two player game

Everything about Sudoku that doesn't fit in one of the other sections
Indeed - a bit confused about the symmetry terminology.

Some questions:

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.

How do both players determine and agree whether these additional cells are actually forced?
Especially when the stronger player applies more advanced technics?

Note that for example in chess, if the stronger player spots a mate in 10 and the other player doesn't there's no problem -
the other player will discover the mate at some point by the most direct constraints of the game!

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.

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.

Just for a good understanding of what you mean: this part is not necessary for the game except when you
want the valid puizzle as a by-product.

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.

What happens when no symmetrical cell is available?

Meanwhile thinking about my next move
evert

Posts: 186
Joined: 26 August 2005

ab wrote: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.

Ah that answers my last question.
Another option might be to allow all symmetries in one game - that gives some freedom...
evert

Posts: 186
Joined: 26 August 2005

Code: Select all
`+-------+-------+-------+| 7 . . | . . . | . .-5 || . 5 3 | . . . | . . . || . . . | 5 . . | . . . |+-------+-------+-------+| . . . | . . . |-6 . . || . . . | . . . | . . . || . . 6 | . . . | . . . |+-------+-------+-------+| . . . | . .-1 | . . . || . . . | . . . |-2 . . || 5 . . | . . . | . .-8 |+-------+-------+-------+`
evert

Posts: 186
Joined: 26 August 2005

Code: Select all
`+-------+-------+-------+| 7 . . | . . . | . .-5 || . 5 3 | . . . | . . . || . . . | 5 . . | . . . |+-------+-------+-------+| . . . | . . . |-6 . . || . . . | . . . | . . . || . . 6 | . . . | . . . |+-------+-------+-------+| . 6 . | . .-1 | . . . || . . . | . . . |-2 . . || 5 . . | . . . | . .-8 |+-------+-------+-------+`

I'll hand you the lead soon evert after that move. I definately think in future games there should be one orbit for each player.
ab

Posts: 451
Joined: 06 September 2005

Code: Select all
`+-------+-------+-------+| 7 . . | . . . | . .-5 ||-6 5 3 | . . . | . . . || . . . | 5 . . | .-6 . |+-------+-------+-------+| . . . | . . . |-6 . . || . . . | . . . | . . . || . . 6 | . . . | . . . |+-------+-------+-------+| . 6 . | . .-1 | . . . || . . . | . . . |-2 .-6 || 5 . . | . . . | . .-8 |+-------+-------+-------+`

...and still interested in your opinion on my questions
evert

Posts: 186
Joined: 26 August 2005

evert wrote:
Code: Select all
`+-------+-------+-------+| 7 . . | . . . | . .-5 ||-6 5 3 | . . . | . . . || . . . | 5 . . | .-6 . |+-------+-------+-------+| . . . | . . . |-6 . . || . . . | . . . | . . . || . . 6 | . . . | . . . |+-------+-------+-------+| . 6 . | . .-1 | . . . || . 4 . | . . . |-2 .-6 || 5 . . | . . . | . .-8 |+-------+-------+-------+`

...and still interested in your opinion on my questions

I wasn't thinking straight! I was hoping to play a 6 at r2c8, but didn't look to see you could play at r3c8 lol

As for your questions. If there is no symmetry available, you can play anywhere, which is when the lead changes hands.

yes the red pens aren't necessary.

I'm sure there are plenty of people here that will back you up if you claim to be using a certain technique
ab

Posts: 451
Joined: 06 September 2005

Code: Select all
`+-------+-------+-------+| 7 . . | . . . | . .-5 ||-6 5 3 | . . . | .-1 . || . . . | 5 . . | .-6 . |+-------+-------+-------+| . . . | . . . |-6 . . || . . . | . . . | . . . || . . 6 | . . . | . . . |+-------+-------+-------+| . 6 . | . .-1 | . . . || . 4 . | . . . |-2 .-6 || 5 . . | . . . |-1 .-8 |+-------+-------+-------+`
evert

Posts: 186
Joined: 26 August 2005

Code: Select all
`+-------+-------+-------+| 7 . . | . . . | . .-5 ||-6 5 3 | . . . | .-1 . || . . . | 5 . . | .-6 . |+-------+-------+-------+| . . . | . . . |-6 . . || . . . | . . . | . . . || . . 6 | . . . | . . . |+-------+-------+-------+| . 6 . | . 5-1 | . . . || . 4 . | . . . |-2 5-6 || 5 . . | . . . |-1 .-8 |+-------+-------+-------+`

That makes it 10-10
ab

Posts: 451
Joined: 06 September 2005

I can't know which 5 you entered first and which was the forced cell.
If R8C8 was the first then I get the lead. If R7C5 was the first then I can choose between R5C7, R3C5, R5C3.

Maybe a nice rule is that I can choose in this case?

Code: Select all
`+-------+-------+-------+| 7 .-4 | . . . | . .-5 ||-6 5 3 | . . . | .-1 . || . . . | 5-4 . | .-6 . |+-------+-------+-------+| . . . | . . . |-6 . . || . . . | . . . | . . . || . . 6 | . . . | . . . |+-------+-------+-------+| . 6 . | . 5-1 | . . . || . 4 . | . . . |-2 5-6 || 5 . . | . . . |-1 .-8 |+-------+-------+-------+`
evert

Posts: 186
Joined: 26 August 2005

evert wrote:I can't know which 5 you entered first and which was the forced cell.

I had to play in r8c8 following the symmetry that was in play, so you had a free choice entirely this go. However I think where you played is to your advantage, but it will give me the lead back!

I'll play 1 in r5c3:
Code: Select all
`+-------+-------+-------+| 7 .-4 | . . . | . .-5 ||-6 5 3 | . . . | .-1 . || . . . | 5-4 . | .-6 . |+-------+-------+-------+| . . 5 | . . . |-6 . . || . . 1 | . . . | . . . || . . 6 | . . . | . . . |+-------+-------+-------+| . 6 . | . 5-1 | . . . || 1 4 . | . . . |-2 5-6 || 5 . . | . . . |-1 .-8 |+-------+-------+-------+`
ab

Posts: 451
Joined: 06 September 2005

1 in R3C2 is yours - and I places the first 9 and forced 2 5s:
Code: Select all
`+-------+-------+-------+| 7 .-4 | . . . | . .-5 ||-6 5 3 | . . . | .-1 . || . 1 . | 5-4 . | .-6 . |+-------+-------+-------+| . . 5 | . . . |-6 . . || . . 1 | . .-5 |-9 . . || . . 6 | . . . |-5 . . |+-------+-------+-------+| . 6 . | . 5-1 | . . . || 1 4 . | . . . |-2 5-6 || 5 . . | . . . |-1 .-8 |+-------+-------+-------+`
evert

Posts: 186
Joined: 26 August 2005

So I get a free choice again! I'll play 8 in r1c5
That forces a 3 in r1c7
a 1 in r1c4
a 6 in r1c6
an 8 in r2c7
a 4 in r7c7
a 7 in r3c7
and a 3 in r3c6
Code: Select all
`+-------+-------+-------+| 7 .-4 | 1 8 6 | 3 .-5 ||-6 5 3 | . . . | 8-1 . || . 1 . | 5-4 3 | 7-6 . |+-------+-------+-------+| . . 5 | . . . |-6 . . || . . 1 | . .-5 |-9 . . || . . 6 | . . . |-5 . . |+-------+-------+-------+| . 6 . | . 5-1 | 4 . . || 1 4 . | . . . |-2 5-6 || 5 . . | . . . |-1 .-8 |+-------+-------+-------+`

Now you can play in r5c1, r5c9 or r9c5
ab

Posts: 451
Joined: 06 September 2005

Code: Select all
`+-------+-------+-------+| 7 .-4 | 1 8 6 | 3 .-5 ||-6 5 3 | . . . | 8-1 4 || . 1 . | 5-4 3 | 7-6 . |+-------+-------+-------+| . . 5 | . . . |-6 . . || . . 1 | .-6-5 |-9 . . || . . 6 | . . . |-5 . . |+-------+-------+-------+| . 6 . |-2 5-1 | 4 . . || 1 4-7 | . . . |-2 5-6 || 5 . . |-6-7-4 |-1 .-8 |+-------+-------+-------+`
evert

Posts: 186
Joined: 26 August 2005

Code: Select all
`+-------+-------+-------+| 7 9-4 | 1 8 6 | 3 2-5 ||-6 5 3 | . . . | 8-1 4 || 2 1 8 | 5-4 3 | 7-6 9 |+-------+-------+-------+| . . 5 | . . . |-6 . . || 3 . 1 | .-6-5 |-9 . . || . . 6 | . . . |-5 . . |+-------+-------+-------+| 8 6 9 |-2 5-1 | 4 . . || 1 4-7 | . . . |-2 5-6 || 5 3 2 |-6-7-4 |-1 9-8 |+-------+-------+-------+`
ab

Posts: 451
Joined: 06 September 2005

Scores update:

55 cells played, 26 cells to go
ab 31 -- evert 24 (leading by 7)

To win:
ab needs 10 cells more, evert needs 17 cells more

Hopefully this game is far from over!
(If Australia can score 434 in 50 overs and still lose, I guess it's never over until the last move...)
udosuk

Posts: 2698
Joined: 17 July 2005

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