The New Sudoku Players' Forum

[AnotherLife]

Hello, colleagues,
HoDoKu gives this puzzle a rating of 1642 and suggests a rather illogical and complicated path (as usual, IMHO). I am sure you can devise a better solution.

Code: Select all

.......4....47.6.9.3...87.1.29.4...8.8.....6.3...5.97.8.59...1.4.3.86....7.......

[AnotherLife]

I see that nobody is willing to react to this post, and I consider three main reasons for this.
1. Nobody understands what I mean by 'devise a better solution than HoDoKu (Andrew Stuart's solver, YZF_Sudoku, etc)'.
2. Nobody wants to solve a rather hard puzzle.
3. Nobody bothers to reply to a 'non-colleague' post.

Which is correct?

[champagne]

Your puzzle is rated 7.1 by skfr. This is not a rating for a hard puzzle.
But It can be difficult to find a one step move (excluding basics)
This can explain that the experts in this field did not react

to solve it skfr, out of basics, uses

a UR
an aligned pair exclusion
and small bi values chains

[AnotherLife]

Your puzzle is rated 7.1 by skfr. This is not a rating for a hard puzzle.
But It can be difficult to find a one step move (excluding basics)
This can explain that the experts in this field did not react

to solve it skfr, out of basics, uses

a UR
an aligned pair exclusion
and small bi values chains

Thanks for your reply, sir. I did not mean only one-step solutions but good ones. Maybe I waste time and energy but let me explain the principles of a good solution from my point of view.

1. Simplicity.
2. Conciseness.
3. Consistency in applying the methods.
4. Similarity of the methods used.

I do not have the complete solution by 'skfr' but I see three groups of methods used:
- uniqueness (UR)
- ALS-based methods (aligned pair exclusion)
- chains.
Maybe the solution is also too long and inconsistent.

As to HoDoKu's solution, I can catch all its details. After the basics, the sudoku state becomes as follows:

Code: Select all

.---------------.-------------------.-----------------.
| 2679  59  278 | 1235  12369  2359 | 2358  4     35  |
| 12    15  128 | 4     7      235  | 6     2358  9   |
| 69    3   4   | 25    69     8    | 7     25    1   |
:---------------+-------------------+-----------------:
| 157   2   9   | 6     4      37   | 135   35    8   |
| 157   8   17  | 237   239    2379 | 1345  6     345 |
| 3     4   6   | 8     5      1    | 9     7     2   |
:---------------+-------------------+-----------------:
| 8     6   5   | 9     23     2347 | 234   1     347 |
| 4     19  3   | 1257  8      6    | 25    259   57  |
| 129   7   12  | 135   13     345  | 3458  3589  6   |
'---------------'-------------------'-----------------'

Here the programme applies three groups of methods that are actually futile (let me omit the details):
- chains (an ER and a W-Wing)
- uniqueness (a UR)
- fish (a finned swordfish).
The sudoku state slightly changes, and here the programme constructs a long AIC with 13 nodes:
Discontinuous Nice Loop: 1/2/3 r1c5 =6= r1c1 =7= r1c3 =8= r1c7 -8- r9c7 =8= r9c8 =9= r9c1 -9- r3c1 -6- r3c5 =6= r1c5 => r1c5<>1, r1c5<>2, r1c5<>3

Code: Select all

.---------------.--------------------.-----------------.
| b267 59 c78   | 1235  a1236  2359  | d2358  4    35  |
| 12   15  18   | 4     7      235   | 6     2358  9   |
| h69   3   4   | 25    i69    8     | 7     25    1   |
:---------------+--------------------+-----------------:
| 157  2   9    | 6     4      37    | 135   35    8   |
| 157  8   17   | 237   239    2379  | 1345  6     345 |
| 3    4   6    | 8     5      1     | 9     7     2   |
:---------------+--------------------+-----------------:
| 8    6   5    | 9     23     247   | 234   1     347 |
| 4    19  3    | 1257  8      6     | 25    259   57  |
| g19  7   2    | 135   13     345   | e3458 f389  6   |
'---------------'--------------------'-----------------'

But this chain was available in the above state, so what was the sense in applying the previous 4 methods? HoDoKu's solution takes 6 steps. Obviously, this solution is long, complicated and inconsistent.

Now let me show two good solutions from my point of view.
1. If we want a short solution, we can make it in two main steps by applying only one relatively simple ALS-based method.
- Almost Locked Set XZ-Rule: A=r1c269 {2359}, B=r2c6,r3c4 {235}, X=2, Z=3,5 => r1c45<>3, r1c4<>5, then Locked Candidates https://disk.yandex.ru/i/HHO-8IH7CFVaDw
After finding 20 singles we can apply this method once again (surely, we can also apply a W-Wing but this is actually a chain):
- Almost Locked Set XZ-Rule: A=r39c4 {235}, B=r34c8 {235}, X=2, Z=3 => r9c8<>3 https://disk.yandex.ru/i/DprBRFShZoqdMQ
Then we have only singles.

2. If we want a simple solution, we can make it in four main steps by applying only short chains:
- W-Wing - 3 times
- A continuous nice loop with 8 nodes.
Let me show only the last one. This chain is obviously shorter than HoDoKu's but it leads to five eliminations!
Continuous Nice Loop: 1/2/3/9 6= r1c5 =1= r9c5 -1- r9c1 -9- r3c1 -6- r3c5 =6= r1c5 =1 => r9c4<>1, r1c5<>2, r1c5<>3, r1c15<>9 https://disk.yandex.ru/i/mLy5gjirc92OEw

I would like to get some feedback. Maybe I am wrong, and the Earth is actually flat.

[pjb]

Here's two simple chains:
(1=9)r8c2 - (9)r8c8 = (9-8)r9c8 = (8)r2c8 - (8)r1c7 = (8-7)r1c3 = (7-6)r1c1 = (6-1)r1c5 = (1)r1c4 => -1 r8c4
Naked pairs of 23 at r5c45 => -3 r5c7
(2=8)r2c8 - (8=3)r9c8 - (3=5)r9c4 - (5=2)r3c4 => -2 r3c8; stte

Phil

[AnotherLife]

Here's two simple chains:
(1=9)r8c2 - (9)r8c8 = (9-8)r9c8 = (8)r2c8 - (8)r1c7 = (8-7)r1c3 = (7-6)r1c1 = (6-1)r1c5 = (1)r1c4 => -1 r8c4

Actually, this chain with 15 nodes is even longer than HoDoKu's chain with 13 nodes.

[Cenoman]

Here is a one-step solution, not that complex:

Code: Select all

 +--------------------+------------------------+----------------------+
 |  2679   59   278   |  1235   12369   2359   |  2358   4     b35    |
 |  12     15   128   |  4      7       235    |  6     a2358   9     |
 |  69     3    4     |yd25     69      8      |  7    ze25     1     |
 +--------------------+------------------------+----------------------+
 |  157    2    9     |  6      4       37     |  135   A3-5    8     |
 |  157    8    17    |  237    239     2379   |  1345   6      345   |
 |  3      4    6     |  8      5       1      |  9      7      2     |
 +--------------------+------------------------+----------------------+
 |  8      6    5     |  9     c23      2347   |  234    1      347   |
 |  4      19   3     | c1257   8       6      |  25     259   b57    |
 |  129    7    12    |xc135  xc13      345    |  3458  w3589   6     |
 +--------------------+------------------------+----------------------+

Kraken column (3)r249c8
(3)r2c8 - (3=57)r18c9 - (7=1235)b8p2478 - r3c4 = (5)r3c8
(3)r4c8
(3)r9c8 - (3=15)r9c45 - r3c4 = (5)r3c8
-----------
=> -5 r4c8; ste

[AnotherLife]

Kraken column (3)r249c8
(3)r2c8 - (3=57)r18c9 - (7=1235)b8p2478 - r3c4 = (5)r3c8
(3)r4c8
(3)r9c8 - (3=15)r9c45 - r3c4 = (5)r3c8
-----------
=> -5 r4c8; ste

Thanks, sir. I can see this solution as a forcing chain contradiction in column 8.
1. The red chain in my picture. If r4c8=5, then r3c8<>5, then r3c4=5, then 7 is locked in the brown ALS b8p2478, then 3 is locked in the yellow ALS r18 c9, then r2c8<>3.
2. The blue strong link. If r4c8=5 then r4c8<>3.
3. The black chain in my picture. If r4=5, then r3c8<>5, then r3c4=5, then 3 is locked in ALS r9c45, then r9c8<>3.
https://disk.yandex.ru/i/3ZOppDrHkcm3oQ
So if r4c8=5 then digit 3 is not present in column 8, but this is a contradiction. This means that r4c8<>5.

Actually, HoDoKu shows this solution only if 'Last Resort' methods are switched on in Edit/Preferences/All possible steps.