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A can of (colored) worms

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keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sun Mar 07, 2010 2:08 am Post subject: A can of (colored) worms

It's been a year, so maybe I can revisit this one:

Code:

Puzzle: M5270971sh(17)
+-------+-------+-------+
| 6 . 5 | 8 . 7 | 4 . 1 |
| 7 . . | 1 . 9 | . . 8 |
| . . . | . 2 . | . . . |
+-------+-------+-------+
| 2 5 . | . . . | . 6 7 |
| . . 8 | . . . | 1 . . |
| 1 7 . | . . . | . 4 2 |
+-------+-------+-------+
| . . . | . 1 . | . . . |
| 5 . . | 2 . 8 | . . 4 |
| 9 . 1 | 3 . 4 | 7 . 6 |
+-------+-------+-------+

Please try to solve it before reading further!

Keith

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sun Mar 07, 2010 2:40 am Post subject:

After basics:

Code:

+-------------------+-------------------+-------------------+
| 6 29 5 | 8 3 7 | 4 29 1 |
| 7 234 234 | 1 46 9 | 2356 235 8 |
| 8 1 349 | 46 2 5 | 369 7 39 |
+-------------------+-------------------+-------------------+
| 2 5 349 | 49 489 1 | 389 6 7 |
| 34 3469 8 | 45679 4679 2 | 1 359 359 |
| 1 7 69 | 569 689 3 | 589 4 2 |
+-------------------+-------------------+-------------------+
| 34 2348 2347 | 79 1 6 | 2359 23589 359 |
| 5 36 367 | 2 79 8 | 39 1 4 |
| 9 28 1 | 3 5 4 | 7 28 6 |
+-------------------+-------------------+-------------------+

Here is the pattern of cells where 3 is unsolved:

Code:

+----------+----------+----------+
| . . . | . . . | . . . |
| . 3 3 | . . . | 3 3 . |
| . . 3 | . . . | 3 . 3 |
+----------+----------+----------+
| . . 3 | . . . | 3 . . |
| 3 3 . | . . . | . 3 3 |
| . . . | . . . | . . . |
+----------+----------+----------+
| 3 3 3 | . . . | 3 3 3 |
| . 3 3 | . . . | 3 . . |
| . . . | . . . | . . . |
+----------+----------+----------+

What, if anything, is wrong with the following logic?:

In C1, one of R57C1 is true. Label R5C1 as R (Red) and R7C1 as G (Green).

R or G is true. r is not R, g is not G. If a cell is both r and g, it is not true (not 3).

Step 1:

Code:

+----------+----------+----------+
| . . . | . . . | . . . |
| . 3 3 | . . . | 3 3 . |
| . . 3 | . . . | 3 . 3 |
+----------+----------+----------+
| . . 3 | . . . | 3 . . |
| 3R 3 . | . . . | . 3 3 |
| . . . | . . . | . . . |
+----------+----------+----------+
| 3G 3g 3g | . . . | 3g 3g 3g |
| . 3g 3g | . . . | 3G . . |
| . . . | . . . | . . . |
+----------+----------+----------+

Step 2:

Code:

+----------+----------+----------+
| . . . | . . . | . . . |
| . 3 3 | . . . | 3g 3 . |
| . . 3 | . . . | 3g . 3 |
+----------+----------+----------+
| . . 3G | . . . | 3g . . |
| 3R 3 . | . . . | . 3 3 |
| . . . | . . . | . . . |
+----------+----------+----------+
| 3G 3g 3g | . . . | 3g 3g 3g |
| . 3g 3g | . . . | 3G . . |
| . . . | . . . | . . . |
+----------+----------+----------+

Step 3:

Code:

+----------+----------+----------+
| . . . | . . . | . . . |
| . 3G 3g | . . . | 3g 3g . |
| . . 3g | . . . | 3g . 3G |
+----------+----------+----------+
| . . 3G | . . . | 3g . . |
|3Rg 3g . | . . . | . 3G 3g |
| . . . | . . . | . . . |
+----------+----------+----------+
| 3G 3g 3g | . . . | 3g 3g 3g |
| . 3g 3g | . . . | 3G . . |
| . . . | . . . | . . . |
+----------+----------+----------+

Starting in R7C1: If G is true, the other G are true, the cells marked g are not true.

Step 4. Let's look at R:

Code:

+----------+----------+----------+
| . . . | . . . | . . . |
| . 3 3 | . . . | 3r 3 . |
| . . 3 | . . . | 3r . 3 |
+----------+----------+----------+
| . . 3r | . . . | 3R . . |
| 3R 3r . | . . . | . 3r 3r |
| . . . | . . . | . . . |
+----------+----------+----------+
| 3r 3 3 | . . . | 3r 3 3 |
| . 3 3 | . . . | 3r . . |
| . . . | . . . | . . . |
+----------+----------+----------+

Starting in R5C1: If R is true, the other R are true, the cells marked r are not true.

Either R or G is true: Any cell that is both r and g is not true.

Step 5: Make the eliminations

Code:

+----------+----------+----------+
| . . . | . . . | . . . |
| . G 3 | . . . |-3 3 . |
| . . 3 | . . . |-3 . G |
+----------+----------+----------+
| . . G | . . . | R . . |
| R -3 . | . . . | . G -3 |
| . . . | . . . | . . . |
+----------+----------+----------+
| G 3 3 | . . . |-3 3 3 |
| . 3 3 | . . . | G . . |
| . . . | . . . | . . . |
+----------+----------+----------+

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sun Mar 07, 2010 2:58 am Post subject:

EDIT: I now believe Step 6 below is incorrect. See the correction in a following message - Keith

So far, so good (I think). We are here:

Code:

+----------+----------+----------+
| . . . | . . . | . . . |
| . 3 3 | . . . | . 3 . |
| . . 3 | . . . | . . G |
+----------+----------+----------+
| . . 3 | . . . | R . . |
| R . . | . . . | . G . |
| . . . | . . . | . . . |
+----------+----------+----------+
| G 3 3 | . . . | . 3 3 |
| . 3 3 | . . . | G . . |
| . . . | . . . | . . . |
+----------+----------+----------+

Step 6:
Continue coloring:

Code:

+----------+----------+----------+
| . . . | . . . | . . . |
| . G -3 | . . . | . R . |
| . . R | . . . | . . G |
+----------+----------+----------+
| . . G | . . . | R . . |
| R . . | . . . | . G . |
| . . . | . . . | . . . |
+----------+----------+----------+
| G -3 -3 | . . . | . -3 R |
| . R -3 | . . . | G . . |
| . . . | . . . | . . . |
+----------+----------+----------+

Leaving us with a minimal net of candidates for 3: Two in each unsolved row, column, and box.

Step 7: End.

Code:

+----------+----------+----------+
| . . . | . . . | . . . |
| . 3 . | . . . | . 3 . |
| . . 3 | . . . | . . 3 |
+----------+----------+----------+
| . . 3 | . . . | 3 . . |
| 3 . . | . . . | . 3 . |
| . . . | . . . | . . . |
+----------+----------+----------+
| 3 . . | . . . | . . 3 |
| . 3 . | . . . | 3 . . |
| . . . | . . . | . . . |
+----------+----------+----------+

I see this as extreme grouped multicoloring. If anyone sees a flaw in the logic, I would appreciate a gentle explanation and correction.

Keith

Last edited by keith on Sun Mar 07, 2010 5:07 pm; edited 1 time in total

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Sun Mar 07, 2010 6:12 am Post subject:

Ignoring all this coloring, the puzzle worked for me as a long BBDB.

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sun Mar 07, 2010 10:27 am Post subject:

keith wrote:

I see this as extreme grouped multicoloring. If anyone sees a flaw in the logic, I would appreciate a gentle explanation and correction.

Keith,

I didn't notice you doing anything wrong. Basically, steps 1-5 are a forcing network on <3> from the bilocation candidates in [c1]. Your step 6 made me nervous, but that's all.

I get confused trying to remember the distinction between various coloring techniques, so I have no idea what name might be associated with your approach.

The important thing to note is that the logic behind your steps must be followed carefully. One slip-up and an error could easily result.

Regards, Danny

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sun Mar 07, 2010 3:33 pm Post subject:

Marty,

After all the coloring there is an XY-wing 46-9 that with transport takes out 9 in R8C7, solving the puzzle.

EDIT: Corrections made in the following

Danny,

Quote:

Your step 6 made me nervous, but that's all.

Me too, that's why I asked. Would you still be nervous if you were to do coloring on this grid, not knowing about Steps 1-5?

Code:

+----------+----------+----------+
| . . . | . . . | . . . |
| . 3 3 | . . . | . 3 . |
| . . 3 | . . . | . . 3 |
+----------+----------+----------+
| . . 3 | . . . | 3 . . |
| 3 . . | . . . | . 3 . |
| . . . | . . . | . . . |
+----------+----------+----------+
| 3 3 3 | . . . | . 3 3 |
| . 3 3 | . . . | 3 . . |
| . . . | . . . | . . . |
+----------+----------+----------+

I think it is ok if you start two threads R and G like I did, and look for cells that are not G in one thread and also not R in the other. Applying that to the grid above yields:

Code:

+----------+----------+----------+
| . . . | . . . | . . . |
| . 3 3 | . . . | . 3 . |
| . . 3 | . . . | . . 3 |
+----------+----------+----------+
| . . r | . . . | R . . |
| R . . | . . . | . r . |
| . . . | . . . | . . . |
+----------+----------+----------+
| r r r | . . . | . 3 3 |
| . 3 3 | . . . | r . . |
| . . . | . . . | . . . |
+----------+----------+----------+

+----------+----------+----------+
| . . . | . . . | . . . |
| . G g | . . . | . g . |
| . . g | . . . | . . G |
+----------+----------+----------+
| . . G | . . . | g . . |
| g . . | . . . | . G . |
| . . . | . . . | . . . |
+----------+----------+----------+
| G g g | . . . | . g g |
| . g g | . . . | G . . |
| . . . | . . . | . . . |
+----------+----------+----------+

R7C23 are "r" because one of R7C89 must be "R".

Note that "g" in B3, R2C8, DOES NOT imply "R" in that cell, even though there are only two candidates in B3.

So, the final pattern is:

Code:

+----------+----------+----------+
| . . . | . . . | . . . |
| . 3 3 | . . . | . 3 . |
| . . 3 | . . . | . . 3 |
+----------+----------+----------+
| . . 3 | . . . | 3 . . |
| 3 . . | . . . | . 3 . |
| . . . | . . . | . . . |
+----------+----------+----------+
| 3 . . | . . . | . 3 3 |
| . 3 3 | . . . | 3 . . |
| . . . | . . . | . . . |
+----------+----------+----------+

Keith

Last edited by keith on Sun Mar 07, 2010 6:47 pm; edited 1 time in total

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Sun Mar 07, 2010 4:43 pm Post subject:

Quote:

After all the coloring there is an XY-wing 46-9 that with transport takes out 9 in R8C7, solving the puzzle.

That exact move was my final step after being preceded by 11 others including X, ERs, XYs, Hidden UR, Finned X, W and multi-coloring.

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sun Mar 07, 2010 7:57 pm Post subject:

Keith, Steps 1-5 are acceptable because they represent a forcing network ... and the eliminations that would follow. I've always had problems with coloring chains once I started to extend the logic beyond the initial coloring of bilocation cells. There's a pitfall where one can incorrectly deduce the coloring of a cell after extending the coloring. Unfortunately, I'm just as likely to make a mistake as get it right. Regards, Danny

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sun Mar 07, 2010 8:00 pm Post subject:

Marty R. wrote:

Quote:

After all the coloring there is an XY-wing 46-9 that with transport takes out 9 in R8C7, solving the puzzle.

That exact move was my final step after being preceded by 11 others including X, ERs, XYs, Hidden UR, Finned X, W and multi-coloring.

Marty,

After basics:

Code:

+-------------------+-------------------+-------------------+
| 6 29 5 | 8 3 7 | 4 29 1 |
| 7 234 234 | 1 46 9 |2-356 235 8 |
| 8 1 349 | 46 2 5 |-369 7 39 |
+-------------------+-------------------+-------------------+
| 2 5 349 | 49 489 1 | 389# 6 7 |
| 34@ 3469 8 | 45679 4679 2 | 1 359 359 |
| 1 7 69 | 569 689 3 | 589 4 2 |
+-------------------+-------------------+-------------------+
| 34@ 2348 2347 | 79 1 6 |2-359 23589 359 |
| 5 36 367 | 2 79 8 | 39# 1 4 |
| 9 28 1 | 3 5 4 | 7 28 6 |
+-------------------+-------------------+-------------------+

The XY-wing is there, except you have to knock out the 3 in R3C7.

One of the cells @ is 3. Coloring in their rows, one of the cells # is 3. Making the eliminations shown.

Will you award me a two-step solution?

Keith

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Sun Mar 07, 2010 8:22 pm Post subject:

Quote:

One of the cells @ is 3. Coloring in their rows, one of the cells # is 3. Making the eliminations shown.

Will you award me a two-step solution?

Absolutely. That's a nice move with the 3s. Got a name for it?

I tried this on Draw/Play, taking out the 3s from c7. Then the 469 XY-Wing takes out the 9 from r4c7. Unfortunately, I don't see where that opens up anything to complete the puzzle.

Code:

+--------------+--------------+---------------+
| 6 29 5 | 8 3 7 | 4 29 1 |
| 7 234 234 | 1 46 9 | 256 235 8 |
| 8 1 349 | 46 2 5 | 69 7 39 |
+--------------+--------------+---------------+
| 2 5 349 | 49 489 1 | 38 6 7 |
| 34 3469 8 | 45679 4679 2 | 1 359 359 |
| 1 7 69 | 569 689 3 | 589 4 2 |
+--------------+--------------+---------------+
| 34 2348 2347 | 79 1 6 | 259 23589 359 |
| 5 36 367 | 2 79 8 | 39 1 4 |
| 9 28 1 | 3 5 4 | 7 28 6 |
+--------------+--------------+---------------+

Play this puzzle online at the Daily Sudoku site

arkietech

Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA

Posted: Sun Mar 07, 2010 9:52 pm Post subject:

Code:

I finished by setting the 3 in col 9. I used an xy chain. Then a swordfish 9 to blow it out.

Excellent puzzle -- even for one who doesn't care for coloring. Very Happy

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sun Mar 07, 2010 10:34 pm Post subject:

Marty R. wrote:

Quote:

One of the cells @ is 3. Coloring in their rows, one of the cells # is 3. Making the eliminations shown.

Will you award me a two-step solution?

Marty,

No, I do not have a name for it.

I should have stated the second step, also grouped coloring.

Code:

+--------------+--------------+---------------+
| 6 29 5 | 8 3 7 | 4 29 1 |
| 7 234 234 | 1 46 9 | 256 235 8 |
| 8 1 349 | 46@ 2 5 | 69# 7 39 |
+--------------+--------------+---------------+
| 2 5 349 | 49# 489 1 | 38 6 7 |
| 34 3469 8 | 45679 4679 2 | 1 359 359 |
| 1 7 69 | 569 689 3 | 589 4 2 |
+--------------+--------------+---------------+
| 34 2348 2347 | 79% 1 6 | 259 23589 359 |
| 5 36 367 | 2 79& 8 |3-9 1 4 |
| 9 28 1 | 3 5 4 | 7 28 6 |
+--------------+--------------+---------------+

The XY-wing has pincers 9 in the cells marked #. R4C4 can be extended to R8C5, taking out 9 in R8C7.

Keith

strmckr

Joined: 18 Aug 2009
Posts: 64

Posted: Sun Mar 07, 2010 11:45 pm Post subject:

keith... off the 3- pattern i found: Franken Swordfish: 3 r48b1 c237 => r237c7,r57c2,r7c3<>3 which leaves a Skyscraper: 3 in r3c9,r4c7 (connected by r34c3) => r5c9<>3 (which accounts for the eliminations you have deduced via coloring)

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