It is currently Thu Mar 28, 2024 7:50 am

All times are UTC - 8 hours [ DST ]




Post new topic Reply to topic  [ 109 posts ]  Go to page Previous  1, 2, 3, 4, 5, 6  Next
Author Message
Offline
 Post subject: Re: Martian problem
Post #61 Posted: Tue Sep 15, 2020 2:07 pm 
Lives in sente

Posts: 1236
Liked others: 21
Was liked: 57
Rank: 1d
Eureka! Reading your different posts with a lot of concentration I begin to understand! Thank you all for your help!

In the phrase "Stones which are alive but possess dame are said to be in seki" I now understand that the word stones is not refering to a chain a stones but to a group of stones. This last term is not defined but the common sense tell us what it is and it is not essential to defined clearly this term provided the intention behind is clear.

Am I now correct?

Top
 Profile  
 
Offline
 Post subject: Re: Martian problem
Post #62 Posted: Tue Sep 15, 2020 2:37 pm 
Honinbo

Posts: 10905
Liked others: 3651
Was liked: 3374
Oops. I accidentally edited my previous note instead of quoting it. That's OK, though.

It uses the rules text to define territory in a single line. :)

Here is the link to it.

https://www.lifein19x19.com/viewtopic.p ... 97#p259797

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Top
 Profile  
 
Offline
 Post subject: Re: Martian problem
Post #63 Posted: Tue Sep 15, 2020 2:46 pm 
Lives in sente

Posts: 1236
Liked others: 21
Was liked: 57
Rank: 1d
Due to my doubts concerning the interperetation of the japonese rule, for a moment, I were not quite sure of my solutions of the martian problem.
Fortunately everythings seems now OK and my two solutions are valide (at least I am persuaded they are!)

Let me remind you the problem:

Find a position considered has the starting position of a game (you are not allowed to create on history for this position in termes of ko or superko) and ask to the martian to play only the first move of the game. The goal is to be able to detect the rule used by the martian (japonese, or chinese PSK, or AGA SSK) by seeing only this first move, knowing that the martian plays always the best move (or one of the best moves) to reach best score.

Good luck for finding yourself a solution for this problem.

Top
 Profile  
 
Offline
 Post subject: Re: Martian problem
Post #64 Posted: Tue Sep 15, 2020 3:16 pm 
Honinbo

Posts: 10905
Liked others: 3651
Was liked: 3374
Gérard TAILLE wrote:
Eureka! Reading your different posts with a lot of concentration I begin to understand! Thank you all for your help!

In the phrase "Stones which are alive but possess dame are said to be in seki" I now understand that the word stones is not refering to a chain a stones but to a group of stones. This last term is not defined but the common sense tell us what it is and it is not essential to defined clearly this term provided the intention behind is clear.

Am I now correct?


You can define such a group this way:

A set of stones of the same color which are either rookwise connected, or which may be made rookwise connected by placing one or more stones on the board on empty points which they surround, after removing dead stones, if necessary.

Note that you only have to place stones, not play them, to avoid the question of whether a play is legal or not, or self atari. Also, a play might capture an opponent's stone which is not dead.

See also: https://senseis.xmp.net/?SpightJapaneseStyleRules#toc6 , article 8.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Top
 Profile  
 
Offline
 Post subject: Re: Martian problem
Post #65 Posted: Tue Sep 15, 2020 6:19 pm 
Dies with sente

Posts: 73
Liked others: 7
Was liked: 17
Rank: 5d
Bill Spight wrote:
Quote:
Maybe the Korean rules / practice could also offer some hints here.

Jaeup is the expert on Korean rules. :)
Looks like there were quite a long discussion on a few issues. Let me clear one thing at a time.

First, the Korean rule "absolutely" allows a ko recapture after two passes. Though (as usual) the rule text is ambiguously written, I am sure about this because I have seen (almost) official examples with such a sequence, recapturing a ko after two passes.

My impression about the Japanese rule is that they also allow a ko recapture after two passes. (Well, the game stop rule makes things more complicated, but I am assuming that the game resumed.)

In the hypothetical play, they ban ko recapture without passing for that ko. I believe the text is supposed to be interpreted that "in the normal situation, you can capture this ko because you passed, but you cannot do so in this hypo mode because you did not pass for this specific ko". But again, the rule text is so ambiguous about this, and I am only guessing.

I can at least say that I will be very surprised if Nihon Ki-in says otherwise. There are hundreds of shapes that can freeze the board when ko recapture is not allowed after two passes, and they surely know such problems.

_________________
Jaeup Kim
Professor in Physics, Ulsan National Institute of Science and Technology, Korea
Author of the Book "Understanding the Rules of Baduk", available at https://home.unist.ac.kr/professor/jukim/bbs/board.php?bo_table=notice&wr_id=5

Top
 Profile  
 
Offline
 Post subject: Re: Martian problem
Post #66 Posted: Tue Sep 15, 2020 6:32 pm 
Dies with sente

Posts: 73
Liked others: 7
Was liked: 17
Rank: 5d
Gérard TAILLE wrote:
Eureka! Reading your different posts with a lot of concentration I begin to understand! Thank you all for your help!

In the phrase "Stones which are alive but possess dame are said to be in seki" I now understand that the word stones is not refering to a chain a stones but to a group of stones. This last term is not defined but the common sense tell us what it is and it is not essential to defined clearly this term provided the intention behind is clear.
"possess dame", "adjacent to dame" or whichever way one translates it, this part of the Japanese rule is problematic. From such one word "adjacent", can one write down a program code identifying when the spread of seki stops? Definitely not.

They surely had the concept of "group" in their minds when writing such a sentence, but not defining or mentioning it makes the situation even worse.

_________________
Jaeup Kim
Professor in Physics, Ulsan National Institute of Science and Technology, Korea
Author of the Book "Understanding the Rules of Baduk", available at https://home.unist.ac.kr/professor/jukim/bbs/board.php?bo_table=notice&wr_id=5

Top
 Profile  
 
Offline
 Post subject: Re: Martian problem
Post #67 Posted: Tue Sep 15, 2020 6:32 pm 
Honinbo

Posts: 10905
Liked others: 3651
Was liked: 3374
jaeup wrote:
I can at least say that I will be very surprised if Nihon Ki-in says otherwise. There are hundreds of shapes that can freeze the board when ko recapture is not allowed after two passes, and they surely know such problems.


Yes, but they handle such situations by hypothetical play instead of resumption. At the very least you can prove that the unfilled ko in many, if not all of such situations, leaves a dead ko stone. Take a look at the official examples. How many such situations are explained by hypothetical play and how many are explained by resumption?

Edit: Besides, they had the example of Ikeda's rules, which use resumption instead of hypothetical play, and the example of Yasunaga's proposal, which requires three consecutive passes to end play.

Also, aside from the mannenko problem in 1928, they had two rules problems with an unfinished ko at the end of play, Go Seigen vs. Iwamoto and Go Seigen vs. Takagawa. In both examples hypothetical play dictates winning the ko.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Top
 Profile  
 
Offline
 Post subject: Re: Martian problem
Post #68 Posted: Tue Sep 15, 2020 7:58 pm 
Lives in gote

Posts: 445
Liked others: 0
Was liked: 37
I forgot this:
Gérard TAILLE wrote:
a definition of a seki which is very difficult to grasp though it is of great importance for understanding what a territory is.

But note that territory can also be defined (transformable to pass-alive vs opposition) without mentioning seki. (OC this is not how current Japanese rules work.)

jaeup wrote:
My impression about the Japanese rule is that they also allow a ko recapture after two passes. (Well, the game stop rule makes things more complicated, but I am assuming that the game resumed.)

In the hypothetical play, they ban ko recapture without passing for that ko. I believe the text is supposed to be interpreted that "in the normal situation, you can capture this ko because you passed, but you cannot do so in this hypo mode because you did not pass for this specific ko".

This is what I meant too. It seems hard to imagine that in one case you can officially pass (for) and thus recapture a ko, yet in another case a pass is some immaterial nothing that have no effect on kos. Either approach could be meaningful and valid - but unlikely both at the same time.

Top
 Profile  
 
Offline
 Post subject: Re: Martian problem
Post #69 Posted: Wed Sep 16, 2020 5:07 am 
Honinbo

Posts: 10905
Liked others: 3651
Was liked: 3374
jann wrote:
It seems hard to imagine that in one case you can officially pass (for) and thus recapture a ko, yet in another case a pass is some immaterial nothing that have no effect on kos. Either approach could be meaningful and valid - but unlikely both at the same time.


Well, it's not both at the same time. Both alternatives depend on the 2 pass rule to end play. Rules that allow a pass to lift ko or superko bans have trouble with the 2 pass rule, because if the first pass lifts a ko ban, but then the opponent's pass ends play, what good does lifting the ko ban do? And if 2 consecutive passes do not end play, how do you end play? Ing has a 4 pass rule; Yasunaga has a 3 pass rule; my rules end play with repetition by the same player, which usually happens with 3 consecutive passes.

AGA rules end play with 2 passes, and preserve any ko ban if play resumes. So do the Japanese rules. But the Japanese rules do not want to leave an unfinished ko on the board. So hypothetical play after play has ended starts with no ko ban. It's not both at the same time, it's either/or. The pass for ko rule during hypothetical play is a way of making kos independent of the rest of the board. OC, they are not independent in regular play, or in a resumption of regular play.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Top
 Profile  
 
Offline
 Post subject: Re: Martian problem
Post #70 Posted: Wed Sep 16, 2020 6:40 am 
Lives in gote

Posts: 445
Liked others: 0
Was liked: 37
Bill Spight wrote:
Rules that allow a pass to lift ko or superko bans have trouble with the 2 pass rule, because if the first pass lifts a ko ban, but then the opponent's pass ends play, what good does lifting the ko ban do? And if 2 consecutive passes do not end play, how do you end play? Ing has a 4 pass rule; Yasunaga has a 3 pass rule

I don't see any real problem here. The pass lifted the ko ban, the second pass stopped (not ended!) play. It may continue / resume (so corrently handling passes and ko bans is necessary). Why force any further logical connection between these?

Top
 Profile  
 
Offline
 Post subject: Re: Martian problem
Post #71 Posted: Wed Sep 16, 2020 6:49 am 
Lives in sente

Posts: 1236
Liked others: 21
Was liked: 57
Rank: 1d
I see another issue with the handling of ko in actual play or in hypothetical play.

Komi O,5 point, White to play
Click Here To Show Diagram Code
[go]$$B
$$ ----------------------------------------
$$ | X X X X X X X X X . O O O O O O O . O|
$$ | X X X X X X X X X O O O O O O O O O .|
$$ | X X X X X X X X X O O O O O O O O O O|
$$ | X X X X X X X X X O O O O O O O O O O|
$$ | X X X X X X X X X O O O O O O O O O O|
$$ | X X X X X X X X X O O O O O O O O O O|
$$ | X X X X X X X X X O O O O O O O O O O|
$$ | X X X X X X X X X O O O O O O O O O O|
$$ | X X X X X X X X X O O O O O O O O O O|
$$ | O O O O O O O O O O O O O O O O O O O|
$$ | X X X X X X X X X X X X X X X X X X X|
$$ | X X X X X X X X X X X X X X X X X X X|
$$ | X X X X X X X X X X X X X X X X X X .|
$$ | X X X X X X X X X X X X X X X X X . X|
$$ | X X X X X X O O O O O . X X X X X X X|
$$ | O O O O O O O O O O O O O O O O O O O|
$$ | O O O O O O O O O O O O O O O O O O O|
$$ | O O O O O O O O O O O O O O O O O O O|
$$ | O O O O O O O O O O O O O O O O O O O|
$$ ----------------------------------------[/go]


In this position the 81 black stones in the upper left corner can be captured and it is the same for the 81 white stones in the bottom.

Assume that both players agreed that, under normal play, these two large groups are dead.

Before 1989 that means that both players agreed that white wins by 0,5 points (81 black stones and 81 white stones are dead).

What happens with the 1989 rule?

White pass, black pass and the game stops.
Assuming that both players agreed to say that the 81 white stones in the bottom are dead by using the hypothetical play it remains only the 81 black stones in the upper left corner.

Here, assuming the two players agreed in their analyse with hypothetical play, 3 scenarios are possible

1) The players agreed that the black group is dead with hypothetical play => everytings is OK, white wins by 0,5 point (same result with the previous rule version)
2) The player agreed that the black group is alive with hypothetical play => white ask for a resumption of the game => black pass and white pass. What is the result? I guess black wins ?
3) The players agreed that it is far to complex to decide whether or not the black group is dead under hypothetical play. What happens? I guess the resumption of the game will be decided but both players will obviously pass. What is the result? Here again I guess black will win

Can we conclude that the 1989 rule changes the result of this game ?


Last edited by Gérard TAILLE on Wed Sep 16, 2020 8:41 am, edited 1 time in total.
Top
 Profile  
 
Offline
 Post subject: Re: Martian problem
Post #72 Posted: Wed Sep 16, 2020 8:40 am 
Honinbo

Posts: 10905
Liked others: 3651
Was liked: 3374
jann wrote:
I don't see any real problem here. The pass lifted the ko ban, the second pass stopped (not ended!) play. It may continue / resume (so corrently handling passes and ko bans is necessary). Why force any further logical connection between these?


That's how the Ing rules work. Play stops after 2 passes, but does not end. 4 passes are necessary to end play. So it's fine for a pass to lift ko bans. AGA rules do not work that way. Neither do Japanese rules. Both AGA rules and Japanese rules allow resumption. Neither allows a pass in actual play to lift ko bans. If you want to criticize Japanese rules, fine. I do, too. Lots of people do.

As my rules indicate, it is possible for play to continue forever if passes lift ko bans and 2 passes do not end play. Unless you have some other way of ending play. Ing classifies some kos as disturbing kos and does not allow infinite play in them. I say if playing a ko does not make progress, but returns to the same position, play ends.

The real problem is how to end play. You can propose a variant reading of the Japanese rules, but if so you have to tackle the question of how to end the game.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Top
 Profile  
 
Offline
 Post subject: Re: Martian problem
Post #73 Posted: Wed Sep 16, 2020 9:23 am 
Lives in gote

Posts: 445
Liked others: 0
Was liked: 37
Bill Spight wrote:
The real problem is how to end play.

Why not simply end at a stop where nobody request resumption, with any kind of limit (left to tournament rules) on the maximum number of resumptions a player can request?

Top
 Profile  
 
Offline
 Post subject: Re: Martian problem
Post #74 Posted: Wed Sep 16, 2020 9:47 am 
Honinbo

Posts: 10905
Liked others: 3651
Was liked: 3374
jann wrote:
Bill Spight wrote:
The real problem is how to end play.

Why not simply end at a stop where nobody request resumption, with any kind of limit (left to tournament rules) on the maximum number of resumptions a player can request?


That would be a different set of rules. :)

I have written a variant of Japanese rules, so has Robert Jasiek, so have others. Someday I hope that the Nihon Kiin will do the same.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Top
 Profile  
 
Offline
 Post subject: Re: Martian problem
Post #75 Posted: Wed Sep 16, 2020 11:36 am 
Lives in gote

Posts: 445
Liked others: 0
Was liked: 37
Bill Spight wrote:
That would be a different set of rules. :)

Would it? Even the current text seems pretty clear that: 1. two passes only stop, 2. in stopped state agreement ends the game, or 3. resumption is requestable.

The only addition seems to be the number of resumptions cannot be unlimited, but this is obvious anyway.

Top
 Profile  
 
Offline
 Post subject: Re: Martian problem
Post #76 Posted: Wed Sep 16, 2020 5:31 pm 
Dies with sente

Posts: 73
Liked others: 7
Was liked: 17
Rank: 5d
Bill Spight wrote:
As my rules indicate, it is possible for play to continue forever if passes lift ko bans and 2 passes do not end play.
Well, it is true only for a few special situations, for example, when there exists a double ko seki on the board. I agree that the Japanese rule, when applying it literally (and assuming a pass lifts ko ban), cannot finish the game. But it does not automatically mean they really meant that a pass cannot lift a ko ban.

_________________
Jaeup Kim
Professor in Physics, Ulsan National Institute of Science and Technology, Korea
Author of the Book "Understanding the Rules of Baduk", available at https://home.unist.ac.kr/professor/jukim/bbs/board.php?bo_table=notice&wr_id=5

Top
 Profile  
 
Offline
 Post subject: Re: Martian problem
Post #77 Posted: Wed Sep 16, 2020 5:49 pm 
Dies with sente

Posts: 73
Liked others: 7
Was liked: 17
Rank: 5d
Bill Spight wrote:
Yes, but they handle such situations by hypothetical play instead of resumption. At the very least you can prove that the unfilled ko in many, if not all of such situations, leaves a dead ko stone.
As you left a reservation, there are situations that not lifting the ko ban really makes things problematic and hypothetical play cannot save all of them.

Here, I brought a figure from my book: Japanese (or Korean) rule, assume a pass does not lift a ko ban, Black's turn, komi W+0.5, what is the best play for each and who wins? My original plan was to explain it, but I just realized that it will be fun to wait for you guys to find the answer.

Attachment:
jpncom49.png
jpncom49.png [ 94.49 KiB | Viewed 9242 times ]

_________________
Jaeup Kim
Professor in Physics, Ulsan National Institute of Science and Technology, Korea
Author of the Book "Understanding the Rules of Baduk", available at https://home.unist.ac.kr/professor/jukim/bbs/board.php?bo_table=notice&wr_id=5

Top
 Profile  
 
Offline
 Post subject: Re: Martian problem
Post #78 Posted: Wed Sep 16, 2020 6:10 pm 
Dies with sente

Posts: 73
Liked others: 7
Was liked: 17
Rank: 5d
Gérard TAILLE wrote:
I see another issue with the handling of ko in actual play or in hypothetical play.

Komi O,5 point, White to play
Click Here To Show Diagram Code
[go]$$B
$$ ----------------------------------------
$$ | X X X X X X X X X . O O O O O O O . O|
$$ | X X X X X X X X X O O O O O O O O O .|
$$ | X X X X X X X X X O O O O O O O O O O|
$$ | X X X X X X X X X O O O O O O O O O O|
$$ | X X X X X X X X X O O O O O O O O O O|
$$ | X X X X X X X X X O O O O O O O O O O|
$$ | X X X X X X X X X O O O O O O O O O O|
$$ | X X X X X X X X X O O O O O O O O O O|
$$ | X X X X X X X X X O O O O O O O O O O|
$$ | O O O O O O O O O O O O O O O O O O O|
$$ | X X X X X X X X X X X X X X X X X X X|
$$ | X X X X X X X X X X X X X X X X X X X|
$$ | X X X X X X X X X X X X X X X X X X .|
$$ | X X X X X X X X X X X X X X X X X . X|
$$ | X X X X X X O O O O O . X X X X X X X|
$$ | O O O O O O O O O O O O O O O O O O O|
$$ | O O O O O O O O O O O O O O O O O O O|
$$ | O O O O O O O O O O O O O O O O O O O|
$$ | O O O O O O O O O O O O O O O O O O O|
$$ ----------------------------------------[/go]


3) The players agreed that it is far to complex to decide whether or not the black group is dead under hypothetical play. What happens? I guess the resumption of the game will be decided but both players will obviously pass. What is the result? Here again I guess black will win

Can we conclude that the 1989 rule changes the result of this game ?
I guess this is also a well-known problem. The hidden question here is, who operates the hypothetical play? Do the players have the right to present the best sequence one can imagine? What if the opponent does not agree?

I believe, even though it is not written anywhere, they had "perfect play" or "God's play" in their minds when writing the rule, assuming that a pro level player will not have a trouble finding such a sequence for the problematic localized area. For this situation, no one can confirm such a sequence, and the only fair decision is to let them "play" the hypothetical play to decide whether Black can make a life on the corner.

Anyway, I do not think that they really cared this type of flaw in their rule-writing. (They will simply say "it won't happen, so don't worry.")

One interesting story is this. The Korean rule is more ambiguous in that it is difficult to see whether the hypothetical play is really inside the rule. I at least interprete it that way, and a few Korean pros I asked agreed. However, when I presented this type of problem to them, they were very reluctant to admit that the Black stones at the corner may get a life. (Yeah, I know. They simply think, well... but... whatever the rule says... its DEAD!!!) So, I think KBA will call it dead if it really occurs. Does Nihon Ki-in have the gut to admit that the corner is alive by seki? I doubt it.

_________________
Jaeup Kim
Professor in Physics, Ulsan National Institute of Science and Technology, Korea
Author of the Book "Understanding the Rules of Baduk", available at https://home.unist.ac.kr/professor/jukim/bbs/board.php?bo_table=notice&wr_id=5

Top
 Profile  
 
Offline
 Post subject: Re: Martian problem
Post #79 Posted: Wed Sep 16, 2020 10:28 pm 
Honinbo

Posts: 10905
Liked others: 3651
Was liked: 3374
jaeup wrote:
Here, I brought a figure from my book: Japanese (or Korean) rule, assume a pass does not lift a ko ban, Black's turn, komi W+0.5, what is the best play for each and who wins? My original plan was to explain it, but I just realized that it will be fun to wait for you guys to find the answer.

Attachment:
jpncom49.png


Nice position. :)

Here is an SGF. I started with no passes as the default and worked from there. :)

Edit: Silly me. :lol:



Black wins by 0.5.
Black makes the second pass to create one of those weird sekis. When White requests resumption, Black passes again, as the ko ban is still in effect. :lol:

As it turns out, this is the optimal result by no pass go with prisoner return without a group tax, Berlekamp's rules.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.


Last edited by Bill Spight on Thu Sep 17, 2020 2:08 am, edited 1 time in total.
Top
 Profile  
 
Offline
 Post subject: Re: Martian problem
Post #80 Posted: Thu Sep 17, 2020 2:03 am 
Lives in sente

Posts: 1236
Liked others: 21
Was liked: 57
Rank: 1d
Click Here To Show Diagram Code
[go]$$B
$$ ----------------------------------------
$$ | X X X X X X X X X . O O O O O O O . O|
$$ | X X X X X X X X X O O O O O O O O O .|
$$ | X X X X X X X X X O O O O O O O O O O|
$$ | X X X X X X X X X O O O O O O O O O O|
$$ | X X X X X X X X X O O O O O O O O O O|
$$ | X X X X X X X X X O O O O O O O O O O|
$$ | X X X X X X X X X O O O O O O O O O O|
$$ | X X X X X X X X X O O O O O O O O O O|
$$ | X X X X X X X X X O O O O O O O O O O|
$$ | O O O O O O O O O O O O O O O O O O O|
$$ | X X X X X X X X X X X X X X X X X X X|
$$ | X X X X X X X X X X X X X X X X X X X|
$$ | X X X X X X X X X X X X X X X X X X .|
$$ | X X X X X X X X X X X X X X X X X . X|
$$ | X X X X X X O O O O O . X X X X X X X|
$$ | O O O O O O O O O O O O O O O O O O O|
$$ | O O O O O O O O O O O O O O O O O O O|
$$ | O O O O O O O O O O O O O O O O O O O|
$$ | O O O O O O O O O O O O O O O O O O O|
$$ ----------------------------------------[/go]

jaeup wrote:

I believe, even though it is not written anywhere, they had "perfect play" or "God's play" in their minds when writing the rule, assuming that a pro level player will not have a trouble finding such a sequence for the problematic localized area. For this situation, no one can confirm such a sequence, and the only fair decision is to let them "play" the hypothetical play to decide whether Black can make a life on the corner.


OK jaeup I agree with your view.
Now assume that the God's play tell us that, due to the special ko rule under hypothetical play, the black group in the upper left corner is alive.
In that case, in one hand you can say the black group is dead under normal God's play and in the other hand you can say the black group is alive under hypothetical God's play.

In that case my understanding of the 1989 japonese rule is that black wins the game though it hurts the common sense of go game doesn't it?

Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 109 posts ]  Go to page Previous  1, 2, 3, 4, 5, 6  Next

All times are UTC - 8 hours [ DST ]


Who is online

Users browsing this forum: No registered users and 1 guest


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group