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boweasel · Joined: 15 May 2006 Posts: 5

Picked up his book the other day, and am having difficulty with this puzzle. Is there a technique beyond guessing I can use to solve it?

Marty R. · Posted: Mon May 15, 2006 9:19 pm Post subject:

In row 9, the only possibilities for "8" are in box 7, therefore, the "8" cannot be in r8c2. That solves r8c9, since that is the only remaining "8" in that row. That will help you solve more cells, but I don't know that that's enough to complete the puzzle. The "7" can't be in r9c7, as that number is already solved in that column, but that's of little help.

There is a unique rectangle in rows 2 and 4, columns 1 and 2. I don't know you or what techniques you're familiar with, but Keith wrote an excellent primer on rectangles here:

http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=744

I think using that rectangle to solve a cell might break the puzzle open.

Good luck.

Guest · Posted: Tue May 16, 2006 12:05 am Post subject:

Somehow I knew I would screw up this entry...
Row 9 col 7 should read 2/5/6/8. I hope that's the only typo I made.

And why do I get the msg 'sorry but this username has already been taken'?

David Bryant · Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

Marty R. · Posted: Tue May 16, 2006 12:56 am Post subject:

David Bryant · Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

You're right, Marty -- it should be r7c7. Thanks for pointing that out. I've edited the original post. dcb Shocked

Guest · Posted: Wed May 17, 2006 1:49 am Post subject:

Wow... unique rectangles! I never would have thought of using a technique based on the principle that the Sudoku puzzle solution must be unique. It just never would've occurred to me.

Using UR enabled me to easily solve the puzzle. Thanks, Marty.

And David, I appreciate your input, although your sentence:

"There's also a coloring argument that allows one to eliminate the "6" at r9c4 -- if r3c1 = 6, then r6c4 = 6; and if r3c1 <> 6, then r9c1 = 6. Either way, there can't be a "6" at r9c4."

is over my head. I mean if I set r3c1 = 6 I have go through a significant number of cells before I finally get to where r6c4 = 6. I'm sure there's simply something I'm not grasping....

David Bryant · Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

boweasel · Joined: 15 May 2006 Posts: 5

Yes. thanks David. It does make sense, although there certainly seems to be more of an educated 'trial and error' quality to coloring than to other logic techniques such as XY Wings, and it might be that very quality that makes me unlikely to use it unless all else fails.

David Bryant · Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

ravel · Joined: 21 Apr 2006 Posts: 536

IMO (multiple) coloring is a systematic way to eliminate candidates. Just follow the well defined rules (color all strong linked cells for a candidate and make the eliminations at the end - if there are any)
So there is not more trial&error than for xy-wings: go to all bivalue cells and try to find appropriate wings.

Lone Cactus · Joined: 12 Jan 2009 Posts: 3 Location: Ranch en BCS Mexico

This is my first time every to post anything. I am working through Longo's book, Black Belt Sudoku. I am currently stumped with this one, Black Belt 2nd Degree Longo #76
If anyone could give me an idea what to try next I would appreciate it.
I have gotten this far:

[code]
+------------+----------------+------------+
| 5 3 9 | 68 4 68 | 7 1 2 |
| 4 12 8 | 12 7 5 | 3 6 9 |
| 26 7 126 | 3 9 12 | 8 5 4 |
+------------+----------------+------------+
| 3 8 12 | 9 26 246 | 14 7 5 |
| 9 12 5 | 247 8 247 | 6 34 13 |
| 7 6 4 | 5 1 3 | 9 2 8 |
+------------+----------------+------------+
| 1 5 37 | 2467 26 9 | 24 8 36 |
| 26 4 26 | 18 3 18 | 5 9 7 |
| 8 9 37 | 247 5 247 | 124 34 136 |
+------------+----------------+------------+

10-Q for any help.

wapati · Posted: Mon Jan 12, 2009 4:23 pm Post subject:

arkietech · Posted: Mon Jan 12, 2009 4:27 pm Post subject:

Lone Cactus · Joined: 12 Jan 2009 Posts: 3 Location: Ranch en BCS Mexico

You are correct I took out the 6's in error,but unfortunately I am still stuck. Any hints or suggestions for my next move...

Code:
.------------------.------------------.------------------.
| 5 3 9 | 68 4 68 | 7 1 2 |
| 4 12 8 | 12 7 5 | 3 6 9 |
| 26 7 126 | 3 9 12 | 8 5 4 |
:------------------+------------------+------------------:
| 3 8 12 | 9 26 246 | 14 7 5 |
| 9 12 5 | 247 8 247 | 6 34 13 |
| 7 6 4 | 5 1 3 | 9 2 8 |
:------------------+------------------+------------------:
| 1 5 37 | 2467 26 9 | 24 8 36 |
| 26 4 26 | 18 3 18 | 5 9 7 |
| 8 9 37 | 2467 5 2467 | 124 34 136 |
'------------------'------------------'------------------'

The only way I can figure out to solve it is my picking an options in one of the cells and seeing if it works, but there must be some method I can apply to eliminate more candidates.

Lone Cactus/Jane

wapati · Posted: Mon Jan 12, 2009 8:16 pm Post subject:

There is a short way to finish using a Unique Rectangle.

Lone Cactus · Joined: 12 Jan 2009 Posts: 3 Location: Ranch en BCS Mexico

Working on Longo 2nd Degree Back Belt, #80.

Have gotten to this point:

keith · Posted: Thu Jan 15, 2009 12:22 am Post subject:

Asellus · Posted: Thu Jan 15, 2009 11:54 pm Post subject:

I agree with Ravel about coloring: no trial and error is involved. The example above is "multi-coloring" because it involves more than one color "cluster", in this case two clusters: =/~ and +/-. The two clusters "see" each other in Box 1 such that + and = cannot both be true. (Some call this weak link connection the "bridge" between the two clusters.) This, in turn, means that - and ~ <6>s cannot both be false. So, any <6> that can see both a - <6> and a ~ <6> can be eliminated, such as the <6> at r9c4.

There is no need to assume that any particular <6> is true or false.