## two player game

Everything about Sudoku that doesn't fit in one of the other sections

### two player game

I've had an idea for a two player sudoku game. it's quite simple, so it wouldn't surprise me if someone else has had a similar idea. The basic idea is you start with an empty grid and take it in turns to fill in an empty cell. however whenever you fill in a cell you also fill in any cells that are set by filling in that cell ie you complete as much of the puzzle as you can given the current state of the grid. You get one point for every cell you fill in. The game finishes when the grid is complete or you cause a contradiction. the winner is the person with the most points.

Now I haven't played this game yet, but the idea of stopping the game by a contradiction is a little worrying. generally it may be quite easy to cause a contradiction, so if you are one or two points ahead it may be easy to win. I think the best way around this problem is to say that if it's possible to fill in a cell without causing an immediate contradiction then you are not allowed to fill in a cell in a way that causes a contradiction.

I think this game would be very interesting if the players agreed on a symmetry for the puzzle at the start of the game. This could be a quarter turn, two reflections (horizontal and vertical or both diagonals) or the whole symmetry of the square. I think to choose the other symmetries would not be so interesting. Then when the first player places his clue the next player is restricted to placing his clue in a cell that is symetrically equivalent to that. This way to play first has a slight advantage. However you can give up that advantage by playing in the central square. It may be advantageous to do this if you get many points for playing there. also it may be possible for the second player to steal the first play advantage. For instance if there are 3 cells that could be played in on a given go, it may be possible to place a clue that fills two of them.

if you play this game with two different coloured pens, say a red one for placing the first clue and a blue one for filling in the consequences, then at the end of the game, if you complete the grid, then the red clues will be a valid sudoku puzzle.
ab

Posts: 451
Joined: 06 September 2005

Why not start a game in this topic?
It's easy to post the grid after each move.
evert

Posts: 186
Joined: 26 August 2005

ok, you're on

let's use a quarter turn as the symmetry and I'll start with a 7 in r1c1
7000000000000000000000000000000000000000000000000000000000000000000000000000000000
I imagine the game won't get interesting for a few moves, we'll see.
ab

Posts: 451
Joined: 06 September 2005

If I may add a suggestion to the game that may affect the strategy:

If a player adds a number that creates a contradiction, then he/she loses his or her turn, the number is withdrawn, all other numbers forced by the last entry are removed, and the OTHER player then gets a turn.

i.e.: Creating a contradiction causes you to lose your turn without affecting the 'game board'.

Obviously, the game can reach an incomplete state where no number can be added. Then whoever is ahead at that point wins.

You'll have to decide if you need a rule for when a contradiction is discovered that was actually created on a previous play, unless you are using software that allows you to check each time to ensure that a valid solution still exists.
tinfoil

Posts: 16
Joined: 06 June 2005

If there is no possible play then missing a go will be no great handicap since the other person will also have to miss a go. Also if there are still valid cells to play in, you shouldn't have picked an invalid cell.

The game will only reach a state where no one can play if someone placed a clue that leads to a contradiction. I think if it's not immediately obvious that a clue leads to a contradiction then you should not be punished for it. ie if it's not spotted that the clue leads to a contradiction before your next play then that clue should be allowed to remain.
ab

Posts: 451
Joined: 06 September 2005

A quarter turn symmetry means I must move in R1C9 since you moved in R1C1?
7000000000000000000000000000000000000000000000000000000000000000000000000000000008
evert

Posts: 186
Joined: 26 August 2005

a half turn means you have to play there. With a quarter tur you could have played in r1c9 or r9c1 too.

I'll play in r9c1 so you are now forced into laying r1c9:
700000000000000000000000000000000000000000000000000000000000000000000000500000008
ab

Posts: 451
Joined: 06 September 2005

Code: Select all
` *-----------* |7..|...|..-5| |...|...|...| |...|...|...| |---+---+---| |...|...|...| |...|...|...| |...|...|...| |---+---+---| |...|...|...| |...|...|...| |5..|...|..-8| *-----------*`

BTW How do we count points?
Is it important to know who placed which number for counting points afterwards? I used +/- for this.
evert

Posts: 186
Joined: 26 August 2005

Code: Select all
` *-----------* |7..|...|.-5| |...|...|...| |...|...|...| |---+---+---| |...|...|...| |...|...|...| |..6|...|...| |---+---+---| |...|...|...| |...|...|...| |5..|...|.-8| *-----------*`

I'll place a 6 in r6c3

+/- will do to score, or we could just keep a tally. At the moment it's ab:3 and evert:2. Might get a bit more interesting soon ;)
ab

Posts: 451
Joined: 06 September 2005

ab wrote:
Code: Select all
` *-----------* |7..|...|.-5| |...|...|...| |...|...|...| |---+---+---| |...|...|-6...| |...|...|...| |..6|...|...| |---+---+---| |...|...|...| |...|...|...| |5..|...|.-8| *-----------*`

I'll place a 6 in r6c3

+/- will do to score, or we could just keep a tally. At the moment it's ab:3 and evert:2. Might get a bit more interesting soon ;)
evert

Posts: 186
Joined: 26 August 2005

Code: Select all
` *-----------* |7..|...|.-5| |...|...|...| |...|5..|...| |---+---+---| |...|...-6...| |...|...|...| |..6|...|...| |---+---+---| |...|...|...| |...|...|...| |5..|...|.-8| *-----------*`
ab

Posts: 451
Joined: 06 September 2005

For god's sake please put some spaces between dots...

Current state (after ab's 4th move):

Code: Select all
` +-------+-------+-------+  | 7 . . | . . . | . .-5 |  | . . . | . . . | . . . |  | . . . | 5 . . | . . . |  +-------+-------+-------+  | . . . | . . . |-6 . . |  | . . . | . . . | . . . |  | . . 6 | . . . | . . . |  +-------+-------+-------+  | . . . | . . . | . . . |  | . . . | . . . | . . . |  | 5 . . | . . . | . .-8 |  +-------+-------+-------+ `
udosuk

Posts: 2698
Joined: 17 July 2005

Code: Select all
` +-------+-------+-------+  | 7 . . | . . . | . .-5 |  | . . . | . . . | . . . |  | . . . | 5 . . | . . . |  +-------+-------+-------+  | . . . | . . . |-6 . . |  | . . . | . . . | . . . |  | . . 6 | . . . | . . . |  +-------+-------+-------+  | . . . |-1 . . | . . . |  | . . . | . . . | . . . |  | 5 . . | . . . | . .-8 |  +-------+-------+-------+ `
evert

Posts: 186
Joined: 26 August 2005

Code: Select all
` +-------+-------+-------+  | 7 . . | . . . | . .-5 |  | . 5 3 | . . . | . . . |  | . . . | 5 . . | . . . |  +-------+-------+-------+  | . . . | . . . |-6 . . |  | . . . | . . . | . . . |  | . . 6 | . . . | . . . |  +-------+-------+-------+  | . . . | . .-1 | . . . |  | . . . | . . . | . . . |  | 5 . . | . . . | . .-8 |  +-------+-------+-------+ `

You have to play in r7c6. I'll assume you still want to play 1. I'll play r2c3=3 and get a 5 in r2c2 for free. Taking a small early lead.

PS thanks for the suggestion udosuk
ab

Posts: 451
Joined: 06 September 2005

I'm wondering if the player playing first has too much of an advantage? It depends how easy it is to take the lead from him. A rule change that would get around this is as follows:

First lets create some terminology. If you place the first number in a group of symmetric cells (whatever the symmetry you're using) we'll say you're starting an orbit. At the moment only one player can start an orbit and he seems to have a big advantage. For instance I could play in r3c4 knowing that evert couldn't play in r2c2 or r2c3 because he had to play in my orbit. An alternative rule could be that each player can start one orbit. Then on any turn you can play in either of the two orbits, but you can only start a new orbit when the orbit you started has been completed. That way you can still sometimes have control over where your opponent plays, but the power does not lie solely with one player.
ab

Posts: 451
Joined: 06 September 2005

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