The New Sudoku Players' Forum

by **Carcul** » Mon Jun 05, 2006 3:57 pm

Claudiarabia wrote:which require a guess

No need to guess:

Code: Select all: *-----------------------------------------------------------* | 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

by **ravel** » Thu Jun 08, 2006 8:05 am

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" ? )

by **daj95376** » Fri Jun 09, 2006 1:22 am

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?

by **Mike Barker** » Fri Jun 09, 2006 4:58 am

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.

Code: Select all: 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<>3 Locked Row Line/Box: r7c89 => r7c123<>4 Grouped Nice Loop: r1c456=6=r1c3-6-ALS:r3c12|r2c3-1-ALS:r379c5-6-r4c5=6=r4c6~6~ => r2c6<>6 top1465 #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<>7 Row X-Wing Fillet-o-Fish: r2c67|r5c678 => r6c7<>7 Row Swordfish Fillet-o-Fish: r1c1389|r4c389|r7c89 => r2c3<>9 Column Swordfish: r139c25|r13c8 => r1c36<>2,r39c4<>2 Nice Loop: r4c9=5=r5c9-5-r5c1=5=r6c1=9=r4c3~9~r4c9 => r4c9<>9 Nice Loop: r6c1=5=r5c1-5-r5c9=5=r4c9=6=r4c8=9=r4c3~9~r6c1 => r6c1<>9 Hidden Single: r4c3 => r4c3=9,r4c8<>9,r1c3<>9 124: 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<>4 Nice Loop: r2c9=2=r2c6=4=r2c7-4-r3c8=4=r9c8=6=r8c9~6~r2c9 => r2c9<>6 Nice Loop: r4c9=3=r2c9=2=r2c6=4=r3c5-4-r4c5=4=r4c2~4~r4c9 => r4c2<>3 ALS xz-rule with A=3 cells: r467c5-4-r23c4|r3c56 => r1c5<>1,r1c5<>8 ALS xy-rule with B=3 cells: r23c4|r3c56-4-r467c5-9-r1c23589 => r1c6<>7,r1c6<>8,r3c12<>1,r1c6<>1 Note: r3c1=1 at this point essentially solves the puzzle 3: 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<>4 Locked Row Line/Box: r6c56 => r6c78<>6 Column Swordfish: r568c14|r56c7 => r5c3<>1,r6c25<>1,r8c35<>1 Grouped Nice Loop: ALS:r239c1-8-r5c1=8=r5c4-8-r3c4-7-r12c6=7=r8c6~7~ => r8c1<>7 4: 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 puzzle Hidden Single: r8c3 => r8c3=3,r8c46<>3 Hidden Single: r6c7 => r6c7=6 Column X-Wing: r24c69 => r2c45<>3,r4c58<>3 Row Swordfish Fillet-o-Fish: r2c137|r5c13|r8c127 => r9c1<>4,r7c3<>4 Nice Loop: r7c9=2=r7c8-2-r6c8-3-r3c8=3=r2c9~3~r7c9 => r2c9<>2 ALS xz-rule with A=3 cells: r8c467-4-r9c1789 => r8c9<>8 ALS xy-rule with B=4 cells: r8c46-7-r7c2356-9-r89c7|r79c89 => r8c9<>5 125: 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 puzzle Hidden Single: r9c4 => r9c4=4,r456c4<>4 Hidden Single: r8c4 => r8c4=6,r8c1379<>6 Hidden Single: r4c4 => r4c4=2,r4c56<>2 Hidden Single: r9c5 => r9c5=3,r9c78<>3,r13c5<>3 Locked Row Line/Box: r7c56 => r7c3<>9 Locked Row Box/Box: r89c17 => r8c6<>2 Naked Single: r8c6 => r8c3<>1,r127c6<>1,r7c5<>1 Row X-Wing: r36c18 => r5c1<>4,r14c8<>4 UR+3KD: r36c45, r6c1278, r1c56 => r3c4<>1 Nice Loop: r6c5=5=r5c6-5-r5c1-9-r5c7=9=r6c7~9~r6c5 => r6c5<>9 5: 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<>1 6: 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 puzzle Hidden Single: r4c1 => r4c1=3,r4c78<>3 Hidden Single: r5c3 => r5c3=9,r12789c3<>9 Hidden Single: r3c9 => r3c9=1,r6c9<>1 Hidden Single: r6c8 => r6c8=1,r45c8<>1 Locked Row Line/Box: r4c23 => r4c45<>1 Locked Row Line/Box: r1c46 => r1c789<>3 Locked Row Line/Box: r1c46 => r1c23<>6 Locked Column Line/Box: r45c7 => r123c7<>8 Naked Block Triple: r3c46|r2c5 => r1c4<>48,r1c6<>89 7: 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<>6 Hidden Single: r4c3 => r4c3=2,r5c31<>2 Hidden Single: r5c4 => r5c4=2,r123c4<>2 Hidden Single: r2c7 => r2c7=5,r2c456<>5 Hidden Single: r6c8 => r6c8=1,r9c8<>1 Empty Column Rectangle : r68c2|r8c4 => r6c4<>5 UR+4C/3SL: r23c14 => r3c4<>1 8: 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 puzzle Hidden Single: r3c5 => r3c5=3,r3c12<>3 Empty Column Rectangle : r35c1|r3c4 => r5c4<>9 9: 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<>7 Hidden Single: r5c9 => r5c9=4,r12c9<>4 Hidden Single: r6c8 => r6c8=7,r6c4<>7,r79c8<>7 Locked Row Line/Box: r2c23 => r2c79<>1 Column Swordfish: r589c14|r89c7 => r5c35<>8,r8c235<>8,r9c25<>8 Nice Loop: r3c7=1=r3c8-1-r9c8-3-r4c8=3=r6c7~3~r3c7 => r6c7<>1 ALS xz-rule with A=3 cells: r6c147-6-r126789c2 => r4c2<>2 126: 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 puzzle Hidden Single: r9c2 => r9c2=4,r9c78<>4 Hidden Single: r8c5 => r8c5=9 Column X-Wing Fillet-o-Fish: r16c5|r126c8 => r1c9<>4 Column Swordfish: r235c14|r23c7 => r2c3<>8,r3c25<>8,r5c3<>8 ALS xz-rule with A=1 cells: r5c6-4-r3679c5 => r4c5<>5 Nice Loop: r1c2=2=r3c2=9=r4c2-9-r4c9-6-r1c9=6=r1c8~6~r1c2 => r1c8<>2 Nice Loop: r5c1=8=r5c4-8-r4c5=8=r1c5=4=r6c5-4-r5c6~5~r5c1 => r5c1<>5 127: 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<>9 ALS xy-rule with B=5 cells: r2c7-2-r6c12457-7-r4679c8 => r13c8<>3 128: 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<>7 Column Swordfish Fillet-o-Fish: r45c3|r2456c6|r245c9 => r4c5<>8,r5c4<>8 VWXYZ-wing: r56c1|r46c2, r5c4 => r5c3<>1 ALS xy-rule with B=5 cells: r5c14-2-r13467c2-6-r9c1278 => r9c4<>1 10: 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 puzzle Hidden Block Pair: r3c1|r1c3 => r3c1=89,r1c3=89 Hidden Block Pair: r1c7|r3c9 => r1c7=78,r3c9=78 Column Swordfish: r36c2|r37c5|r67c8 => r3c6<>3,r6c37<>3,r7c6<>3 Column Swordfish: r47c2|r17c5|r14c8 => r4c17<>2,r7c14<>2,r1c4<>2 Nice Loop: r1c5=2=r1c8-2-r2c7=2=r5c7=3=r8c7-3-r8c6=3=r7c5~3~r1c5 => r7c5<>2 Hidden Single: r7c2 => r7c2=2,r4c2<>2,r8c1<>2 Hidden Single: r5c1 => r5c1=2,r5c7<>2 Hidden Single: r8c4 => r8c4=2,r2c4<>2 Hidden Single: r1c5 => r1c5=2,r1c8<>2 Hidden Single: r2c7 => r2c7=2 Hidden Single: r4c8 => r4c8=2 Row X-Wing Fillet-o-Fish: r5c469|r8c69 => r4c6<>5 Column X-Wing Fillet-o-Fish: r469c5|r69c8 => r6c4<>5 Column Big Fin Jellyfish: r246c1|r146c2|r469c5|r69c8 => r46c9<>5,r9c46<>5 Nice Loop: r7c5=3=r8c6=5=r9c5-5-r9c8=5=r6c8=3=r7c8-3-r7c5 => r8c6=35,r6c8=35 Locked Row Line/Box: r9c46 => r9c23<>1 Locked Column Line/Box: r46c9 => r2c9<>1 ALS xz-rule with A=3 cells: r8c13|r9c2-7-r8c79|r79c8 => r9c7<>4 Locked Column Box/Box: r1379c8|r27c9 => r456c9<>4 Grouped 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<>4 11: 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<>2 Hidden Single: r4c3 => r4c3=5,r8c3<>5 Locked Row Line/Box: r6c13 => r6c45<>4 12: 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<>1 Hidden Single: r2c4 => r2c4=3,r13c5<>3,r2c129<>3 Hidden Single: r2c7 => r2c7=2,r46c7<>2 Hidden Single: r9c8 => r9c8=7,r9c5<>7 Locked Column Line/Box: r45c6 => r78c6<>5 Locked Column Box/Box: r3456c56 => r79c5<>4,r7c6<>4 Locked Column Box/Box: r135c5|r1235c6 => r79c5<>9,r78c6<>9 Empty Row Rectangle : r7c29|r3c9 => r3c2<>3 ALS xz-rule with A=4 cells: r1379c3-7-r23489c2 => r7c2<>2 13: 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<>5 Hidden Single: r4c6 => r4c6=3,r4c23<>3 Locked Column Line/Box: r23c3 => r678c3<>3 ALS xz-rule with A=2 cells: r4c23-6-r5c178 => r4c9<>5,r5c3<>5,r1c8<>5 Hidden Single: r5c8 => r5c8=5,r6c8<>5 Hidden Single: r5c7 => r5c7=4,r1389c7<>4 Hidden Single: r1c9 => r1c9=5 Column X-Wing Fillet-o-Fish: r378c3|r38c9 => r8c2<>4 Grouped Nice Loop: ALS:r149c2-9-ALS:r9c678-4-r1c8=4=r3c89-4-r3c3=4=r78c3~4~ => r7c2<>4 14: 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<>5 ALS xz-rule with A=1 cells: r2c3-8-r1c2789 => r2c89<>7 15: 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<>8 Hidden Single: r7c2 => r7c2=8,r7c46<>8 Hidden Single: r9c4 => r9c4=8,r9c6<>8 Hidden Single: r5c6 => r5c6=8 Hidden Single: r3c8 => r3c8=8 Empty Column Rectangle : r36c1|r3c9 => r6c9<>4 Column X-Wing Fillet-o-Fish: r68c2|r678c8 => r8c7<>9 Row Swordfish Fillet-o-Fish: r3c19|r4c1789|r7c89 => r6c8<>4 Locked Row Line/Box: r4c789 => r4c1<>4 Column Swordfish: r68c2|r78c4|r678c8 => r6c39<>9,r8c3<>9,r7c9<>9 Grouped Nice Loop: ALS:r3c24-6-r3c5=6=r9c5-6-ALS:r9c13|r8c2|r7c1-2-ALS:r57c5~7~ => r3c5<>7 16: 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<>2 Locked Row Line/Box: r2c23 => r2c79<>5 Locked Row Line/Box: r5c23 => r5c56<>9 Locked Row Box/Box: r4c35|r5c235 => r4c7<>5,r5c89<>5 Nice Loop: r8c6=2=r8c7=4=r8c3-4-r4c3-5-r4c5=5=r5c5=8=r5c6~8~r8c6 => r8c6<>8 Grouped Nice Loop: ALS:r1256c6-6-r3c5-8-r123c4=8=r89c4~8~ => r7c6<>8 Grouped Nice Loop: ALS:r2c1236-9-r1c5=9=r8c5=8=r89c4~8~ => r2c4<>8 Grouped Nice Loop: r3c5-6-ALS:r1256c6-1-r3c4=1=r3c89-1-ALS:r1789c8~8~ => r3c8<>8

by **daj95376** » Fri Jun 09, 2006 9:30 am

Message dropped. Puzzles not appropriate for this thread. Thanks to those who reviewed them!!!

by **Carcul** » Fri Jun 09, 2006 9:39 am

Hi Daj95376.

What is the hardest puzzle of your list?

Carcul

by **ravel** » Fri Jun 09, 2006 12:32 pm

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).

by **daj95376** » Fri Jun 09, 2006 3:45 pm

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.

by **JPF** » Wed Jun 28, 2006 11:04 pm

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

by **tso** » Thu Jun 29, 2006 3:12 am

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..7 29: 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.

by **ravel** » Fri Jun 30, 2006 7:27 am

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?

by **JPF** » Fri Jun 30, 2006 2:55 pm

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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

Your feedback will be appreciated.
Thanks.
JPF

by **ravel** » Fri Jun 30, 2006 7:15 pm

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

by **JPF** » Sat Jul 01, 2006 10:27 pm

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 # 070200000004005000008000000301800009500670002000030000000090027600000540000300608 02 # 000006000500000973010092005004009000300000160160000007680057000005800000400060000 03 # 400000700000058040010600000080000007200073000041000230320005010000809000006000004 04 # 000000074000000092000061850000037500005400080900010000317002000080000000209700000 05 # 000000021006000000002000930000907380000300709000020040780406000065010000010030000 06 # 096000200000007580800000014200030050048000000000001000000025047300000600050900100 07 # 300000710000250400500000300027900040000000030006001020000307001600000000090680000 08 # 480102000200060800970000062010900070000000093000600020800000004600010000050203000 09 # 000007900008350060040802000907003006002000107000000004054030000020005080006000000 10 # 000000704870900002000400038100000000009350000580060070010800000300610890000000600 11 # 050000840010070000904003000601008500507090000000060030000042001000900300072001000 12 # 005000000070095004000600080040709000710008403006000908400300000000080109600010000 13 # 000000301000000049029000600000600803000001007000085060053794000100003000807020000 14 # 030000000900020500080005602200010000100004000000870900050100400009007080000000039 15 # 000030800000509040065000000530070000004000030078000020000907000089050301100000950 16 # 005002700000000030090780601100400250007000000200000908000000507901006000800000090 17 # 089370100150040026000006007000000000003050004206000080020000000000700009005060010 18 # 003000569008000000000060100000150002000000030000082710960027000400009600200600090 19 # 600000000009000203850020900002040030010670040000900000040050800000800050000006001 20 # 000805009008609050030000000400003096000000200050410070800000000007000001591000067 21 # 090000030600007020008000014000050090004200051020300006000802009900461000010500000 22 # 000000023000000109000000670070030000400000080008201900004059000782006000501007000 23 # 800570000560000000003000107040000090000001008200784000000000509000002030300106000 24 # 000080705095430000010000400300020000050600907004050000000007002040500003009300100 25 # 006408021000000000009000000060000000000009476040250090057001600000030080200070005 26 # 000002070007396000600000120000058904005000000086003000070000000010800705000001090 27 # 000001000200560080009000000006300004740026300500040000000000170050903800000080003 28 # 000000030000006807000008590000065009001300000086700300160089000050020000903100000 29 # 000007018002900050040000900000075000500000040900306070000200700180700003050004000 30 # 800040000060000501304000000000900700009500060003001050400005970000290010000000206 31 # 000080340030009500170500020006048100200003050000006090001000009040000730000000000 32 # 000400060000060080400100900300040109800020036000000020108000500630000000005809002 33 # 000000150000010002060400090000050013480600200070009000340060000700000080010070006 34 # 097620005580000000400001090004000000000750000008000460000003010006080009000009200 35 # 000000013007000092020000700000030000000096070000007430008741000400300000319802000 36 # 210000050600750800400900060002800300000000506080300002700200030000009007043006000 37 # 007900268000030007600000050260000080009100000504008006050080740400200000000005001 38 # 003000008008704060000600007100475200000090000004286009400007000010302400600000800 39 # 104000070000002806008700050060028003009000000200001004000009020700000309902000040 40 # 603000000090010000100036002007061000500000000000000450005090000304702006020005700

JPF

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

by **ravel** » Sun Jul 02, 2006 11:32 am

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.

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