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[ArkieTech]

Code: Select all

 *-----------*
 |2.5|6.8|...|
 |...|.43|.6.|
 |.9.|.7.|...|
 |---+---+---|
 |81.|...|..6|
 |.39|...|18.|
 |4..|...|.59|
 |---+---+---|
 |...|.3.|.9.|
 |.6.|91.|...|
 |...|4.6|5.1|
 *-----------*


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[eleven]

Code: Select all

+----------------------+----------------------+----------------------+
| 2      4      5      | 6      9      8      | 7      1      3      |
| 7      8      1      |#25     4      3      | 9      6     #25     |
| 6      9      3      | 125    7     b12     | 248    24     2458   |
+----------------------+----------------------+----------------------+
| 8      1      27     | 237    5      9      | 234    247    6      |
| 5      3      9      |#27     6      4      | 1      8     #27     |
| 4      27     6      |c12378 a28     127    | 23     5      9      |
+----------------------+----------------------+----------------------+
| 1      5      248    | 278    3      27     | 6      9      248    |
| 3      6      248    | 9      1      5      | 248    247    2478   |
| 9      27     278    | 4      28     6      | 5      3      1      |
+----------------------+----------------------+----------------------+

Hard not to use the x-wings in 2. So i extended it:
Either r2c4 or r5c4 must be 2.
r5c4=2 -> r6c5=8
r2c4=2 -> r3c6=1 -> r6c4=1 -> r6c5=8

[ArkieTech]

Code: Select all

 *--------------------------------------------------------------------*
 | 2      4      5      | 6      9      8      | 7      1      3      |
 | 7      8      1      |c25     4      3      | 9      6     b25     |
 | 6      9      3      | 125    7     c12     | 248    24     2458   |
 |----------------------+----------------------+----------------------|
 | 8      1      27     | 37-2   5      9      | 234    247    6      |
 | 5      3      9      |a27     6      4      | 1      8     b27     |
 | 4      27     6      | 1378-2 8-2   c127    | 23     5      9      |
 |----------------------+----------------------+----------------------|
 | 1      5      248    | 278    3      27     | 6      9      248    |
 | 3      6      248    | 9      1      5      | 248    247    2478   |
 | 9      27     278    | 4      28     6      | 5      3      1      |
 *--------------------------------------------------------------------*
(2=7)r5c4-(7=5)r25c9-(5=7)r2c4,r3c6-(7=2)r5c4,r6c6 => -2r46c4,r6c5; stte

[tlanglet]

AXY-wing(27-8)r5c4,r6c5,r7c4 with (78=2)r7c4
[xy-wing(27-8)r5c4,r6c5,r7c4 => r6c4<>8] = [2r7c4-r5c4=r5c9-r23c9=r3c78-(2=1)r3c6-r6c6=1r6c4 => r6c4<>8] => r6c4<>8

[Marty R.]

Code: Select all

+----------+--------------+--------------+
| 2 4  5   | 6     9  8   | 7   1   3    |
| 7 8  1   | 25    4  3   | 9   6   25   |
| 6 9  3   | 125   7  12  | 248 24  2458 |
+----------+--------------+--------------+
| 8 1  27  | 237   5  9   | 234 247 6    |
| 5 3  9   | 27    6  4   | 1   8   27   |
| 4 27 6   | 12378 28 127 | 23  5   9    |
+----------+--------------+--------------+
| 1 5  248 | 278   3  27  | 6   9   248  |
| 3 6  248 | 9     1  5   | 248 247 2478 |
| 9 27 278 | 4     28 6   | 5   3   1    |
+----------+--------------+--------------+


Play this puzzle online at the Daily Sudoku site

The potential DP 48 in r78c39 does it. Notationally, it's too much of a challenge.

Pseudo cell 27 in r78c9 combines with r5c9 to form a 27 pair. This=>r2c9=5=>r2c4=2=>r5c4=7=>r7c4=8
One of r78c3=2=>r9c2=7=>r9c3=8=>r9c5<>8=>r7c4=8

R7c4=8

[eleven]

The potential DP 48 in r78c39 does it.

Nice

Code: Select all

 *--------------------------------------------------------------------*
 | 2      4      5      | 6      9      8      | 7      1      3      |
 | 7      8      1      |c25     4      3      | 9      6     b25     |
 | 6      9      3      | 125    7     c12     | 248    24     2458   |
 |----------------------+----------------------+----------------------|
 | 8      1      27     | 37-2   5      9      | 234    247    6      |
 | 5      3      9      |a27     6      4      | 1      8     b27     |
 | 4      27     6      | 1378-2 8-2   c127    | 23     5      9      |
 |----------------------+----------------------+----------------------|
 | 1      5      248    | 278    3      27     | 6      9      248    |
 | 3      6      248    | 9      1      5      | 248    247    2478   |
 | 9      27     278    | 4      28     6      | 5      3      1      |
 *--------------------------------------------------------------------*
(2=7)r5c4-(7=5)r25c9-(5=7)r2c4,r3c6-(7=2)r5c4,r6c6 => -2r46c4,r6c5; stte

I neither understand the notation nor the logic, please explain.

[DonM]

Code: Select all

+----------+--------------+--------------+
| 2 4  5   | 6     9  8   | 7   1   3    |
| 7 8  1   | 25    4  3   | 9   6   25   |
| 6 9  3   | 125   7  12  | 248 24  2458 |
+----------+--------------+--------------+
| 8 1  27  | 237   5  9   | 234 247 6    |
| 5 3  9   | 27    6  4   | 1   8   27   |
| 4 27 6   | 12378 28 127 | 23  5   9    |
+----------+--------------+--------------+
| 1 5  248 | 278   3  27  | 6   9   248  |
| 3 6  248 | 9     1  5   | 248 247 2478 |
| 9 27 278 | 4     28 6   | 5   3   1    |
+----------+--------------+--------------+


Play this puzzle online at the Daily Sudoku site

The potential DP 48 in r78c39 does it. Notationally, it's too much of a challenge.

Pseudo cell 27 in r78c9 combines with r5c9 to form a 27 pair. This=>r2c9=5=>r2c4=2=>r5c4=7=>r7c4=8
One of r78c3=2=>r9c2=7=>r9c3=8=>r9c5<>8=>r7c4=8

R7c4=8

Here's one suggestion for notation. Some time ago, Steve K introduced the term 'quantum' to apply to constructs such as the 'effective' naked pair in your solution. There was some discussion over the use of the term 'quantum', but I think it serves to give us a way to notate these constructs. A 'q' is used to denote a 'quantum'.

The chain I use does not follow your logic flow above exactly, but it results in r7c4=8 as yours does.

sis: AUR(48)r78c39[(2)r78c3=(27)r78c9]
(8)r7c4=(8-2)r9c5=grp(2)r9c23-(2)r78c3=qnp(27)r578c9-r2c9=r2c4-(2=1)r3c6-r6c6=(1)r6c4 =>r6c4<>8 -> r7c4=8

Starting the notation with the sis (strong inference set) simply shows the reader what is the basis for your 'effective' naked pair (27). The underlined part is the 'critical' premise of your solution: simply put: if not (2)r78c3 then you have an 'effective' naked pair 27 in r578c9 (signified by 'q' for quantum). The rest of the chain is just a regular AIC.

[ronk]

Some time ago, Steve K introduced the term 'quantum' to apply to constructs such as the 'effective' naked pair in your solution.

This usage for the quantum term was actually first introduced by MadOverlord in 2005.

[DonM]

Some time ago, Steve K introduced the term 'quantum' to apply to constructs such as the 'effective' naked pair in your solution.

This usage for the quantum term was actually first introduced by MadOverlord in 2005.

Perhaps you didn't notice that the sentence does not say 'Steve K first introduced the term 'quantum'. So, unless you are saying that MadOverlord introduced the term 'quantum' to apply to constructs such as the 'effective' naked pair in [the] solution then my point is correct as stated.

[ArkieTech]

Used as an example Here