The New Sudoku Players' Forum

[mareng]

This is a high difficulty puzzle generated
by an unknown computer program. I would
like to solve it without guessing/t&e…
just with pattern recognition...anyone see
a pattern(s)??

1256-8-1269-4679-679-45679-3-469-14679
1356-139-4-6789-36789-2-578-689-1679
356-39-7-4689-1-34569-58-2-469
2347-5-123-12679-23679-13679-49-36-8
1234-6-23-5-239-8-49-7-23
9-237-8-267-4-367-1-5-236
12378-4-1239-12789-5-179-6-389-379
1678-179-169-3-6789-14679-2-489-5
23678-2379-5-246789-26789-4679-78-1-3479

[Hud]

It's kinda hard to see as it's presented. I tried to dub it into the Pappocom program and it rejected it. Maybe you could repost the puzzle in its original form for us?

[lb2064]

This is a high difficulty puzzle generated by an unknown computer program. I would like to solve it without guessing/t&e… just with pattern recognition...anyone see a pattern(s)??

I see a lot of singles! But towards the end it doesn't look like a solvable puzzle - I get a contradiction. Try entering the puzzle into one of the many available programs to see it provides you with any useful hints.

[lb2064]

It's kinda hard to see as it's presented. I tried to dub it into the Pappocom program and it rejected it. Maybe you could repost the puzzle in its original form for us?

Hud - here's the code I managed to decipher from the puzzle

. 8 . | . . . | 3 . .
. . 4 | . . 2 | . . .
. . 7 | . 1 . | . 2 .
-------+-------+------
. 5 . | . . . | . . 8
. 6 . | 5 . 8 | . 7 .
9 . 8 | . 4 . | 1 5 .
-------+-------+------
. 4 . | . 5 . | 6 . .
. . . | 3 . . | 2 . 5
. . 5 | . . . | . 1 .


1256 8 1269 | 4679 679 45679 | 3 469 14679
1356 139 4 | 6789 36789 2 | 578 689 1679
356 39 7 | 4689 1 34569 | 58 2 469
----------------------+----------------------+----------------------
2347 5 123 | 12679 23679 13679 | 49 36 8
1234 6 23 | 5 239 8 | 49 7 23
9 237 8 | 267 4 367 | 1 5 236
----------------------+----------------------+----------------------
12378 4 1239 | 12789 5 179 | 6 389 379
1678 179 169 | 3 6789 14679 | 2 489 5
23678 2379 5 | 246789 26789 4679 | 78 1 3479

[tso]

Please type [code] before your diagrams and [/code] after. Click PREVIEW before SUBMIT. Make sure DISABLE BBCODE IN THIS POST is UNchecked.

That being said, I cannot be of much help solving this.

[edit: I posted the wrong puzzle before.]

Code: Select all

+-------+-------+-------+
| . 8 . | . . . | 3 . . |
| . . 4 | . . 2 | . . . |
| . . 7 | . 1 . | . 2 . |
+-------+-------+-------+
| . 5 . | . . . | . . 8 |
| . 6 . | 5 . 8 | . 7 . |
| 9 . 8 | . 4 . | 1 5 . |
+-------+-------+-------+
| . 4 . | . 5 . | 6 . . |
| . . . | 3 . . | 2 . 5 |
| . . 5 | . . . | . 1 . |
+-------+-------+-------+

Code: Select all

+----------------------+----------------------+----------------------+
| 1256   8      1269   | 4679   679    45679  | 3      469    14679  |
| 1356   139    4      | 6789   36789  2      | 5789   689    1679   |
| 356    39     7      | 4689   1      34569  | 4589   2      469    |
+----------------------+----------------------+----------------------+
| 12347  5      123    | 12679  23679  13679  | 49     3469   8      |
| 1234   6      123    | 5      239    8      | 49     7      2349   |
| 9      237    8      | 267    4      367    | 1      5      236    |
+----------------------+----------------------+----------------------+
| 12378  4      1239   | 12789  5      179    | 6      389    379    |
| 1678   179    169    | 3      6789   14679  | 2      489    5      |
| 23678  2379   5      | 246789 26789  4679   | 4789   1      3479   |
+----------------------+----------------------+----------------------+

[lb2064]

Thanks tso. I always wondered how that was done.

[Hud]

Here's my feeble attempt at organizing this candidates list. Note that my 1s in box 4 differ from the original:

Code: Select all

+---------------+------------------+-------------+
|1256  8    1269|4679   679   45679|3   469 14679| 
|1356  139  4   |6789   36789 2    |578 689 1679 |
|356   39   7   |4689   1     34569|58  2   469  |
+---------------+------------------+-------------+
|2347  5    23  |12679  23679 13679|49  36  8    |
|1234  6    123 |5      239   8    |49  7   23   |
|9     237  8   |267    4     367  |1   5   236  |
+---------------+------------------+-------------+
|12378 4    1239|12789  5     179  |6   389 379  |
|1678  179  169 |3      6789  14679|2   489 5    |
|23678 2379 5   |246789 26789 4679 |78  1   3479 |
+---------------+------------------+-------------+

I thought I'd found a swordfish of 2s but it didn't pan out. I'd like to see if it's a valid puzzle also.

I just looked again, and maybe it is there. Is it a valid swordfish of 2s in columns 2, 5, and 9? Thus elim 2s at R5C1,3, R6C4, and R9C1,4

Even if it works, I'm still pretty much dead.

I believe I forgot that the 2s in the 3 columns must also only occupy 3 rows. Release that swordfish matey.

[lb2064]

..... Is it a valid swordfish of 2s in columns 2, 5, and 9? Thus elim 2s at R5C1,3, R6C4, and R9C1,4......

Not quite a swordfish Hud. You have 4 rows in 4,5,6 and row 9 however you need just 3 for the swordfish. In your revised puzzle, you do have an empty rectangle though which eliminates all the 2's in box 8 thus making r6c4<>2. After that there are a few forced chains but that doesnt seem to help either. Maybe a triple or quadriple chain is needed but my skills arent there for that level of complexity.

[mareng]

Here's the solution (the only one) for this puzzle.... sorry, I should have posted it originally. Thanks for your input... I'm still trying to see what could be done with it, but haven't spotted a pattern yet.
Code:
| 2 8 6 |9 7 5 |3 4 1 |
| 3 1 4 |6 8 2 |5 9 7 |
| 5 9 7 |4 1 3 |8 2 6 |
|7 5 3 |2 9 1 |4 6 8 |
|4 6 1 |5 3 8 |9 7 2 |
|9 2 8 |7 4 6 |1 5 3 |
|8 4 2 |1 5 7 |6 3 9 |
|1 7 9 |3 6 4 |2 8 5 |
|6 3 5 |8 2 9 |7 1 4 |
/ Code:

[Mike Barker]

If you don't mind being a guinea pig, here's one possible solution. I (along with hundreds of others) have been writing my own solver. Basically is to answer what step I should take when I get stuck. It’s still under development, but I ran your puzzle through it and here are the results. No guarantees that the program wrote the steps correctly as well as a couple of other caveats:
1) With apologies to Carcul, I haven't gotten all of his nice loop notation implemented (especially for discontinuous loops where I use a "~" to show discontinuities
2) The solver only prints one elimination for each step (it graphically shows the rest), so you still need to determine other eliminations
3) There is still a lot I could do to make simpler eliminations earlier
4) I use a "Disjoint Strong Link" algorithms for Turbot Chains (3 strong links define a 7-node Turbot Chain)
5) mYZ-wings (XYZ-wing, WXYZ-wing, etc) are generalized (they don't require 3-cell, 4-cell, etc pilot cells)
Hope this helps and please let me know if you see something wrong since this is the first time that I've tried this.

Naked Column Pair: r45c7 => r2c7<>49
Naked Block Pair: r45c7 => r4c8<>49
Locked Row: r4c46 => r4c1<>1
Column X-Wing Fillet-o-Fish: r69c2|r459c5 => r6c4<>2
Column X-Wing Fillet-o-Fish: r457c3|r47c8 => r4c1<>3
Almost Locked Set: xz-rule with A=2 cells: r4c38, r6c246 => r4c4<>6
Hidden Single: r4c8 => r4c8=6
Hidden Single: r7c8 => r7c8=3
Locked Column Box: r239c12 => r5c1<>3
Three Strong Links : r7c14|r3c47|r28c8 => r8c1<>8
WXYZ-wing: r6c246|r4c3 => r4c5<>3
Hidden Single: r4c3 => r4c3=3
Almost Locked Set: xz-rule with A=3 cells: r7c369, r2389c2 => r7c1<>7
Almost Locked Set: xz-rule with A=3 cells: r3c7|r12c8, r123c4|r12c5|r3c6 => r1c6<>4
Almost Locked Set: xz-rule with A=4 cells: r7c3469, r8c1235 => r7c1<>1
Almost Locked Set: xz-rule with A=4 cells: r2389c2, r9c45679 => r9c1<>7
Almost Locked Set: xy-rule with A=2 cells: r9c7|r7c9, r8c12368, r7c1346 => r8c5<>7
Nice Loop: r9c2=2=r6c2-2-r6c9-3-r6c6=3=r3c6-3-r3c2~9~r9c2 => r9c2<>9
Nice Loop: r9c1=3=r9c2=2=r6c2-2-r6c9-3-r6c6=3=r3c6~3~ => r3c1<>3
VWXYZ-wing: r3c179|r12c8 => r3c4<>6
VWXYZ-wing: r3c179|r12c8 => r3c6<>5
Hidden Single: r1c6 => r1c6=5
Almost Locked Set: xz-rule with A=2 cells: r3c17, r12c8|r3c9 => r2c7<>8
Almost Locked Set: xy-rule with A=1 cells: r3c1, r3c7|r12c8, r35679c9 => r1c9<>4
Row X-Wing Fillet-o-Fish: r1c48|r8c68 => r9c4<>4
Locked Column: r89c6 => r3c6<>4
Naked Row Pair: r3c26 => r3c4<>39
Almost Locked Set: xy-rule with A=1 cells: r3c1, r3c7|r12c8, r35679c9 => r1c9<>9
Almost Locked Set: xz-rule with A=2 cells: r9c7|r8c8, r34678c6 => r9c6<>7
Nice Loop: r8c6=4=r9c6-4-r9c9=4=r3c9=6=r3c1-6-r1c3=6=r8c3~6~r8c6 => r8c6<>6
Almost Locked Set: xy-rule with A=4 cells: r3478c6, r3c12479, r28c8 => r2c2<>9
Almost Locked Set: xy-rule with A=1 cells: r3c6, r6c246, r123c1|r23c2 => r4c1<>2
Locked Row Box: r5c39|r6c29 => r5c5<>2
Almost Locked Set: xz-rule with A=1 cells: r2c2, r23458c1 => r1c1<>1
Almost Locked Set: xy-rule with A=2 cells: r57c3, r1c13458, r7c9 => r1c9<>7
Locked Row: r2c79 => r2c4<>7
VWXYZ-wing: r3c469|r2c45 => r2c9<>6
Almost Locked Set: xz-rule with A=2 cells: r9c7|r8c8, r1c13589 => r9c5<>7
Almost Locked Set: xz-rule with A=3 cells: r2c458, r46c4|r45c5|r4c6 => r1c4<>6
Almost Locked Set: xy-rule with A=2 cells: r6c46, r24589c5, r3c14679 => r1c5<>9
Almost Locked Set: xy-rule with A=2 cells: r57c3, r23c12|r1c3, r12567c9 => r1c1<>6
Naked Single: r1c1 => r1c3<>2
Naked Single: r7c1 => r7c4<>8
Almost Locked Set: xy-rule with A=1 cells: r6c2, r89c12|r8c3, r6c46|r5c5 => r8c5<>9
Almost Locked Set: xz-rule with A=2 cells: r8c58, r1c389 => r1c5<>6
Naked Single: r1c5 => r1c4<>7
Naked Row Pair: r1c48 => r1c3<>49
Hidden Single: r3c2 => r3c2=9
Naked Single: r3c6 => r6c6<>3
Hidden Single: r5c5 => r5c5=3

The rest is singles

[re'born]

Mike,

I went through your solver's derivation and it seems to check out. One thing worth noting is that your solver is not getting the biggest "bang for its buck" out the ALS. As your solver output does not give all of the deductions, I'm sure where the first instance it misses something is exactly, but in Step 23 and Step 24 you have:

Almost Locked Set: xz-rule with A=2 cells: r3c17, r12c8|r3c9 => r2c7<>8

Almost Locked Set: xy-rule with A=1 cells: r3c1, r3c7|r12c8, r35679c9 => r1c9<>4

From this, I concluded that in Step 23, r1c9<>4 is not one of the hidden deductions. However, it can be deduced from precisely the same set as was used in Step 23. This is because the 5 cells in that step contain 5 candidates and hence is a locked set. Therefore, we may conclude r2c7<>8 (which you concluded from the xz-rule) as well as r1c9<>4 and r12c9<>9. Naturally, these extra deductions do not come from the xz-rule, but from aeb's subset principle (see
http://forum.enjoysudoku.com/viewtopic.php?t=3479&highlight=subset+principle). One of the beauties of the principle is that it does not only apply when the cells form a locked set, but even almost locked sets (or worse). For instance, one could now replace the deduction in Step 24 with r8c8<>9 (from the same ALS) which will create locked 9's in box 9 which will lead to r3c9<>9.

I'm sure there are other places where it might be useful, I just can't say exactly where since I don't know precisely what your solver deduced at each step. As I am not a programmer, it is not clear to me whether or not this would be difficult to add to a solver, but given the relative ease with which I can find the deductions (having been given the appropriate sets), I can't imagine it being so bad.

[Edit: I don't know why I didn't see this before, but you use the exact same locked set in the two VWXYZ steps (Steps 20 and 21). So you can, starting from just after Step 19, make all of the deductions at once from that one locked set, namely: r3c46<>6, r3c6<>5, r1c9<>4, r2c7<>8, r12c9<>9. Not bad.]

[Mike Barker]

Thanks for the feedback. I agree I could get more bang for my buck and will look into it in the future although I'm not sure which more advanced techniques I'll implement. The idea for the solver is an aid for me to identify what technique I should use to help me hand solve a puzzle. Unlike you I'm not sure I could actually identify one of aeb's subsets!

[re'born]

Mike,

Oh I think it would be a bit of a stretch to say that I can identify aeb's subsets. What I can do is once given the subset (as your output did), I can identify all of the eliminations using his principle. Though there are probably lots of examples of the principle that are not based on the standard ALS rules, even if you just test for ALS's and then use the subset principle instead of, say, the xz-rule, you will be better off.

[ronk]

Naturally, these extra deductions do not come from the xz-rule, but from aeb's subset principle (see
http://forum.enjoysudoku.com/viewtopic.php?t=3479&highlight=subset+principle).

Au contraire! It is indeed the xz-rule for the special case where x and z are interchangeable. IOW both x and z are 'restricted common' in bennys' original terms. Although his examples weren't the best, it's what Bob Hanson first described as almost-locked sets -- doubly weakly linked last December. It's also a generalized case of the Two-Sector Disjoint Sets described by Sue de Coq last October.

[re'born]

Ron,

Help me out here. Please explain how to use the ALS xz-rule on

Almost Locked Set: xz-rule with A=2 cells: r3c17, r12c8|r3c9 => r2c7<>8

to obtain r12c9<>9. I can do it if I set up the sets as

A={r3c17, r2c8}, B = {r1c8, r3c9} with the restricted common as x = 6 and the other common as z = 9.

But with the sets gven as above, I don't see it, for 9 does not appear to me to be a common candidate.

Thanks for your help.