple, Single, or Zero. If Zero, the digit is disallowed and it becomes the opponent's turn. If Multiple, the digit is allowed and it becomes the opponent's turn. If Single, the player wins.

To prevent players from stalling (sometimes a player might prefer to "pass" to force the opponent to move, but "passing" is illegal, sort of like zugzwang in chess), you'd have to make it illegal to place a digit which immediately creates a duplicate digit in a row, column, or box. You'd also have to make it illegal to place a digit in a cell where that digit in that cell has previously been disallowed.

Bill Smythe
Smythe Dakota

Posts: 546
Joined: 11 February 2006

### Re: Sudothello

Isn't "number of solutions = zero" the same as screening the move for validity?
Isn't "previously been disallowed" the same as Mr Computer saying "no, RnCn is not N" in the list of moves in a game of known starting grid?

You're saying that if Mr Computer determines there is a unique solution, game is over, regardless of what that solution is?
Is that because to determine that, he must have resolved the grid?

I'm not sure if you're saying anything I haven't. But at any rate, it seems some sort of gains must be made by the players in the interactions of the digits as structures or
by tactical movement during the course of the game as the players are heading toward a resolution of the grid.
Some sort of score.

Maybe the discussion should break into two parts.
One for finding a pleasing meld of Sudoku and Reversi.
One for speculating about a competitive game which generates strictly a Sudoku puzzle.
Plattso.ver2.0

Posts: 18
Joined: 21 January 2013

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