The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |3.2|..7|465|
 |7..|..3|...|
 |...|6..|...|
 |---+---+---|
 |8..|4..|...|
 |..3|.1.|9..|
 |...|..6|..4|
 |---+---+---|
 |...|..8|...|
 |...|2..|..7|
 |967|5..|1.2|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*-----------------------------------------------------------------------*
| 3      18     2       | 18     9      7       | 4      6      5       |
| 7      5      6       | 18     4      3       | 28     12     9       |
|b14     9      48      | 6      25     25      | 378    137   b13      |
|-----------------------+-----------------------+-----------------------|
| 8      127    5-1     | 4      25     9       | 2367   12357 a136     |
| 6      4      3       | 7      1      25      | 9      25     8       |
| 125    127    9       | 3      8      6       | 27     1257   4       |
|-----------------------+-----------------------+-----------------------|
| 125    123   c15      | 9      7      8       | 356    4     a36      |
|c45     38     48      | 2      6      1       | 35     9      7       |
| 9      6      7       | 5      3      4       | 1      8      2       |
*-----------------------------------------------------------------------*

ALS XY Wing: (1=3) r47c9 - (3=4) r3c19 - (4=1) r8c1,r7c3 => - 1 r4c3; stte

Leren

[tlanglet]

I didn't find a useful AHS(), so I settled for an ANS()...........

Code: Select all

 *--------------------------------------------------------------------*
 | 3     b18     2      |c18     9      7      | 4      6      5      |
 | 7      5      6      |d18     4      3      | 28    d12     9      |
 | 14     9      48     | 6      25     25     | 378    137    13     |
 |----------------------+----------------------+----------------------|
 | 8      127   h15     | 4     g25     9      | 2367   12357  136    |
 | 6      4      3      | 7      1     f25     | 9     e25     8      |
 | 125    127    9      | 3      8      6      | 27     1257   4      |
 |----------------------+----------------------+----------------------|
 |*125   *12=3 *i15     | 9      7      8      | 36-5   4      36     |
 | 45    a38     48     | 2      6      1      | 35     9      7      |
 | 9      6      7      | 5      3      4      | 1      8      2      |
 *--------------------------------------------------------------------*


ANT(125=3)r7c132-(3=8)r8c2-r1c2=r1c4-(8=12)r2c48-(2=5)r5c8-r5c6=r4c5-r4c3=5r7c3 => r7c7<>5

Ted

[Leren]

tlanglet wrote: ANT(125=3)r7c132-(3=8)r8c2-r1c2=r1c4-(8=12)r2c48-(2=5)r5c8-r5c6=r4c5-r4c3=5r7c3 => r7c7<>5

Also r8c1 <> 5

Leren

[SteveG48]

Basic moves followed by:
Double coloring on 1's: r1c2-r1c4-r2c4-r2c8 and r3c9-r4c9 => r4c2<>1
BUG 2/5: r3c56, r4c4, r5c67 =>r4c7 <>2/5
ur r47c79 => r4c7<>3
XY-wing r3c1, r7c3, pivot r8c1 => r7c1<>1
Double coloring on 1's: r3c1-r6c1 and r3c9-r4c9 => r4c3/r6c8 <>1

[pjb]

Code: Select all

 3      18     2      | 18     9      7      | 4      6      5     
 7      5      6      | 18     4      3      | 28     12     9     
b14     9      48     | 6      25     25     | 378    137   c13     
 ---------------------+----------------------+---------------------
 8      127   e15     | 4      25     9      | 2367   12357 d136   
 6      4      3      | 7      1      25     | 9      25     8     
 12-5   127    9      | 3      8      6      | 27     1257   4     
 ---------------------+----------------------+---------------------
 125    123    1-5    | 9      7      8      | 356    4      36     
a45     38     48     | 2      6      1      | 35     9      7     
 9      6      7      | 5      3      4      | 1      8      2

(5=4) r8c1 - (4=1) r3c1 - r3c9 = r4c9 - (1=5) r4c3 => -5 r6c1, r7c3; stte

Phil

[ArkieTech]

Code: Select all

 *--------------------------------------------------------------------*
 | 3      18     2      | 18     9      7      | 4      6      5      |
 | 7      5      6      | 18     4      3      | 28     12     9      |
 |b14     9      48     | 6      25     25     | 378    137   b13     |
 |----------------------+----------------------+----------------------|
 | 8      127    5-1    | 4      25     9      | 2367   12357 a136    |
 | 6      4      3      | 7      1      25     | 9      25     8      |
 | 125    127    9      | 3      8      6      | 27     1257   4      |
 |----------------------+----------------------+----------------------|
 | 125    123   c15     | 9      7      8      | 356    4     a36     |
 |c45     38     48     | 2      6      1      | 35     9      7      |
 | 9      6      7      | 5      3      4      | 1      8      2      |
 *--------------------------------------------------------------------*
(1=63)r47c9-(3=4)r3c19-(4=1)r8c1,r7c3 => -1r4c3; ste

[tlanglet]

tlanglet wrote: ANT(125=3)r7c132-(3=8)r8c2-r1c2=r1c4-(8=12)r2c48-(2=5)r5c8-r5c6=r4c5-r4c3=5r7c3 => r7c7<>5

Also r8c1 <> 5

Leren

Thanks, Leren. Details can be a pain but are critical.

Ted

[tlanglet]

Code: Select all

 *-----------*
 |3.2|..7|465|
 |7..|..3|...|
 |...|6..|...|
 |---+---+---|
 |8..|4..|...|
 |..3|.1.|9..|
 |...|..6|..4|
 |---+---+---|
 |...|..8|...|
 |...|2..|..7|
 |967|5..|1.2|
 *-----------*


Play/Print this puzzle online

Dan,

So, what was the significance of the title for this puzzle? Did "AHS" refer to "Almost Hidden Set" or ???

In any case, I want to thank you for all your efforts in posting these puzzles daily. I am not able to always participate but definitely look forward to joining your group of followers on this forum.

Ted

[ArkieTech]

So, what was the significance of the title for this puzzle? Did "AHS" refer to "Almost Hidden Set" or ???

I also am trying to learn about almost hidden sets and the difference between AHS and ALS. I think (1=63)r47c9 is an AHS in this puzzle. In this forum a way to learn is to try something and generally if it is wrong someone will tell you.

[daj95376]

Code: Select all

 +-----------------------------------------------------------------------+
 |  3      18     2      |  18     9      7      |  4      6      5      |
 |  7      5      6      |  18     4      3      |  28     12     9      |
 |  14     9      48     |  6      25     25     |  378    137    13     |
 |-----------------------+-----------------------+-----------------------|
 |  8      127    15     |  4      25     9      |  2367   12357  136    |
 |  6      4      3      |  7      1      25     |  9      25     8      |
 |  125    127    9      |  3      8      6      |  27     1257   4      |
 |-----------------------+-----------------------+-----------------------|
 |  125    123    15     |  9      7      8      |  356    4      36     |
 |  45     38     48     |  2      6      1      |  35     9      7      |
 |  9      6      7      |  5      3      4      |  1      8      2      |
 +-----------------------------------------------------------------------+
 # 49 eliminations remain


I'd like to express my opinion on AHS versus ANS. [Box 9] offers trivial examples.

Code: Select all

<356> ALS r78c7, <356> ALS r7c79, and <356> ALS r7c9,r8c7   (non-chain related)


... = (3  )r7c9 - (3=ANS= 56)r78c7 ...
... = (3-6)r7c9     =AHS= 56)r78c7 ...

... - (3  )r7c9     =AHS=(35)r78c7 ...
... - (3=6)r7c9 - (6=ANS= 35)r78c7 ...


Both sides of an AHS strong inference contain at least one digit in common. This makes Dan's "(1=63)r47c9" an ANS.



An AHS/ANS based on an ALS in (N-1) cells of an N-cell unit is absurd. Except for shortening the notation, an ALS consisting of bivalue cells is also absurd. When reduced to simpler terms, Dan's chain becomes an XY-Chain with an initial SL extension:

Code: Select all

(1)r4c9 = r3c9 - (1=4)r3c1 - (4=5)r8c1 - (5=1)r7c3  =>  r4c3<>1


[ArkieTech]

This would make Dan's "(1=63)r47c9" an ANS.

Thanks Danny,

Now I am really confused. If you remove the 1 from r47c9 you have a 36 pair ANP not ANS.

ANS is almost naked set not almost naked single. Is there a difference between ALS and ANS?

[daj95376]

This would make Dan's "(1=63)r47c9" an ANS.

Thanks Danny,

Now I am really confused. If you remove the 1 from r47c9 you have a 36 pair ANP not ANS.

If you remove <1> from r47c9, you end up with the <36> Naked Pair. No almost about it.

Thus, the ANS can be qualified as an ANP. Something Ted tends to do in his descriptions. For example:

Code: Select all

(1=ANS=63)r47c9 -or- (1=ANP=63)r47c9 -or- ANP(1=63)r47c9   -OR-   (1)r4c9 = NP(63)r47c9


[Marty R.]

Code: Select all

+------------+----------+----------------+
| 3   18  2  | 18 9  7  | 4    6     5   |
| 7   5   6  | 18 4  3  | 28   12    9   |
| 14  9   48 | 6  25 25 | 378  137   13  |
+------------+----------+----------------+
| 8   127 15 | 4  25 9  | 2367 12357 136 |
| 6   4   3  | 7  1  25 | 9    25    8   |
| 125 127 9  | 3  8  6  | 27   1257  4   |
+------------+----------+----------------+
| 125 123 15 | 9  7  8  | 356  4     36  |
| 45  38  48 | 2  6  1  | 35   9     7   |
| 9   6   7  | 5  3  4  | 1    8     2   |
+------------+----------+----------------+


Play this puzzle online at the Daily Sudoku site

Same elimination of 1 as a few others.

(1=5)r7c3-(5=4)r8c1-(4=1)r3c1-r3c89=r2c8-r6c8=r6c12=>r4c3<>1

[daj95376]

Is there a difference between ALS and ANS?

Not to my knowledge. IIRC, the distinction arose when DPB wanted to use AHS and ANS instead of AHS and ALS. Ted also favors the qualified ANS over ALS. As long as you are consistent, I don't see a problem. As an example, I almost always use unit instead of house.