banquo's_bumble_puppy

2005-Dec-04, 07:49 PM

Anybody else play this game? Never heard of it before. Is it fun? Sorta looks like a cross-word puzzle with numbers instead of letters.

View Full Version : Sudoku?

banquo's_bumble_puppy

2005-Dec-04, 07:49 PM

Anybody else play this game? Never heard of it before. Is it fun? Sorta looks like a cross-word puzzle with numbers instead of letters.

TheBlackCat

2005-Dec-04, 08:14 PM

I like it, but don't do it that often. My mom is obsessed with it, she does them all the time (at least she was last time I saw her).

Fram

2005-Dec-04, 09:03 PM

They are fun for a while. I just don't get it why they also make them with letters though, as they are exactly identical to the numbers' ones. I do them for about half an hour a day, as a warming up to my working day...

Joff

2005-Dec-04, 10:00 PM

I do Sudoku puzzles occasionally for a bit of fun. The hardest grade of puzzle can be very challenging and (for me at least) involves long exploration down the consequences of alternative choices to establish which is correct. I do more of the slightly easier grade.

Here (http://www.dailysudoku.co.uk/sudoku/index.shtml) is a daily sudoku puzzle if you can't find one anywhere else. Here (http://www.daily-sudoku.com/daily_suduko.php) are some you can (attempt to) solve online.

Here (http://www.dailysudoku.co.uk/sudoku/index.shtml) is a daily sudoku puzzle if you can't find one anywhere else. Here (http://www.daily-sudoku.com/daily_suduko.php) are some you can (attempt to) solve online.

Gillianren

2005-Dec-05, 12:00 AM

I've been doing them for years, though they haven't been called that. They appear in those books of word puzzles and such that you can buy at the supermarket. I enjoy them, but I find crossword puzzles more interesting.

kashi

2005-Dec-05, 12:17 AM

Joff...you should never need to experiment with alternatives...ever.

Joff

2005-Dec-05, 12:24 AM

Joff...you should never need to experiment with alternatives...ever.Well, you'll have to share your secrets on the hard grade of puzzle then, because the grid often reaches a point where all remaining squares have multiple alternatives and every row column and square has multiple positions for all remaining numbers.

Parrothead

2005-Dec-05, 12:26 AM

I enjoy doing them. Several of the papers carry multiple puzzles daily. It took me awhile to get the hang of them at first.

Parrothead

2005-Dec-05, 12:27 AM

Well, you'll have to share your secrets on the hard grade of puzzle then, because the grid often reaches a point where all remaining squares have multiple alternatives and every row column and square has multiple positions for all remaining numbers.

Just remember each 3x3 grid should also have the numbers 1-9, along with each horizontal and vertical line.

Just remember each 3x3 grid should also have the numbers 1-9, along with each horizontal and vertical line.

Donnie B.

2005-Dec-05, 02:22 AM

Just remember each 3x3 grid should also have the numbers 1-9, along with each horizontal and vertical line.Joff is right. The hardest puzzles are "underspecified" -- you have to try alternative solutions (much like chess).

Joff

2005-Dec-05, 02:30 AM

Just remember each 3x3 grid should also have the numbers 1-9, along with each horizontal and vertical line.Come on, P'head, I do solve the puzzles. :naughty: :doh: anyway, kashi's the one with the secrets, not you.

Andromeda321

2005-Dec-05, 02:37 AM

I do them during classes that are boring.:shifty: I can now do them all within a half hour or so now except for the hardest ones on Fridays.

paulie jay

2005-Dec-05, 06:12 AM

They are a challenge, but I prefer a good crossword :)

crosscountry

2005-Dec-05, 07:04 AM

I do well with SuDoKus until 5 stars. With 4 you are only required 1 "guess" if you do it right. Thus, if you are wrong with that guess change all the others. trick is to pick whick square tells you the most information with just 1 guess.

5 stars takes 2 or more "guesses" I don't like to spend that much time although I have guessed correctly the first try.

I prefer them over crosswords because I know all the characters. Crosswords often have definitions that excape me.

5 stars takes 2 or more "guesses" I don't like to spend that much time although I have guessed correctly the first try.

I prefer them over crosswords because I know all the characters. Crosswords often have definitions that excape me.

Andromeda321

2005-Dec-05, 07:09 AM

crosscountry I agree with you. Regarding the star rating system, however, it's not completely true regarding guesses: I never do them on principle and have solved a 4 or 5 star one despite this. It involves usually leaving the puzzle alone for awhile then returning to it with a fresh mind to get the completely random hidden clue that is not at all obvious.

Parrothead

2005-Dec-05, 04:19 PM

I like crosswords too. In regards to sudoko puzzles, there will always be a piece of the answer available. It just takes time to see it at times. I pencil in possible numbers for given squares, if nothing pops out at me. Usually, I'll start looking at individual numbers that I'm missing from individual 3x3 grids. Process of elimination leaves fewer spaces that missing numbers will fill, eventually something pops up as a definate, from which point you move on again. :)

crosscountry

2005-Dec-05, 04:28 PM

you're right about coming back after a while. That helps me forget the few points I was stuck on for so long.

so far there was only 1 I could not get. it was a 5.

I do every square I know for sure. Then I mark the possibilities in the corners. Next, I take a red pen and write over the known squares. guessing time. BUT, pick the square that gives you the most information.

A poor guess may actually be correct, but if it tells you nothing but that square then it was worthless. Pick one that finishes a row/column/ or box. Make sure it tells you at least 2 other squares. AND has only 1 other option. if you do that, you cannot mess up.

as always, write the guesses lightly. if you were wrong you'll have to erase (thus the need for pen) since you chose a square with only one other option you'll have everything you need.

after a good guess (not necessarily correct the first try) all the others will fall into place. like I said, some guesses can be correct but un-usefull.

so far there was only 1 I could not get. it was a 5.

I do every square I know for sure. Then I mark the possibilities in the corners. Next, I take a red pen and write over the known squares. guessing time. BUT, pick the square that gives you the most information.

A poor guess may actually be correct, but if it tells you nothing but that square then it was worthless. Pick one that finishes a row/column/ or box. Make sure it tells you at least 2 other squares. AND has only 1 other option. if you do that, you cannot mess up.

as always, write the guesses lightly. if you were wrong you'll have to erase (thus the need for pen) since you chose a square with only one other option you'll have everything you need.

after a good guess (not necessarily correct the first try) all the others will fall into place. like I said, some guesses can be correct but un-usefull.

crosscountry

2005-Dec-05, 04:30 PM

eventually something pops up as a definate, from which point you move on again. :)

that hasn't been my case. it seems that the higher levels often are missing one clue necessary. read above about guessing.

I may not know every strategy however... But I still like to think I do:)

that hasn't been my case. it seems that the higher levels often are missing one clue necessary. read above about guessing.

I may not know every strategy however... But I still like to think I do:)

Fram

2005-Dec-05, 04:38 PM

If there is only one solution (as it should be), then you have per definition enough information. The question then is (a bit like chess) how many steps you can think ahead, how many combinations you can see without actually trying them.

I am not able to do this for the hardest sudoku's either without at least writing down all the still possible outcomes per square, and I can understand for the hardest sudokus that you have to guess (I don't think I have done the equivalent of your 5 star ones yet), but that is not a "fault" of the sudoku, not a case of missing info, but of limits to our brains.

I am not able to do this for the hardest sudoku's either without at least writing down all the still possible outcomes per square, and I can understand for the hardest sudokus that you have to guess (I don't think I have done the equivalent of your 5 star ones yet), but that is not a "fault" of the sudoku, not a case of missing info, but of limits to our brains.

ToSeek

2005-Dec-05, 04:40 PM

I've never had to guess with a Sudoku puzzle printed in a newspaper - there's always some sort of trick to it. The toughest example was something along the lines of the following:

- The middle (fifth) row of the puzzle needed a 9 somewhere, but the only place a nine could go was in one of the first three positions, i.e., in the middle left-hand block of nine.

- This means that the only place a 9 could go in that left-hand block was one of those three middle positions.

- This ruled out a 9 in the fourth row inside the left-hand block.

- Which meant that the only place in the fourth row a 9 could go was in a position in the right-hand block. Once I got that, everything else cascaded into place.

The biggest roadblocks in the toughest puzzles I've dealt with tend to be along the same lines: realizing there's some sort of conjunction between rows/columns and blocks that focuses the options elsewhere.

- The middle (fifth) row of the puzzle needed a 9 somewhere, but the only place a nine could go was in one of the first three positions, i.e., in the middle left-hand block of nine.

- This means that the only place a 9 could go in that left-hand block was one of those three middle positions.

- This ruled out a 9 in the fourth row inside the left-hand block.

- Which meant that the only place in the fourth row a 9 could go was in a position in the right-hand block. Once I got that, everything else cascaded into place.

The biggest roadblocks in the toughest puzzles I've dealt with tend to be along the same lines: realizing there's some sort of conjunction between rows/columns and blocks that focuses the options elsewhere.

crosscountry

2005-Dec-05, 05:23 PM

The biggest roadblocks in the toughest puzzles I've dealt with tend to be along the same lines: realizing there's some sort of conjunction between rows/columns and blocks that focuses the options elsewhere.

Exactly. You have 3 areas to fill: the rows, columns, and the blocks.

I often get to a part where many boxes are filled but there are still about 1/2 left. I put in every possible number for each block (as described by your post) and look. Often I can eliminate a few more leaving me with just one option. BUT, that doesn't always work.

there are lots of stragegies, and you have to employ them all to finish a hard Sudoku. Sometimes I think that is not enough.

either that, or my guessing technique is just faster :wink:

Exactly. You have 3 areas to fill: the rows, columns, and the blocks.

I often get to a part where many boxes are filled but there are still about 1/2 left. I put in every possible number for each block (as described by your post) and look. Often I can eliminate a few more leaving me with just one option. BUT, that doesn't always work.

there are lots of stragegies, and you have to employ them all to finish a hard Sudoku. Sometimes I think that is not enough.

either that, or my guessing technique is just faster :wink:

gwiz

2005-Dec-05, 05:32 PM

They are a challenge, but I prefer a good crossword :)

I'm with you there, the novelty wore off after I'd done a few and I went back to the crossword, which is somehow much more satisfying.

I'm with you there, the novelty wore off after I'd done a few and I went back to the crossword, which is somehow much more satisfying.

Donnie B.

2005-Dec-05, 06:32 PM

My most frustrating moment with a sudoku puzzle (a 4-star) went like this:

I finished the puzzle, and went over it to check my answer. Big mistake! I found that:

All 3x3 boxes were correct and complete.

All rows were correct and complete.

All but two columns were correct and complete. But those two were wrong: one had two 7s and no 3, the other had two 3s and no 7.

Naturally, it wasn't possible to simply swap one of the 7s for one of the 3s, because that would have broken either rows or 3-boxes.

Obviously I'd made a serious mistake early on in the process. There was no way to backtrack, other than erasing everything and starting over. Arrgh!

I finished the puzzle, and went over it to check my answer. Big mistake! I found that:

All 3x3 boxes were correct and complete.

All rows were correct and complete.

All but two columns were correct and complete. But those two were wrong: one had two 7s and no 3, the other had two 3s and no 7.

Naturally, it wasn't possible to simply swap one of the 7s for one of the 3s, because that would have broken either rows or 3-boxes.

Obviously I'd made a serious mistake early on in the process. There was no way to backtrack, other than erasing everything and starting over. Arrgh!

crosscountry

2005-Dec-05, 07:39 PM

then the 3x3 blocks couldn't have been right.

ToSeek

2005-Dec-05, 07:56 PM

My most frustrating moment with a sudoku puzzle (a 4-star) went like this:

I finished the puzzle, and went over it to check my answer. Big mistake! I found that:

All 3x3 boxes were correct and complete.

All rows were correct and complete.

All but two columns were correct and complete. But those two were wrong: one had two 7s and no 3, the other had two 3s and no 7.

Naturally, it wasn't possible to simply swap one of the 7s for one of the 3s, because that would have broken either rows or 3-boxes.

Obviously I'd made a serious mistake early on in the process. There was no way to backtrack, other than erasing everything and starting over. Arrgh!

That's the one real problem I have with Sudoku: if you make any mistake at all, you pretty much have to start over again from scratch because there's no way of telling where you went wrong.

I finished the puzzle, and went over it to check my answer. Big mistake! I found that:

All 3x3 boxes were correct and complete.

All rows were correct and complete.

All but two columns were correct and complete. But those two were wrong: one had two 7s and no 3, the other had two 3s and no 7.

Naturally, it wasn't possible to simply swap one of the 7s for one of the 3s, because that would have broken either rows or 3-boxes.

Obviously I'd made a serious mistake early on in the process. There was no way to backtrack, other than erasing everything and starting over. Arrgh!

That's the one real problem I have with Sudoku: if you make any mistake at all, you pretty much have to start over again from scratch because there's no way of telling where you went wrong.

HenrikOlsen

2005-Dec-05, 09:38 PM

That's why I normally solve them with a pen rather than a pencil, it makes you focus a lot more to prevent mistakes, which helps with spotting connections.

ToSeek

2005-Dec-05, 11:01 PM

That's why I normally solve them with a pen rather than a pencil, it makes you focus a lot more to prevent mistakes, which helps with spotting connections.

I make intermediate notes to myself in pencil, then put the final answers down with a pen.

I make intermediate notes to myself in pencil, then put the final answers down with a pen.

The Supreme Canuck

2005-Dec-06, 12:48 AM

I use the dot system for temporary notations. A dot in the top left corner is a 1, centre-top is a 2, top-right is a 3, left-centre is a 4, centre is a 5, right-centre is a 6, and so on.

Andromeda321

2005-Dec-06, 12:59 AM

TSC, I like that! I'll have to give it a try as it's hard to write much info in those boxes; thanks for the tip! :D

The Supreme Canuck

2005-Dec-06, 01:03 AM

Hey, no problem. I thought it was pretty neat, too, when I read about it.

Donnie B.

2005-Dec-06, 06:12 AM

then the 3x3 blocks couldn't have been right.Actually, they could be and were.

The transposed values were both in the same 3x3, and canceled each other out (if you see what I mean). It was not unlike the situation in Rubik's Cube when all faces are correct except that one block on each of two faces are the wrong color (e.g. one red block on a green face and vice versa). You think you're close to a solution, but really you're not close at all.

I never did get very good at Rubik's Cube... :mad:

The transposed values were both in the same 3x3, and canceled each other out (if you see what I mean). It was not unlike the situation in Rubik's Cube when all faces are correct except that one block on each of two faces are the wrong color (e.g. one red block on a green face and vice versa). You think you're close to a solution, but really you're not close at all.

I never did get very good at Rubik's Cube... :mad:

crosscountry

2005-Dec-06, 09:02 AM

I've done something similar but it didn't mess up the entire puzzle.

kashi

2005-Dec-06, 09:54 AM

Joff,

Find a diffiicult one that you believe requires experimentation with alternate solutions and I'll have a crack at it.

There are some supposedly very difficult ones here: http://www.websudoku.com/?level=4

Find a diffiicult one that you believe requires experimentation with alternate solutions and I'll have a crack at it.

There are some supposedly very difficult ones here: http://www.websudoku.com/?level=4

crosscountry

2005-Dec-07, 04:00 AM

thanks for the link

I only have one test tomorrow :doh:

I only have one test tomorrow :doh:

kashi

2005-Dec-07, 10:21 AM

Come on Joff! Put your money where your mouth is!

Fram

2005-Dec-07, 10:43 AM

I got stuck on the evil one (without guessing, and without pencil or whatever), so I tried a hard one, and solved it straight in 6 minutes 50 seconds. Restored my selfrespect a little bit :-)

Joff

2005-Dec-07, 03:48 PM

Come on Joff! Put your money where your mouth is!

I tried a few on that site but I solved them without the alternatives technique... :mad: ...wait, I guess I should be happy? ;) I'll let you know when I find one.

I tried a few on that site but I solved them without the alternatives technique... :mad: ...wait, I guess I should be happy? ;) I'll let you know when I find one.

kashi

2005-Dec-08, 09:51 AM

Hehe. No worries.

Fram

2005-Dec-08, 11:11 AM

I solved evil puzle 6,486,707,143 from kashi's link in 15 minutes and 40 seconds, with taking 1 guess (out of two choices to fill a cube). I had no idea how to progress at that point otherwise, I don't seem to be able to think that far ahead... Probably lost a few minutes pondering how to proceed without guessing, as the puzzle was quite easy before and after the guess.

Fram

2005-Dec-08, 11:26 AM

And puzzle 7,602,333,059 in 13 minutes 57 without guessing. I'm getting smarter! (or the puzzles are of uneven difficulty of course).

kylenano

2005-Dec-08, 12:14 PM

Although I often can't do the harder 9x9 sodoku, I prefer the 16x16 The Independent publishes. They're numbered from 0-F (hexadecimal) and I find they help with insomnia. Takes me ages to finish them though.

I use a 4B pencil and a soft white eraser, never a pen!

I use a 4B pencil and a soft white eraser, never a pen!

crosscountry

2005-Dec-08, 03:39 PM

I solved evil puzle 6,486,707,143 from kashi's link in 15 minutes and 40 seconds, with taking 1 guess (out of two choices to fill a cube). I had no idea how to progress at that point otherwise, I don't seem to be able to think that far ahead... Probably lost a few minutes pondering how to proceed without guessing, as the puzzle was quite easy before and after the guess.

yea, I get to a point where I feel the need to guess and make the guess with the most information attached.

yea, I get to a point where I feel the need to guess and make the guess with the most information attached.

Joff

2006-Jan-01, 05:37 PM

Joff,

Find a diffiicult one that you believe requires experimentation with alternate solutions and I'll have a crack at it.

The original grid:

. . . . 7 1 6 . 9

9 4 6 3 . 2 . . .

. 2 . . . . . 4 .

. . . . . 9 2 . 4

. 9 . . . . . 8 .

1 . 4 5 . . . . .

. 1 . . . . . 6 .

. . . 1 . 7 5 3 8

8 . 7 9 6 . . . .

I filled in twenty-one more entries before I reached the point where I believe experimentation is the only way forward.

Find a diffiicult one that you believe requires experimentation with alternate solutions and I'll have a crack at it.

The original grid:

. . . . 7 1 6 . 9

9 4 6 3 . 2 . . .

. 2 . . . . . 4 .

. . . . . 9 2 . 4

. 9 . . . . . 8 .

1 . 4 5 . . . . .

. 1 . . . . . 6 .

. . . 1 . 7 5 3 8

8 . 7 9 6 . . . .

I filled in twenty-one more entries before I reached the point where I believe experimentation is the only way forward.

mickal555

2006-Jan-01, 06:34 PM

Anybody else play this game? Never heard of it before. Is it fun? Sorta looks like a cross-word puzzle with numbers instead of letters.

I like it, it's kinda fun...

Gets boring after a while though....

I like it, it's kinda fun...

Gets boring after a while though....

turbo-1

2006-Jan-01, 08:01 PM

Try evil puzzle 4,945,418,525

http://www.websudoku.com/

I can usually zip through them, but that bad boy took me over an hour.

http://www.websudoku.com/

I can usually zip through them, but that bad boy took me over an hour.

mickal555

2006-Jan-01, 08:47 PM

Try evil puzzle 4,945,418,525

http://www.websudoku.com/

I can usually zip through them, but that bad boy took me over an hour.

Congratulations! You solved the Sudoku in 12 minutes, 2 seconds!

Evil puzzles solved:1 Your average time:12:02 Your fastest time:12:02 Puzzles solved on this computer since 1 Jan 2006.

45978216317395682462843175938567924196132457874251 8396236195487597843612814267935 Evil Puzzle 4,945,418,525

Maybe you had a mindblock

http://www.websudoku.com/

I can usually zip through them, but that bad boy took me over an hour.

Congratulations! You solved the Sudoku in 12 minutes, 2 seconds!

Evil puzzles solved:1 Your average time:12:02 Your fastest time:12:02 Puzzles solved on this computer since 1 Jan 2006.

45978216317395682462843175938567924196132457874251 8396236195487597843612814267935 Evil Puzzle 4,945,418,525

Maybe you had a mindblock

suntrack2

2006-Jan-02, 05:14 PM

sudoku is a japnese word?

sudoku is a puzzle word game?

sudoku is a number game to arrange it in sequence?

or what?

sudoku is a puzzle word game?

sudoku is a number game to arrange it in sequence?

or what?

snarkophilus

2006-Jan-02, 05:58 PM

Well, you'll have to share your secrets on the hard grade of puzzle then, because the grid often reaches a point where all remaining squares have multiple alternatives and every row column and square has multiple positions for all remaining numbers.

That's when they really get fun! The way I solve them is to build what I call "exclusion matrices." Basically, you get a bunch of blanks that are all dependent upon one another and put them in a group. Put the logical dependencies in a matrix. Do this for all the blanks you have left. Then you study how those groups interact and eliminate possibilities.

The simplest one is where you have two blanks left in a square (or row or column). Suppose you're missing 4 and 7. Then you know that exactly one square is a 4, and exactly one is a 7. Now, you might have another square elsewhere in the puzzle that's also missing a 4 and a 7. Those two squares are related by a pair of linear equations (really formal logical equations, but I treat them as linear algebra for notational convenience). Put those equations in a matrix. Once you do this for all of those groups, you can usually just look and see that some blank must contain some particular number (otherwise there's a logical contradiction), but in the worst case you can just solve the equations.

I've seen a couple of puzzles where I had to do this twice, and once where I had to do it three times. There were groups of groups, and to solve one group of groups, I first had to solve another to get enough information.

It's usually faster to just guess, though. The key to guessing is intelligently picking which one to guess -- usually you should take the number that has the most direct consequences, so if it fails it will fail right away. For most puzzles, a single failed guess in the right place will give enough information to solve the rest of the puzzle.

So much fun!

That's when they really get fun! The way I solve them is to build what I call "exclusion matrices." Basically, you get a bunch of blanks that are all dependent upon one another and put them in a group. Put the logical dependencies in a matrix. Do this for all the blanks you have left. Then you study how those groups interact and eliminate possibilities.

The simplest one is where you have two blanks left in a square (or row or column). Suppose you're missing 4 and 7. Then you know that exactly one square is a 4, and exactly one is a 7. Now, you might have another square elsewhere in the puzzle that's also missing a 4 and a 7. Those two squares are related by a pair of linear equations (really formal logical equations, but I treat them as linear algebra for notational convenience). Put those equations in a matrix. Once you do this for all of those groups, you can usually just look and see that some blank must contain some particular number (otherwise there's a logical contradiction), but in the worst case you can just solve the equations.

I've seen a couple of puzzles where I had to do this twice, and once where I had to do it three times. There were groups of groups, and to solve one group of groups, I first had to solve another to get enough information.

It's usually faster to just guess, though. The key to guessing is intelligently picking which one to guess -- usually you should take the number that has the most direct consequences, so if it fails it will fail right away. For most puzzles, a single failed guess in the right place will give enough information to solve the rest of the puzzle.

So much fun!

snarkophilus

2006-Jan-02, 06:06 PM

I use the dot system for temporary notations. A dot in the top left corner is a 1, centre-top is a 2, top-right is a 3, left-centre is a 4, centre is a 5, right-centre is a 6, and so on.

I do something like this for harder puzzles, but I hate putting a dot in the middle of the box, so I go clockwise around, starting in the top left. 8 and 9 are sandwiched on the left side. I use open circles to signify that a number is possible, and fill the circle in when the number is eliminated from consideration.

I also use a system of triangles. If there are two blanks in the same 3x3 box, one of which must contain a number, both blanks get an upward-pointing triangle in that position. If there are two blanks in different boxed with the same criteria, they get a down triangle. A square is used in lieu of both upward and downward triangles.

I've been trying to do puzzles without any notation lately, just for more of a challenge. Eventually, I'm going to try to learn to solve them entirely in my head before writing anything, and totally impress people when I seem to sit down, glance at the page, and solve the puzzle instantly! :shhh:

I do something like this for harder puzzles, but I hate putting a dot in the middle of the box, so I go clockwise around, starting in the top left. 8 and 9 are sandwiched on the left side. I use open circles to signify that a number is possible, and fill the circle in when the number is eliminated from consideration.

I also use a system of triangles. If there are two blanks in the same 3x3 box, one of which must contain a number, both blanks get an upward-pointing triangle in that position. If there are two blanks in different boxed with the same criteria, they get a down triangle. A square is used in lieu of both upward and downward triangles.

I've been trying to do puzzles without any notation lately, just for more of a challenge. Eventually, I'm going to try to learn to solve them entirely in my head before writing anything, and totally impress people when I seem to sit down, glance at the page, and solve the puzzle instantly! :shhh:

Gillianren

2006-Jan-03, 02:31 AM

sudoku is a japnese word?

sudoku is a puzzle word game?

sudoku is a number game to arrange it in sequence?

or what?

The point of Sudoku (yes, the word is Japanese) and Sudoku-like games is to arrange the numbers (usually) 1-9 in boxes. Each Sudoku grid is (usually) nine numbers across and nine numbers down, with heavy lines dividing it into nine boxes of nine squares. The goal is to arrange it so that each horizontal, each vertical, and each smaller grid contains the digits 1-9. I've seen versions that require the digits 1-9 on the diagonal as well, and of course there are the larger versions in hexadecimal--0-9 plus A-F, generally, though I suppose 1-9 plus A-G is also possible.

The game, as I've said, is not new; I've been doing them for years in those books of puzzles you can buy on the magazine rack.

sudoku is a puzzle word game?

sudoku is a number game to arrange it in sequence?

or what?

The point of Sudoku (yes, the word is Japanese) and Sudoku-like games is to arrange the numbers (usually) 1-9 in boxes. Each Sudoku grid is (usually) nine numbers across and nine numbers down, with heavy lines dividing it into nine boxes of nine squares. The goal is to arrange it so that each horizontal, each vertical, and each smaller grid contains the digits 1-9. I've seen versions that require the digits 1-9 on the diagonal as well, and of course there are the larger versions in hexadecimal--0-9 plus A-F, generally, though I suppose 1-9 plus A-G is also possible.

The game, as I've said, is not new; I've been doing them for years in those books of puzzles you can buy on the magazine rack.

ToSeek

2006-Jan-03, 03:37 AM

I've been trying to do puzzles without any notation lately, just for more of a challenge. Eventually, I'm going to try to learn to solve them entirely in my head before writing anything, and totally impress people when I seem to sit down, glance at the page, and solve the puzzle instantly! :shhh:

The Washington Post categorizes the puzzles into levels: very easy, easy, medium, and hard. I try to do all but the hard ones without any notes. (I can't imagine picking up some of the necessary patterns in the hard ones just in my head.)

I have a couple of different notations:

- If I'm noting the numbers that can go in a specific box, I write them at the bottom.

- If I'm noting that a number can only go in a few boxes, I put it in different places depending on the underlying constraint:

- If the few boxes are in a 3x3 block, then the number goes in the upper middle.

- If the few boxes are in a row, then the number goes at the top.

- If the few boxes are in a column, then the number goes at the side.

I've also had some oddball situations, such as realizing that the number in column 1, row 3, has to be the same number as the one in column 3, row 7. In that case, I just lightly circled each box and drew a dotted line between them.

The Washington Post categorizes the puzzles into levels: very easy, easy, medium, and hard. I try to do all but the hard ones without any notes. (I can't imagine picking up some of the necessary patterns in the hard ones just in my head.)

I have a couple of different notations:

- If I'm noting the numbers that can go in a specific box, I write them at the bottom.

- If I'm noting that a number can only go in a few boxes, I put it in different places depending on the underlying constraint:

- If the few boxes are in a 3x3 block, then the number goes in the upper middle.

- If the few boxes are in a row, then the number goes at the top.

- If the few boxes are in a column, then the number goes at the side.

I've also had some oddball situations, such as realizing that the number in column 1, row 3, has to be the same number as the one in column 3, row 7. In that case, I just lightly circled each box and drew a dotted line between them.

ToSeek

2006-Jan-03, 03:40 AM

I should add that the Post had a special Sudoku puzzle in their New Year's issue. Imagine that in addition to the usual 9x9 Sudoku puzzle that each corner block of a central 9x9 is also the opposite corner block of a peripheral 9x9, so that you have 5 of the usual Sudoku puzzles all jammed together and overlapping. I haven't worked it yet, but it looks interesting. The implication in the directions is that you can't solve just one of the 9x9's, that you have to work on all of them.

SeanF

2006-Jan-03, 03:17 PM

It was not unlike the situation in Rubik's Cube when all faces are correct except that one block on each of two faces are the wrong color (e.g. one red block on a green face and vice versa). You think you're close to a solution, but really you're not close at all.

Hey, I missed this before!

Donnie, if you've ever had a Rubik's Cube that has the situation you described, two and only two wrong squares, somebody's been funnin' with you. It's actually impossible to create that situation without taking the cube apart (or peeling the colored stickers off), and it's just as impossible to solve it without doing the same. :)

Hey, I missed this before!

Donnie, if you've ever had a Rubik's Cube that has the situation you described, two and only two wrong squares, somebody's been funnin' with you. It's actually impossible to create that situation without taking the cube apart (or peeling the colored stickers off), and it's just as impossible to solve it without doing the same. :)

farmerjumperdon

2006-Jan-03, 03:32 PM

My daughter got a book of these for Christmas. She does one every 3 or 4 days. She sticks to the less difficult ones, but still pretty impressive.

I did a couple and they were pretty fun for a short bit, but got boring quickly. I find reading almost anything to be more entertaining.

I did a couple and they were pretty fun for a short bit, but got boring quickly. I find reading almost anything to be more entertaining.

suntrack2

2006-Jan-03, 05:03 PM

thanks gillian for the information, it is related with maths only and using for the brain power to test ?

Joff

2006-Jan-03, 06:36 PM

thanks gillian for the information, it is related with maths only and using for the brain power to test ?It's nothing to do with maths. You could have a sudoku with letters just as well. It's really a logic puzzle, and some of the puzzles certainly test your brain power. For those who zip through the regular version, there's always megasudoku (25x25) or killer sudoku (starts with area sums rather than individual numbers) to keep testing the brain cells!

Gillianren

2006-Jan-03, 07:42 PM

After all, if it were purely math, I wouldn't do them, not being a math person. Almost all the math problems in my puzzle books get left blank.

Donnie B.

2006-Jan-03, 09:32 PM

Donnie, if you've ever had a Rubik's Cube that has the situation you described, two and only two wrong squares, somebody's been funnin' with you. It's actually impossible to create that situation without taking the cube apart (or peeling the colored stickers off), and it's just as impossible to solve it without doing the same. :)Ah, you're right. I'd heard about people doing that to drive other people crazy.

For the record, I never owned a Rubik's cube, though I did play with one for a bit. It never really caught my interest.

In any case, it was just an illustration, and as such I think it's sorta valid. It's possible to get a Sudoku solved almost right... but that could still be far from the correct solution.

For the record, I never owned a Rubik's cube, though I did play with one for a bit. It never really caught my interest.

In any case, it was just an illustration, and as such I think it's sorta valid. It's possible to get a Sudoku solved almost right... but that could still be far from the correct solution.

crosscountry

2006-Jan-04, 03:54 PM

I've also had some oddball situations, such as realizing that the number in column 1, row 3, has to be the same number as the one in column 3, row 7. In that case, I just lightly circled each box and drew a dotted line between them.

that is quite an idea. I haven't had the need for it yet, that I can recall.

I also like your idea of using different sides of the box for your notes. I had been just putting the numbers anywhere.

that is quite an idea. I haven't had the need for it yet, that I can recall.

I also like your idea of using different sides of the box for your notes. I had been just putting the numbers anywhere.

crosscountry

2006-Jan-04, 03:56 PM

thanks gillian for the information, it is related with maths only and using for the brain power to test ?

as the others said, sudoku really has nothing to do with numbers. I liken it to puzzles that they make us take on standardized exams in the US.

first they give some scenario: Jill is taller than Robert, and Robert is shorter than Tim. Then they give several others clues about other characters and their height or something else and ask "Who is taller Jill or Tim?"

well, it's just about finding which number goes where and you use the clues given to solve the puzzle.

as the others said, sudoku really has nothing to do with numbers. I liken it to puzzles that they make us take on standardized exams in the US.

first they give some scenario: Jill is taller than Robert, and Robert is shorter than Tim. Then they give several others clues about other characters and their height or something else and ask "Who is taller Jill or Tim?"

well, it's just about finding which number goes where and you use the clues given to solve the puzzle.

ToSeek

2006-Jan-04, 04:05 PM

that is quite an idea. I haven't had the need for it yet, that I can recall.

I've only seen it the once, and I don't remember the exact situation that created it, just that it was obvious to me that two not-particularly-related open boxes had to have the same number.

I've only seen it the once, and I don't remember the exact situation that created it, just that it was obvious to me that two not-particularly-related open boxes had to have the same number.

Joff

2006-Jan-05, 01:02 AM

I rarely resort to annotating boxes but I find it very useful to keep tabs on the numbers still required in rows and columns with only a few entries left to get. I note these at bottom and right. Generally I track all with 2 or 3 blanks; 4 if things are grinding to a halt.

SeanF

2006-Jan-05, 08:49 PM

The original grid:

. . . . 7 1 6 . 9

9 4 6 3 . 2 . . .

. 2 . . . . . 4 .

. . . . . 9 2 . 4

. 9 . . . . . 8 .

1 . 4 5 . . . . .

. 1 . . . . . 6 .

. . . 1 . 7 5 3 8

8 . 7 9 6 . . . .

I filled in twenty-one more entries before I reached the point where I believe experimentation is the only way forward.

Joff, this puzzle is driving me crazy! I was able to get 22 additional numbers filled in, but I can't find the logic to let me determine any more... :evil:

. . . . 7 1 6 . 9

9 4 6 3 . 2 . . .

. 2 . . . . . 4 .

. . . . . 9 2 . 4

. 9 . . . . . 8 .

1 . 4 5 . . . . .

. 1 . . . . . 6 .

. . . 1 . 7 5 3 8

8 . 7 9 6 . . . .

I filled in twenty-one more entries before I reached the point where I believe experimentation is the only way forward.

Joff, this puzzle is driving me crazy! I was able to get 22 additional numbers filled in, but I can't find the logic to let me determine any more... :evil:

Joff

2006-Jan-05, 09:22 PM

Yes, well, that was my point really (it may have been 22 for me also, I only counted them up quickly). The next step involves taking one of the boxes which has a choice of two numbers and picking one of them, then carrying that through until either the grid is completed in accordance with the rules, or a contradiction occurs. If the latter then you know your assumption was wrong. You erase everything since that point and fill in the other alternative as definite and proceed from there.

More thoroughly perhaps, I sometimes use different corners of the boxes for different assumptions, which allows me to test them all rather than assume that one that works is the unique answer. That can get visually very confusing though.

If you need the answer I could PM it.

More thoroughly perhaps, I sometimes use different corners of the boxes for different assumptions, which allows me to test them all rather than assume that one that works is the unique answer. That can get visually very confusing though.

If you need the answer I could PM it.

SeanF

2006-Jan-05, 09:36 PM

If you need the answer I could PM it.

I'm confident I could get the answer through trial-and-error.

I don't think it's "right," though, that the puzzle would be set up where trial-and-error is the only way to solve it. There's got to be some piece of logic that I'm missing... :think:

I'm confident I could get the answer through trial-and-error.

I don't think it's "right," though, that the puzzle would be set up where trial-and-error is the only way to solve it. There's got to be some piece of logic that I'm missing... :think:

HenrikOlsen

2006-Jan-05, 10:22 PM

By definition, if one of the alternatives lead to a contradiction later, then it can be eliminated logically.

It's just that you have to consider too many things at once to see it.

The problem is if both guesses lead to solutions

It's just that you have to consider too many things at once to see it.

The problem is if both guesses lead to solutions

SeanF

2006-Jan-05, 10:47 PM

By definition, if one of the alternatives lead to a contradiction later, then it can be eliminated logically.

It's just that you have to consider too many things at once to see it.

Yeah, I suppose when you think about it, it's all trial-and-error, it's just that usually the "error" is immediately obvious from the "trial." In this case, the logic to solve it ends up involving five boxes:

F6 could, apparently, take an 8. However, putting an 8 in F6 would require you to put a 7 in B6 and an 8 in D3. The 7 in B6 would then require a 3 in G6, while the 8 in D3 would require a 3 in D6. Since D6 and G6 are in the same column, they can't both have a 3. Therefore, that eliminates the possibility of an 8 going in F6.

So to solve this puzzle, you've got to "see" two layers deep. Maybe one of those professional chess players who can see two or three moves down into a game could do it. :evil:

It's just that you have to consider too many things at once to see it.

Yeah, I suppose when you think about it, it's all trial-and-error, it's just that usually the "error" is immediately obvious from the "trial." In this case, the logic to solve it ends up involving five boxes:

F6 could, apparently, take an 8. However, putting an 8 in F6 would require you to put a 7 in B6 and an 8 in D3. The 7 in B6 would then require a 3 in G6, while the 8 in D3 would require a 3 in D6. Since D6 and G6 are in the same column, they can't both have a 3. Therefore, that eliminates the possibility of an 8 going in F6.

So to solve this puzzle, you've got to "see" two layers deep. Maybe one of those professional chess players who can see two or three moves down into a game could do it. :evil:

Joff

2006-Jan-05, 11:14 PM

Provided there is only one solution, I would argue that the Sudoku is valid. How you get to that one solution is up to the solver. Imagine the following process:

1. Fill every unspecfied box randomly with a digit in 1-9

2. Check if the resulting grid is valid

3. If not, erase all boxes filled at (1) and try again.

In theory this will lead to the solution - it'll just take a ludicrously long time (reminds me of anti-optimum sorting methods). The better your "tools" are, the quicker you'll solve it; but it still may require a variety of methods.

1. Fill every unspecfied box randomly with a digit in 1-9

2. Check if the resulting grid is valid

3. If not, erase all boxes filled at (1) and try again.

In theory this will lead to the solution - it'll just take a ludicrously long time (reminds me of anti-optimum sorting methods). The better your "tools" are, the quicker you'll solve it; but it still may require a variety of methods.

Joff

2006-Jan-05, 11:26 PM

Here's another one with an experimentation (or "extended look-ahead") challenge - significantly more than the previous puzzle when I tried it (although I do sometimes overlook simple stuff)

. . . . . . . . .

. . . . . 6 5 . .

. 3 . 7 . 1 . 9 2

9 2 . . 1 . . 7 6

. . 8 5 . 7 3 . .

3 7 . . 9 . . 2 5

5 1 . 9 . 2 . 3 .

. . 2 4 . . . . .

. . . . . . . . .

let me know how you get on... ;)

. . . . . . . . .

. . . . . 6 5 . .

. 3 . 7 . 1 . 9 2

9 2 . . 1 . . 7 6

. . 8 5 . 7 3 . .

3 7 . . 9 . . 2 5

5 1 . 9 . 2 . 3 .

. . 2 4 . . . . .

. . . . . . . . .

let me know how you get on... ;)

SeanF

2006-Jan-06, 01:49 AM

Here's another one with an experimentation (or "extended look-ahead") challenge - significantly more than the previous puzzle when I tried it (although I do sometimes overlook simple stuff)

. . . . . . . . .

. . . . . 6 5 . .

. 3 . 7 . 1 . 9 2

9 2 . . 1 . . 7 6

. . 8 5 . 7 3 . .

3 7 . . 9 . . 2 5

5 1 . 9 . 2 . 3 .

. . 2 4 . . . . .

. . . . . . . . .

let me know how you get on... ;)

You must've missed something. I was able to solve this one without doing any guessing...

Which now has me thinking again that there's something I'm missing in that other one! :wall:

. . . . . . . . .

. . . . . 6 5 . .

. 3 . 7 . 1 . 9 2

9 2 . . 1 . . 7 6

. . 8 5 . 7 3 . .

3 7 . . 9 . . 2 5

5 1 . 9 . 2 . 3 .

. . 2 4 . . . . .

. . . . . . . . .

let me know how you get on... ;)

You must've missed something. I was able to solve this one without doing any guessing...

Which now has me thinking again that there's something I'm missing in that other one! :wall:

ToSeek

2006-Jan-06, 02:08 AM

Joff, this puzzle is driving me crazy! I was able to get 22 additional numbers filled in, but I can't find the logic to let me determine any more... :evil:

The computer helper program I use resorts to a forcing chain (i.e., sophisticated guessing) at this point:

Puzzle: Joff's puzzle #1 from BAUT

+-------+-------+-------+

| . . . | 4 7 1 | 6 2 9 |

| 9 4 6 | 3 . 2 | . . . |

| 7 2 1 | . 9 . | . 4 . |

+-------+-------+-------+

| . . . | . 1 9 | 2 . 4 |

| . 9 2 | . 3 4 | . 8 . |

| 1 . 4 | 5 2 . | . 9 . |

+-------+-------+-------+

| 4 1 . | 2 . . | 9 6 7 |

| 2 6 9 | 1 4 7 | 5 3 8 |

| 8 . 7 | 9 6 . | 4 1 2 |

+-------+-------+-------+

So I don't think it's just you.

The computer helper program I use resorts to a forcing chain (i.e., sophisticated guessing) at this point:

Puzzle: Joff's puzzle #1 from BAUT

+-------+-------+-------+

| . . . | 4 7 1 | 6 2 9 |

| 9 4 6 | 3 . 2 | . . . |

| 7 2 1 | . 9 . | . 4 . |

+-------+-------+-------+

| . . . | . 1 9 | 2 . 4 |

| . 9 2 | . 3 4 | . 8 . |

| 1 . 4 | 5 2 . | . 9 . |

+-------+-------+-------+

| 4 1 . | 2 . . | 9 6 7 |

| 2 6 9 | 1 4 7 | 5 3 8 |

| 8 . 7 | 9 6 . | 4 1 2 |

+-------+-------+-------+

So I don't think it's just you.

ToSeek

2006-Jan-06, 02:21 AM

Here's another one with an experimentation (or "extended look-ahead") challenge - significantly more than the previous puzzle when I tried it (although I do sometimes overlook simple stuff)

. . . . . . . . .

. . . . . 6 5 . .

. 3 . 7 . 1 . 9 2

9 2 . . 1 . . 7 6

. . 8 5 . 7 3 . .

3 7 . . 9 . . 2 5

5 1 . 9 . 2 . 3 .

. . 2 4 . . . . .

. . . . . . . . .

let me know how you get on... ;)

There's one tough step with that one, but it doesn't require guessing.

. . . . . . . . .

. . . . . 6 5 . .

. 3 . 7 . 1 . 9 2

9 2 . . 1 . . 7 6

. . 8 5 . 7 3 . .

3 7 . . 9 . . 2 5

5 1 . 9 . 2 . 3 .

. . 2 4 . . . . .

. . . . . . . . .

let me know how you get on... ;)

There's one tough step with that one, but it doesn't require guessing.

ToSeek

2006-Jan-06, 02:25 AM

My computer program had this in its list of puzzles. It's marked as "Toughest known puzzle." Good luck!

Puzzle: Toughest Known Puzzle

+-------+-------+-------+

| . . . | . 7 . | 9 4 . |

| . . . | . 9 . | . . 5 |

| 3 . . | . . 5 | . 7 . |

+-------+-------+-------+

| . . 7 | 4 . . | 1 . . |

| 4 6 3 | . . . | . . . |

| . . . | . . 7 | . 8 . |

+-------+-------+-------+

| 8 . . | . . . | . . . |

| 7 . . | . . . | . 2 8 |

| . 5 . | 2 6 . | . . . |

+-------+-------+-------+

Puzzle: Toughest Known Puzzle

+-------+-------+-------+

| . . . | . 7 . | 9 4 . |

| . . . | . 9 . | . . 5 |

| 3 . . | . . 5 | . 7 . |

+-------+-------+-------+

| . . 7 | 4 . . | 1 . . |

| 4 6 3 | . . . | . . . |

| . . . | . . 7 | . 8 . |

+-------+-------+-------+

| 8 . . | . . . | . . . |

| 7 . . | . . . | . 2 8 |

| . 5 . | 2 6 . | . . . |

+-------+-------+-------+

Dragon Star

2006-Jan-06, 02:30 AM

My computer program had this in its list of puzzles. It's marked as "Toughest known puzzle." Good luck!

E=MC^2!

I'd crap if that was right....:p

Lost of places say they have the "toughest known puzzle", I might dig some up later.

E=MC^2!

I'd crap if that was right....:p

Lost of places say they have the "toughest known puzzle", I might dig some up later.

SeanF

2006-Jan-06, 02:45 PM

The computer helper program I use resorts to a forcing chain (i.e., sophisticated guessing) at this point:

Puzzle: Joff's puzzle #1 from BAUT

+-------+-------+-------+

| . . . | 4 7 1 | 6 2 9 |

| 9 4 6 | 3 . 2 | . . . |

| 7 2 1 | . 9 . | . 4 . |

+-------+-------+-------+

| . . . | . 1 9 | 2 . 4 |

| . 9 2 | . 3 4 | . 8 . |

| 1 . 4 | 5 2 . | . 9 . |

+-------+-------+-------+

| 4 1 . | 2 . . | 9 6 7 |

| 2 6 9 | 1 4 7 | 5 3 8 |

| 8 . 7 | 9 6 . | 4 1 2 |

+-------+-------+-------+

So I don't think it's just you.

Yeah, that's exactly where I end up and look to guessing.

But that just means your program is missing the logic, too. ;)

Puzzle: Joff's puzzle #1 from BAUT

+-------+-------+-------+

| . . . | 4 7 1 | 6 2 9 |

| 9 4 6 | 3 . 2 | . . . |

| 7 2 1 | . 9 . | . 4 . |

+-------+-------+-------+

| . . . | . 1 9 | 2 . 4 |

| . 9 2 | . 3 4 | . 8 . |

| 1 . 4 | 5 2 . | . 9 . |

+-------+-------+-------+

| 4 1 . | 2 . . | 9 6 7 |

| 2 6 9 | 1 4 7 | 5 3 8 |

| 8 . 7 | 9 6 . | 4 1 2 |

+-------+-------+-------+

So I don't think it's just you.

Yeah, that's exactly where I end up and look to guessing.

But that just means your program is missing the logic, too. ;)

ToSeek

2006-Jan-06, 02:59 PM

But that just means your program is missing the logic, too. ;)

It's got a whole list of algorithms that it runs through in order, and the "forcing chain" is after all the "non-guessing" ones. I don't think there's anything not on the list that I've come up with yet.

It's got a whole list of algorithms that it runs through in order, and the "forcing chain" is after all the "non-guessing" ones. I don't think there's anything not on the list that I've come up with yet.

Joff

2006-Jan-06, 10:07 PM

I guess this is the "tough step" point for the one I think is hard (& you guys don't)...

. 5 . . . 9 . . .

. . 9 . . 6 5 . .

. 3 . 7 5 1 . 9 2

9 2 5 . 1 . . 7 6

. . 8 5 2 7 3 . 9

3 7 . 6 9 . . 2 5

5 1 . 9 . 2 . 3 .

. . 2 4 . . 9 . .

. 9 3 1 . . 2 . .

soo if you (ToSeek or SeanF) can tell me what digit you enter next, and why if possible, maybe that will improve my ability at sudoku...

. 5 . . . 9 . . .

. . 9 . . 6 5 . .

. 3 . 7 5 1 . 9 2

9 2 5 . 1 . . 7 6

. . 8 5 2 7 3 . 9

3 7 . 6 9 . . 2 5

5 1 . 9 . 2 . 3 .

. . 2 4 . . 9 . .

. 9 3 1 . . 2 . .

soo if you (ToSeek or SeanF) can tell me what digit you enter next, and why if possible, maybe that will improve my ability at sudoku...

SeanF

2006-Jan-07, 04:32 AM

soo if you (ToSeek or SeanF) can tell me what digit you enter next, and why if possible, maybe that will improve my ability at sudoku...

I sent you a PM, Joff.

Ironically enough, earlier in this thread ToSeek mentioned:

I've only seen it the once, and I don't remember the exact situation that created it, just that it was obvious to me that two not-particularly-related open boxes had to have the same number.

That's actually part of the key to this puzzle. And I wonder if it's not the key to that other one we've reduced to guessing, also... :)

EDIT: I couldn't go to bed without checking it, and it is in fact the key. Two squares in that other puzzle that were narrowed down to either a 5 or 8 in one case and either a 5 or 7 in the other case had to be the same number - thus, they both had to be 5. The rest of it just falls into place after that. :dance:

I sent you a PM, Joff.

Ironically enough, earlier in this thread ToSeek mentioned:

I've only seen it the once, and I don't remember the exact situation that created it, just that it was obvious to me that two not-particularly-related open boxes had to have the same number.

That's actually part of the key to this puzzle. And I wonder if it's not the key to that other one we've reduced to guessing, also... :)

EDIT: I couldn't go to bed without checking it, and it is in fact the key. Two squares in that other puzzle that were narrowed down to either a 5 or 8 in one case and either a 5 or 7 in the other case had to be the same number - thus, they both had to be 5. The rest of it just falls into place after that. :dance:

Joff

2006-Jan-07, 05:55 AM

Good job - and thanks for the walk-through on the other puzzle.

:dance: :lol: ;)

:dance: :lol: ;)

ToSeek

2006-Jan-07, 06:33 AM

EDIT: I couldn't go to bed without checking it, and it is in fact the key. Two squares in that other puzzle that were narrowed down to either a 5 or 8 in one case and either a 5 or 7 in the other case had to be the same number - thus, they both had to be 5. The rest of it just falls into place after that. :dance:

You'll have to walk me through that one when you're next awake because I don't see it right now.

You'll have to walk me through that one when you're next awake because I don't see it right now.

Powered by vBulletin® Version 4.2.3 Copyright © 2019 vBulletin Solutions, Inc. All rights reserved.