The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |.8.|..4|93.|
 |4.6|...|.1.|
 |...|...|...|
 |---+---+---|
 |3.1|...|7..|
 |89.|71.|...|
 |...|..2|...|
 |---+---+---|
 |...|.25|.87|
 |..9|13.|5..|
 |...|...|...|
 *-----------*


Play/Print this puzzle online

[pjb]

Code: Select all

 1       8       257    | 256    567    4      | 9      3      256   
 4       2357    6      | 2358   5789   379    | 28     1      258   
 9       235     235    | 23568  568    1      | 2468   7      24568 
------------------------+----------------------+---------------------
 3       2456    1      | 4568   45689 a69     | 7     b24569  2468-9 
 8       9       245    | 7      1     a36     |b2346  b2456  b2346   
 57      4567    457    | 34568  45689  2      | 13468 b4569   134689
------------------------+----------------------+---------------------
 6       134     34     | 9      2      5      | 134    8      7     
 27      47      9      | 1      3      8      | 5      246    246   
 25      135     8      | 46     467    67     | 123    29     1239   



(9=3)r45c6 - (3=24569)r4c8,r5c789,r6c8 => -9 r4c9; lclste

Phil

[SteveG48]

Code: Select all

 *------------------------------------------------------------------------------*
 | 1       8       257     | 256     567     4       |  9       3       256     |
 | 4      f2357    6       |f2358    5789   e379     | f28      1      f258     |
 | 9       235     235     | 23568   568     1       |  2468    7       24568   |
 *-------------------------+-------------------------+--------------------------|
 | 3       2456    1       | 4568    45689   69      |  7       24569   24689   |
 | 8       9       245     | 7       1      d36      |bc2346    2456   d2346    |
 | 57      4567    457     | 34568   45689   2       | b13468   4569   c134689  |
 *-------------------------+-------------------------+--------------------------|
 | 6       134     34      | 9       2       5       | a134     8       7       |
 | 27     g47      9       | 1       3       8       |  5     ag246   ag246     |
 | 25      135     8       | 46      467     67      | a123     9-2     139-2   |
 *------------------------------------------------------------------------------*


(2=4631)b9p1567 - (31)r56c7* = (1-3)r6c9,r5c*7 = r5c9 - r5c6 = r2c6 - (3=2587)r2c2479 - (7=462)r8c289 => -2 r9c89 ; lclste

Wow! Nicely done, Phil!

And another Wow! for Leren. What great ALSs we're seeing tonight.

[Leren]

Code: Select all

*--------------------------------------------------------------------------------*
| 1       8       257      | 256     567     4        | 9       3      c256      |
| 4       2357    6        | 2358    5789    379      | 28      1      c258      |
| 9       235     235      | 23568   568     1        | 2468    7      c24568    |
|--------------------------+--------------------------+--------------------------|
| 3      b2456    1        |b4568   b45689  b69       | 7      b24569  c24689    |
| 8       9       245      | 7       1       6-3      | 2346    2456   c2346     |
|a57     a4567   a457      |a34568  a45689   2        | 1468-3 a4569    14689-3  |
|--------------------------+--------------------------+--------------------------|
| 6       134     34       | 9       2       5        | 134     8       7        |
| 27      47      9        | 1       3       8        | 5       246    c246      |
| 25      135     8        | 46      467     67       | 123     29      1239     |
*--------------------------------------------------------------------------------*

ALS XY Wing: (3=8) r6c123458 - (8=9) r4c24568 - (9=3) r123458c9 => - 3 r5c7, r6c79; stte

Leren

[JC Van Hay]

Code: Select all

+---------------+-------------------+----------------------------+
| 1   8     257 | 256    567    4   | 9         3      256       |
| 4   2357  6   | 2358   5789   379 | 28        1      258       |
| 9   235   235 | 23568  568    1   | 2468      7      24568     |
+---------------+-------------------+----------------------------+
| 3   2456  1   | 4568   45689  69  | 7         24569  246(89)   |
| 8   9     245 | 7      1      36  | 2346      2456   2346      |
| 57  4567  457 | 34568  45689  2   | 46-3(18)  4569   -346(189) |
+---------------+-------------------+----------------------------+
| 6   134   34  | 9      2      5   | 4(13)     8      7         |
| 27  47    9   | 1      3      8   | 5         246    246       |
| 25  135   8   | 46     467    67  | 2(13)     29     2(139)    |
+---------------+-------------------+----------------------------+


HT(189)r6c7,r46c9 = (9-13)r9c9 = HP(13)r97c7 - 1r6c7=1r6c9 :=> -3r6c7, -346r6c9, +3r6c4; UP81

[daj95376]

Code: Select all

 1       8       257    | 256    567    4      | 9      3      256   
 4       2357    6      | 2358   5789   379    | 28     1      258   
 9       235     235    | 23568  568    1      | 2468   7      24568 
------------------------+----------------------+---------------------
 3       2456    1      | 4568   45689 a69     | 7     b24569  2468-9 
 8       9       245    | 7      1     a36     |b2346  b2456  b2346   
 57      4567    457    | 34568  45689  2      | 13468 b4569   134689
------------------------+----------------------+---------------------
 6       134     34     | 9      2      5      | 134    8      7     
 27      47      9      | 1      3      8      | 5      246    246   
 25      135     8      | 46     467    67     | 123    29     1239   



(9=3)r45c6 - (3=24569)r4c8,r5c789,r6c8 => -9 r4c9; lclste

Very nice! However, as I've done to many posts with an ALS in five cells, I looked for an alternate description. The first step was realizing that your <24569> eliminated every candidate in r4c9 except <8>. I worked backwards from there linking <8> to the remaining <3>s in [b6]. Spotting the SL on <1> completed the conversion.

Code: Select all

(9=3)r45c6 - 3r5c79 = (31-18)r6c79 = 8r4c9  =>  -9 r4c9


My third term's notation was chosen to indicate the SL on <1> in r6c79. It creates a pseudo-weak link between <3> and <8>.

_

[bat999]

Code: Select all

.-----------------.-------------------.----------------------.
| 1   8     *25-7 | 256    567    4   | 9      3      256    |
| 4   2357   6    | 2358   5789   379 | 28     1      258    |
| 9   235    235  | 23568  568    1   | 2468   7      24568  |
:-----------------+-------------------+----------------------:
| 3   2456   1    | 4568   45689  69  | 7      24569  24689  |
| 8   9      245  | 7      1      36  | 2346   2456   2346   |
| 57  4567   457  | 34568  45689  2   | 13468  4569   134689 |
:-----------------+-------------------+----------------------:
| 6   134    34   | 9      2      5   | 134    8      7      |
| 27  47     9    | 1      3      8   | 5      246    246    |
| 25  135    8    | 46     467    67  | 123    29     1239   |
'-----------------'-------------------'----------------------'

Hi
I found if r1c3 is set to "not 7" then everything works out OK.
=> - 7 r1c3; stte
Is this a dumb way of going about it?

[SteveG48]

Hi, Bat. It's not dumb, but it is simple trial and error. It's frowned on because you don't learn anything about solving puzzles by relying on guesswork.

[bat999]

... but it is simple trial and error...

OK
When I use this method I hope to come to a contradiction after a few steps (if not a dead end).
So I could say for example, if r1c3 <> 7 it causes a contradiction so therefore r1c3 must be a 7.
But with this puzzle it went on and on to the very end.
Not so much a proof by contradiction, it's a proof by exhaustion.

I agree it's trial and error, but that's not guesswork (imho).

[SteveG48]

Not so much a proof by contradiction, it's a proof by exhaustion.

I agree it's trial and error, but that's not guesswork (imho).

Yes, there's a fine line there. In the end, it all comes down to what pleases you.

[ronk]

Very nice! However, as I've done to many posts with an ALS in five cells, I looked for an alternate description.
...
(9=3)r45c6 - 3r5c79 = (31-18)r6c79 = 8r4c9 => -9 r4c9

It might be better to label the (almost) hidden pair:

(9=3)r45c6 - 3r5c9 = (hp13-8)r6c79 = 8r4c9 ==> r4c9<>9

[daj95376]

It might be better to label the (almost) hidden pair:

(9=3)r45c6 - 3r5c9 = (hp13-8)r6c79 = 8r4c9 ==> r4c9<>9

After the recent fiasco about naming various "pairs", I wouldn't go there with a 10' pole. I was more interested in showing the role of <1> on the weak link between <3> and <8>. Althought AICs may be bidirectional, Eureka notation sometimes seems to fall short on portraying this property. So, I also aimed for a notation that tried to support this property.

_

[bat999]

Hi, Bat. It's not dumb, but it is simple trial and error. It's frowned on because you don't learn anything about solving puzzles by relying on guesswork.

Hi
I think this method is known as a "Forcing Net".
You set a value to a square and run with it.
Look for a contradiction or a verity.
In this puzzle there was no contradiction when I set r1c3 to "not 7".
It ran and ran till all the squares were accounted for, so that is a verity (imho).

It's not guesswork, but it seems to be trial and error which square to choose.
I enquired about this in another thread, how to choose a start square intelligently instead of trial and error.
There was mention about a "b/b plot" but I couldn't get a handle on it.

[JC Van Hay]

I enquired about this in another thread, how to choose a start square intelligently instead of trial and error.
There was mention about a "b/b plot" but I couldn't get a handle on it.

As a starting point, have a look at SteveK's blog, particularly here.

[bat999]

... particularly here.

OK
I think he has circled all the candidates that are in two squares of a house (two squares in the house means they are strongly linked / conjugate linked).
(He says "Candidates limited to two locations in a large container")

Then he has looked for a square that contains two (or more) circles.
In his example, f7 (r3c6) has 2 and 5 cirled.
So he thinks this is a good place to look for a "forbidding chain" utilizing the 2 and 5.
And he found the Continuous Nice Loop.

I think this is the notation:
-[r3c6]-5-[r1c5]=5=[r9c5]=2=[r9c6]-2-[r3c6]- => r1c4<>5, r45c6<>2, r9c5<>6
From left to right, if r3c6 is 5 then r3c6 is not 2.
From right to left, if r3c6 is 2 then r3c6 is not 5.

Is this what the "b/b plot" is all about then, two squares in a house is the meaning of bi-location?
When you find a square with two (or more) of those circles, go for it, look here first?


This is a quote from his blog...
How does one spot forbidding chains? The method that I use is progressive. I start looking where I believe chains are most likely to exist, and progress towards the least likely...
Since forbidding chains use strong sets as their primary building block, it is logical to look at the native strong sets first.
I begin by identifying the strongest of the native strong sets. Of these, there are two types:
1 Cells limited to two candidates
2 Candidates limited to two locations in a large container

EDIT
He also says "Start with the candidate that is circled most often".
So maybe he also looked to see whether 2 or 5 appeared very often in his drawing before deciding on f7 (r3c6).