## The hardest sudokus

Everything about Sudoku that doesn't fit in one of the other sections
Claudiarabia wrote:which require a guess

No need to guess:

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` *-----------------------------------------------------------* | 34    13    9     | 6     137   8     | 5     347   2     | | 35    6     7     | 59    4     2     | 8     139   13    | | 3458  1358  2     | 59    137   13    | 6     3479  347   | |-------------------+-------------------+-------------------| | 6     37    5     | 8     13    4     | 17    2     9     | | 37    9     48    | 13    2     6     | 17    5     48    | | 1     2     48    | 7     5     9     | 3     48    6     | |-------------------+-------------------+-------------------| | 9     4     6     | 13    8     137   | 2     17    5     | | 578   578   3     | 2     9     17    | 4     6     178   | | 2     78    1     | 4     6     5     | 9     378   378   | *-----------------------------------------------------------*`

[r8c9](-8-[r8c12]=8=[r9c2]-8-[r3c2]=8=[r3c1]=4=[r1c1]-4-[r1c8])-8-
[r5c9]-4-[r3c9]=4=[r3c8]=9=[r2c8]-9-[r2c4]-5-[r2c1]=5=[r3c2]-5-
[r8c2]-7-[r4c2]=7=[r5c1]=3=[r5c4]=1=[r7c4]-1-[r8c6]=1=[r8c9],
=> r8c9<>8 and the puzzle is solved.

Carcul
Carcul

Posts: 724
Joined: 04 November 2005

There is a new sudoku book announced for end of August: Mensa Guide to Solving Sudoku: Hundreds of Puzzles & Techniques to Help You Crack Them All (Peter Gordon, Frank Longo). It says:
"Hidden pairs, naked pairs, X-wings, jellyfish, squirmbag, bivalue and bilocation graphs, turbot fish, grid coloring, chains: every single one is here, and much more too, including the exclusive Gordonian logic methods (Gordonian rectangles and Gordonian polygons) that will turn even the hardest puzzles into a breeze."
So i am curious, how these exclusive methods will crack the puzzles here
(is "Gordonian" a synonym for "unique" ? )
ravel

Posts: 998
Joined: 21 February 2006

I have a collection of 56 puzzles from my still-in-development generator. I doubt any qualify as hardest, but I'm hoping some of them will qualify as hard. May I post them to this thread and get feedback on any that may prove difficult?
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

In order to try to start to understand the magic which makes a tough puzzle tough I ran Ravel's 6-10 steppers through my solver to see what is left after it has eliminated everything that it can. In most cases not much was eliminated. One thing that was very clear was that analysis of most of the puzzles was completed very quickly indicating very few strong links, bivalue cells, ALS and grouped strong links. This is probably critical which got me thinking - if these are so important how can I demonstrate this. I've started to go through the puzzles identify bivalue cells, identify the candidate which doesn't go into the bivalue cell, and set this value in the cell which does contain it. Although it didn't always work with just one BFE, in many cases one placement was all that was needed to crack the puzzle. This supports the theory of the importance of bivalued cells. I've started to note these in the results below (#124, #4, #125, #6, #8, #126, and #10) and will look into the rest of the puzzles over the coming days. It wouldn't surprise me if the same thing holds for strong links - basically a butterfly affect - no butterfly then no tsunami, but one correct flap of the wings and surfs up.

By the way daj, I'd be happy to look at your puzzles.

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`1: top1465 #77  "the toughest known", +----------------------+---------------------+---------------------+|       7  1589    568 |  1269  13569  23569 |      4   125    123 ||   14569     2    456 |  1469      7   3459 |    156     8     13 ||    1456   145      3 |  1246    156      8 |  12567  1257      9 |+----------------------+---------------------+---------------------+|    2489  4789   2478 |     5   1689    469 |      3  1247  12478 ||    3458     6   4578 |   148      2     34 |   1578     9   1478 ||  234589  4589      1 |   489    389      7 |    258   245      6 |+----------------------+---------------------+---------------------+|   12568  1578  25678 |     3    568    256 |      9  1247  12478 ||    1258     3   2578 |  2789      4    259 |   1278     6   1278 ||    2468   478      9 |  2678     68      1 |    278     3      5 |+----------------------+---------------------+---------------------+Hidden Single: r9c8 => r9c8=3,r1c8<>3Locked Row Line/Box: r7c89 => r7c123<>4Grouped Nice Loop: r1c456=6=r1c3-6-ALS:r3c12|r2c3-1-ALS:r379c5-6-r4c5=6=r4c6~6~ => r2c6<>6top1465 #89  +-------------------+----------------------+---------------------+|  1469  1248   468 |      3   267      78 |     5  246789  4689 ||   469     5  2468 |   2689     1     278 |  6789       3  4689 ||   369   238     7 |   5689   256       4 |   689    2689     1 |+-------------------+----------------------+---------------------+|     2   378     9 |    158   357   13578 |     4    1678  3568 ||   345     6   348 |  12458     9  123578 |  1378     178   358 ||   345  3478     1 |    458  3457       6 |   389     789     2 |+-------------------+----------------------+---------------------+|     8   134   346 |      7  3456     135 |     2    1469  3469 ||     7     9  2346 |   1246     8     123 |   136       5   346 ||  1346  1234     5 |    146  2346       9 |  1368    1468     7 |+-------------------+----------------------+---------------------+Hidden Single: r8c1 => r8c1=7,r56c1<>7Row X-Wing Fillet-o-Fish: r2c67|r5c678 => r6c7<>7Row Swordfish Fillet-o-Fish: r1c1389|r4c389|r7c89 => r2c3<>9Column Swordfish: r139c25|r13c8 => r1c36<>2,r39c4<>2Nice Loop: r4c9=5=r5c9-5-r5c1=5=r6c1=9=r4c3~9~r4c9 => r4c9<>9Nice Loop: r6c1=5=r5c1-5-r5c9=5=r4c9=6=r4c8=9=r4c3~9~r6c1 => r6c1<>9Hidden Single: r4c3 => r4c3=9,r4c8<>9,r1c3<>9124:  Ruud #13/15 +--------------------+-----------------------+--------------------+|      4    17   168 |      3    269      29 |     5    678  2678 ||    378     9   368 |    678      5    2478 |  3478      1  2378 ||   3578   357     2 |   1678   1468     178 |   378   4678     9 |+--------------------+-----------------------+--------------------+|      9   145  1358 |      2    148    1578 |     6    578  1378 ||    158     6  1458 |  15789      3  145789 |  1789      2   178 ||  12358  1235     7 |   1589    189       6 |  1389    589     4 |+--------------------+-----------------------+--------------------+|      6  1357  1359 |      4    189    1589 |     2    789   178 ||    125     8  1459 |   1569      7    1259 |   149      3    16 ||    127  1247    19 |   1689  12689       3 |  1789  46789     5 |+--------------------+-----------------------+--------------------+Column Swordfish: r49c2|r34c5|r39c8 => r4c36<>4,r9c37<>4,r3c67<>4Nice Loop: r2c9=2=r2c6=4=r2c7-4-r3c8=4=r9c8=6=r8c9~6~r2c9 => r2c9<>6Nice Loop: r4c9=3=r2c9=2=r2c6=4=r3c5-4-r4c5=4=r4c2~4~r4c9 => r4c2<>3ALS xz-rule with A=3 cells: r467c5-4-r23c4|r3c56 => r1c5<>1,r1c5<>8ALS xy-rule with B=3 cells: r23c4|r3c56-4-r467c5-9-r1c23589 => r1c6<>7,r1c6<>8,r3c12<>1,r1c6<>1Note: r3c1=1 at this point essentially solves the puzzle3: top1465 #130 +---------------------+--------------------+----------------------+|     5   1379  13679 |     4   236    367 |      8  23679  23679 ||   478   3478    367 |  2578     9  35678 |    236      1  23467 ||  4789  34789      2 |    78   368      1 |    369  34679      5 |+---------------------+--------------------+----------------------+|     6  12789    179 |     3  1258    589 |      4   2579    279 ||  1289      5     39 |  1289     7      4 |  12369   2369   2369 ||  1279   2379      4 |  1259   256    569 |  12359  23579      8 |+---------------------+--------------------+----------------------+|     3   1249    159 |     6  1458    589 |      7   2459    249 ||  1249      6    579 |  1579   345   3579 |   2359      8   2349 ||   479    479      8 |   579   345      2 |   3569  34569      1 |+---------------------+--------------------+----------------------+Hidden Single: r5c6 => r5c6=4,r78c6<>4Locked Row Line/Box: r6c56 => r6c78<>6Column Swordfish: r568c14|r56c7 => r5c3<>1,r6c25<>1,r8c35<>1Grouped Nice Loop: ALS:r239c1-8-r5c1=8=r5c4-8-r3c4-7-r12c6=7=r8c6~7~ => r8c1<>74: top1465 #201 +---------------------+---------------------+--------------------+|      3  2469    469 |     5    789   2678 |     1  2479    279 ||  12459     7  14569 |   269     19    236 |   245     8    359 ||   1259  1259      8 |  2379   1379      4 |   257  2379      6 |+---------------------+---------------------+--------------------+|      6  1258     15 |     4    578  23578 |     9   127  12378 ||   1249     3    149 |  2789      6    278 |   278     5   1278 ||    259  2589      7 |  2389   3589      1 |     6    23      4 |+---------------------+---------------------+--------------------+|      8  4569    569 |     1    457    567 |     3  2479   2579 ||  14579  1459      3 |    78      2    578 |  4578     6    179 ||    157  1456      2 |  3678  34578      9 |  4578   147   1578 |+---------------------+---------------------+--------------------+Note: r4c9=3 essentially solves the puzzleHidden Single: r8c3 => r8c3=3,r8c46<>3Hidden Single: r6c7 => r6c7=6Column X-Wing: r24c69 => r2c45<>3,r4c58<>3Row Swordfish Fillet-o-Fish: r2c137|r5c13|r8c127 => r9c1<>4,r7c3<>4Nice Loop: r7c9=2=r7c8-2-r6c8-3-r3c8=3=r2c9~3~r7c9 => r2c9<>2ALS xz-rule with A=3 cells: r8c467-4-r9c1789 => r8c9<>8ALS xy-rule with B=4 cells: r8c46-7-r7c2356-9-r89c7|r79c89 => r8c9<>5125:  Ruud #7/15 +---------------------+------------------+--------------------+|      8  1356  13456 |     9  125    25 |     7   356   3456 ||    567     9   1356 |  1378    4    57 |  1368     2   3568 ||    457  1357      2 |   378  158     6 |   138  3458      9 |+---------------------+------------------+--------------------+|      1   368  34689 |     2   89   479 |     5  3678  34678 ||     59     2  34589 |    78    6  4579 |   389     1   3478 ||   4569   568      7 |    18  158     3 |   689   468      2 |+---------------------+------------------+--------------------+|      3  1678    168 |     5   29    29 |     4   678    678 ||     25     4     58 |     6    7     1 |   238     9    358 ||  25679   567    569 |     4    3     8 |    26   567      1 |+---------------------+------------------+--------------------+Note: r1c5=2 essentially solves the puzzleHidden Single: r9c4 => r9c4=4,r456c4<>4Hidden Single: r8c4 => r8c4=6,r8c1379<>6Hidden Single: r4c4 => r4c4=2,r4c56<>2Hidden Single: r9c5 => r9c5=3,r9c78<>3,r13c5<>3Locked Row Line/Box: r7c56 => r7c3<>9Locked Row Box/Box: r89c17 => r8c6<>2Naked Single: r8c6 => r8c3<>1,r127c6<>1,r7c5<>1Row X-Wing: r36c18 => r5c1<>4,r14c8<>4UR+3KD: r36c45, r6c1278, r1c56 => r3c4<>1Nice Loop: r6c5=5=r5c6-5-r5c1-9-r5c7=9=r6c7~9~r6c5 => r6c5<>95: top1465 #125 +---------------------+---------------------+---------------------+|      4  2579   2579 |      6     19   158 |     3  25789    289 ||     37     1   3579 |   3459      2  3458 |  4789      6    489 ||    236  2569      8 |   3459    349     7 |   249    259      1 |+---------------------+---------------------+---------------------+|      9   267  12367 |      8  13467  1346 |     5     23   2346 ||  23678     4   2367 |    379      5    36 |   289      1  23689 ||   1368   568   1356 |   1349  13469     2 |   489    389      7 |+---------------------+---------------------+---------------------+|      5  2789  12479 |  12347   1347   134 |     6  23789   2389 ||   1267     3  12679 |   1257      8    56 |  1279      4     29 ||  12678  2678  12467 |  12347   3467     9 |  1278   2378      5 |+---------------------+---------------------+---------------------+Column Swordfish Fillet-o-Fish: r689c1|r6789c4|r89c7 => r8c6<>1,r9c5<>16: top1465 #280 +-------------------+---------------------+----------------------+|     1    49  2478 |     36     5     36 |   2479    249    248 ||  4789  4569  4678 |      2   489      1 |  34579   3459   3458 ||  2489   459     3 |     48     7     89 |   2459      6      1 |+-------------------+---------------------+----------------------+|     3    14   147 |  45678   248  25678 |  24568    245      9 ||     6     2     9 |   1458   148     58 |   3458    345      7 ||    47     8     5 |      9     3    267 |    246      1    246 |+-------------------+---------------------+----------------------+|   249     3   124 |    157     6   2579 |   2459      8    245 ||  2489     7  2468 |    358   289  23589 |      1  23459  23456 ||     5   169  1268 |    138  1289      4 |   2369      7    236 |+-------------------+---------------------+----------------------+Note: r3c1=9 essentially solves the puzzleHidden Single: r4c1 => r4c1=3,r4c78<>3Hidden Single: r5c3 => r5c3=9,r12789c3<>9Hidden Single: r3c9 => r3c9=1,r6c9<>1Hidden Single: r6c8 => r6c8=1,r45c8<>1Locked Row Line/Box: r4c23 => r4c45<>1Locked Row Line/Box: r1c46 => r1c789<>3Locked Row Line/Box: r1c46 => r1c23<>6Locked Column Line/Box: r45c7 => r123c7<>8Naked Block Triple: r3c46|r2c5 => r1c4<>48,r1c6<>897: top1465 #303 +-------------------+-------------------+---------------------+|    239    39    6 |  3458  4589  2345 |      7  2489      1 ||   1279    79    4 |  1678  1689    26 |      5     3    289 ||  12379     8    5 |   347   149   234 |     49     6    249 |+-------------------+-------------------+---------------------+|      6  3457    2 |     9   458     1 |    348   478   3478 ||    349     1  389 |     2   468     7 |  34689   489      5 ||   4579  4579  789 |   468     3   456 |      2     1  46789 |+-------------------+-------------------+---------------------+|   3479     2  379 |  1346   146     8 |  13469     5  34679 ||      8  3457    1 |  3456     2     9 |    346    47   3467 ||   3459     6   39 |  1345     7   345 |  13489  2489  23489 |+-------------------+-------------------+---------------------+Hidden Single: r1c3 => r1c3=6,r1c456<>6Hidden Single: r4c3 => r4c3=2,r5c31<>2Hidden Single: r5c4 => r5c4=2,r123c4<>2Hidden Single: r2c7 => r2c7=5,r2c456<>5Hidden Single: r6c8 => r6c8=1,r9c8<>1Empty Column Rectangle : r68c2|r8c4 => r6c4<>5UR+4C/3SL: r23c14 => r3c4<>18: top1465 #113 +----------------------+---------------------+--------------------+|      5   4678  14689 |     2    169    179 |     3   178    147 ||    134   3467   1346 |   567      8    157 |  1257     9  12457 ||    189     78      2 |   579      3      4 |  1578  1578      6 |+----------------------+---------------------+--------------------+|      6  23458    348 |     1    245   2578 |     9   357   2357 ||   2389      1    389 |  5678   2569  25789 |  2567     4   2357 ||    249    245      7 |  4569  24569      3 |  1256   156      8 |+----------------------+---------------------+--------------------+|      7    268    168 |     3   1259  12589 |     4  1568     15 ||   1348      9  13468 |   458      7    158 |  1568     2    135 ||  12348   2348      5 |    48    124      6 |   178  1378      9 |+----------------------+---------------------+--------------------+Note: r1c3=8 essentially solves the puzzleHidden Single: r3c5 => r3c5=3,r3c12<>3Empty Column Rectangle : r35c1|r3c4 => r5c4<>99: top1465 #200 +--------------------+----------------------+----------------------+|      6  2458  2358 |     1   23459    234 |       7    49    259 ||   2345  1245  1235 |  3569       7   2346 |     269     8   2569 ||    245     7     9 |    56    2456      8 |     126   146      3 |+--------------------+----------------------+----------------------+|      7  1689   128 |     4  123689   1236 |       5  1369    169 ||    589     3    15 |  6789     169    167 |     169     2      4 ||     29  1269     4 |   369   12369      5 |     369     7      8 |+--------------------+----------------------+----------------------+|      1   589  3578 |     2    3568    367 |       4   369    679 ||  23489   249   237 |  3678    1346  13467 |  123689     5  12679 ||  23458   245     6 |  3578    1345      9 |    1238    13    127 |+--------------------+----------------------+----------------------+Hidden Single: r3c2 => r3c2=7,r789c2<>7Hidden Single: r5c9 => r5c9=4,r12c9<>4Hidden Single: r6c8 => r6c8=7,r6c4<>7,r79c8<>7Locked Row Line/Box: r2c23 => r2c79<>1Column Swordfish: r589c14|r89c7 => r5c35<>8,r8c235<>8,r9c25<>8Nice Loop: r3c7=1=r3c8-1-r9c8-3-r4c8=3=r6c7~3~r3c7 => r6c7<>1ALS xz-rule with A=3 cells: r6c147-6-r126789c2 => r4c2<>2126:  Ruud #11/15 +---------------------+--------------------+----------------------+|      1   278    578 |     9  4578   2457 |      3    467    267 ||  35789     6    357 |  2358     1  23457 |    478   2479   2479 ||   3789  2379      4 |   238    37      6 |    178   1279      5 |+---------------------+--------------------+----------------------+|      4   389   3568 |     7   368    135 |      2   1569     69 ||   6789     1    567 |   568     2     45 |   4567      3   4679 ||   3567    37      2 |  1356  3456      9 |  14567  14567      8 |+---------------------+--------------------+----------------------+|      2   378  13678 |     4  3567   1357 |      9    567    367 ||    367     5   1367 |  1236     9   1237 |    467      8  23467 ||    367     4      9 |  2356  3567      8 |    567   2567      1 |+---------------------+--------------------+----------------------+Note: r4c2=3 solves the puzzleHidden Single: r9c2 => r9c2=4,r9c78<>4Hidden Single: r8c5 => r8c5=9Column X-Wing Fillet-o-Fish: r16c5|r126c8 => r1c9<>4Column Swordfish: r235c14|r23c7 => r2c3<>8,r3c25<>8,r5c3<>8ALS xz-rule with A=1 cells: r5c6-4-r3679c5 => r4c5<>5Nice Loop: r1c2=2=r3c2=9=r4c2-9-r4c9-6-r1c9=6=r1c8~6~r1c2 => r1c8<>2Nice Loop: r5c1=8=r5c4-8-r4c5=8=r1c5=4=r6c5-4-r5c6~5~r5c1 => r5c1<>5127:  Ruud #14/15 +----------------------+--------------------+-------------------+|   3468  23678  24678 |     9  1468   1348 |     5   247  1237 ||    346      1    246 |  3456     7    345 |    23     8     9 ||   3489   3789      5 |   134   148      2 |   137    47     6 |+----------------------+--------------------+-------------------+|      2    368    168 |     7  1589  13589 |     4   356   135 ||  13468      5  14678 |   134     2   1348 |  1367     9   137 ||    134     37      9 |  1345   145      6 |  1237  2357     8 |+----------------------+--------------------+-------------------+|      7     26    126 |     8  1456    145 |     9  2356   235 ||   5689      4    268 |   256     3     59 |  2678     1   257 ||  15689   2689      3 |  1256  1569      7 |   268   256     4 |+----------------------+--------------------+-------------------+Hidden Single: r2c9 => r2c9=9,r2c1<>9ALS xy-rule with B=5 cells: r2c7-2-r6c12457-7-r4679c8 => r13c8<>3128:  Ruud #4/13+--------------------+---------------------+----------------------+|      8  1579    15 |     6    139    139 |       4   2359  2579 ||   4579     3  1456 |  1458      2   1489 |    5679    589  5689 ||    459   569     2 |  3458   3489      7 |    3569   3589     1 |+--------------------+---------------------+----------------------+|      6  1257  1358 |     9   1347  12348 |     125  12458   258 ||     23     4    38 |    13      5  12368 |    1269      7  2689 ||    257   125     9 |  1478   1468  12468 |    1256  12458     3 |+--------------------+---------------------+----------------------+|      1   569  3456 |     2  34679   3469 |       8    359   579 ||  23459     8   345 |  1347   1349   1349 |  123579      6   259 ||    239   269     7 |    38  13689      5 |    1239   1239     4 |+--------------------+---------------------+----------------------+Column Swordfish: r26c1|r68c4|r28c7 => r2c9<>7,r6c25<>7,r8c59<>7Column Swordfish Fillet-o-Fish: r45c3|r2456c6|r245c9 => r4c5<>8,r5c4<>8VWXYZ-wing: r56c1|r46c2, r5c4 => r5c3<>1ALS xy-rule with B=5 cells: r5c14-2-r13467c2-6-r9c1278 => r9c4<>110: gfroyle's beauty +---------------------+---------------------+------------------+|      6   145     89 |  14579     2  14579 |    78   14     3 ||    145     7    134 |    156     8   1356 |     2    9    46 ||     89   134      2 |  14679  3679  14679 |     5  146    78 |+---------------------+---------------------+------------------+|  14579   156  14679 |      3  5679  46789 |  4689    2  1689 ||      2     8   3469 |   4569     1   4569 |  3469    7   569 ||  14579  1356  14679 |  46789  5679      2 |  4689   35  1689 |+---------------------+---------------------+------------------+|    478     2      5 |   6789  3679   6789 |     1  346   479 ||     17     9    167 |      2     4     35 |   367    8   567 ||      3    46    478 |  16789  5679  16789 |    79  456     2 |+---------------------+---------------------+------------------+Note: r8c7=7 solves the puzzleHidden Block Pair: r3c1|r1c3 => r3c1=89,r1c3=89Hidden Block Pair: r1c7|r3c9 => r1c7=78,r3c9=78Column Swordfish: r36c2|r37c5|r67c8 => r3c6<>3,r6c37<>3,r7c6<>3Column Swordfish: r47c2|r17c5|r14c8 => r4c17<>2,r7c14<>2,r1c4<>2Nice Loop: r1c5=2=r1c8-2-r2c7=2=r5c7=3=r8c7-3-r8c6=3=r7c5~3~r1c5 => r7c5<>2Hidden Single: r7c2 => r7c2=2,r4c2<>2,r8c1<>2Hidden Single: r5c1 => r5c1=2,r5c7<>2Hidden Single: r8c4 => r8c4=2,r2c4<>2Hidden Single: r1c5 => r1c5=2,r1c8<>2Hidden Single: r2c7 => r2c7=2Hidden Single: r4c8 => r4c8=2Row X-Wing Fillet-o-Fish: r5c469|r8c69 => r4c6<>5Column X-Wing Fillet-o-Fish: r469c5|r69c8 => r6c4<>5Column Big Fin Jellyfish: r246c1|r146c2|r469c5|r69c8 => r46c9<>5,r9c46<>5Nice Loop: r7c5=3=r8c6=5=r9c5-5-r9c8=5=r6c8=3=r7c8-3-r7c5 => r8c6=35,r6c8=35Locked Row Line/Box: r9c46 => r9c23<>1Locked Column Line/Box: r46c9 => r2c9<>1ALS xz-rule with A=3 cells: r8c13|r9c2-7-r8c79|r79c8 => r9c7<>4Locked Column Box/Box: r1379c8|r27c9 => r456c9<>4Grouped Nice Loop: r2c13=4=r13c2-4-ALS:r9c2|r8c13-7-ALS:r8c79|r79c8-4-r13c8=4=r2c9-4-r2c13 => r46c2<>4,r9c37<>6,r7c9<>6,r2c46<>411: top1465 #187 +-------------------+----------------------+--------------------+|     6   189  1479 |  124578   1478  2458 |      3  1257   147 ||   347     5  1347 |    1247      9   234 |   1246     8  1467 ||   347   138     2 |   14578  13478     6 |     14   157     9 |+-------------------+----------------------+--------------------+|     8  1369     5 |    2469    346  2349 |      7  1239   136 ||   239     7  1369 |    2689      5  2389 |  12689     4  1368 ||  2349   369  3469 |   26789   3678     1 |   2689   239     5 |+-------------------+----------------------+--------------------+|     1     2   679 |       3    468   489 |      5    79   478 ||  3579     4   379 |    1589      2   589 |    189     6  1378 ||   359   369     8 |   14569    146     7 |    149   139     2 |+-------------------+----------------------+--------------------+Hidden Single: r7c2 => r7c2=2,r46c2<>2Hidden Single: r4c3 => r4c3=5,r8c3<>5Locked Row Line/Box: r6c13 => r6c45<>412: top1465 #372 +--------------------+-------------------+--------------------+|   3569     4  3679 |    2   679   1679 |   569   135      8 ||    689   678     1 |    3     5    679 |     2     4     69 ||      2    56   369 |    8   469   1469 |     7   135  13569 |+--------------------+-------------------+--------------------+|    346   236     8 |    1   234    245 |   456     9      7 ||     14   127    27 |    6  2489  24589 |     3  1258    145 ||   1346     9     5 |    7  2348    248 |   468   128    146 |+--------------------+-------------------+--------------------+|  13589  1358   239 |  459   278    278 |  4589     6   3459 ||      7  3568     4 |   59     1     68 |   589   358      2 ||   5689  2568   269 |  459   268      3 |     1     7    459 |+--------------------+-------------------+--------------------+Hidden Single: r4c4 => r4c4=1,r456c6<>1,r4c12<>1Hidden Single: r2c4 => r2c4=3,r13c5<>3,r2c129<>3Hidden Single: r2c7 => r2c7=2,r46c7<>2Hidden Single: r9c8 => r9c8=7,r9c5<>7Locked Column Line/Box: r45c6 => r78c6<>5Locked Column Box/Box: r3456c56 => r79c5<>4,r7c6<>4Locked Column Box/Box: r135c5|r1235c6 => r79c5<>9,r78c6<>9Empty Row Rectangle : r7c29|r3c9 => r3c2<>3ALS xz-rule with A=4 cells: r1379c3-7-r23489c2 => r7c2<>213: top1465 #388 +-------------------+----------------------+---------------------+|    16   146     2 |       3   6789  6789 |    1679   4678    5 ||     8     5   136 |     267      4  2679 |  123679   2367  127 ||     9     7   346 |       5    268     1 |     236  23468   24 |+-------------------+----------------------+---------------------+|     4    16   156 |     267   2567     3 |       8      9  127 ||    67     2    68 |       9      1   678 |       4      5    3 ||   137  1389  1589 |     278   2578     4 |     127     27    6 |+-------------------+----------------------+---------------------+|  1236  1368  1468 |  124678   2678  2678 |       5  23467    9 ||   236  3689  4689 |   24678  26789     5 |    2367      1  247 ||     5  1469     7 |    1246      3   269 |      26    246    8 |+-------------------+----------------------+---------------------+Hidden Single: r9c1 => r9c1=5,r56c1<>5Hidden Single: r4c6 => r4c6=3,r4c23<>3Locked Column Line/Box: r23c3 => r678c3<>3ALS xz-rule with A=2 cells: r4c23-6-r5c178 => r4c9<>5,r5c3<>5,r1c8<>5Hidden Single: r5c8 => r5c8=5,r6c8<>5Hidden Single: r5c7 => r5c7=4,r1389c7<>4Hidden Single: r1c9 => r1c9=5Column X-Wing Fillet-o-Fish: r378c3|r38c9 => r8c2<>4Grouped Nice Loop: ALS:r149c2-9-ALS:r9c678-4-r1c8=4=r3c89-4-r3c3=4=r78c3~4~ => r7c2<>414: top1465 #246 +---------------------+---------------------+------------------------+|     9     68      4 |   178   1238      5 |    2367    2367     37 ||     2      5     78 |     6   3489   3478 |       1      34    349 ||     3      1     67 |    79    249    247 |  245679   24567      8 |+---------------------+---------------------+------------------------+|    68      7   2368 |   158   1358      9 |    2346  123468    134 ||     4    389   3589 |     2      6    138 |    3579   13578  13579 ||   568  23689      1 |     4      7     38 |   23569   23568    359 |+---------------------+---------------------+------------------------+|     7   3689  35689 |  1589  14589   1468 |     345    1345      2 ||    15     29    259 |     3  12459   1247 |       8    1457      6 ||  1568      4  23568 |  1578   1258  12678 |     357       9   1357 |+---------------------+---------------------+------------------------+Locked Row Line/Box: r4c45 => r4c13789<>5ALS xz-rule with A=1 cells: r2c3-8-r1c2789 => r2c89<>715: top1465 #460 +-------------------+---------------------+---------------------+|     8     6   124 |    135   235   1234 |  23459     7  23459 ||     9   157  1247 |   1357     8  12347 |   2345   345      6 ||  2457    57     3 |    567   256      9 |      1     8    245 |+-------------------+---------------------+---------------------+|   167   137     8 |    367     9      5 |   2347   134  12347 ||   157     2   179 |      4    37      8 |   3579     6  13579 ||  4567  3579   467 |      2     1    367 |      8   359    357 |+-------------------+---------------------+---------------------+|   127     8     5 |   1379   237   1237 |      6  1349   1347 ||     3   179  1267 |  15679     4   1267 |     57   159      8 ||   167     4  1679 |      8  3567   1367 |   3579     2  13579 |+-------------------+---------------------+---------------------+Hidden Single: r1c1 => r1c1=8,r379c1<>8,r3c2<>8Hidden Single: r7c2 => r7c2=8,r7c46<>8Hidden Single: r9c4 => r9c4=8,r9c6<>8Hidden Single: r5c6 => r5c6=8Hidden Single: r3c8 => r3c8=8Empty Column Rectangle : r36c1|r3c9 => r6c9<>4Column X-Wing Fillet-o-Fish: r68c2|r678c8 => r8c7<>9Row Swordfish Fillet-o-Fish: r3c19|r4c1789|r7c89 => r6c8<>4Locked Row Line/Box: r4c789 => r4c1<>4Column Swordfish: r68c2|r78c4|r678c8 => r6c39<>9,r8c3<>9,r7c9<>9Grouped Nice Loop: ALS:r3c24-6-r3c5=6=r9c5-6-ALS:r9c13|r8c2|r7c1-2-ALS:r57c5~7~ => r3c5<>716: top1465 #573 +-------------------+----------------------+----------------------+|  1468     3     2 |  146789  6789  14689 |   5789  15678  15679 ||   168    58   156 |   13679     2   1689 |   3789      4   1679 ||     9    48     7 |   13468    68      5 |    238    136    126 |+-------------------+----------------------+----------------------+|     2     1    45 |     467   567      3 |     47      9      8 ||   347   459  3459 |       2   578     48 |      6    137    147 ||   347     6     8 |     479     1     49 |   3457      2    457 |+-------------------+----------------------+----------------------+|  1468  2489  1469 |       5     3   1269 |  24789    678  24679 ||     5     7  1469 |    1689   689   1269 |   2489     68      3 ||   368   289   369 |     689     4      7 |      1    568   2569 |+-------------------+----------------------+----------------------+Hidden Single: r4c1 => r4c1=2,r79c1<>2Locked Row Line/Box: r2c23 => r2c79<>5Locked Row Line/Box: r5c23 => r5c56<>9Locked Row Box/Box: r4c35|r5c235 => r4c7<>5,r5c89<>5Nice Loop: r8c6=2=r8c7=4=r8c3-4-r4c3-5-r4c5=5=r5c5=8=r5c6~8~r8c6 => r8c6<>8Grouped Nice Loop: ALS:r1256c6-6-r3c5-8-r123c4=8=r89c4~8~ => r7c6<>8Grouped Nice Loop: ALS:r2c1236-9-r1c5=9=r8c5=8=r89c4~8~ => r2c4<>8Grouped Nice Loop: r3c5-6-ALS:r1256c6-1-r3c4=1=r3c89-1-ALS:r1789c8~8~ => r3c8<>8`
Mike Barker

Posts: 458
Joined: 22 January 2006

Message dropped. Puzzles not appropriate for this thread. Thanks to those who reviewed them!!!
Last edited by daj95376 on Fri Jun 09, 2006 11:47 am, edited 1 time in total.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

Hi Daj95376.

What is the hardest puzzle of your list?

Carcul
Carcul

Posts: 724
Joined: 04 November 2005

Thanks for the list, daj95376.

The hardest for my program are numbers 8, 13, 24, 42, 45, 49, 50 with 3 steps (easiest 15 and 25 with 1 step).
ravel

Posts: 998
Joined: 21 February 2006

Carcul: Apparently none of them are as difficult as I'd hoped.

Ravel: Thank you for checking them!

Havard: Thank you for checking them and sending the PM.

I'm going to drop my message because the puzzles aren't appropriate for this thread.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

Hi Ravel,
Could you give me a rating of this one :
Code: Select all
` . . . | . . . | . 7 4 . . . | . . . | . 9 2 . . . | . 6 1 | 8 5 .-------+-------+------- . . . | . 3 7 | 5 . . . . 5 | 4 . . | . 8 . 9 . . | . 1 . | . . .-------+-------+------- 3 1 7 | . . 2 | . . . . 8 . | . . . | . . . 2 . 9 | 7 . . | . . .`
Thanks.
JPF
JPF
2017 Supporter

Posts: 4382
Joined: 06 December 2005
Location: Paris, France

Which, if any, of these puzzles are as hard as those on the 'hard list', and why (or why not)?

(The ratings number before each puzzle is from suexrat9.exe)
Code: Select all
`01:  507,  ..1..5..9...9..6...8..1......7..6...5..2..4...2..4..9......7..32..4..5...6..8..4.02:  526,  ..1..6...7..8..3...9..2..4...4..1..31..6..2...8..5..1...6..7..59..5..7......3..2.03:  541,  ..1..6..27..8..3...9..2..4...4..1..31..6..2...8.....1...6..7..59..5..7......3..2.04:  571,  ..2..3...4.....9...3..9..1...6..4..58..7..4...4..8..2......7..25..6..3...1..3..9.05:  605,  ...3..9...6..1..8...1..8..44..9..7...2.....9...3..7..55..7..2...8..6..3...6..4...06:  486,  ..4..1..21..6.........5......5..8..64..9..7...9..1..2...2..3..18..7..9...6.....3.07:  674,  ...5..7...2..6..4...6..1..39..2..4...3.....1...7..3..81..7..6...5..4..7...9..8...08:  484,  ..6..2..81..8..4...5..7......1..3..7...4..6...7..1..9...9..5..26..7......2.....3.09:  526,  ..6..3..83..5..7......9..6...8..2..64..7..1...5..1..3...4.....35..8..6...9.....2.10:  478,  ..7..3..94..1..5......8..7...4..1..6...7......3..2..9...9..2..16..8..4...2.....8.11:  377,  ...7..8...2.....3...3..1..64..6..1...5..7..6...6..9..28..5..4...7.....1...9..4...12:  602,  ..7..9..13..1.........4..9...4..6..39..7..2...1..5..7...5.....91..8..6...2..7..8.13:  636,  ..7..9..13..1..5......4..9...4..6..3...7..2...1..5..7...5.....91..8..6...2..7..8.14:  462,  ..8.....4...6..5......2..9...4.....61..9..3...7..3..1...7..8..99..5..1...2..1..7.15:  571,  ...8..1...9..2..4...2..5..66..7..5...8.....1...1..4..97..6..4...1..5..3...5..3...16:  384,  ...8..4...1..2......9..6..28..4..7...3..1..9...5..8..62..7..9......4..3...7..5...17:  415,  ..8..5..34..9..8...9.....2...9..6...2..7..4...1..3..7...1..4..26..8..3...5..1..4.18:  439,  ...8..6...5..2..7...1..7..56..3..2...1.....3...7..4..95..1..8...9..4..1...4..6...19:  456,  ..8..7..1...9..4...4..1..8...4..1...5..3..6...2..5..9...2..3..63..1..9...8..2..7.20:  488,  ..8..7..93..9..6...4..5......3..2..42..1..3...6..9..2...2..1..76.....5...3.....4.21:  435,  ..8..9..31..4..8......5..7...2..5..78..6..9...3.....1...4..6..27..2..6...2..7..3.22:  458,  ..8..9..36..1..8...7..6..4...2..8..45.....1...9..3......5..4..9...6..7......9..2.23:  700,  ..9..6......7..4...5..2..3...3..5..47..6..1...2..7..9......1..88..4..6...3..6....24:  470,  ..9..8..5...5..4...7..4..2...3..5...9..4..2......6..1...7..9..22..3..1...6..7..3.25:  530,  ...1..6...6..3..4...5..8...8..6..2...9.....7...3..2..85..9..4...2..7..9...7..5...26:  634,  ...2..9...3..4..6...8..6...1..8..6...5..2..7...2..4..35..6..4...2..7..5...9..1...27:  568,  ...3..1...1..5..7...9..6..41..4..9...6.....8...7..2..36..7..5...8.....6...2..9...28:  478,  9..5..2...4..3..9...3..8..65..3..8...9.....6...1..7..48..4..6...6..2..8...9..6..729:  383,  ...9..6...9..4..3...8..7..41..3..9...6..8..2...2..5..15..4..2......3..1...7..6...30:  525,  ...7..2...1..9..4...6..4..58..1..3...4.....7...1..6..23..4..9...6..7..2...8..5...31:  595,  ...7..2...1..9..4...6..4..58.....3...4.....7...1..6..23..4..9...6..7..2...8..5...`

(I don't know how suexrat9 works, but it gives slightly different ratings each time it is run.)

Notes:

#27 -- Sudoku Susser 2.4.3, using it's default settings, finds 2 Nishio (coloring) making a grand total of 2 exclusions and can go no further. It rates only mid-500s on suexrate -- while #23 hits 700 though Susser *does* solve it, using 4 "Trebors Tables" and nothing else but naked singles (aka "forced moves") However, both Into Sudoku and SudoCue rate #27 substantially harder than #23. (It's very hard to find puzzles that stump Susser on it's default settings; many puzzle rated much near the top of the hardest lists do not stump it; e.g. 124: Ruud #13/15, the third one from the top of this post.)

#'s 4, 5, 7, 9, 26, 28, 29 and 31 also stump Susser at default settings. All the rest were solved using either tabling, "Bowman's Bingo", or both.

#31 is just #30 minimized -- just once clue less. Susser solves the first, not the second.

Oh, and Pappocom says they're all invalid.
tso

Posts: 798
Joined: 22 June 2005

Tso, thanks for this great heavy weight collection.

My program ran for hours to verify them. This diagonal pattern really is most viperish.

And we have a new leader !
No 7 is a very extreme puzzle. Though one guess (r1c2=4) could solve the puzzle with singles, it needed 12 steps.

The BF ratings are
5, 6, 7, 4, 6, 3,12, 4, 8, 4,
3, 5, 5, 5, 5, 5, 5, 5, 4, 5,
4, 3, 5, 4, 8, 6, 6, 6, 4, 6,
6

As i had it for the (old) 2 top hardest, the recent susser version was stumped with them, but not the old susser version 1.2.9. This also solved the following puzzles with tabling (in brackets the number of tabling steps needed):
4 (2), 5(4), 7(3), 9(3), 26(3), 28(4), 29(3) and 31(3)
So i dont know, in which version there is a bug. Maybe someone else, who has implemented tabling, could verify it.

But v1.2.9 is stumped with #27 also. I assume, that means that it cannot be solved with chains, that dont use multiple inference. Does anybody know?
ravel

Posts: 998
Joined: 21 February 2006

Hi Ravel,

In an effort to find new types of patterns for your list, I sent you one puzzle to get your rating.
Here are some more :
Code: Select all
`000000074000000092000061850000037500005400080900010000317002000080000000209700000000000021006000000002000930000907380000300709000020040780406000065010000010030000030000000900020500080005602200010000100004000000870900050100400009007080000000039600000000009000203850020900002040030010670040000900000040050800000800050000006001000000023000000109000000670070030000400000080008201900004059000782006000501007000800570000560000000003000107040000090000001008200784000000000509000002030300106000000000030000006807000008590000065009001300000086700300160089000050020000903100000800040000060000501304000000000900700009500060003001050400005970000290010000000206000000013007000092020000700000030000000096070000007430008741000400300000319802000000409007023000006100005000400500200002000800080000000000001050004007003030900060003000008008704060000600007100475200000090000004286009400007000010302400600000800`

Thanks.
JPF
JPF
2017 Supporter

Posts: 4382
Joined: 06 December 2005
Location: Paris, France

Oh, sorry, i overlooked it, only saw tso's post. I will check them on Monday.
ravel

Posts: 998
Joined: 21 February 2006

ravel wrote:Oh, sorry, i overlooked it, only saw tso's post. I will check them on Monday.

It's OK.
It gave me more time to add some puzzles.
My final sample is :
Code: Select all
`01 # 07020000000400500000800000030180000950067000200003000000009002760000054000030060802 # 00000600050000097301009200500400900030000016016000000768005700000580000040006000003 # 40000070000005804001060000008000000720007300004100023032000501000080900000600000404 # 00000007400000009200006185000003750000540008090001000031700200008000000020970000005 # 00000002100600000000200093000090738000030070900002004078040600006501000001003000006 # 09600020000000758080000001420003005004800000000000100000002504730000060005090010007 # 30000071000025040050000030002790004000000003000600102000030700160000000009068000008 # 48010200020006080097000006201090007000000009300060002080000000460001000005020300009 # 00000790000835006004080200090700300600200010700000000405403000002000508000600000010 # 00000070487090000200040003810000000000935000058006007001080000030061089000000060011 # 05000084001007000090400300060100850050709000000006003000004200100090030007200100012 # 00500000007009500400060008004070900071000840300600090840030000000008010960001000013 # 00000030100000004902900060000060080300000100700008506005379400010000300080702000014 # 03000000090002050008000560220001000010000400000087090005010040000900708000000003915 # 00003080000050904006500000053007000000400003007800002000090700008905030110000095016 # 00500270000000003009078060110040025000700000020000090800000050790100600080000009017 # 08937010015004002600000600700000000000305000420600008002000000000070000900506001018 # 00300056900800000000006010000015000200000003000008271096002700040000960020060009019 # 60000000000900020385002090000204003001067004000090000004005080000080005000000600120 # 00080500900860905003000000040000309600000020005041007080000000000700000159100006721 # 09000003060000702000800001400005009000420005102030000600080200990046100001050000022 # 00000002300000010900000067007003000040000008000820190000405900078200600050100700023 # 80057000056000000000300010704000009000000100820078400000000050900000203030010600024 # 00008070509543000001000040030002000005060090700405000000000700204050000300930010025 # 00640802100000000000900000006000000000000947604025009005700160000003008020007000526 # 00000207000739600060000012000005890400500000008600300007000000001080070500000109027 # 00000100020056008000900000000630000474002630050004000000000017005090380000008000328 # 00000003000000680700000859000006500900130000008670030016008900005002000090310000029 # 00000701800290005004000090000007500050000004090030607000020070018070000305000400030 # 80004000006000050130400000000090070000950006000300105040000597000029001000000020631 # 00008034003000950017050002000604810020000305000000609000100000904000073000000000032 # 00040006000006008040010090030004010980002003600000002010800050063000000000580900233 # 00000015000001000206040009000005001348060020007000900034006000070000008001007000634 # 09762000558000000040000109000400000000075000000800046000000301000608000900000920035 # 00000001300700009202000070000003000000009607000000743000874100040030000031980200036 # 21000005060075080040090006000280030000000050608030000270020003000000900704300600037 # 00790026800003000760000005026000008000910000050400800605008074040020000000000500138 # 00300000800870406000060000710047520000009000000428600940000700001030240060000080039 # 10400007000000280600870005006002800300900000020000100400000902070000030990200004040 # 603000000090010000100036002007061000500000000000000450005090000304702006020005700`

JPF

PS : I don't understand how you calculate the number of steps...
JPF
2017 Supporter

Posts: 4382
Joined: 06 December 2005
Location: Paris, France

JPF wrote:I don't understand how you calculate the number of steps...

I only explained it more detailed in other threads.

The program has only some basic methods implemented: tuples, box interactions, x-wings and UR type 1. When getting stuck with them the first time, it "tries" each candidate.

If this leads to a contradiction (i.e. neither it gets stuck again nor it solves the puzzle), it is dropped (one step) and the puzzle continued until it gets stuck the next time. Then all candidates are tried. Out of the candidates that can be eliminated then, i take the (first) one, that reduced the number of candidates most, when it was dropped.

So from each starting candidate (first time stuck) i keep a list of eliminations, until it is solved (or it gives up after a maximum number). At the end i take the minimum number of needed eliminations as the number of BF steps.

Since often several candidates lead to the same progress, scrambling the puzzle can lead to different results. This is the more probable, the more steps are needed. For all 3 of the current puzzles in the list, that needed more than 9 steps, i had even more steps without changing the order to get the next candidate to be dropped. They are so hard that most eliminations did not make any progress, i.e. no other candidate could be eliminated. The different "solutions" (orders of eliminations) often dont have anything in common.

PS:
ravel wrote:But v1.2.9 is stumped with #27 also. I assume, that means that it cannot be solved with chains, that dont use multiple inference. Does anybody know?

susser 2.5.4 solves all of them with tabling, when "Aggressive Forces and Pins" is selected.
ravel

Posts: 998
Joined: 21 February 2006

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