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krazydad puzzle, book 100 puzzle # 1

 
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Thu Oct 18, 2007 5:53 pm    Post subject: krazydad puzzle, book 100 puzzle # 1 Reply with quote

this is from book 100 puzzle number 1 on his toughest list.

x x 2 6 x x 9 x x

x 6 8 9 1 x x x 2

x 5 x x x x x x x

5 1 x 8 x x x x x

x x 9 x 2 x 1 x x

x x x x x 1 x 4 3

x x x x x x x 1 x

1 x x x 6 7 3 9 x

x x 6 x x 9 5 x x


enjoy,

Norm
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Thu Oct 18, 2007 9:05 pm    Post subject: Reply with quote

after an XYZ wing (2,3,4) removes 4 from r7c56, this is where it ends - for now:

Code:

+--------------------------+--------------------------+--------------------------+
| 347     347     2        | 6       34578   3458     | 9       3578    1        |
| 347     6       8        | 9       1       345      | 47      357     2        |
| 9       5       1        | 2347    3478    2348     | 4678    3678    4678     |
+--------------------------+--------------------------+--------------------------+
| 5       1       34       | 8       347     346      | 267     267     9        |
| 3468    348     9        | 347     2       346      | 1       678     5        |
| 268     28      7        | 5       9       1        | 68      4       3        |
+--------------------------+--------------------------+--------------------------+
| 23478   9       34       | 234     358     2358     | 24678   1       4678     |
| 1       248     5        | 24      6       7        | 3       9       48       |
| 23478   23478   6        | 1       348     9        | 5       278     478      |
+--------------------------+--------------------------+--------------------------+


Now the real fun starts ...

but not tonight. nohow

I think I'll start some coloring tomorrow.
That 24 in r8c4 looks real promising, expanding into 4 and 8 right away, and those 2s form long strongly connected chains.

yea, I'm into chains, that's for sure
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Fri Oct 19, 2007 6:25 am    Post subject: Reply with quote

update on progress:

started coloring a bit.
managed to eliminate 3 from r4c5 using a group instead of a single cell to create a strong link between r4c3 and r9c5:
if r4c3 not 3 then r7c3=3, then none of r7c456 can be 3 then r9c5=3.

A similar argument removes 8 from r3c6, and also 3 can be removed from that cell. (I cannot re-create the chains without some effort, I used the
GEM (graded equivalence marks, http://www.sudopedia.org/wiki/Graded_Equivalence_Marks) method because it is rather easy to do on paper)

But then - nothing more (might be some ALS/APE but I cannot find those so I don't try - yet)

That's it. I give up.

Code:

+--------------------------+--------------------------+--------------------------+
| 347     347     2        | 6       34578   3458     | 9       3578    1        |
| 347     6       8        | 9       1       345      | 47      357     2        |
| 9       5       1        | 2347    3478    24       | 4678    3678    4678     |
+--------------------------+--------------------------+--------------------------+
| 5       1       34       | 8       47      346      | 267     267     9        |
| 3468    348     9        | 347     2       346      | 1       678     5        |
| 268     28      7        | 5       9       1        | 68      4       3        |
+--------------------------+--------------------------+--------------------------+
| 23478   9       34       | 234     358     2358     | 24678   1       4678     |
| 1       248     5        | 24      6       7        | 3       9       48       |
| 23478   23478   6        | 1       348     9        | 5       278     478      |
+--------------------------+--------------------------+--------------------------+
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Fri Oct 19, 2007 11:29 am    Post subject: sorry Reply with quote

sorry for the post out of nowhere, I am new to the forum but not new to the site. I love the insight in this particular forum because it seems everyone is moving along with the difficulty of the puzzles. hence my learning curve has skyrocketed over the last couple months. since the puzzles have included xy wings, x wings, simple coloring as of late, my feelings about sudoku have deepened and I am in the same camp of those who can't get enough.

anyways, enough blabber, the reason for posting this puzzle is because I was told that these puzzles are great for looking for chains and I need help on chains in the worst way.

Norm
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Fri Oct 19, 2007 1:32 pm    Post subject: Reply with quote

no reason to be sorry. On the contrary, I was looking for a challenge anyway, and judging from some of the posts here I am not the only one. I do hope someone comes up with a solution path (death blossom, anyone?). As for chains I rather doubt they will get us over the barrier here. Except of course the (bad, bad!Evil or Very Mad ) forcing chains (e.g. cell r8c4: setting it to "2" leads to a contradiction, "4" solves the puzzle easily)
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Fri Oct 19, 2007 5:43 pm    Post subject: Reply with quote

ok, took it to work, had about 5 people stare at it for a while. we all agree that there is some kind of overlapping als in r6c1,2... r5,c1,2
and over at r4,c5 and r5c4, and possibly in r4,c6 and r5,c6...

so we see the commons as the 6's in the first two columns, the 3's in the 5th row and but the 4's in column 6 don't match up.
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Sat Oct 20, 2007 12:14 am    Post subject: Reply with quote

I solved it using a branched AIC that led to a contradiction. But, since many would object that is too close to forcing, I looked for another way of describing the underlying constraint. I suspect that there is some Sue de Coq way of describing this, but I couldn't come up with it. (Perhaps someone more proficient in Sue de Coq methods can find such an explanation.) Some of those ALSs are the key, in any case. I have used a coloring approach.

But first...
nataraj: Your <3> elimination in R4C5 can also be described as an ER elimination; the ER is in Box 8.

I start coloring with the {34} pair in C3:
Code:
+---------------------+------------------------+--------------------+
| 347    347    2     | 6       34578  3458    | 9      3578   1    |
| 347    6      8     | 9       1      345     | 47     357    2    |
| 9      5      1     | 2347    3478   24      | 4678   3678   4678 |
+---------------------+------------------------+--------------------+
| 5      1      3g4r  | 8       47     3r46    | 267    267    9    |
| 3468   348    9     | 347     2      34r6    | 1      678    5    |
| 268    28     7     | 5       9      1       | 68     4      3    |
+---------------------+------------------------+--------------------+
| 23478  9      3r4g  | 234     358    2358    | 24678  1      4678 |
| 1      248    5     | 24      6      7       | 3      9      48   |
| 23478  23478  6     | 1       348    9       | 5      278    478  |
+---------------------+------------------------+--------------------+

The <3> in R4C6 is easily determined as "red". One of the <4>s in R5C46 must be red; but, which?

If the "red" <3> at R7C3 is true, then R78C4 becomes a {24} Locked Pair. So, the <4> at R5C4 cannot be red: the <4> at R5C6 must be red.

However, there is a strongly linked pair of <6>s in R45C6. So, it is impossible for "red" to be true since it requires these cells to be <3> and <4>. Thus, the "greens" can be placed and all "reds" eliminated.

After this, there is a 9-cell XY Chain with pincers at R4C6 and R6C7 that eliminates <6>s and breaks the puzzle open.
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