The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|..1|.4.|
 |.5.|3..|91.|
 |1..|4..|7.2|
 |---+---+---|
 |...|...|.8.|
 |8.6|.7.|5.3|
 |.7.|...|...|
 |---+---+---|
 |5.1|..3|..9|
 |.63|..7|.2.|
 |.4.|1..|...|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*--------------------------------------------------------------*
| 6     239   29     | 7     59    1      | 38    4     58     |
| 47    5     47     | 3     28    28     | 9     1     6      |
| 1    d389  e89     | 4     569   569    | 7    c35    2      |
|--------------------+--------------------+--------------------|
| 234   29    2459   | 569   13    56     | 124   8     7      |
| 8     1     6      | 2     7     4      | 5     9     3      |
| 234   7     59     | 589   13    58     | 124   6     14     |
|--------------------+--------------------+--------------------|
| 5     28    1      | 68    2468  3      | 468   7     9      |
| 9     6     3      | 58    458   7      | 148   2     14     |
| 27    4     27-8   | 1     2689  2689   | 368  b35   a58     |
*--------------------------------------------------------------*

(8=5) r9c9 - r9c8 = (5-3) r3c8 = (3-8) r3c2 = (8) r3c3 => - 8 r9c3; stte

Leren

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 | 6     239   29    | 7    c59    1     | 38    4     8-5   |
 | 47    5     47    | 3     28    28    | 9     1     6     |
 | 1     389   89    | 4     569   569   | 7     35    2     |
 *-------------------+-------------------+-------------------|
 | 234   29    2459  | 569   13    56    | 124   8     7     |
 | 8     1     6     | 2     7     4     | 5     9     3     |
 | 234   7     59    | 589   13    58    | 124   6     14    |
 *-------------------+-------------------+-------------------|
 | 5    b28    1     |b68    2468  3     | 468   7     9     |
 | 9     6     3     | 58    458   7     | 148   2     14    |
 |a27    4    a278   | 1    c2689  2689  | 368   35   a58    |
 *-----------------------------------------------------------*


(5=28*)r9c139 - (2=6)r7c24 - (6*28=5)r19c5 => -5 r1c9 ; stte

Or a variation on the theme:

(5=28)r9c139 - (28=69)r9c56 - (6=8)r7c4 - r7c2 = (8)r9c3 => -8 r9c9 ; stte

[bat999]

And my noob version...
What happens when r3c8 or r9c8 is 5.
When r3c8 is 5.. r3c56 are 69 (ALS) and r3c3 is not 9, it's 8.
So r9c3 is not 8.
When r9c8 is 5, r9c9 is 8 so again r9c3 is not 8.
=> - 8 r9c3; stte

This is probably a longwinded version of Leren's solution.

[SteveG48]

And my noob version...
What happens when r3c8 or r9c8 is 5.
When r3c8 is 5.. r3c56 are 69 (ALS) and r3c3 is not 9, it's 8.
So r9c3 is not 8.
When r9c8 is 5, r9c9 is 8 so again r9c3 is not 8.
=> - 8 r9c3; stte

This is probably a longwinded version of Leren's solution.

Not quite. This is Leren's:

(8=5) r9c9 - r9c8 = (5-3) r3c8 = (3-8) r3c2 = (8) r3c3 => - 8 r9c3; stte

And this is yours:

(8=5)r9c9 - r9c8 = r3c8 - (5=69)r3c56 - (9=8)r3c3 => -8 r9c3 ; stte

They're quite similar, but Leren uses r3c2 and you use the pair r3c56 for another nice solution. Both establish the strong link between 8's in r9c9 and r3c3. Keep at it. Try to express your solutions as AI chains.

[bat999]

.. but Leren uses r3c2...

I see, when r3c8 makes r3c2 the 3, only r3c3 can be an 8 in that box.

[SteveG48]

.. but Leren uses r2c2...

I think you mean r3c2.
I see, when r3c8 makes r3c2 the 3, only r3c3 can be an 8 in that box.

Right, thanks! I fixed the typo in my post.

[Leren]

Hi Bat,

I've noticed that you tend to look for Kraken constructions. In this case your wordy argument can be expressed as :

Code: Select all

Kraken Column 8 Digit 5:

5 r3c8 - (5=69)r3c56 - (9=8)r3c3 - 8 r9c3;

5 r9c8 - (5=8) r9c9              - 8 r9c3; => - 8 r9c3

There is nothing wrong with this logic, but when a Kraken construction has only 2 branches it can always be re-expressed more elegantly as a linear (non-branching) Alternating Inference Chain (AIC).

All you have to do is reverse the sign of the second leg and append it to the first leg as follows:

8 r9c3 - (8=5) r9c9 - r9c8 = r3c8 - (5=69)r3c56 - (9=8)r3c3 - 8 r9c3; => - 8 r9c3

In this form it is a discontinuous loop that assumes that 8 r9c3 is True and shows that it is False, so it must be False.

This AIC is still regarded as slightly inelegant because it starts and ends on Weak links involving the same single digit.

Aficionados of elegance tend to drop the first and last terms so that the AIC starts and ends on Strong links:

(8=5) r9c9 - r9c8 = r3c8 - (5=69)r3c56 - (9=8)r3c3; => - 8 r9c3

The logic of this form is slightly different - at least one of the 8's in the first and last terms must be True, so any 8 that can see both of the 8's in the first and last terms must be False.

Hope this helps, Leren

PS Have a look at the following Hodoku page on chains and loops.

http://hodoku.sourceforge.net/en/tech_chains.php#nl