FAQ   Search   Memberlist   Usergroups   Register   Profile   Log in          Games  Calendar Log in to check your private messages    Why Unsolvable Goto page Previous  1, 2, 3  Next          Sudoku Programmers Forum Index -> Solving sudoku View previous topic :: View next topic   Author Message Mark Joined: 19 Oct 2005 Posts: 30 : Location: Arizona Items Posted: Tue Jan 03, 2006 1:10 am    Post subject: Ruud wrote: Other promising techniques, like Constraint Subsets, do not seem to survive, while brand new techniques like Broken Wings still need to be fleshed out by the player community. A very interesting observation, Ruud. One thing that bothers me about the state of sudoku is the current rat's nest of solving techniques. The large number of these techniques contributes to the confusion, and it's no longer obvious whether a newly-proposed method is logically distinct, or simply a combination of existing methods. Add to that the exotic naming, and the whole subject begins to look like a zoo. I applaud you for not immediately jumping on the bandwagon simply because a new method rears its head. Perhaps soon there'll be an analysis that reduces each proposed technique to a set of provably independent patterns. Cycles (loops) are fascinating, since they allow possible eliminations of candidates which otherwise would result in a given value occurring twice in the same unit. The underlying logical rule is exactly the same as for subsets, which are simply cycles that occur wholly in a single unit. Mark Back to top Ruud Site Admin Joined: 17 Sep 2005 Posts: 708 : Location: Netherlands Items Posted: Wed Jan 04, 2006 11:17 am    Post subject: Carcul wrote: I have just a small request for you, if you allow me to do so: I wonder if you could post in this forum the two most difficult puzzles that your Sudo Cue program can generate? I have a separate program that does mass-generation of puzzles for me, because Sudo Cue only generates one puzzle at a time. However, I do use Sudo Cue to rate the difficulty of these mass-generated puzzles, as I have rated other collections posted here and on other forums. The most difficult Sudokus were found in the top1465 by dukuso. 3 puzzles require advanced techniques embedded in tabling, something not yet implemented in Sudo Cue, so it solves them with DLX. These 3 are #2, #3 and #77 of top1465. The most difficult ones generated by my own generator and rated by Sudo Cue are these 2, but keep in mind that this rating is mainly based on the number of tabling steps required (and a quick manual check): Code: . . .|. . 8|. 2 . . 1 .|3 . .|. . . 2 . 6|. . 7|9 . . -----+-----+----- 5 . .|. . 1|. . 3 . . 7|. 9 .|6 . . 1 . .|6 . .|. . 7 -----+-----+----- . . 1|7 . .|8 . 2 . . .|. . 2|. 5 . . 4 .|8 . .|. . . and Code: . . .|. . .|. . . 8 . .|9 . .|2 4 . . 3 7|. . 4|. 1 . -----+-----+----- . . 4|. . .|. . 7 . . .|5 8 9|. . . 9 . .|. . .|8 . . -----+-----+----- . 4 .|6 . .|5 3 . . 6 3|. . 7|. . 2 . . .|. . .|. . . Mark wrote: One thing that bothers me about the state of sudoku is the current rat's nest of solving techniques. I fully agree with you on this one. What makes it more difficult is that they are introduced and discussed on different forums, with lots of interference by "Help, I'm stuck" and "Newbie found the ultimate solving method" topics. It is hard to keep up with all this. Ruud. _________________ Meet me at sudocue.net Back to top Carcul Joined: 29 Dec 2005 Posts: 50 : Location: Coimbra, Portugal Items Posted: Thu Jan 05, 2006 8:49 am    Post subject: Ruud wrote: The most difficult ones generated by my own generator and rated by Sudo Cue are these 2, Thanks for providing these puzzles. Ruud wrote: but keep in mind that this rating is mainly based on the number of tabling steps required (and a quick manual check): That's right: these two puzzles are indeed not very hard to solve. Regards, Carcul Back to top rkral Joined: 21 Oct 2005 Posts: 233 : Items Posted: Thu Jan 05, 2006 11:08 am    Post subject: Ruud wrote: Carcul wrote: I have just a small request for you, if you allow me to do so: I wonder if you could post in this forum the two most difficult puzzles that your Sudo Cue program can generate? The most difficult ones generated by my own generator and rated by Sudo Cue are these 2, but keep in mind that this rating is mainly based on the number of tabling steps required. How do you define a "tabling step"? Are you counting at a high level, e.g., the eliminations made by tabling ... or are you counting iterations at a lower level? How many "tabling steps" does each puzzle require? Thanks in advance, Ron Back to top Ruud Site Admin Joined: 17 Sep 2005 Posts: 708 : Location: Netherlands Items Posted: Thu Jan 05, 2006 12:39 pm    Post subject: rkral wrote: How do you define a "tabling step"? Are you counting at a high level, e.g., the eliminations made by tabling ... or are you counting iterations at a lower level? Unlike the Susser, that does upto 7 eliminations in a tabling stap, Sudo Cue does a single elimination in each step. After this step it first goes through all 'lower' solving methods before it continues with the next tabling step. Quote: How many "tabling steps" does each puzzle require? These 2 require 16 and 14 steps, respectively. This is still not the optimal solving path, but I am selecting the eliminations based on the lowest constraint count (pairs before triples, etc.) Ruud. _________________ Meet me at sudocue.net Back to top rkral Joined: 21 Oct 2005 Posts: 233 : Items Posted: Thu Jan 05, 2006 1:59 pm    Post subject: Ruud wrote: Sudo Cue does a single elimination in each step. After this step it first goes through all 'lower' solving methods before it continues with the next tabling step. That's the only method that makes sense to me, since it best emulates a solution by a human. If a solver doesn't attempt "best emulation", it might as well use DLX. Well, that's a bit extreme, but I'm sure you understand. Ruud wrote: These 2 require 16 and 14 steps, respectively. [1-11-2006 edit: The following was 100% rewritten to reflect a change in the T&E section of my solver.] My (unpublished) solver requires 5 and 2 T&E eliminations (was 11 and 8), respectively ... but, relative to your solver, that probably doesn't mean much. It's likely just stumbling upon magic candidates earlier. The T&E step finds double implication chains that cause a contradiction (two placements of the same digit in one row, col, or 3x3 box) by asserting each candidate as true. If a contradiction is found, the asserted candidate is eliminated and "basic techniques" are again used until another T&E step is required. The T&E step now first asserts candidates in bivalued cells, then trivalued cells, etc. ... with a scanning order of smallest digit first, columns left-to-right, and rows top-to-bottom. It previously did the identical scan without regard to the number of candidates in a cell. FWIW, the T&E eliminations in sequence are ... Puzzle #1: pzl 1, implication: pass 1, excludes 8 from r4c3 = 89 pzl 1, implication: pass 2, excludes 3 from r6c3 = 34 pzl 1, implication: pass 3, excludes 5 from r1c3 = 35 pzl 1, implication: pass 4, excludes 7 from r1c1 = 47 pzl 1, implication: pass 5, excludes 9 from r1c2 = 79 Puzzle #2: pzl 1, implication: pass 1, excludes 2 from r3c4 = 28 pzl 1, implication: pass 2, excludes 9 from r3c7 = 69 Ron Last edited by rkral on Wed Jan 11, 2006 11:06 am; edited 2 times in total Back to top mugnyte Joined: 07 Dec 2005 Posts: 13 : Location: portland, or Items Posted: Wed Jan 11, 2006 1:16 am    Post subject: Funny, my solver repeatedly solves puzzle #2 with no backups using only basic rules and subset elimination... then again, it may have found a "machine made" side-effect by discovering the pattern of required values (out of several possibilities that are always the min/max/middle of the possibilities)- yeah, that side effect is out there! weird _________________ thanks Back to top rkral Joined: 21 Oct 2005 Posts: 233 : Items Posted: Wed Jan 11, 2006 4:01 am    Post subject: mugnyte wrote: Funny, my solver repeatedly solves puzzle #2 with no backups using only basic rules and subset elimination... Are you talking about Ruud's most difficult #2 or unsolvable #2? Quote: then again, it may have found a "machine made" side-effect by discovering the pattern of required values (out of several possibilities that are always the min/max/middle of the possibilities)- yeah, that side effect is out there! That sure doesn't sound like a solver that is "using only basic rules and subset elimination". Do you mean it only uses basic rules and subset elimination during its T&E step(s)? [edit: links added] Last edited by rkral on Thu Jan 12, 2006 2:32 pm; edited 1 time in total Back to top mugnyte Joined: 07 Dec 2005 Posts: 13 : Location: portland, or Items Posted: Wed Jan 11, 2006 7:50 am    Post subject: Sorry. I was talking about Ruud's above. You inspired me to finish the code for rating puzzles in bulk since I'd never run against the "classics" yet. From dusoku's site: My "ratings" are number of forward moves required to solve. My solver uses logic backed up with T&E. "top1465" 3072: ..1.....7...89..........6..26..3.......5...749...........1.4.5.83.............2.. 2245: 7.8...3.....6.1...5.........4.....263...8.......1...9..9.2....4....7.5........... 2120: 1.....7.2.3.1......9..........39..6.5.8...2...........2....85.....6...9.....4.... "topn234" and "topn87" had many duplicates, and the toughest were identical. It averaged solving about 10/sec. About only 10-15% required no backups by my solver. This is expected, since I've only completed Basic Rules and Subsets as yet. It should be great to see how these change going forward. I'm curious if folks using just basic rules (+/- some logic routine) arrive at the similar numbers. i can't be the only one counting moves, right? Jim _________________ thanks Back to top rkral Joined: 21 Oct 2005 Posts: 233 : Items Posted: Wed Jan 11, 2006 11:33 am    Post subject: mugnyte wrote: My "ratings" are number of forward moves required to solve. My solver uses logic backed up with T&E. [snip][/snip] I'm curious if folks using just basic rules (+/- some logic routine) arrive at the similar numbers. i can't be the only one counting moves, right? I'm considering adding that. Although the difference in counts would be small, are you counting ... just placements, or placements plus eliminations? just unsuccessful placements, or successful ones as well? just moves of the T&E section, or moves of "basic techniques" as well? mugnyte wrote: "top1465" 3072: ..1.....7...89..........6..26..3.......5...749...........1.4.5.83.............2.. 2245: 7.8...3.....6.1...5.........4.....263...8.......1...9..9.2....4....7.5........... 2120: 1.....7.2.3.1......9..........39..6.5.8...2...........2....85.....6...9.....4.... Those are puzzles #29, #3, and #393 of the top1465, respectively. It's mildly interesting that my solver solves those three, but not puzzles #2 and #77. Ruud, as you likely recall, I changed the T&E section of my solver to try bivalued cells first. Therefore, I edited the reported results in a prior post. Ron Back to top tarek Joined: 31 Dec 2005 Posts: 153 : Location: London, UK Items Posted: Wed Jan 11, 2006 12:13 pm    Post subject: Hi mugnyte, mugnyte wrote: Funny, my solver repeatedly solves puzzle #2 with no backups using only basic rules and subset elimination... I must say that that sounds strange. my solver first goes into basic rules first & subset eliminations ........ T&E occurs just at the end & #2 required not just simple T&E (forward checking with single elinations) but it needed complex T&E (forward checking using all possible logical techniques). what level of subset elimination did you reach before cracking the puzzle ? the other queries are same as rkral's: what do you mean by counting forward moves? when do you start counting ? what do you count from then ? are there are any exclusions ? tarek Back to top mugnyte Joined: 07 Dec 2005 Posts: 13 : Location: portland, or Items Posted: Wed Jan 11, 2006 8:54 pm    Post subject: Counting Good questions. First the counting: I count from the first move of the game. Any placement of a value on the board is a "move". I do NOT count backups, but neither do I decrement the count. There are not exceptions. So, when no backups, there are 81-starts "moves". I understand the amount of analysis between moves is the grey area. To explain that, here's the entire pseuocode for my solver. After you guys help me clarify anything obtuse, I'll post it as a topic if wanted. Code: Solver Summary:  pluggable logic modules with full T&E backup when presented with multiple choices Details: There's lots of text-generation code skipped to allow re-use of this    logic for different purposes (generate,solve,hint).    Also unshown, the are optimization switches to interpret naked singles    as values and just keep cranking on the inner routines - which defeats "human-style"    solving style but is great for counting solutions or ripping through puzzle collections.    I have changed names of many routines and variables to protect the innocent ;) Legend:     - for clarity, subroutines named "fnXXX"    - variables are all caps    - comments are after "//"    - conditionals and loops have end markers    - sets unioned with a capital U fnSOLVE:    count GIVENS // places on board with starting #'s    MOVES_TOGO = 81 - GIVENS    SOL_COUNT = 0    WHILE( SOL_COUNT < FIND_SOLS )       WHILE( MOVES_TOGO > 0 )          fnSCAN(CANDIDATE)          if ( CANDIDATE isn't a valid cell )             CANDIDATE = BOARD.CELL with the least number of AVAIL          end if          if ( CANDIDATE isnt valid cell)             fnBACKUP(MOVED)             IF ( MOVED = FALSE )                // cannot back up any further                // there are 0 solutions!                RETURN failure             END IF          else             // save the path we're taking on the cell's choices             AVAILNDX = 0             MOVE_HISTORY.PUSH( BOARD.CELL, AVAILNDX )             // change the board             BOARD.CELL.VAL = CANDIDATE             CELL.AVAIL.CLEAR             MOVES_TOGO--          end if       end while    end while :fnSOLVE fnBACKUP:    WHILE ( MOVE_HISTORY.COUNT > 0 ) and (MOVED = false)       MOVE_HISTORY.POP( BOARD.CELL, AVAILNDX )                 // we privously made a move from       // the BOARD.CELL.AVAIL set at AVAILNDX       // so now we increment it and make another       if ( AVAILNDX < BOARD.CELL.AVAIL.COUNT )          // now we can move          AVAILNDX += 1          MOVE_HISTORY.PUSH( BOARD.CELL, AVAILNDX )          return true       else          // no move moves possible for this cell,          // so we must back up further until we          // can go foward again or until we reach the          // first game move (which indicates 0 solutions)       end if    END WHILE :fnBACKUP fnSCAN(SINGLE):        FIRST = true    DO       BOARDCHANGED = false       // calculate what's available in every cell       for each CELL (0,0) to (8,8)          if FIRST = true             CELL.AVAIL = all values from 1..9             FIRST = false          end if          // note: user chooses modules          for each LM in CHOSEN_LOGIC             // always given in order below             if LM = CHS                fnCHS(BOARDCHANGED)                 else if LM = RC                fnRC(BOARDCHANGED)                 else if LM = SE                fnSE(BOARDCHANGED)             else                // further modules go here             end if             // after any module is applied:             if (board has a naked single)                // we have enough to continue, exit                return SINGLE             end if          end for       end for       // if BOARDCHANGE == false:       // we don't have a naked single, but we've changed the       // board marks during a pass from 0,0 to 8,8       // so, like a human, we re-scan and look for the effects of logic    WHILE ( BOARDCHANGED = true )    // board wasn't changed by a pass of all our logic, so we'll have to guess :fnSCAN        // Cross-Hatch Scanning fnCHS:    for each CHSCELL in (region U row U col coordinates) intersecting CELL // skip CELL itself       remove CHSCELL.ENTERED from CELL.AVAIL       BOARDCHANGED = true    end for :fnEND // Range Checking fnRC:    foreach SET in (region,row,col coordinates) intersecting CELL // skip CELL itself       if a *any* of CELL.AVAIL not found in SET:          remove all other AVAIL from CELL          for each CELL2 in (region U row U col coordinates) intersecting CELL // skip CELL itself             remove single value from CELL2.AVAIL          end for          BOARDCHANGED = true       end if    end for :RC // Subuset Elimination - a bit more detailed SE:    foreach SET in (region,row,col coordinates) intersecting CELL // skip CELL itself       // this is key to finding the smallest sets first       sort SET by each member's AVAIL count ascending       for each CHECKCELL in SET          store CHECKCELL in CELLSET          for each V in CHECKCELL.AVAIL             if V in CELL.AVAIL                store that value in VALUESET             end if          end if                       // if this isn't a single, which should be remove by RC          //    and if values count == cells count          //    and if the set count is less than our entire domain          if (CELLSET.COUNT > 1) and             ( CELLSET.COUNT == VALUESET.COUNT ) and             (CELLSET.COUNT < SET.COUNT )              // loop through the domain again             for each REMOVECELL in SET                // if not part of our subset..                if (REMOVECELL not in CELLSET)                   for each REMOVEAVAIL in REMOVECELL.AVAIL                      // .. but has a value from that set..                      if (REMOVEAVAILVAL in VALUESET)                         // ..remove said value                         remove REMOVEAVAILVAL from REMOVECELL.AVAIL                         BOARDCHANGED = true                      end if                   end for                end if             end for          end if       end for    end for :SE The real code for this is available on my site. Jim [edited to update the logic in a second review. sheesh] _________________ thanks Back to top tarek Joined: 31 Dec 2005 Posts: 153 : Location: London, UK Items Posted: Thu Jan 12, 2006 1:34 am    Post subject: mugnyte wrote: I understand the amount of analysis between moves is the grey area. To explain that, here's the entire pseuocode for my solver. After you guys help me clarify anything obtuse, I'll post it as a topic if wanted. The pseudocode looks nice to me, however I'm not good in reading pseudocodes in the first place. Is it possible just to post the logic that made you make the statement mugnyte wrote: my solver repeatedly solves puzzle #2 with no backups using only basic rules and subset elimination... Tarek Back to top mugnyte Joined: 07 Dec 2005 Posts: 13 : Location: portland, or Items Posted: Thu Jan 12, 2006 6:07 am    Post subject: tarek wrote: Is it possible just to post the logic that made you make the statement Tarek Tarek, Sorry for the delay. I scanned the entire topic again and realized that we may be speaking of different puzzles. Ruud mentions 2 different "second" puzzles - one in reference to the "unsolveable" heading, and one of his own. the first: Code: .1.|.7.|... .26|...|.57 5..|...|..3 ----------- ..8|2..|... .5.|..4|3.2 4..|.37|.8. ----------- ...|.53|4.. ..5|...|..8 .8.|...|.96 was what i typed in a found to take only my sovler's trivial logic. (55 moves) the second: Code: ...|...|... 8..|9..|24. .37|..4|.1. ----------- ..4|...|..7 ...|589|... 9..|...|8.. ----------- .4.|6..|53. .63|..7|..2 ...|...|... indeed, took 3 guesses & 93 moves: the 8th entry was found to be best at: Code: x..|...|... x..|xx.|xx. .xx|..x|.x. ----------- .xx|...|... .x.|xxx|... x..|xx.|x.. ----------- xx.|x..|xx. Oxx|..x|..x ...|...|... small x are prior entries, large O is current chosen entry location (its choices are least across board) offering a choice of 1 or 5. it took 1 and headed off to make 2 more guesses later before coming back here to try the (correct) 5. sorry for the confusion! i hope i didn't send you on a wild goose chase. However, I'm most curious that Ruud's rating system found such a puzzle to be the "very difficult". From what I can tell, these 3 decision points (2 values apiece) were the entire tree using just my limited modules. Ruud, can you enlighten us about that? Jim _________________ thanks Back to top Ruud Site Admin Joined: 17 Sep 2005 Posts: 708 : Location: Netherlands Items Posted: Thu Jan 12, 2006 8:15 am    Post subject: Hi, To add a bit to the confusion, this puzzle: Code: .1.|.7.|... .26|...|.57 5..|...|..3 ----------- ..8|2..|... .5.|..4|3.2 4..|.37|.8. ----------- ...|.53|4.. ..5|...|..8 .8.|...|.96 Was the second puzzle, dubbed unsolvable, from this site: http://www.smackedassintosh.net/sudoku/unsolvable_boards.html With Sudo Cue, I could solve this without guessing, but it still required 8 tabling steps, making it "interesting". Here is my solver log summary on this puzzle (I colored the 8 tabling steps): log wrote: Row 6 Digit 2 must be placed in R6C3 Row 7 Digit 8 must be placed in R7C4 Row 5 Digit 8 must be placed in R5C5 Column 8 Digit 3 must be placed in R8C8 Column 2 Digit 3 must be placed in R4C2 Row 9 Digit 5 must be placed in R9C7 R7C9 has Digit 1 as the only remaining candidate Row 2 only has candidates for Digit 4 in Box 2 Row 7 only has candidates for Digit 6 in Box 7 Row 7 only has candidates for Digit 9 in Box 7 1 candidates for Digit 1 eliminated by a template check Placing Digit 4 in R1C3 forces 2 different Digits in R7C8 Row 1 only has candidates for Digit 4 in Box 3 Box 1 found a Hidden Pair with Digits {4,7} Column 2 found a Naked Pair with Digits {4,7} Placing Digit 3 in R1C1 forces 2 different Digits in R9C3 Placing Digit 9 in R1C4 forces 2 different cells to Digit 9 in Column 4 Placing Digit 6 in R1C4 forces 2 different cells to Digit 1 in Column 4 Placing Digit 6 in R1C6 forces 2 different cells to Digit 7 in Row 8 Row 1 only has candidates for Digit 6 in Box 3 Placing Digit 2 in R1C6 forces 2 different cells to Digit 9 in Row 6 Row 1 only has candidates for Digit 2 in Box 3 R3C8 has Digit 1 as the only remaining candidate Box 3 found a Naked Pair with Digits {8,9} R1C9 has Digit 4 as the only remaining candidate Column 8 Digit 4 must be placed in R4C8 Column 9 only has candidates for Digit 9 in Box 6 Coloring value 7 found a connected pair Placing Digit 9 in R1C1 forces 2 different Digits in R7C3 R1C1 has Digit 8 as the only remaining candidate Placing Digit 9 in R1C6 forces 2 different cells to Digit 7 in Column 3 Row 1 Digit 9 must be placed in R1C3 R1C6 has Digit 5 as the only remaining candidate Row 1 Digit 3 must be placed in R1C4 Column 3 Digit 3 must be placed in R9C3 Box 1 Digit 3 must be placed in R2C1 R7C3 has Digit 7 as the only remaining candidate Column 4 Digit 5 must be placed in R6C4 Row 4 Digit 5 must be placed in R4C9 Column 3 Digit 1 must be placed in R5C3 Column 3 Digit 4 must be placed in R3C3 Box 7 Digit 4 must be placed in R8C2 Row 9 Digit 7 must be placed in R9C4 Row 3 Digit 7 must be placed in R3C2 Column 8 Digit 7 must be placed in R5C8 Box 9 Digit 7 must be placed in R8C7 R7C8 has Digit 2 as the only remaining candidate Column 1 Digit 7 must be placed in R4C1 Row 6 Digit 1 must be placed in R6C7 Row 6 Digit 6 must be placed in R6C2 Row 6 Digit 9 must be placed in R6C9 R5C1 has Digit 9 as the only remaining candidate R5C4 has Digit 6 as the only remaining candidate Column 4 Digit 4 must be placed in R2C4 Box 8 Digit 4 must be placed in R9C5 Column 8 Digit 6 must be placed in R1C8 Box 6 Digit 6 must be placed in R4C7 Column 7 Digit 2 must be placed in R1C7 R7C1 has Digit 6 as the only remaining candidate Column 2 Digit 9 must be placed in R7C2 R3C4 has Digit 9 as the only remaining candidate R8C4 has Digit 1 as the only remaining candidate Row 2 Digit 9 must be placed in R2C7 R2C5 has Digit 1 as the only remaining candidate R2C6 has Digit 8 as the only remaining candidate R3C7 has Digit 8 as the only remaining candidate Column 1 Digit 1 must be placed in R9C1 R8C1 has Digit 2 as the only remaining candidate Column 6 Digit 1 must be placed in R4C6 R9C6 has Digit 2 as the only remaining candidate R4C5 has Digit 9 as the only remaining candidate R3C6 has Digit 6 as the only remaining candidate Column 5 Digit 2 must be placed in R3C5 R8C5 has Digit 6 as the only remaining candidate R8C6 has Digit 9 as the only remaining candidate All Cells Solved Now I was a little surprised to read this: mugnyte wrote: (...) was what i typed in a found to take only my solver's trivial logic. (55 moves) With 8 tabling steps required in my solver, how do you define "trivial logic"? Can you show us a solver log, so that we can see what shortcuts you have found? Ruud. _________________ Meet me at sudocue.net Back to top Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year Oldest FirstNewest First         Sudoku Programmers Forum Index -> Solving sudoku All times are GMT Goto page Previous  1, 2, 3  Next Page 2 of 3   Jump to: Select a forum Sudoku----------------Solving sudokuSetting sudokuProgramming sudokuThe mathematics of sudokuExotic sudoku Library----------------PuzzlesSoftwareSudoku elsewhere Not sudoku----------------Random thoughtsForum feedback  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 vote in polls in this forum   Powered by phpBB © 2001, 2005 phpBB Group Igloo Theme Version 1.0 :: Created By: Andrew Charron