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By ReallyEvilCanine (Thu Apr 26, 2007 at 02:19:56 AM EST) A Day in the Life, sudoku, Uniqueness, pie (all tags)
Solving a Difficult Sudoku

I can't sit in the Cube at the Desk of Hate all day long. When it's time for this monkey to have a smoke, I usually take a sudoku puzzle with me. I do 'em in the train to and from work as well. I've done so many that I can do most puzzles at the hardest level in under 10 minutes. Luckily, Berti hates smoke and so avoids the smoking room which means I'm not subject to his opinions on how the puzzles work.

Warning: This diary contains nothing about fuckwits, only a method for solving difficult standard sudoku puzzles.

x-posted to da brog, sans poll.



I don't use strategies such as "Advanced cross-hatching", "X-wing", "Swordfish" and the like; to me they're obvious and nothing more than long names and descriptions for what I already do: scan numbers in rows and columns and when those are all set, start looking for pairs and triplets. However, there's a rule I came up with a year ago which I call "Uniqueness". No other site ever explained this, and when I sent it to the guy with the former Numbah Wun sudoku strategy site, he gave me nothing but a "Pish and tosh". Fine. Fuck 'im. He's wrong, I'm right, you benefit.

This can be demonstrated with Websudoku's Evil Puzzle #7,645,498,690.

First we get some preliminary numbers out of the way:

In looking for pairs we have two blocks with 5 and 6. If all four of those boxes are either 5 or 6 then this is an illegal puzzle. It would have two answers.

One square also has an additional alternative Since Uniqueness demands that it cannot be either 5 or 6, this alternative must be the answer.

After that one certainty, we can fill in a lot of numbers, starting with the 1 in the bottom left quadrant since 5 and 6 are still blocked in that row, forcing the top to be a 6, forcing the number below the newly-placed 1 to be a 6, and so on. From 45 open spaces we're down to 29.

On Monday I came across Websudoku's Evil Puzzle #8,351,019,029:

After some quick scanning to fill in the obvious, we've got this:

Pretty simple, but now what?

I noticed the 1 and 9 in the bottom middle block, and this is significant because there's a 1/9 pair in the top middle block:

Now that still leaves three empty spaces for which I only know two numbers but then Uniqueness comes into play. In the example, blocks A and B both include the same 1/9 pair while block D has the 1/9 and a third number. :

There's only one of three possible ways to fill two of the circles with 1/9 which gives a legal result. Circles B and C can't be 1/9 since there's already a box in that column which can only be a 1/9. Circles A and C can't be 1/9: this would violate the Uniqueness property allowing two different ways to solve for 1 and 9. That leaves A and C:

Since the 3 and 8 in the second row from the bottom can only be placed on the top of this bottom middle box, position B must be a 4.

This is the first time that I've come across Uniqueness being a factor early on. It normally appears fairly late in a puzzle with a pair somewhere and the same pair mirrored elsewhere but with a third possibility for one of them. The Uniqueness strategy always works (by definition it must), and is often the last recourse before guessing.

While extremely rare, Uniqueness can also be used if nine spaces house the same pairs/triplets over three rows or columns, along with one extra possible digit in one of those spaces. If I see it again I'll add it here.

These days I'm doing "Killer", "Greater-Than", and "Greater-Than Killer" sudokus. These fuckers aren't kidding when they call their weekly puzzles "mind-bending". I'm grateful to Websudoku (as well as to Sudoku.org.uk) for all the puzzles they've provided me but these days I'm getting more challenging stuff from Killer Sudoku Online. If anyone has any links to sites which offer regular supplies of other sudoku variants (pips and shared cell, for example) please let me know in the comments.

Note: These graphics gave me a chance to try out Paint.NET for the down-and-dirty crap I normally do in PaintShop Pro 3. While it's still young, it's pretty damned good. An imitation Photoshop to be sure, the features it lacks are made up for by the ease of use. They need to make layers copyable and savable; I had to draw the red shading for each graphic individually. The learning curve's very shallow if you know Photoshop and still not terribly steep if you don't.

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A Day in the Life | 11 comments (11 topical, 0 hidden) | Trackback
My wife uses that technique by TPD (2.00 / 0) #1 Thu Apr 26, 2007 at 04:26:17 AM EST
but when she explained it, she explained it really poorly.

She's a bit of an addict - there's a daily sudoku here: http://www.guardian.co.uk/sudoku

why sit, when you can sit and swivel with The Ab-SwivellerTM

I'm reasonably sure by skippy (2.00 / 0) #9 Thu Apr 26, 2007 at 09:28:59 AM EST
that my brain is using the same method - but I wouldn't have been able to explain it.

"You know, I just find like the patterns of numbers and stuff?  And then I put in the numbers in the boxes when I figure it out."

[ Parent ]
Got any play online Killer sites? by ambrosen (2.00 / 0) #2 Thu Apr 26, 2007 at 05:03:54 AM EST


As an amateur Sudoku guy . . . by slozo (2.00 / 0) #3 Thu Apr 26, 2007 at 05:43:11 AM EST
. . . I am confused with your first example: You state that for two boxes, we have 5 and 6. Yet in the left center box, there are clearly three possibilites for 5 and 6 . . . your example of uniqueness forgets that 7 could have also gone in the top left hand corner of that same box. Hence, it is a bad example perhaps?

That being said, I have used your uniqueness technique a few times myself with success.

The issue is that by ambrosen (4.00 / 1) #4 Thu Apr 26, 2007 at 06:12:42 AM EST
in the bottom left square, there's a pair of boxes that have to be 5 or 6, and in the middle left square, directly above that, there's one box that's also 5 or 6, and the one that's 5, 6 or 7.

If all four of those boxes contained just 5s and 6s, then the puzzle would be ambiguous, because you wouldn't be able to tell which column had the 5 above the 6 and which had it below, so the one box that contains a third option must be filled with that to make the puzzle solvable.

And yes, Mr Canine did explain better than me.

[ Parent ]
Exactly. by ReallyEvilCanine (2.00 / 0) #7 Thu Apr 26, 2007 at 07:30:10 AM EST
Maybe I should call this "Disambiguity" rather than "Uniqueness".

the internet: amplifier of stupidity -- discordia

[ Parent ]
ah, I see now . . . by slozo (2.00 / 0) #8 Thu Apr 26, 2007 at 08:34:48 AM EST
. . . the third suare doesn't come into play, right. Fair enough. BTW - I never knew about the "two possible solutions makes it illegal" thing . . .

[ Parent ]
sudoku techniques by Merekat (3.00 / 1) #5 Thu Apr 26, 2007 at 06:52:04 AM EST
Am I missing something or isn't it just a series of varyingly complex simultaneous equations?

It's not really simultaneous equations. by ambrosen (2.00 / 0) #6 Thu Apr 26, 2007 at 06:55:49 AM EST
They're more basic elimination problems. But I like them for keeping the brain working.

[ Parent ]
To irk my wife by sasquatchan (2.00 / 0) #10 Fri Apr 27, 2007 at 06:43:00 AM EST
I wrote a brute force sudoku solver. Was from the math challenge web site (now the Euler project web site). Re wrote it a few times to brute force depth/breadth first, from 0,0 or 9,9, and one that just does simple iterative "fill in the obvious". Though "fill in the obvious" only completes easy puzzles. Was an interesting exercise, but didn't bother making it 'smarter' for better set elimination.

How long has the <small> tag worked here? by ammoniacal (2.00 / 0) #11 Sat Apr 28, 2007 at 08:57:21 AM EST

"To this day that was the most bullshit caesar salad I have every experienced..." - triggerfinger

A Day in the Life | 11 comments (11 topical, 0 hidden) | Trackback