The New Sudoku Players' Forum

[Plattso.ver2.0]

So my "Mr Computer can completely resolve the grid now because of this latest move" is like
Smythe Dakota's "Mr Computer says there is now one solution"
In my Red player above example- it's like checkmate, game over, player wins.

and if Mr Computer cannot resolve it yet, after this latest move is like
Smythe Dakota's "Mr Computer says there is now multiple solutions"

Do I have this right?

So If the purpose of the game is for this counter play to create a tough Sudoku puzzle, then a "good" move
would be one which, although it creates a solving structure, and perhaps gives the player some sort
of game value, it resolves only one or few cells, and the game continues.

Does Mr Computer then display these newly resolved cells to the players?

[Plattso.ver2.0]

It's one thing to start with a known array, in a completely filled-in grid.
Then carefully choose those handful which you will reveal to the solver.
So that he may figure out the rest.

It's another for the array to not yet exist
but is being created, one at a time perhaps along that same handful,
perhaps not,
through some process, as the diminishing degrees-of-freedom snap the rest of them into place.

[Plattso.ver2.0]

This reminds me of the old pencil-paper game of 64 Dots.
Two players, Red and Green. Blank Sudoku grid.
Referee is a simple-single-solver.
Players must place a digit alternately on a cell; no passing or skipping.

When Player marks a cell with his digit, that cell belongs to Player.
If Player's cell-mark causes Referee to resolve a chain of one or more cells, those cells belong to Opponent.

And so, until all cells are marked. Player with most cells wins.

[Smythe Dakota]

Isn't "number of solutions = zero" the same as screening the move for validity? ....

Yup. But, since we're starting with an empty grid, and gradually working our way up into reasonable territory, about the only way Mr. Computer could screen for validity is to try to solve the puzzle.

.... 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? ....

I'm not sure what you're saying here. Another way of saying "previously been disallowed" is to say "You already tried that". (Or "your opponent already tried that".)

.... You're saying that if Mr Computer determines there is a unique solution, game is over, regardless of what that solution is? ....

Yes, the computer would have to try to solve the puzzle anew at each turn. If it finds there is no solution, disallow the entry. If it finds a solution, then it would have to look for a second solution, or prove there is none. Once a second solution is found, that's good enough, we don't care how many solutions there are if there are at least two.

....I'm not sure if you're saying anything I haven't. ....

Maybe I'm not. Not sure.

.... 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. ....

My idea was to try to be the first player to reduce the number of solutions to 1. I'm thinking along the following lines. Eventually, in many newspaper puzzles near the end of the week, one often gets to a position where there are only 15 or so unresolved cells, many of which have only two candidates, some three, few if any with four. In many such situations, guessing one of them will lead immediately to filling in most of the rest. One must be careful, then, not to hand an easy solution to the opponent. Jockeying around, sort of like trying to avoid zugzwang in chess.

I'm not at all sure this idea is even workable, though.

.... 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.

Yeh, I guess I was straying a bit far from the original topic here.

Bill Smythe

[JasonLion]

It would be more playable if the players are trying to leave the puzzle with multiple solutions and the first person to create a puzzle with only one solution loses.

[Plattso.ver2.0]

It would be more playable if the players are trying to leave the puzzle with multiple solutions and the first person to create a puzzle with only one solution loses.

Yeah, I think I'm ineptly struggling toward something like that.

[Plattso.ver2.0]

Let's look again for a second at this simple-singles game.
let's say instead of a referee, both players have a simple-single-finder machine.
For humor's sake, let's call it the Single Sucker.
You're Green, and Red has just made a move, placing a digit onto some cell, thereby claiming his ownership of that cell.
Before you make your digit-placing move, as is the rule, you hit your button on your Sucker Machine.
It finds any possible chain of one or more simple singles and then adds those resolved cells to your tally.
Now you make your digit-placing move.

[Plattso.ver2.0]

Okay:

Two players, Red and Green. Blank Sudoku board.
Mr. Computer, henceforth known as MC, does the digit and tile handling and is a solver.
Players take turns by declaring some chosen cell to contain a digit 1-9.
MC checks if valid, and resolves that cell to the players chosen digit (now a tile) of Player's color.
Moves are made with a mind toward not-necessarily-contiguous bookending and flipping of opponent's tiles
along row, column and diagonal.
After each move is made, MC attempts to solve this sudoku puzzle as it stands so far.
If a chain of one or more cells are resolved by MC, they are noted on MC's "copy" of board, but not shown on Player's board.
If Player declares a digit which is incorrect because that cell is resolved on MC's board
the correct digit is displayed on Player's board and tile is awarded to opponent
plus any tile flipping that would have occurred if opponent had made that move is awarded to opponent.
Then it's opponent's move.

When all cells are resolved, color tally determines winner.

[Plattso.ver2.0]

Game settings which may be toggled on or off by player agreement.
1) Any of one or more special techniques on top of the regular simple singles can be On for MC/Solver.
2) Tiles may be worth their face value as numerals.

Example of Super Tiles:
Face Value turned Off (makes this example easier)
Only Xwing is turned On over regular singles.
After last move, MC attempts a solve with singles only to no avail, doesn't resolve a cell.
Goes to Xwing routine and finds one involving digit X.
Those cells between-the-wings, as it were, are ruled out for X.
But two of those cells only had two candidates apiece.
So they are now resolved and are Super Cells, the direct results of a special technique.
Further resolved cells by singles after that don't count as Super.
Red declares a digit correctly on a Super Cell, he earns a Super Tile, which is worth more.
If Green later flips that tile it resets back to normal value.
But if Red flips it again, it goes back to Super Value. Red has sort of earned that tile by recognizing the special technique.

3) MC announces the existence of Super Cells
3a) MC shows Players the location of Super Cells
3b) MC names the special technique which earns these Super Cells

4) Super Tile Multiplication Factor.
If STMF=9 and Face Value=On, Player nails a Super Tile of numeral 9 gets a whopping 81 points.

Okay there were two Super Cells in that last example. What if Green now nails the other one?
If after Red's last Super Move, MC finds one or more singles, that cell loses its Super status.
If MC finds no singles, and the Xwing is still "active", that second cell is still Super.

[Plattso.ver2.0]

So, at some point MC's board will be ahead of the Player's in number of cells resolved.
MC might announce the existence of Super Cells, but that is from its perspective.
The Player's might not be able to see the special technique yet.
It's like he's saying, Hey, if your singles fall down like on my board, soon there will be a special technique.
If Player decides to declare some wild cell off somewhere because it flips some good tiles
and he's just going to take a chance. He figures there's 3 candidates there and he's behind and he's going to go for it.
MC checks MC's board for any sudoku contradictions by this declaration, and if that cell has not been resolved already,
and if that candidate digit has not been ruled out for that cell,
MC assigns the digit (resolves that cell) and tile is awarded to player
and any resultant flips are done.
Now if MC re-evaluates this new board and singles fall down all over
what would have been that special technique area
those Super Cells are no longer.