The New Sudoku Players' Forum

by **Ruud** » Tue Apr 11, 2006 2:35 pm

Hi fellow Sudoku fanatics,

At several occasions we discussed the usefulness of a benchmark set of sudokus. Many programmers are using dukuso's top1465, top95 or Gordon Royle's minimal sudoku list to test their solvers.

This thread will be used to offer a benchmark set of sudokus to be used by our members to test their solvers (solving skills). It must be a predictable testset, so I invite you to run this against your solver and report the failures.

The list is expandable. When new or alternative solving techniques are developed, we can add new examples. The list of solving techniques is based on those currently supported by SudoCue. It is not complete, but it is a start.

Singles only (no candididate grids used at this stage)

# Completed grid (solver must report puzzle complete)

Code: Select all: 429316578867524193513897246931785624682941735745263981354672819178459362296138457

# 19 Full house singles (last empty spot in a row/column/box)

Code: Select all: 305420810487901506029056374850793041613208957074065280241309065508670192096512408

# 56 hidden singles (when not tested for naked singles)

Code: Select all: 300000600000050180000601700000070506050030070401020000006802000098010000002000004

# 55 hidden singles, 1 naked single

Code: Select all: 900000120002300000400005960080200600000050000001009030076900001000001700098000004

# 46 hidden singles, 11 naked singles

Code: Select all: 082050000700009060000040000009306007200000003600205800000070000010400008000030410

# 55 naked singles (when not tested for hidden singles)

Code: Select all: 005079003200000000348000000050680000070204080000013020000000471000000006800790300

Locked candidates , pointing pairs, line-box interaction

# 1 row-box interaction for digit 2 (pointing pair type)

Code: Select all: 090700400100600070600030080850006000006000300000400058040020006030001002002003090 .------------------.------------------.------------------. | 235 9 35 | 7 158 258 | 4 6 135 | | 1 8 345 | 6 59 2459 |*259 7 359 | | 6 27 457 | 1259 3 2459 |*1259 8 159 | :------------------+------------------+------------------: | 8 5 79 | 3 179 6 |-1279 12 4 | | 4 127 6 | 12589 15789 2589 | 3 12 179 | | 2379 127 379 | 4 179 29 | 6 5 8 | :------------------+------------------+------------------: | 59 4 1 | 589 2 7 | 58 3 6 | | 579 3 8 | 59 6 1 | 57 4 2 | | 57 6 2 | 58 4 3 | 1578 9 157 | '------------------'------------------'------------------'

# 1 column-box interaction for digit 2 (2 candidates locked)

Code: Select all: 000907300080065040000000009060040015100000002540090080200000000090250070006408000 .---------------------.---------------------.---------------------. | 46 *125 -1245 | 9 128 7 | 3 256 168 | | 379 8 -12379 | 13 6 5 | 127 4 17 | | 367 *12357 -12357 | 138 1238 4 | 125678 256 9 | :---------------------+---------------------+---------------------: | 3789 6 23789 | 378 4 23 | 79 1 5 | | 1 37 3789 | 5 378 36 | 4 369 2 | | 5 4 237 | 1367 9 1236 | 67 8 367 | :---------------------+---------------------+---------------------: | 2 1357 134578| 1367 137 9 | 1568 356 13468 | | 348 9 1348 | 2 5 136 | 168 7 13468 | | 37 1357 6 | 4 137 8 | 1259 2359 13 | '---------------------'---------------------'---------------------'

# 1 row-box interaction for digit 6 (3 candidates locked)

Code: Select all: 000004009009000020172009005000000800300070006005000000400500698090000700600300000 .---------------------.---------------------.---------------------. | 58 3568 368 |-12678 -123568 4 | 13 13678 9 | | 58 4 9 |*1678 *13568 *135678| 13 2 137 | | 1 7 2 |-68 -368 9 | 34 3468 5 | :---------------------+---------------------+---------------------: | 279 126 1467 | 12469 123456 12356 | 8 13457 12347 | | 3 128 148 | 12489 7 1258 | 12459 145 6 | | 2789 1268 5 | 124689 123468 12368 | 12349 1347 12347 | :---------------------+---------------------+---------------------: | 4 123 137 | 5 12 127 | 6 9 8 | | 258 9 138 | 12468 12468 1268 | 7 1345 1234 | | 6 1258 178 | 3 9 1278 | 1245 145 124 | '---------------------'---------------------'---------------------'

# 1 row-box interaction (block-block type) for digit 3

Code: Select all: 658000003040050000001027006080000007000005600006040050037080100000971300009002000 .---------------------.---------------------.---------------------. | 6 5 8 | 14 19 49 | 2479 12479 3 | | 7 4 2 | 1368 5 3689 | 89 189 189 | | 3 9 1 | 48 2 7 | 5 48 6 | :---------------------+---------------------+---------------------: | 12459 8 *345 |-1236 -1369 -369 | 249 *12349 7 | | 1249 127 *34 |-12378 -139 5 | 6 *123489 12489 | | 129 127 6 | 12378 4 389 | 289 5 1289 | :---------------------+---------------------+---------------------: | 245 3 7 | 456 8 46 | 1 2469 2459 | | 2458 26 45 | 9 7 1 | 3 2468 2458 | | 1458 16 9 | 3456 36 2 | 478 4678 458 | '---------------------'---------------------'---------------------'

# 16 line-box interactions

Code: Select all: 080020006000806000300000901409000000050307060000000805205000009000403000100070030

Subsets (disjoint, naked, hidden, number) (pairs, triples, quads)

# 1 naked pair in a column and box combination

Code: Select all: 005100000600003000300000706000030601009050400802090000401000005000500008000007200 .-------------------.------------------.------------------. | 279 -24789 5 | 1 6 2489 | 389 234 349 | | 6 -12489 *48 | 289 7 3 | 1589 1245 49 | | 3 -12489 *48 | 289 248 5 | 7 124 6 | :-------------------+------------------+------------------: | 57 457 -47 | 28 3 28 | 6 9 1 | | 1 3 9 | 7 5 6 | 4 8 2 | | 8 6 2 | 4 9 1 | 35 35 7 | :-------------------+------------------+------------------: | 4 2789 1 | 23689 28 289 | 39 367 5 | | 279 279 367 | 5 124 249 | 139 13467 8 | | 59 589 -368 | 3689 148 7 | 2 1346 349 | '-------------------'------------------'------------------'

# 1 naked pair in a row and box combination

Code: Select all: 300004005008207000002090000080000402430000017206000050000010800000903600700600001 .---------------.---------------.---------------. | 3 679 79 | 1 68 4 | 2 89 5 | | 569 4569 8 | 2 356 7 | 1 349 369 | | 156 1456 2 | 35 9 568 | 7 348 36 | :---------------+---------------+---------------: | 19 8 79 |-357 -357 159 | 4 6 2 | | 4 3 5 | 8 26 26 | 9 1 7 | | 2 -179 6 |*47 *47 19 | 3 5 8 | :---------------+---------------+---------------: | 569 2569 349 | 457 1 25 | 8 2379 39 | | 8 25 1 | 9 257 3 | 6 27 4 | | 7 29 349 | 6 248 28 | 5 239 1 | '---------------'---------------'---------------'

# 3 naked pairs, 1x row, 1x box, 1x column (no combinations)

Code: Select all: 000000004090007005030009080010008079000040000680500010050600020100800030200000000 # First in row 6 .---------------------.---------------------.---------------------. | 578 267 125678| 123 123568 12356 | 1237 9 4 | | 48 9 1248 | 1234 1238 7 | 123 6 5 | | 457 3 124567| 124 1256 9 | 127 8 127 | :---------------------+---------------------+---------------------: | 345 1 2345 | 23 236 8 | 246 7 9 | | 379 27 2379 | 12379 4 1236 | 268 5 2368 | | 6 8 -23479 | 5 -2379 *23 |-24 1 *23 | :---------------------+---------------------+---------------------: | 3789 5 3789 | 6 1379 4 | 1789 2 178 | | 1 4 679 | 8 2579 25 | 5679 3 67 | | 2 67 36789 | 1379 13579 135 | 156789 4 1678 | '---------------------'---------------------'---------------------' # Second in box 5 .---------------------.---------------------.---------------------. | 578 267 125678| 123 123568 12356 | 1237 9 4 | | 48 9 1248 | 1234 1238 7 | 123 6 5 | | 457 3 124567| 124 1256 9 | 127 8 127 | :---------------------+---------------------+---------------------: | 345 1 2345 |*23 -236 8 | 26 7 9 | | 379 27 2379 |-12379 4 -1236 | 268 5 2368 | | 6 8 79 | 5 79 *23 | 4 1 23 | :---------------------+---------------------+---------------------: | 3789 5 3789 | 6 1379 4 | 1789 2 178 | | 1 4 679 | 8 2579 25 | 5679 3 67 | | 2 67 36789 | 1379 13579 135 | 156789 4 1678 | '---------------------'---------------------'---------------------' # Third in column 3 .------------------.------------------.------------------. | 578 27 -12578| 12 1358 6 | 137 9 4 | | 48 9 1248 | 124 138 7 | 13 6 5 | | 457 3 6 | 14 15 9 | 17 8 2 | :------------------+------------------+------------------: | 45 1 45 | 3 6 8 | 2 7 9 | | 379 27 -2379 | 79 4 1 | 68 5 68 | | 6 8 *79 | 5 79 2 | 4 1 3 | :------------------+------------------+------------------: | 3789 5 -3789 | 6 179 4 | 89 2 178 | | 1 4 *79 | 8 2 5 | 69 3 67 | | 2 6 -789 | 179 179 3 | 5 4 178 | '------------------'------------------'------------------'

# 1 naked triple in a column

Code: Select all: 500000008000029700063070000600800007850000091900007005000040380001980000300000009 .---------------.---------------.---------------. | 5 7 9 |-1346 136 146 | 126 126 8 | | 1 4 8 |*56 2 9 | 7 56 3 | | 2 6 3 |*15 7 8 | 9 15 4 | :---------------+---------------+---------------: | 6 1 24 | 8 9 5 | 24 3 7 | | 8 5 7 |-2346 36 46 | 246 9 1 | | 9 3 24 |-1246 16 7 | 8 246 5 | :---------------+---------------+---------------: | 7 9 5 |*16 4 16 | 3 8 2 | | 4 2 1 | 9 8 3 | 5 7 6 | | 3 8 6 | 7 5 2 | 14 14 9 | '---------------'---------------'---------------'

# 1 naked triple in a row

Code: Select all: 000060000000020054800049100087005600060000080005100430001750008670030000000010000 .------------------.------------------.------------------. |-4579 -13459*39 |-358 6 17 |-2389 *29 *239 | | 79 139 6 | 38 2 17 | 389 5 4 | | 8 235 23 | 35 4 9 | 1 7 6 | :------------------+------------------+------------------: | 3 8 7 | 4 9 5 | 6 12 12 | | 1 6 4 | 2 7 3 | 59 8 59 | | 29 29 5 | 1 8 6 | 4 3 7 | :------------------+------------------+------------------: | 249 2349 1 | 7 5 24 | 239 6 8 | | 6 7 28 | 9 3 248 | 25 124 125 | | 2459 23459 2389 | 6 1 248 | 7 249 239 | '------------------'------------------'------------------'

# 1 naked quad in a box

Code: Select all: 910008040400307000000006000008000010130904087060000300000500000000809004050600029 .---------------------.---------------------.----------------------. | 9 1 367 | 2 5 8 |*67 4 *36 | | 4 28 256 | 3 19 7 |-125689 *56 -12568 | | 235 278 2357 | 4 19 6 |-125789 *357 -12358 | :---------------------+---------------------+----------------------: | 25 9 8 | 7 236 235 | 4 1 256 | | 1 3 25 | 9 26 4 | 256 8 7 | | 7 6 4 | 1 8 25 | 3 9 25 | :---------------------+---------------------+----------------------: | 2368 4 9 | 5 237 123 | 1678 367 1368 | | 236 27 1237 | 8 237 9 | 1567 3567 4 | | 38 5 137 | 6 4 13 | 178 2 9 | '---------------------'---------------------'----------------------'

# 2 naked quads

Code: Select all: 008090706031600000200000000000005000009010300000400000000000004000007820706030100

# 1 hidden pair (1,7) in row 7

Code: Select all: 590006078401000300000000000000870400307000902004012000000000000002000701710600085 .---------------.---------------.---------------. | 5 9 3 | 24 24 6 | 1 7 8 | | 4 67 1 | 579 589 578 | 3 2 69 | | 2 67 8 | 179 39 137 | 5 49 469 | :---------------+---------------+---------------: | 1 2 6 | 8 7 9 | 4 5 3 | | 3 8 7 | 45 6 45 | 9 1 2 | | 9 5 4 | 3 1 2 | 8 6 7 | :---------------+---------------+---------------: | 8 34 5 |*1279 29 *17 | 6 349 49 | | 6 34 2 | 59 589 58 | 7 349 1 | | 7 1 9 | 6 34 34 | 2 8 5 | '---------------'---------------'---------------'

# 1 hidden pair (3,8) in column 1

Code: Select all: 000000070900007456003006001290001000000040000000500082400200600619800007050000000 .------------------.------------------.------------------. | 15 246 1456 | 149 1259 8 | 239 7 39 | | 9 28 18 | 3 12 7 | 4 5 6 | | 57 247 3 | 49 259 6 | 8 29 1 | :------------------+------------------+------------------: | 2 9 567 | 67 8 1 | 357 346 345 | |*13578 3678 15678| 679 4 2 | 1579 169 59 | | 17 467 1467 | 5 679 3 | 179 8 2 | :------------------+------------------+------------------: | 4 378 78 | 2 17 59 | 6 139 3589 | | 6 1 9 | 8 3 45 | 25 24 7 | |*378 5 2 | 167 167 49 | 139 1349 3489 | '------------------'------------------'------------------'

# 3 hidden pairs

Code: Select all: 001050000090600007200300000006000200004107900008000500000005004500009020000030600 # Box 2 hidden pair (7,9) = & # Column 3 and box 7 combined hidden pair (2,9) = * .---------------.---------------.---------------. | 4678 3468 1 |&4789 5 48 | 348 369 2 | | 48 9 35 | 6 14 2 | 1348 135 7 | | 2 468 57 | 3 &1479 148 | 148 1569 59 | :---------------+---------------+---------------: | 9 7 6 | 5 8 3 | 2 4 1 | | 3 5 4 | 1 2 7 | 9 8 6 | | 1 2 8 | 49 49 6 | 5 7 3 | :---------------+---------------+---------------: | 678 1368*2379| 278 167 5 | 137 139 4 | | 5 1346 37 | 47 1467 9 | 137 2 8 | | 478 148 *279 | 2478 3 148 | 6 159 59 | '---------------'---------------'---------------' # Column 4 and box 8 combined hidden pair (2,8) .---------------.---------------.---------------. | 4678 3468 1 | 79 5 48 | 348 369 2 | | 48 9 35 | 6 14 2 | 1348 135 7 | | 2 468 57 | 3 79 148 | 148 1569 59 | :---------------+---------------+---------------: | 9 7 6 | 5 8 3 | 2 4 1 | | 3 5 4 | 1 2 7 | 9 8 6 | | 1 2 8 | 49 49 6 | 5 7 3 | :---------------+---------------+---------------: | 678 1368 29 |*278 167 5 | 137 139 4 | | 5 1346 37 | 47 1467 9 | 137 2 8 | | 478 148 29 |*2478 3 14 | 6 159 59 | '---------------'---------------'---------------'

# 1 hidden triple (4,6,7) in column 3

Code: Select all: 020003000160700040008000000000910002003060010800000070000400300740500000600100700 .---------------------.---------------------.---------------------. | 459 2 *4579 | 68 589 3 | 15689 5689 156789| | 1 6 59 | 7 2589 2589 | 2589 4 3 | | 3 579 8 | 26 4 1 | 2569 2569 5679 | :---------------------+---------------------+---------------------: | 45 57 *4567 | 9 1 4578 | 4568 3 2 | | 2459 579 3 | 28 6 24578 | 4589 1 589 | | 8 1 *24569 | 3 25 245 | 4569 7 569 | :---------------------+---------------------+---------------------: | 259 8 1259 | 4 7 269 | 3 2569 1569 | | 7 4 129 | 5 3 2689 | 12689 2689 1689 | | 6 3 259 | 1 289 289 | 7 2589 4 | '---------------------'---------------------'---------------------'

# 1 hidden triple (2,6,9) in box 2

Code: Select all: 002000960030100000000000005000002008000600004725003000080006090000009001200470000 .---------------------.---------------------.---------------------. | 1458 1457 2 | 357 358 4578 | 9 6 37 | | 45689 3 46789 | 1 *25689 4578 | 2478 2478 27 | | 4689 4679 46789 |*2379 *23689 478 | 1 23478 5 | :---------------------+---------------------+---------------------: | 13469 1469 13469 | 579 159 2 | 357 357 8 | | 1389 19 1389 | 6 159 157 | 2357 2357 4 | | 7 2 5 | 8 4 3 | 6 1 9 | :---------------------+---------------------+---------------------: | 1345 8 1347 | 235 1235 6 | 23457 9 237 | | 3456 4567 3467 | 235 2358 9 | 234578 234578 1 | | 2 159 139 | 4 7 158 | 358 358 6 | '---------------------'---------------------'---------------------'

# 1 naked pair (1,8) in row 9, 1 hidden quad (1,3,6,8) in box 9

Code: Select all: 000005004000000910000900038000304507070080060803502000490003000025000000600700000 .------------------.------------------.------------------. | 12379 8 12679| 26 123 5 | 267 27 4 | | 237 4 267 | 268 23 678 | 9 1 5 | | 127 5 1267 | 9 4 167 | 267 3 8 | :------------------+------------------+------------------: | 29 1 29 | 3 6 4 | 5 8 7 | | 5 7 4 | 1 8 9 | 23 6 23 | | 8 6 3 | 5 7 2 | 14 49 19 | :------------------+------------------+------------------: | 4 9 178 | 268 125 3 |*1278 257 *126 | | 17 2 5 | 4 19 168 |*1378 79 *1369 | | 6 3 18 | 7 259 18 | 24 2459 29 | '------------------'------------------'------------------'

X-Wings, Swordfish, Jellyfish

# X-Wing digit 1 in rows

Code: Select all: 028700050054003980000000007001090000006300000090004300000050000502000006600170009 .------------------.------------------.------------------. | 13 2 8 | 7 -14 9 | 6 5 -134 | | 7 5 4 | 26 *126 3 | 9 8 *12 | | 13 6 9 | 258 -1248 15 | 124 23 7 | :------------------+------------------+------------------: | 248 3 1 | 258 9 7 | 248 6 2458 | | 248 7 6 | 3 -128 15 | 1248 9 -12458| | 28 9 5 | 268 *1268 4 | 3 7 *128 | :------------------+------------------+------------------: | 9 1 7 | 4 5 6 | 28 23 238 | | 5 4 2 | 9 3 8 | 7 1 6 | | 6 8 3 | 1 7 2 | 5 4 9 | '------------------'------------------'------------------'

# X-Wing digit 7 in columns

Code: Select all: 000500094000007000006009203203000400060070020004000109801400500000700000350002000 .---------------------.---------------------.---------------------. |-17 -12378 *278 | 5 12368 1368 |*678 9 4 | | 1459 12389 2589 | 12368 123468 7 | 68 1568 1568 | | 1457 178 6 | 18 148 9 | 2 1578 3 | :---------------------+---------------------+---------------------: | 2 1789 3 | 1689 15689 1568 | 4 5678 5678 | | 159 6 589 | 1389 7 4 | 38 2 58 | | 57 78 4 | 2368 23568 3568 | 1 35678 9 | :---------------------+---------------------+---------------------: | 8 279 1 | 4 369 36 | 5 367 267 | | 6 4 29 | 7 13589 1358 | 389 138 128 | | 3 5 *79 | 1689 1689 2 |*6789 4 -1678 | '---------------------'---------------------'---------------------'

# Swordfish digit 7 in rows

Code: Select all: 200000005000010300780004000900003000605040902000600008000400081006020000500000007 .---------------.---------------.---------------. | 2 6 1 |*79 3 *79 | 8 4 5 | | 4 5 9 | 28 1 28 | 3 7 6 | | 7 8 3 | 5 6 4 | 12 12 9 | :---------------+---------------+---------------: | 9 -27 8 |-127 57 3 | 1567 156 4 | | 6 *37 5 |*178 4 *178 | 9 13 2 | | 1 -2347 247 | 6 579 -2579| 57 35 8 | :---------------+---------------+---------------: | 3 -279 27 | 4 579 -5679| 256 8 1 | | 8 *1479 6 |*179 2 *1579| 45 59 3 | | 5 1249 24 | 3 8 169 | 246 269 7 | '---------------'---------------'---------------'

# Swordfish digit 9 in columns

Code: Select all: 008007060140000200060050000030180006004000800500073020000010080009000032020400500 .---------------.---------------.---------------. | 239 59 8 | 239 4 7 | 139 6 159 | | 1 4 357 |-3689*39 *689 | 2 *79 -5789| | 2379 6 237 | 2389 5 1 | 379 4 789 | :---------------+---------------+---------------: | 279 3 27 | 1 8 4 | 79 5 6 | |-679 -179 4 |-569 2 *569 | 8 *179 3 | | 5 8 16 | 69 7 3 | 149 2 149 | :---------------+---------------+---------------: | 347 57 357 | 3579 1 2 | 6 8 479 | | 478 157 9 | 578 6 58 | 147 3 2 | | 3678 2 16 | 4 *39 *89 | 5 *179 -179 | '---------------'---------------'---------------'

# Jellyfish digit 9 in rows

Code: Select all: 003100005850400000006050009025006080000000000070800430500020600000008014100003500 .---------------.---------------.---------------. |*279 4 3 | 1 8 *279 | 27 6 5 | | 8 5 *279 | 4 6 *279 | 13 27 13 | | 27 1 6 | 3 5 27 | 8 4 9 | :---------------+---------------+---------------: | 4 2 5 | 79 3 6 | 179 8 17 | |-39 389 -189 | 2 -179 4 | 79 5 6 | | 6 7 *19 | 8 *19 5 | 4 3 2 | :---------------+---------------+---------------: | 5 38 4 | 79 2 1 | 6 79 38 | |*2379 6 *279 | 5 *79 8 | 237 1 4 | | 1 89 -2789| 6 4 3 | 5 279 78 | '---------------'---------------'---------------'

# 1 Jellyfish in rows, 1 Swordfish

Code: Select all: 007050000000001034120300000400200080200080005010004003000003041690700000000020600

# 1 Jellyfish in rows, 1 X-Wing

Code: Select all: 000000210051080000600000045000200300807050401003001000240000006000040570095000000

# Beyond this point, there is no agreed order of techniques. Your solver may find another technique to advance the listed puzzles. The listed techniques should be found when your solver is configured to detect the mentioned technique before anything past Jellyfish.

XY-Wing, XYZ-Wing, remote pairs

# XY-Wing X=3 Y=9 Z=1

Code: Select all: 300090040050008000097300002000000800900625003006000000200007980000200010040080005 .------------------.------------------.------------------. | 3 6 1 | 57 9 2 | 57 4 8 | | 4 5 2 | 17 167 8 | 1367 369 1679 | | 8 9 7 | 3 1456 146 | 156 56 2 | :------------------+------------------+------------------: | 157 1237 345 | 1479 1347 1349 | 8 2569 1469 | | 9 18 48 | 6 2 5 | 14 7 3 | | 157 1237 6 | 8 1347 1349 | 1245 259 149 | :------------------+------------------+------------------: | 2 *13 35 |-145 -13456 7 | 9 8 46 | | 567 378 3589 | 2 3456 3469 | 3467 1 467 | |-167 4 *39 |*19 8 1369 | 2367 236 5 | '------------------'------------------'------------------'

# 3 XY-Wings (only 2 required)

Code: Select all: 004000080300000072000000305900010000100842000000009700200081056000200004609500000

# XYZ-Wing X=4 Y=9 Z=6 (beautiful example)

Code: Select all: 049070000207000900030006000520700000000809000000004068000100020003000105000040370 .------------------.------------------.------------------. | 168 4 9 | 235 7 12358| 2568 1358 1236 | | 2 168 7 | 345 1358 1358 | 9 13458 1346 | | 18 3 5 | 249 1289 6 | 278 148 1247 | :------------------+------------------+------------------: | 5 2 8 | 7 6 13 | 4 139 139 | | 3467 67 46 | 8 1235 9 | 257 135 1237 | | 379 79 1 | 235 235 4 | 257 6 8 | :------------------+------------------+------------------: | 46789 56789*46 | 1 3589 3578 |-68 2 *469 | | 46789 6789 3 | 269 289 278 | 1 489 5 | | 1689 15689 2 | 569 4 58 | 3 7 *69 | '------------------'------------------'------------------'

# Remote pair (6,9) chain length = 4

Code: Select all: 000810000060500304700000000070000023090108050420000080000000002205001040000032000 .------------.------------.------------. |-39 5 349| 8 1 346| 2 7 *69 | | 8 6 2 | 5 7 9 | 3 1 4 | | 7 1 349| 2 46 346| 8 *69 5 | :------------+------------+------------: | 5 7 8 | 69 469 46 | 1 2 3 | | 36 9 36 | 1 2 8 | 4 5 7 | | 4 2 1 | 3 5 7 | 69 8 69 | :------------+------------+------------: | 1 4 69 | 679 8 5 | 679 3 2 | | 2 3 5 | 679 69 1 | 679 4 8 | |*69 8 7 | 4 3 2 | 5 *69 1 | '------------'------------'------------'

# 4 Remote pairs

Code: Select all: 003054070000000800026009000500002063000000000640800009000900640002000000080230900

Single digit advanced techniques

# Finned X-Wing digit 4 (2 fin cells)

Code: Select all: 048003006000500000020086007300000000056070120000000004200360010000009000900200430 .------------------.------------------.------------------. | 157 4 8 | 17 129 3 | 259 59 6 | | 6 379 379 | 5 249 247 | 2389 489 1 | | 15 2 1359 | 14 8 6 | 359 459 7 | :------------------+------------------+------------------: | 3 1789 *12479|#1468 #1245 *12458| 56789 56789 589 | | 48 5 6 | 9 7 -48 | 1 2 3 | | 178 1789 1279 | 168 3 1258 | 56789 56789 4 | :------------------+------------------+------------------: | 2 78 *457 | 3 6 *4578 | 5789 1 589 | | 14578 1378 13457| 1478 145 9 | 5678 5678 2 | | 9 6 157 | 2 15 1578 | 4 3 58 | '------------------'------------------'------------------'

# Finned Sashimi X-Wing digit 7

Code: Select all: 000004052000060300070000060607300500010090020002001604050000030004010000320700000 .---------------------.---------------------.---------------------. | 189 689 13689 | 189 #378 *4 |*1789 5 2 | | 124589 489 1589 | 12589 6 -25789 | 3 14789 1789 | | 124589 7 13589 | 12589 2358 2589 | 1489 6 189 | :---------------------+---------------------+---------------------: | 6 489 7 | 3 248 28 | 5 189 189 | | 458 1 58 | 4568 9 *5678 |*78 2 3 | | 589 3 2 | 58 578 1 | 6 789 4 | :---------------------+---------------------+---------------------: | 1789 5 1689 | 24689 248 2689 | 124789 3 16789 | | 789 689 4 | 25689 1 3 | 2789 789 56789 | | 3 2 1689 | 7 458 5689 | 1489 1489 15689 | '---------------------'---------------------'---------------------'

# Finned Sashimi X-Wing digit 5 (2 fin cells)

Code: Select all: 000080400501900000090003000106400020800070009050006304000600030000007502003090000 .---------------------.---------------------.---------------------. | 3 267 27 |#1257 *8 #125 | 4 9 *1567 | | 5 24678 1 | 9 246 24 | 2678 678 3 | | 2467 9 2478 | 1257 -12456 3 | 12678 15678 15678 | :---------------------+---------------------+---------------------: | 1 37 6 | 4 *35 9 | 78 2 *578 | | 8 234 24 | 1235 7 125 | 16 156 9 | | 279 5 279 | 8 12 6 | 3 17 4 | :---------------------+---------------------+---------------------: | 247 12478 5 | 6 124 1248 | 9 3 178 | | 469 1468 489 | 13 134 7 | 5 1468 2 | | 2467 124678 3 | 125 9 12458 | 1678 14678 1678 | '---------------------'---------------------'---------------------'

# Finned Swordfish digit 9 (also a regular swordfish for digit 8 present)

Code: Select all: 070500910000001800009708003000000102060070030504000000900603500007800000035007060 .------------------.------------------.------------------. | 238 7 268 | 5 236 26 | 9 1 4 | | 234 245 26 |*2349 *23469 1 | 8 257 57 | | 124 1245 9 | 7 24 8 | 6 25 3 | :------------------+------------------+------------------: | 7 89 3 |-49 -45689 4569 | 1 589 2 | | 128 6 128 | 129 7 #259 | 4 3 *589 | | 5 1289 4 |-1239 -12389 29 | 7 89 6 | :------------------+------------------+------------------: | 9 1248 128 | 6 124 3 | 5 478 178 | | 6 124 7 | 8 12459 2459 | 3 49 19 | | 148 3 5 |*149 *149 7 | 2 6 *189 | '------------------'------------------'------------------'

# Finned Sashimi Swordfish digit 3

Code: Select all: 003400000000025009040700060801000090070050010060000703080006020600170000000003500 .------------------.------------------.------------------. | 259 259 3 | 4 6 189 | 128 578 12578| | 7 1 6 | 38 2 5 | 348 #348 9 | | 259 4 8 | 7 *139 19 |-123 6 125 | :------------------+------------------+------------------: | 8 *235 1 | 236 *34 7 | 246 9 245 | | 2349 7 249 | 23689 5 2489 | 2468 1 248 | | 2459 6 2459 | 289 1489 12489| 7 458 3 | :------------------+------------------+------------------: | 349 8 479 | 5 49 6 | 1349 2 147 | | 6 *2359 2459 | 1 7 2489 | 3489 *348 48 | | 1 29 2479 | 289 489 3 | 5 478 6 | '------------------'------------------'------------------'

#Finned jellyfish

Code: Select all: 027000000010908006000000400200400095003020600570003004005000000400602030000000860 #one view: Jellyfish with 2 tentacles digit 1 .---------------.---------------.---------------. | 689 2 7 |*13 1346 146 |-19 5 *1389| | 3 1 4 | 9 5 8 | 7 2 6 | | 689 5 689 | 2 1367 167 | 4 #18 #1389| :---------------+---------------+---------------: | 2 68 168 | 4 1678 167 | 3 9 5 | |*189 4 3 |*158 2 159 | 6 7 18 | | 5 7 69 |*18 69 3 | 2 *18 4 | :---------------+---------------+---------------: | 678 368 5 | 378 38 19 | 19 4 2 | | 4 89 18 | 6 189 2 | 5 3 7 | |*17 39 2 |*1357 1349 1459| 8 6 *19 | '---------------'---------------'---------------' #alternative view: Sashimi Jellyfish digit 1 .---------------.---------------.---------------. | 689 2 7 | 13 1346 146 |-19 5 1389| | 3 1 4 | 9 5 8 | 7 2 6 | | 689 5 689 | 2 *1367*167 | 4 #18 #1389| :---------------+---------------+---------------: | 2 68 *168 | 4 *1678*167 | 3 9 5 | | 189 4 3 | 158 2 159 | 6 7 18 | | 5 7 69 | 18 69 3 | 2 18 4 | :---------------+---------------+---------------: | 678 368 5 | 378 38 *19 |*19 4 2 | | 4 89 *18 | 6 *189 2 | 5 3 7 | | 17 39 2 | 1357 1349 1459| 8 6 19 | '---------------'---------------'---------------'

# Simple Coloring digit 8 (4 eliminations)

Code: Select all: 300000000009630700002700090000002435500000009634500000080009300003047600000000004 .---------------.---------------.---------------. | 3 457 57 | 9 2 -158 |A18 -148 6 | |a18 45 9 | 6 3 158 | 7 -1248-128 | |A18 6 2 | 7 a18 4 | 5 9 3 | :---------------+---------------+---------------: | 79 179 a178 |A18 6 2 | 4 3 5 | | 5 2 A18 | 4 7 3 |a18 6 9 | | 6 3 4 | 5 9 a18 | 2 178 178 | :---------------+---------------+---------------: | 4 8 6 | 12 15 9 | 3 1257 127 | | 29 159 3 |a128 4 7 | 6 1258 128 | | 27 157 157 | 3 A158 6 | 9 a1258 4 | '---------------'---------------'---------------'

# Multi Coloring digit 7 (3 chains, A!B, a!c, b!c => c!c)

Code: Select all: 980300002000001306000060070003040000400209001000010500030090000102500000500002068 .------------.------------.------------. | 9 8 6 | 3 5 7 | 4 1 2 | | 7 45 45 | 89 2 1 | 3 89 6 | | 3 2 1 | 489 6 48 | 89 7 5 | :------------+------------+------------: | 268 1 3 |A678 4 5 |a678 28 9 | | 4 567 578| 2 B78 9 | 678 3 1 | | 268 679 789| 678 1 3 | 5 248c47 | :------------+------------+------------: | 68 3 c478| 1 9 46 | 2 5 C47 | | 1 467 2 | 5 b78 468|c79 49 3 | | 5 479 479|B47 3 2 | 1 6 8 | '------------'------------'------------'

# Multi Coloring digit 5 (2 chains, a!b)

Code: Select all: 600007005120400030000000040000040208000050000309020000070000000090006053200900006 .------------------.------------------.------------------. | 6 348 348 | 138 1389 7 | 189 2 5 | | 1 2 A578 | 4 689 a58 | 6789 3 79 | | 9 358 3578 |A1358 1368 2 | 1678 4 17 | :------------------+------------------+------------------: |B57 156 -15 | 1367 4 139 | 2 1679 8 | | 478 1468 2 | 1678 5 189 | 3 1679 1479 | | 3 1468 9 | 1678 2 18 | 5 167 147 | :------------------+------------------+------------------: |b458 7 6 |a1358 138 13458| 149 189 2 | | 48 9 148 | 2 178 6 | 147 5 3 | | 2 13458 13458| 9 178 1458 | 147 178 6 | '------------------'------------------'------------------'

# Template check, Nishio (3 candidates for digit 9 eliminated)
# Alternative 1: Combined Frankenfish type 1 & 2.
# Alternative 2: Empty Rectangle (ER) eliminates R7C8 digit 9.
# Alternative 3: Grouped coloring (fork pattern) eliminates R7C8 digit 9.

Code: Select all: 000000040060300100400908500020030001007000600800070030008106005003009070050000000 .------------------.------------------.------------------. | 13579 8 159 | 25 6 257 | 29 4 2379 | | 579 6 59 | 3 245 2457 | 1 289 2789 | | 4 37 2 | 9 1 8 | 5 6 37 | :------------------+------------------+------------------: | 569 2 4569 | 4568 3 45 | 7 589 1 | | 135 134 7 | 2458 9 1245 | 6 258 248 | | 8 149 14569| 2456 7 1245 | 249 3 249 | :------------------+------------------+------------------: | 279 479 8 | 1 24 6 | 3 -29 5 | | 126 14 3 | 245 2458 9 | 248 7 246 | |-269 5 -469 | 7 248 3 | 2489 1 2469 | '------------------'------------------'------------------'

Techniques that depend on a unique solution

# Uniqueness test 1

Code: Select all: 004000016200010000000002403041708000000000000000205390502400000000030005760000800 .------------.------------.------------. | 8 *57 4 | 3 *57 9 | 2 1 6 | | 2 357 36 | 68 1 4 | 9 578 78 | | 1 *579 69 | 68 *57 2 | 4 578 3 | :------------+------------+------------: | 3 4 1 | 7 9 8 | 5 6 2 | | 9 2 5 | 1 6 3 | 7 48 48 | | 6 8 7 | 2 4 5 | 3 9 1 | :------------+------------+------------: | 5 39 2 | 4 8 6 | 1 37 79 | | 4 1 8 | 9 3 7 | 6 2 5 | | 7 6 39 | 5 2 1 | 8 34 49 | '------------'------------'------------'

# Uniqueness test 2

Code: Select all: 000610000003000500095000078000004005042030760800500000410000620009000300000096000 .------------.------------.------------. | 7 8 4 | 6 1 5 | 9 3 2 | | 1 2 3 |*789-78 *789| 5 4 6 | | 6 9 5 | 34 24 23 | 1 7 8 | :------------+------------+------------: | 9 3 16 | 17 67 4 | 2 8 5 | | 5 4 2 |*89 3 *89 | 7 6 1 | | 8 7 16 | 5 26 12 | 4 9 3 | :------------+------------+------------: | 4 1 8 | 37 5 37 | 6 2 9 | | 2 6 9 | 148 48 18 | 3 5 7 | | 3 5 7 | 2 9 6 | 8 1 4 | '------------'------------'------------'

# Uniqueness test 3

Code: Select all: 000501003209004800040000500010960000002000100000017080008000020003400706500709000 .---------------.---------------.---------------. | 67 8 67 | 5 29 1 | 249 49 3 | | 2 5 9 | 3 7 4 | 8 6 1 | | 3 4 1 | 6 289 28 | 5 79 279 | :---------------+---------------+---------------: | 8 1 457 | 9 6 *35 | 24 *3457 2457| | 679 679 2 | 8 4 *35 | 1 *3579 579 | | 49 3 45 | 2 1 7 | 6 8 459 | :---------------+---------------+---------------: | 479 79 8 | 1 35 6 | 349 2 459 | | 1 29 3 | 4 258 28 | 7 -59 6 | | 5 26 46 | 7 23 9 | 34 1 8 | '---------------'---------------'---------------'

# Uniqueness test 4

Code: Select all: 000410000020090105006700090802000000000803000000000309080004500507080060000072000 .------------.------------.------------. |*79 *79 5 | 4 1 8 | 6 3 2 | | 4 2 8 | 3 9 6 | 1 7 5 | | 3 1 6 | 7 2 5 | 8 9 4 | :------------+------------+------------: | 8 3 2 | 19 46 179| 47 5 16 | |*679*579 14 | 8 456 3 | 47 2 16 | | 67 57 14 | 2 456 17 | 3 8 9 | :------------+------------+------------: | 2 8 9 | 6 3 4 | 5 1 7 | | 5 4 7 | 19 8 19 | 2 6 3 | | 1 6 3 | 5 7 2 | 9 4 8 | '------------'------------'------------'

# BUG+1 (5 is the surplus candidate)

Code: Select all: 609000000000006541700001000803009000040000020000300607000400002592600000000000903 .------------.------------.------------. | 6 1 9 | 25 4 25 | 7 3 8 | | 2 3 8 | 9 7 6 | 5 4 1 | | 7 5 4 | 8 3 1 | 2 9 6 | :------------+------------+------------: | 8 67 3 | 27 26 9 | 4 1 5 | | 1 4 67 | 57 56 8 | 3 2 9 | | 9 2 5 | 3 1 4 | 6 8 7 | :------------+------------+------------: | 3 67 1 | 4 9 57 | 8 56 2 | | 5 9 2 | 6 8 3 | 1 7 4 | | 4 8 67 | 1 25 -257| 9 56 3 | '------------'------------'------------'

#Reversed BUG digits 2 & 9 in starting grid (example by RW)

Code: Select all: 000070502000001060040560310012000609000000103009000420081040730050700000006038000 .---------------------.---------------------.---------------------. | 13689 369 38 | 3489 7 349 | 5 -489 *2 | | 235789 2379 3578 | 23489 289 1 | 89 6 478 | | 2789 4 78 | 5 6 29 | 3 1 78 | :---------------------+---------------------+---------------------: | 34578 1 *2 | 348 58 3457 | 6 578 *9 | | 45678 67 4578 | 24689 2589 245679| 1 578 3 | | 35678 367 *9 | 1368 158 3567 | 4 *2 578 | :---------------------+---------------------+---------------------: | 29 8 1 | 269 4 2569 | 7 3 56 | | 2349 5 34 | 7 129 269 | 289 489 1468 | | 2479 279 6 | 129 3 8 | 29 459 145 | '---------------------'---------------------'---------------------'

Forcing chains, Tabling, Bowman's Bingo

# My solver does not make a distinction between 'clean' chains and messy ones, so I just post a few samples here, but feel free to correct me in this section.

# Single short chain

Code: Select all: 000052000100000702042080600000001000230070058000300000004060910906000003000830000 # Chain starting position .------------.------------.------------. | 6 9 3 | 7 5 2 | 8 4 1 | | 1 5 8 | 69 49 46 | 7 3 2 | | 7 4 2 | 1 8 3 | 6 9 5 | :------------+------------+------------: | 8 67 79 | 5 249 1 | 3 267 469| | 2 3 19 | 69 7 46 | 14 5 8 | | 4 167 5 | 3 29 8 | 12 267 69 | :------------+------------+------------: | 3 8 4 | 2 6 5 | 9 1 7 | | 9 2 6 | 4 1 7 | 5 8 3 | | 5 17 17 | 8 3 9 | 24 26 46 | '------------'------------'------------'

# Single long chain

Code: Select all: 005200000013000004940800070000100620000704000059002000020006045700000360000001700

# 5 chains used

Code: Select all: 000010006307800009000600070000305400040000090001908000050002000400009208200070000

Extremely tough puzzles

# Original toughest known

Code: Select all: 000070940070090005300005070087400100463080000000007080800700000700000028050268000

# Top1465 #2

Code: Select all: 708000300000201000500000000040000026300080000000100090090600004000070500000000000

# Top1465 #77

Code: Select all: 700000400020070080003008009000500300060020090001007006000300900030040060009001005

Invalid Puzzles (your solver must start complaining here)

# Empty grid

Code: Select all: 000000000000000000000000000000000000000000000000000000000000000000000000000000000

# Zen sudoku (solution can only be found by staring at the 1 in the center)

Code: Select all: 000000000000000000000000000000000000000010000000000000000000000000000000000000000

# 3673 solutions

Code: Select all: 000306500800500000010000040900080020000000000040060001050000010000009002006108000

# 2 solutions

Code: Select all: 000010000702409000040300060179000000035000100000000578020006040000704302000090000

# No solution, cell with no candidates left

Code: Select all: 009028700806004005003000004600000000020713450000000002300000500900400807001250300

# No solution, box with no candidates for a digit

Code: Select all: 090300001000080046000000800405060030003275600060010904001000000580020000200007060

# No solution, duplicate digit in row

Code: Select all: 030067100690000000081382050000700008010000020900005000050193800000000034007650010

All samples are from my own collection, except for the toughest puzzles, which have been posted in the public domain already. Thanks to Gaby for a description of the 'zen' sudoku.

I hope this will help you test your solvers (programmers) and solving skills (players). This corner of the forum is not so busy, but if needed, we can make this a sticky.

Ruud.

PS. It took me almost 4 days to assemble this list, have mercy if you find any errors.
PPS. Candidate grids of the 'moment supreme' have been added, comment lines prefixed with #

by **tarek** » Thu Apr 13, 2006 9:25 pm

I've posted this in the effortless thread too...but it should work here as it has only one non single step (a 5 node ALS xy rule):

Code: Select all: . . 9 | . . . | 4 . . . . . | . 7 . | . . . 7 . 4 | . . 2 | 6 . 1 -------+-------+------ . . 5 | 7 . 1 | . . . . 8 . | 4 6 . | . 2 . . . . | 5 . 8 | 3 . . -------+-------+------ 4 . 7 | 6 . . | 2 . 9 . . . | . 3 . | . . . . . 6 | . . . | 1 . . *-----------------------------------------------* | 8 12 9 | 13 5 6 | 4 37 237 | |*12 6 3 | 19 7 4 | 8 59 ^25 | | 7 5 4 | 39 8 2 | 6 39 1 | |---------------+---------------+---------------| | 3 4 5 | 7 2 1 | 9 6 8 | | 9 8 1 | 4 6 3 |-57 2 ^57 | | 6 7 2 | 5 9 8 | 3 1 4 | |---------------+---------------+---------------| | 4 3 7 | 6 1 5 | 2 8 9 | |%15 19 8 | 2 3 79 |%57 4 6 | | 25 29 6 | 8 4 79 | 1 357 -357 | *-----------------------------------------------* Eliminating 7 from r5c7(ALS-XY A=12 in r2c1 B=257 in r5c9,r2c9 C=157 in r8c7,r8c1 x=2 y=1 z=7) Eliminating 7 from r9c9(ALS-XY A=12 in r2c1 B=257 in r5c9,r2c9 C=157 in r8c7,r8c1 x=2 y=1 z=7)

This one is even simpler, the only non single move is a 4 node ALS xy rule...(also not by me)...

Code: Select all: . 5 . | . . . | . . 6 . . 6 | 7 4 . | 3 1 . 2 . . | . 8 . | . 4 . -------+-------+------ . 1 . | 3 . . | . 2 4 . . . | 8 . . | . 7 . . . . | . . 4 | 1 . . -------+-------+------ . . 2 | 6 . . | . . . . 6 . | . . 9 | . 8 1 5 . . | . . 8 | . . . *-----------------------------------------------------------------* | 47 5 47 |^12 3 12 | 8 9 6 | | 8 9 6 | 7 4 5 | 3 1 2 | | 2 3 1 | 9 8 6 | 57 4 57 | |---------------------+---------------------+---------------------| | 69 1 8 | 3 569 7 | 569 2 4 | | 3469 %24 345 | 8 12569 12 | 569 7 35 | | 3679 27 357 |-25 2569 4 | 1 36 8 | |---------------------+---------------------+---------------------| | 1 8 2 | 6 7 3 | 4 5 9 | | 347 6 347 | 245 25 9 | 27 8 1 | | 5 *47 9 |^124 12 8 | 267 36 37 | *-----------------------------------------------------------------* Eliminating 2 from r6c4(ALS-XY A=47 in r9c2 B=124 in r1c4,r9c4 C=27 in r6c2 x=4 y=7 z=2)

tarek

by **Ocean** » Fri Apr 14, 2006 4:02 pm

Good work on the benchmark list, Ruud!. Think it will be useful. My own logical solver is not too sophisticated - originally written as a tool for 'finding x-wings'. Later incremented for 'detecting xy-chains' (finds all potential xy-chains in the bivalue graph and sorts them by length). Since the XY-wing is an xy-chain of length 3, it also finds XY-wings:

Ruud wrote:# 3 XY-Wings (probably only 2 required)
Code: Select all
004000080300000072000000305900010000100842000000009700200081056000200004609500000

This puzzle can be solved with 2 XY-wings. (At stage 59 there is a choice between two XY-wings. If the one eliminating candidate '6' from r5c3 is applied, then there is a second (new) XY-wing a few steps later that finishes the 'hard' jobs).

Else my 'solver' performs 'as expected' on those puzzles from your benchmark list that I tested so far - it reports less (or different) details than you do, and some methods are not implemented (fishes, colouring), which means it either finds other methods or fails. (In general - with the implemented techniques - it finds a solution to 98.8% of 'random symmetrical puzzles', but only about 70% of 'minimal puzzles with low number of clues'.)

by **Havard** » Sun Apr 16, 2006 1:40 pm

Ruud wrote:# Template check, Nishio (3 candidates for digit 9 eliminated)
Code: Select all
000000040060300100400908500020030001007000600800070030008106005003009070050000000 .------------------.------------------.------------------. | 13579 8 159 | 25 6 257 | 29 4 2379 | | 579 6 59 | 3 245 2457 | 1 289 2789 | | 4 37 2 | 9 1 8 | 5 6 37 | :------------------+------------------+------------------: | 569 2 4569 | 4568 3 45 | 7 589 1 | | 135 134 7 | 2458 9 1245 | 6 258 248 | | 8 149 14569| 2456 7 1245 | 249 3 249 | :------------------+------------------+------------------: | 279 479 8 | 1 24 6 | 3 -29 5 | | 126 14 3 | 245 2458 9 | 248 7 246 | |-269 5 -469 | 7 248 3 | 2489 1 2469 | '------------------'------------------'------------------'

the "big fish" thread has contributed to downsize the importance of nishio:

Code: Select all: Combined frankenfish type 1 and type 2: . . . | . . . | # . # . . . | . . . | | . # . . . | . . . | | . | ------+-------+-|---| . . . | . . . | | . | . . . | . . . | | . | . X . | . . . | X . X --|---+-------+-|---| . H . | . . . | | * | . . . | . . . | | . | * . * | . . . | X . X

by **Steve R** » Sun Apr 16, 2006 3:51 pm

Nishio? Fishio?

The empty rectangle constructed from box 6 and the conjugates with respect to 9 in column 2 also excludes 9 from r7c8. Perhaps the empty rectangle could be added to the list.

In fact, a much more elementary argument that I call a fork will make the same elimination here. There are only two places for 9 in the fourth row, r4c8 and b4 ex c2. There are also just two places for it in the second column, r7c2 and b4c2. So r7c8 cannot contain a 9.

Steve

by **Ruud** » Sun Apr 16, 2006 6:14 pm

Thanks for the alternative solving methods.

Any pattern technique is favored by me to replace the Template check / Nishio, but I would really like to see the effective range of each method.

In this case, we have a combined Frankenfish competing with 2 techniques put forward by Steve. I see different applications of grouped coloring in both methods, Steve.

Is it possible to come up with an example where only one of the techniques works, with no alternatives but Nishio? Those are the ones I would like to add to the list. Otherwise, we must confirm that these alternative methods are equivalent.

Ocean wrote:This puzzle can be solved with 2 XY-wings.

I will edit the list accordingly. Thanks.

Ruud.

by **ronk** » Sun Apr 16, 2006 7:19 pm

Ruud wrote:
Code: Select all
# Template check, Nishio (3 candidates for digit 9 eliminated) # Alternative 1: Combined Frankenfish type 1 & 2. # Alternative 2: Empty Rectangle (ER) eliminates R7C8 digit 9. # Alternative 3: Grouped coloring (fork pattern) eliminates R7C8 digit 9. .------------------.------------------.------------------. | 13579 8 159 | 25 6 257 | 29 4 2379 | | 579 6 59 | 3 245 2457 | 1 289 2789 | | 4 37 2 | 9 1 8 | 5 6 37 | :------------------+------------------+------------------: | 569 2 4569 | 4568 3 45 | 7 589 1 | | 135 134 7 | 2458 9 1245 | 6 258 248 | | 8 149 14569| 2456 7 1245 | 249 3 249 | :------------------+------------------+------------------: | 279 479 8 | 1 24 6 | 3 -29 5 | | 126 14 3 | 245 2458 9 | 248 7 246 | |-269 5 -469 | 7 248 3 | 2489 1 2469 | '------------------'------------------'------------------'

[edit: Corrected logic error, which reduced exclusions from five to three. Bogus exclusions were r6c7 and r6c9.]

Three eliminations with grouped coloring ...

Code: Select all: 9 . 9 | . . . | 9 . 9 9 . 9 | . . . | . 9 9 . . . | . . . | . . . - - - + - - - + - - - 9 . 9 | . . . | . b . . . . | . . . | . . . . A 9 | . . . | B . B - - - + - - - + - - - 9 a . | . . . | .-C . . . . | . . . | . . . -9 .-9 | . . . | c . c

... and two applications of the same coloring rule:
1. Since 'A' excludes 'B' and 'b' excludes 'C', any candidate that sees both 'a' and 'c' may be excluded (r9c1,r9c3).
2. Since 'A' excludes 'B', any candidate that sees both 'a' and 'b' may be excluded (r7c8).

Note: The grouped coloring uses the strong links of two empty rectangles (hinges).

by **Ruud** » Sun Apr 16, 2006 7:40 pm

[edit] obsolete now

by **Myth Jellies** » Sun Apr 16, 2006 9:58 pm

edit - no longer needed after ronk edited his post

by **ronk** » Sun Apr 16, 2006 10:12 pm

Ruud wrote:So why is R6C7 eliminated by your grouped coloring? And what forms the strong pairing between b and B, with candidates in every column in box 3?

Thanks, that "strong pairing" is definitely bogus. The ER in box 9 is a conjugate link of a 3rd color, which means the eliminations at r6c7 and r6c9 are invalid. I'll edit my post.

by RW » Tue Apr 18, 2006 8:10 pm

Here's a reverse-BUG example. It might not be the most common pattern, but it shouldn't be too hard to program either:

Code: Select all: 000070500000001060040560310012000600000000103009000420081040730050700000006038000 *--------------------------------------------------------------------* | 1 6 38 | 3489 7 349 | 5 -489 *2 | | 35 29 357 | 34 289 1 | 89 6 47 | | 29 4 78 | 5 6 29 | 3 1 78 | |----------------------+----------------------+----------------------| | 458 1 *2 | 348 58 34 | 6 7 *9 | | 4568 7 45 | 24689 2589 249 | 1 58 3 | | 568 3 *9 | 68 1 7 | 4 *2 58 | |----------------------+----------------------+----------------------| | 29 8 1 | 29 4 5 | 7 3 6 | | 34 5 34 | 7 29 6 | 289 89 1 | | 7 29 6 | 1 3 8 | 29 45 45 | *--------------------------------------------------------------------*

RW

by **Ruud** » Tue Apr 18, 2006 8:59 pm

RW wrote:Here's a reverse-BUG example.

Thanks. I've checked your example and it contains:
4(3) naked pairs,
1 naked triple,
2(1) hidden pairs,
1(0) remote pair,
2(0) swordfish,
1(0) XYZ-wing,
1(0) chain.

The numbers in parentheses are the result of using the reverse-BUG.

Even when it is rare, it cuts the number of required techniques in half.

For the benchmark list, I prefer isolated cases. If you can find a case with only singles and a reverse-BUG, I would appreciate it.

cheers,
Ruud.

by **Ocean** » Wed Apr 19, 2006 7:34 am

In case you need an XY-chain example in your benchmark list, here is a candidate.
It should need only singles, plus an xy-chain (discontinuous nice loop) (@53):
409000701000903000100040008040307020006000800050104060600070003000806000204000906
-3-[r3c2]-6-[r3c7]-5-[r4c7]-1-[r4c3]-8-[r4c1]-9-[r6c1]-7-[r5c1]-3- =>r5c2<>3
#

Code: Select all: Candidate list when 53 cells are filled. Cells in the xy-chain labeled #, loop discontinuity labeled *. {4} {2} {9} {6} {5} {8} {7} {3} {1} {578} {678} {578} {9} {1} {3} {456} {45} {2} {1} {36}# {35} {7} {4} {2} {56}# {9} {8} {89}# {4} {18}# {3} {6} {7} {15}# {2} {59} {37}# -{137}* {6} {2} {9} {5} {8} {147} {47} {79}# {5} {2} {1} {8} {4} {3} {6} {79} {6} {18} {158} {4} {7} {9} {2} {158} {3} {357} {9} {1357} {8} {2} {6} {145} {1457} {457} {2} {78} {4} {5} {3} {1} {9} {78} {6}

by **Havard** » Wed Apr 19, 2006 7:12 pm

Hi Ruud.

Your finned jellyfish has a smaller skyscraper / 2-strong links / fillet'o' / finned x-wing counterpart:

Code: Select all: 9 68 1 | 46 5 3 | 2 7 48 5 28 26 | 467 147 1467 | 3 9 48 7 3 4 | 2 8 9 | 6 5 1 ---------------+----------------+--------------- 8 7 3 | 5 6 2 | 14 14 9 46X 1 5 | 9 3 47X | 8 2 67 2 46- 9 | 1 47 8 | 5 3 67 ---------------+----------------+--------------- 1 24X 26 | 3 9 46X | 7 8 5 3 9 7 | 8 14 5 | 14 6 2 46- 5 8 | 467 2 1467 | 9 14 3 . . . | 4 . . | . . 4 . . . | 4 4 4 | . . 4 . . 4 | . . . | . . . ---------+----------+--------- . . . | . . . | 4 4 . 4X . . | . . 4X | . . . . 4- . | . 4 . | . . . ---------+----------+--------- . 4X . | . . 4X | . . . . . . | . 4 . | 4 . . 4- . . | 4 . 4 | . 4 .

This post-initiative is great! Hope someone can find a worthy jellyfish substitute...

One question though... Where does really Unique Rectangles fit into the solving hierarchy? Most manual solver I know say that they are among the first thing they look for, but it seems like a lot of computer-solvers puts them towards the end of their list. If you promote the UR's up front with the locked sets a list like this becomes quite different.... Any thoughts?

Havard

by **Ruud** » Wed Apr 19, 2006 7:48 pm

Havard wrote:Your finned jellyfish has a smaller skyscraper / 2-strong links / fillet'o' / finned x-wing counterpart

Thanks. I will update the entry.

I may have a replacement here:

Code: Select all: 027000000010908006000000400200400095003020600570003004005000000400602030000000860 #Jellyfish with 2 tentacles .---------------.---------------.---------------. | 689 2 7 |*13 1346 146 |-19 5 *1389| | 3 1 4 | 9 5 8 | 7 2 6 | | 689 5 689 | 2 1367 167 | 4 #18 #1389| :---------------+---------------+---------------: | 2 68 168 | 4 1678 167 | 3 9 5 | |*189 4 3 |*158 2 159 | 6 7 18 | | 5 7 69 |*18 69 3 | 2 *18 4 | :---------------+---------------+---------------: | 678 368 5 | 378 38 19 | 19 4 2 | | 4 89 18 | 6 189 2 | 5 3 7 | |*17 39 2 |*1357 1349 1459| 8 6 *19 | '---------------'---------------'---------------' #alternative view: Sashimi Jellyfish digit 1 .---------------.---------------.---------------. | 689 2 7 | 13 1346 146 |-19 5 1389| | 3 1 4 | 9 5 8 | 7 2 6 | | 689 5 689 | 2 *1367*167 | 4 #18 #1389| :---------------+---------------+---------------: | 2 68 *168 | 4 *1678*167 | 3 9 5 | | 189 4 3 | 158 2 159 | 6 7 18 | | 5 7 69 | 18 69 3 | 2 18 4 | :---------------+---------------+---------------: | 678 368 5 | 378 38 *19 |*19 4 2 | | 4 89 *18 | 6 *189 2 | 5 3 7 | | 17 39 2 | 1357 1349 1459| 8 6 19 | '---------------'---------------'---------------'

Please can you verify it before I put another misser in the list?

Where does really Unique Rectangles fit into the solving hierarchy?

In this list it does not really matter. So far, I've been able to find examples for uniqueness-based methods with most other techniques enabled in my solver. I try to select examples that have as few as possible other techniques (preferable singles only).

Ruud.

The New Sudoku Players' Forum

Benchmark Sudoku List

Benchmark Sudoku List

Re: Benchmark Sudoku List

# Template check, Nishio