"hidden-3" 2 9 7 | 1 6 58 | 3 4 58 456 1 456 | 2 3 4589 | 569 89 7 8 3 456 | 7 49 459 | 569 2 1 ---------------+---------------+--------------- 345 478 9 | 6 147 2 | 45 18 358 46 2 1468 | 5 149 3 | 49 7 68 3456 47 1456 | 8 1479 49 | 2 19 356 ---------------+---------------+--------------- 1 5 2 | 9 8 6 | 7 3 4 9 48 48 | 3 5 7 | 1 6 2 7 6 3 | 4 2 1 | 8 5 9 "x-wing" 47 249 1 | 8 5 3 | 6 247 249 5 369 789 | 2 4 16 | 1789 378 19 3468 2346 28 | 7 9 16 | 18 23458 1245 ------------------+------------------+------------------ 9 7 3 | 1 2 8 | 5 46 46 2 8 5 | 9 6 4 | 3 1 7 16 16 4 | 5 3 7 | 2 9 8 ------------------+------------------+------------------ 3478 2349 2789 | 46 1 5 | 789 2678 269 1478 1245 278 | 46 78 9 | 178 25678 3 178 159 6 | 3 78 2 | 4 578 159 "x-wing" 146 8 14 | 7 169 5 | 2 149 3 7 369 5 | 2 1369 469 | 48 1489 19 134 39 2 | 134 8 49 | 6 5 7 ------------------+------------------+------------------ 9 5 7 | 6 4 2 | 1 3 8 8 4 6 | 15 15 3 | 9 7 2 2 1 3 | 9 7 8 | 45 46 56 ------------------+------------------+------------------ 14 2367 9 | 345 2356 467 | 3578 168 156 36 2367 8 | 35 23569 1 | 357 69 4 5 367 14 | 8 369 4679 | 37 2 169 "swordfish" 8 47 1 | 67 3 46 | 2 5 9 3 6 79 | 79 2 5 | 8 1 4 5 2 49 | 89 48 1 | 7 3 6 ------------+------------+------------ 19 5 47 | 26 18 26 | 3 49 78 6 8 3 | 4 9 7 | 1 2 5 19 47 2 | 13 5 38 | 49 6 78 ------------+------------+------------ 2 19 8 | 5 147 49 | 6 479 3 7 19 5 | 13 6 349 | 49 8 2 4 3 6 | 28 78 289 | 5 79 1 "swordfish" 457 8 459 | 247 347 2347 | 6 1 79 1 3 46 | 467 9 478 | 2 5 78 2 679 69 | 1 678 5 | 89 3 4 ---------------+---------------+--------------- 9 26 8 | 45 45 1 | 3 7 26 57 57 1 | 3 2 6 | 489 48 89 3 4 26 | 79 78 789 | 5 26 1 ---------------+---------------+--------------- 6 259 2459 | 8 457 2479 | 1 24 3 48 29 3 |2469 1 249 | 7 2468 5 458 1 7 |2456 3456 234 | 48 9 26 "swordfish" 489 89 2 | 1 46 5 | 3 7 469 7 35 345 | 9 46 23 | 256 1 8 6 1 3459 | 23 7 8 | 25 29 459 ---------------+---------------+--------------- 2349 2359 8 | 56 1 49 | 7 269 369 1249 7 469 | 68 3 49 | 268 5 169 139 359 3569 | 568 2 7 | 4 689 1369 ---------------+---------------+--------------- 89 6 7 | 4 589 1 | 58 3 2 5 2389 39 | 23 89 6 | 1 4 7 23 4 1 | 7 58 23 | 9 68 56 "swordfish" 267 1 2679 | 257 45 247 | 8 579 3 5 378 278 | 237 9 6 | 1 47 24 237 379 4 | 2357 8 1 | 579 6 29 ------------------+------------------+------------------ 9 578 1578 | 4 12 3 | 25 58 6 348 2 58 | 79 6 79 | 35 1 48 346 34 16 | 8 12 5 | 239 49 7 ------------------+------------------+------------------ 278 6 25789 | 259 3 289 | 4 789 1 248 489 289 | 1 7 2489 | 6 3 5 1 45789 3 | 6 45 489 | 79 2 89 "swordfish" 267 26 8 | 37 9 23 | 1 4 5 5 3 1 | 6 4 28 | 2789 789 289 4 9 27 | 1578 2578 128 | 28 36 36 ------------------+------------------+------------------ 12679 12468 46 | 3789 2378 5 | 2789 13789 2389 279 5 3 | 789 1 289 | 6 789 4 1279 128 27 | 4 2378 6 | 5 13789 2389 ------------------+------------------+------------------ 1236 1246 456 |13589 358 1389 | 89 689 7 136 16 56 |13589 358 7 | 4 2 689 8 7 9 | 2 6 4 | 3 5 1 "swordfish/x-wing" 269 2679 679 | 1 3 467 | 678 4789 5 3 4 1679 | 678 78 5 | 2 79 179 8 5 167 | 9 47 2 | 1367 347 1347 ------------------+------------------+------------------ 146 678 4678 |23478 5 147 | 9 23678 12378 1569 6789 2 | 378 789 179 | 4 35678 1378 1459 789 3 | 2478 6 1479 | 1578 2578 1278 ------------------+------------------+------------------ 249 289 489 | 457 1 3 | 57 24579 6 246 3 5 | 467 479 4679 | 78 1 2478 7 1 469 | 456 2 8 | 35 3459 349 "jellyfish/x-wing" 7 58 6 | 2 3 9 | 58 1 4 1 589 2 | 6 58 4 | 7 59 3 589 4 3 | 58 7 1 |5689 2 68 ---------------+---------------+--------------- 58 2 58 | 3 6 7 | 1 4 9 6 3 9 | 1 4 5 | 28 7 28 4 1 7 | 9 2 8 | 3 6 5 ---------------+---------------+--------------- 25 7 1 | 4 9 3 | 256 8 26 3 568 4 | 7 58 26 | 259 59 1 29 69 58 | 58 1 26 | 4 3 7 "jellyfish" 5 13 12 | 67 89 67 | 239 18 4 124 8 9 | 145 45 3 | 25 7 6 134 6 7 | 2 89 145 | 359 18 359 ---------------+---------------+--------------- 6 159 3 | 59 7 8 | 15 4 2 17 2 8 | 345 6 45 |1357 9 357 79 579 4 | 359 1 2 | 8 6 357 ---------------+---------------+--------------- 127 17 56 | 156 25 9 | 4 3 8 39 4 12 | 8 23 17 | 6 5 79 8 39 56 |4567 345 4567 | 79 2 1 "jellyfish" 35 18 35 | 4 7 9 | 6 2 18 178 178 4 | 26 26 18 | 3 9 5 9 2 6 | 35 18 35 | 148 47 1478 ---------------+---------------+--------------- 57 3 1 | 257 248 578 | 45 6 9 258 48 25 | 9 3 6 | 145 47 147 567 467 9 | 157 14 157 | 2 8 3 ---------------+---------------+--------------- 23 5 23 | 8 9 4 | 7 1 6 4 16 8 | 37 16 37 | 9 5 2 16 9 7 | 16 5 2 | 48 3 48 "xy-wing" 13 2 6 | 349 35 7 | 149 59 8 8 9 5 | 6 2 14 | 14 7 3 13 7 4 | 39 8 15 |1269 259 169 ---------------+---------------+--------------- 4 5 7 | 1 9 3 | 8 6 2 9 8 3 | 2 4 6 | 5 1 7 6 1 2 | 5 7 8 | 39 39 4 ---------------+---------------+--------------- 2 36 9 | 34 1 45 | 7 8 56 5 4 8 | 7 36 9 |1236 23 16 7 36 1 | 8 356 2 | 369 4 569 "coloring" 2 5 3 | 49 7 1 | 49 6 8 9 4 7 | 2 8 6 | 1 3 5 6 8 1 | 3 45 59 | 2 49 7 ------------+------------+------------ 3 7 6 |149 14 8 | 49 5 2 8 1 2 | 45 3 59 | 7 49 6 5 9 4 | 6 2 7 | 3 8 1 ------------+------------+------------ 4 6 9 | 15 15 2 | 8 7 3 1 3 8 | 7 6 4 | 5 2 9 7 2 5 | 8 9 3 | 6 1 4 "coloring" 6 9 4 | 7 5 1 | 2 3 8 2 3 5 | 48 48 69 | 7 1 69 7 1 8 | 2 69 3 | 69 4 5 ------------+------------+------------ 1 4 7 | 69 3 69 | 5 8 2 8 2 6 | 45 47 57 | 3 9 1 3 5 9 | 1 2 8 | 4 6 7 ------------+------------+------------ 9 7 2 | 68 1 4 | 68 5 3 4 8 3 |569 67 57 | 1 2 69 5 6 1 | 3 89 2 | 89 7 4 "coloring" 29 29 1 | 7 3 6 | 4 5 8 7 6 4 | 8 5 12 | 3 12 9 5 3 8 | 4 12 9 | 12 6 7 ---------------+---------------+--------------- 289 2459 3 | 6 7 125 | 12 128 45 28 45 7 | 9 12 3 | 6 128 45 1 25 6 | 25 4 8 | 9 7 3 ---------------+---------------+--------------- 6 1 59 | 3 8 45 | 7 49 2 3 7 59 | 25 6 245 | 8 49 1 4 8 2 | 1 9 7 | 5 3 6 "coloring" 5 2 7 | 16 3 16 | 4 9 8 3 9 4 | 2 7 8 | 6 1 5 6 8 1 | 5 9 4 | 2 7 3 ------------+------------+------------ 9 4 25 | 68 1 26 | 3 58 7 1 3 25 | 4 28 7 | 58 6 9 8 7 6 | 3 5 9 | 1 2 4 ------------+------------+------------ 27 6 8 | 9 24 3 | 57 45 1 4 1 9 | 78 6 5 | 78 3 2 27 5 3 |178 248 12 | 9 48 6 "coloring" 7 13 6 | 8 2 5 | 13 9 4 5 9 4 | 3 1 7 | 6 2 8 2 138 38 | 6 4 9 | 5 13 7 ------------+------------+------------ 89 4 5 | 2 3 18 | 7 6 19 6 7 38 | 9 5 18 | 13 4 2 39 2 1 | 7 6 4 | 8 5 39 ------------+------------+------------ 4 5 7 | 1 9 3 | 2 8 6 38 6 9 | 5 78 2 | 4 17 13 1 38 2 | 4 78 6 | 9 37 5 "coloring" 2 6 5 | 147 147 147 | 9 8 3 7 4 8 | 6 3 9 | 15 15 2 3 1 9 | 5 8 2 | 4 7 6 ---------------+---------------+--------------- 6 27 12 | 3 45 45 | 17 9 8 19 79 4 | 17 2 8 | 6 3 5 8 5 3 | 9 17 6 | 127 12 4 ---------------+---------------+--------------- 459 29 6 | 8 457 3457 | 235 25 1 145 8 12 | 14 9 1345 | 235 6 7 15 3 7 | 2 6 15 | 8 4 9 "fillet-o-fish" 58 58 6 | 17 147 2 | 47 3 9 1 9 3 | 5 8 47 | 47 2 6 2 4 7 | 3 9 6 | 58 58 1 ---------------+---------------+--------------- 9 257 25 | 17 1357 8 | 6 4 23 6 3 458 | 2 45 9 | 1 7 58 578 1 2458 | 6 3457 457 | 58 9 23 ---------------+---------------+--------------- 4 57 9 | 8 6 3 | 2 1 57 578 6 258 | 9 257 1 | 3 58 4 3 2578 1 | 4 257 57 | 9 6 578 "finned-x-wing" 156 7 15 | 2 4 3 | 9 18 168 16 4 3 | 5 9 8 | 2 7 16 9 2 8 | 67 67 1 | 3 4 5 ---------------+---------------+--------------- 4 158 1579 |1679 167 2 | 56 3 18 2 158 159 |1469 3 56 | 456 18 7 3 6 157 | 147 8 57 | 45 2 9 ---------------+---------------+--------------- 17 9 2 | 3 167 67 | 8 5 4 78 3 6 | 78 5 4 | 1 9 2 158 15 4 | 18 2 9 | 7 6 3 "finned-x-wing" 4 6 138 | 7 1238 123 | 9 5 12 18 2 9 | 4 5 18 | 6 3 7 13 5 7 | 6 123 9 | 8 4 12 ---------------+---------------+--------------- 5 37 238 | 23 2378 4 | 1 9 6 128 4 6 | 128 9 1278 | 3 27 5 9 137 123 | 5 6 1237 | 4 27 8 ---------------+---------------+--------------- 6 8 4 | 239 23 5 | 7 1 39 1237 13 123 |1389 4 1378 | 5 6 39 137 9 5 | 13 137 6 | 2 8 4 "finned-x-wing" 4678 9 168 | 2 3 146 | 78 5 16 236 18 236 | 9 7 5 | 4 18 26 2467 157 1256 | 16 8 146 | 27 9 3 ---------------+---------------+--------------- 68 3 68 | 5 2 7 | 1 4 9 1 4 9 | 8 6 3 | 5 2 7 5 2 7 | 4 1 9 | 36 36 8 ---------------+---------------+--------------- 9 6 128 | 3 4 18 | 28 7 5 2378 178 4 | 16 5 168 | 9 138 12 38 158 1358 | 7 9 2 | 36 1368 4 "finned-x-wing" 467 9 178 | 2 3 146 | 78 5 16 26 128 3 | 9 7 5 | 4 18 126 2467 1257 1257 | 16 8 146 | 27 9 3 ---------------+---------------+--------------- 8 3 6 | 5 2 7 | 1 4 9 1 4 9 | 8 6 3 | 5 2 7 5 27 27 | 4 1 9 | 3 6 8 ---------------+---------------+--------------- 9 6 128 | 3 4 18 | 28 7 5 27 1278 4 | 16 5 168 | 9 3 12 3 158 158 | 7 9 2 | 6 18 4 "finned-x-wing" 189 359 38 |15689 159 2 | 7 4 68 1289 259 7 |15689 4 156 | 56 3 268 248 245 6 | 58 7 3 | 1 25 9 ------------------+------------------+------------------ 7 8 1 | 245 25 9 | 3 26 246 3 24 9 | 124 6 14 | 8 7 5 5 6 24 | 7 3 8 | 9 1 24 ------------------+------------------+------------------ 6 239 5 | 129 129 17 | 4 8 37 49 1 34 | 4569 8 4567 | 2 569 37 2489 7 248 | 3 259 456 | 56 569 1 "finned-x-wing" 2 8 9 | 5 6 47 | 47 1 3 56 7 3 | 489 12 12 | 4568 4569 568 4 15 16 | 3 89 789 | 5678 569 2 ------------------+------------------+------------------ 567 1459 16 | 2 14589 14689 | 3 456 15678 3 145 8 | 46 7 146 | 9 2 156 567 1459 2 | 4689 14589 3 | 4568 456 15678 ------------------+------------------+------------------ 1 2 45 | 7 48 468 | 56 3 9 8 3 45 | 469 249 2469 | 1 7 56 9 6 7 | 1 3 5 | 2 8 4 "ocean : xwing required : (XW @52)" 578 35 37 | 1 34 6 | 489 79 2 168 2 4 | 5 9 7 | 3 16 18 167 9 1367 | 8 34 2 | 46 5 147 ---------------+---------------+--------------- 2 4 5 | 3 6 1 | 7 8 9 19 6 19 | 7 8 4 | 2 3 5 3 7 8 | 2 5 9 | 1 4 6 ---------------+---------------+--------------- 69 1 369 | 4 7 5 | 689 2 38 467 8 2 | 9 1 3 | 5 67 47 4579 35 379 | 6 2 8 | 49 179 1347 "ocean : xwing required : (XW @50)" 9 37 8 | 6 1 4 | 2 35 357 2 6 1 | 5 3 7 | 89 89 4 5 37 4 | 89 89 2 | 37 6 1 ---------------+---------------+--------------- 368 1 356 | 89 4 59 | 35 7 2 4 9 7 | 2 58 3 | 6 1 58 38 2 35 | 7 6 1 | 359 4 3589 ---------------+---------------+--------------- 1 4 2 | 3 579 59 | 578 58 6 367 5 36 | 4 2 8 | 1 39 379 37 8 9 | 1 57 6 | 4 2 357 "ocean : xwing required : (XW @40)" 5 19 169 | 12 8 7 | 126 4 3 123 7 13 | 9 4 6 | 5 8 12 126 8 4 | 1235 125 123 | 7 9 126 ------------------+------------------+------------------ 369 2 3679 |34568 5679 3489 | 468 1 689 8 4 1369 | 1236 1269 1239 | 26 7 5 169 5 1679 |12468 12679 12489 | 2468 3 2689 ------------------+------------------+------------------ 7 3 2 | 1468 16 148 | 9 5 18 19 6 8 | 7 19 5 | 3 2 4 4 19 5 | 128 3 1289 | 18 6 7 "ocean : xwing required : (XW @40)" 12569 256 269 | 8 7 4 | 1235 235 135 58 3 48 | 2 1 9 | 458 6 7 128 248 7 | 3 6 5 | 9 248 18 ------------------+------------------+------------------ 7 2568 1268 | 56 3 18 | 58 9 4 358 9 38 | 7 4 2 | 358 1 6 4 568 1368 | 56 9 18 | 7 358 2 ------------------+------------------+------------------ 2389 248 5 | 1 28 7 | 6 2348 389 2389 1 2389 | 4 5 6 | 238 7 389 268 7 2468 | 9 28 3 |12458 2458 158 "ocean : xwing required : (XW @38)" 36 4 8 | 9 36 5 | 2 1 7 2356 2359 23579 | 1 4 237 | 3568 3568 68 1 235 2357 | 2378 368 237 | 3456 3456 9 ------------------+------------------+------------------ 4 3568 35 | 358 7 9 | 568 2 1 2358 7 235 | 6 358 1 | 458 9 48 9 568 1 | 58 2 4 | 7 568 3 ------------------+------------------+------------------ 7 238 234 | 23 9 236 | 1 3468 5 2358 23589 23459 | 2357 1 2367 | 3468 3468 468 35 1 6 | 4 35 8 | 9 7 2 "ocean : xwing required : (XW @34)" 134578 3478 1458 | 268 24678 26 | 4679 25 245679 457 6 2 | 9 47 3 | 1 8 457 478 9 48 | 5 24678 1 | 467 3 2467 ---------------------+---------------------+--------------------- 59 1 7 | 3 569 8 | 2 4 69 234589 348 4589 | 26 1 59 | 69 7 38 29 38 6 | 4 29 7 | 5 1 38 ---------------------+---------------------+--------------------- 168 5 18 | 7 268 4 | 3 9 12 47 2 3 | 1 59 59 | 8 6 47 146789 478 1489 | 268 3 26 | 47 25 125 "ocean : xwing required : (XW @32)" 123578 12578 135 | 1345 6 9 | 1247 237 1347 12356 125 9 | 1345 7 345 | 8 236 1346 1367 4 136 | 2 13 8 | 167 5 9 ---------------------+---------------------+--------------------- 1348 18 7 | 136 9 2 | 5 368 346 9 6 345 | 8 34 357 | 47 1 2 13458 158 2 | 13567 134 3567 | 9 3678 3467 ---------------------+---------------------+--------------------- 567 3 56 | 9 2 1 | 67 4 8 12467 1279 8 | 467 5 467 | 3 2679 167 12467 1279 146 | 3467 8 3467 | 1267 2679 5 "ocean : xy chain" "xy chain length 5" 259 1 259 | 4 37 8 | 3579 6 59 7 4589 24589 | 29 6 235 |34589 389 1 569 45689 3 | 19 17 5 | 2 789 4589 ------------------+------------------+------------------ 1 369 69 | 5 2 4 | 3689 389 7 2359 7 259 | 6 8 1 | 3589 4 589 8 456 456 | 3 9 7 | 56 1 2 ------------------+------------------+------------------ 3569 35689 7 | 28 348 236 | 1 289 4689 4 689 1689 | 128 5 26 | 6789 2789 3 36 2 168 | 7 1348 9 | 468 5 468 "xy chain length 5" 18 238 4 | 6 5 9 | 7 23 12 1678 2578 2568 | 4 128 3 | 1269 2569 129 9 235 2356 | 2 7 1 | 1236 23456 8 ------------------+------------------+------------------ 4 1 389 | 239 289 68 | 289 7 5 2 389 7 | 359 189 158 | 4 89 6 5 6 89 | 279 2489 78 | 289 1 3 ------------------+------------------+------------------ 3 25789 2589 | 579 6 57 | 1289 289 4 678 45789 5689 | 1 9 2 | 3689 3689 79 67 279 1 | 8 3 4 | 5 269 279 "xy chain length 5" 567 3 567 | 1 45678 9 | 4568 2 4568 4 5678 12567 | 257 3 2678 | 568 15 9 156 568 9 | 25 24568 2468 | 7 1345 4568 ---------------------+---------------------+--------------------- 8 67 367 | 4 279 5 | 2369 39 1 13567 2 134567 | 379 79 7 | 34569 8 456 9 45 345 | 6 28 1 | 2345 345 7 ---------------------+---------------------+--------------------- 3567 45679 8 | 2579 245679 2467 | 1 4579 245 2 45679 4567 | 579 1 467 | 4589 4579 3 57 1 457 | 8 24579 3 | 2459 6 245 "xy chain length 5" 4 1 2359 | 389 358 389 | 2358 6 7 8 25 2359 | 6 135 7 | 1235 359 4 3679 567 3569 | 3489 2 13489 | 1358 3589 135 ------------------+------------------+------------------ 9 3 2459 | 478 6 48 | 2578 1 25 16 46 7 | 5 138 2 | 9 38 36 16 8 1256 | 37 9 13 |23567 4 2356 ------------------+------------------+------------------ 1367 67 1368 |23789 4 3689 |13567 357 1356 2 467 3468 | 1 378 5 | 3467 37 9 5 9 1346 | 37 37 36 |13467 2 8 "xy chain length 5" 6 167 5 | 4 68 3 | 2 168 189 2346 2346 23468 | 1 7 9 | 3458 4568 38 9 12346 123468 | 25 2568 26 | 13458 14568 7 ---------------------+---------------------+--------------------- 7 8 246 | 3 26 1 | 4 9 5 346 5 346 | 7 69 67 | 1478 2 18 1 9 2 | 8 25 4 | 7 3 6 ---------------------+---------------------+--------------------- 8 1236 12369 | 27 23 27 | 13579 157 4 2345 234 2349 | 6 1 8 | 3579 57 239 234 1234 7 | 9 234 5 | 6 18 1238 "xy chain length 5" 8 1346 3567 | 245 3457 237 | 1245 1257 9 1457 14 2 | 9 457 6 | 3 1578 1458 3457 9 357 | 8 3457 1 | 245 6 245 ------------------+------------------+------------------ 47 5 1 | 46 2 7 | 9 3 68 479 46 679 | 3 45679 8 | 125 125 1256 39 2 8 | 56 1 9 | 7 4 56 ------------------+------------------+------------------ 235 7 35 | 1 368 4 | 258 9 2358 1239 138 4 | 7 389 5 | 6 128 1238 6 138 359 | 2 389 239 |12458 1258 7 "xy chain length 5" 124689 12 2469 | 3478 24578 258 | 34678 567 345678 48 3 7 | 1 458 6 | 2 9 458 2468 5 246 | 3478 9 28 | 34678 1 34678 ---------------------+---------------------+--------------------- 167 9 6 | 5 148 3 | 14678 2 14678 12357 127 8 | 4 6 12 | 9 57 1457 1256 4 256 | 9 128 7 | 168 3 1568 ---------------------+---------------------+--------------------- 2579 8 259 | 67 3 159 | 167 4 12679 379 6 1 | 2 7 4 | 5 8 379 234579 27 23459 | 678 1578 1589 | 1367 67 123679 "xy chain length 6" 1 56789 578 | 2 69 3 | 58 78 4 28 589 3 | 458 7 4589 | 6 128 258 2678 4 2578 | 568 1 568 | 2358 9 2358 ---------------------+---------------------+--------------------- 9 3578 2578 |345678 2346 45678 | 238 268 1 2378 1 6 | 378 239 789 | 4 5 2389 4 358 258 | 13568 2369 15689 | 2389 268 7 ---------------------+---------------------+--------------------- 678 2 1478 | 1467 5 1467 | 189 3 89 36 36 9 | 1346 8 146 | 7 124 25 5 378 1478 | 9 34 2 | 18 148 6 "xy chain length 6" 8 159 59 | 7 6 2 | 145 4 3 56 7 4 | 1 5 3 | 8 9 25 59 3 259 | 4589 458 489 |12457 6 2457 ------------------+------------------+------------------ 2 8 59 | 459 1457 479 | 47 3 6 7 59 3569 |24589 23458 4689 | 24 248 1 1 4 36 | 28 2378 678 | 27 5 9 ------------------+------------------+------------------ 359 6 35789 | 248 2478 478 | 2345 1 245 3 2 1 | 6 48 5 | 9 7 4 4 5 57 | 3 9 1 | 256 2 8 "xy chain length 6" 1268 368 4 | 15 9 2358 | 7 1235 138 128 389 2389 | 6 123458 7 | 1258 12345 1348 5 38 7 | 14 12348 238 | 9 1234 6 ---------------------+---------------------+--------------------- 47 1 59 | 3 257 6 | 2 8 47 3 46789 89 | 179 127 29 | 126 12467 5 67 2 5 | 8 157 4 | 16 9 137 ---------------------+---------------------+--------------------- 9 3578 6 | 57 3578 358 | 4 157 2 478 34578 358 | 2 34578 1 | 568 567 789 2478 4578 1 | 4579 6 589 | 3 57 789 "xy chain length 6" 47 9 3 | 178 1278 247 | 6 5 1248 2 467 678 | 5 1678 9 | 14 48 3 1 46 568 | 368 2368 2346 | 249 489 7 ------------------+------------------+------------------ 457 8 157 | 37 9 357 |23457 6 24 45679 3467 5679 | 2 35678 1 |34579 34789 489 5679 2 5679 | 3678 4 3567 | 3579 1 89 ------------------+------------------+------------------ 8 17 1279 | 1379 12357 2357 |13479 3479 6 3 167 12679 | 4 1267 8 | 179 79 5 679 5 4 |13679 1367 367 | 8 2 19 "xy chain length 6" 6 135 25 | 8 1345 9 | 45 1245 7 1357 13578 4 | 157 1357 13 | 6 12589 1259 157 9 578 | 6 1457 2 | 458 3 145 ---------------------+---------------------+--------------------- 2 457 3 | 45 9 48 | 1 458 6 145 1456 56 | 3 12458 7 | 4589 24589 2459 8 145 9 | 145 6 14 | 7 245 3 ---------------------+---------------------+--------------------- 345 2 58 | 9 1348 6 | 345 7 145 3457 345678 1 | 47 3478 348 | 2 4569 459 9 3467 67 | 2 1347 5 | 34 146 8 "xy chain length 7" 1 289 2589 | 6 579 3 | 2578 278 4 3456 7 3456 | 2 15 8 | 156 9 156 356 2689 235689 | 157 4 179 |125678 2378 1256 ---------------------+---------------------+--------------------- 9 3 15 | 157 1257 147 | 124 6 8 56 16 7 | 15 8 1469 | 3 24 129 2 4 168 | 13 139 169 | 19 5 7 ---------------------+---------------------+--------------------- 347 129 12349 | 1378 6 17 |245789 2478 259 367 5 369 | 4 37 2 | 6789 1 69 8 126 1246 | 9 17 5 | 2467 247 3 "xy chain length 9" 69 8 1369 | 2 13 7 | 1346 5 1349 4 137 135 | 9 138 6 | 1378 37 2 679 1367 12369 | 1348 5 148 |134678 34679 1349 ---------------------+---------------------+--------------------- 1 5 4689 | 348 3689 48 | 34 2 7 68 46 7 | 1348 12368 12458 | 9 34 1345 3 2 49 | 147 179 145 | 145 8 6 ---------------------+---------------------+--------------------- 5678 1367 13568 | 178 4 128 | 23567 3679 359 2 1347 1345 | 6 17 9 | 3457 347 8 678 9 468 | 5 278 3 | 2467 1 4 "xy chain length 10" 5 2 36 | 3678 4 36 | 3678 9 1 1 7 369 | 2368 239 369 | 368 5 4 89 3689 4 |35678 1379 13569 | 2 78 367 ------------------+------------------+------------------ 27 34 1237 | 9 5 8 | 1367 147 367 6 389 1359 | 4 3 7 |13589 18 2 789 3489 3579 | 1 6 2 |35789 478 357 ------------------+------------------+------------------ 279 69 8 |23567 12379 13569 | 4 127 57 4 5 2679 | 267 1279 169 | 17 3 8 3 1 27 | 257 8 45 | 57 6 9 "xy chain length 10" 12479 1247 5 | 1478 147 678 | 3 2468 4689 1234 8 24 | 1345 9 356 | 245 7 456 6 47 479 |34578 2 3578 | 4589 48 1 ------------------+------------------+------------------ 2789 257 2789 | 6 357 4 | 1258 1238 358 248 3 1 | 258 5 258 | 7 9 4568 2478 24567 24678 | 9 357 1 | 2458 23468 34568 ------------------+------------------+------------------ 5 1467 467 | 1347 8 379 | 149 134 2 12478 9 2478 |12347 6 237 | 148 5 3478 12478 1247 3 |12457 1457 2579 | 6 148 4789 "xy chain" 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 "mythjellies : alternating inference chains" "either the 8 in A (r9c6) or the 8 in H (r8c3) is true, therefore no 8's can exist in r8c456 or r9c123" 247 5 28 | 479 4789 1 | 6 379 3789 3 147 6 | 479 45789 2 | 578 179 5789 17 178 9 | 3 578 6 | 2 157 4 ------------------+------------------+------------------ 79 6 4 | 5 3 79 | 1 8 2 129 1239 23 | 8 6 4 | 57 3579 359 8 379 5 | 1 2 79 | 4 6 39 ------------------+------------------+------------------ 6 248 1 | 479 479 5 | 3 27 78 245 2348 238 | 6 47 38 | 9 257 1 59 39 7 | 2 1 38 | 58 4 6 "either a 1 in A (r2c2) or a 1 in E (r7c6), therefore there can be no 1 in either r2c6 or r7c2" 39 2 39 | 6 1 8 | 5 4 7 7 156 4 | 25 235 9 | 12 36 8 156 156 8 | 2457 23457 24 | 9 36 12 ------------------+------------------+------------------ 2689 3 69 | 1 2489 7 | 248 5 2469 1259 1589 1579 | 24 249 6 | 2347 789 2349 2689 4 679 | 3 289 5 | 278 1 269 ------------------+------------------+------------------ 139 189 2 | 4578 457 14 | 6 789 39 4 1689 1369 | 278 27 12 | 137 789 5 158 7 15 | 9 6 3 | 148 2 14 "AIC [36][35][38][88][97][96] : [36] and [96] share a group (column 6) => 36=6 or 96=8 => 36^8 96^6" 247 5 28 | 479 4789 1 | 6 379 3789 3 1478 6 | 479 45789 2 | 578 179 5789 17 178 9 | 3 5678 68 | 2 157 4 ------------------+------------------+------------------ 79 679 4 | 5 3 679 | 1 8 2 129 12369 23 | 8 69 4 | 57 35679 359 8 3679 5 | 1 2 679 | 4 369 39 ------------------+------------------+------------------ 6 2489 1 | 479 4789 5 | 3 27 78 245 2348 238 | 6 478 38 | 9 257 1 59 39 7 | 2 1 389 | 58 4 6 "pure bilocation loop" 7 58 1 | 2 3 9 | 6 4 58 6 38 2 | 1 4 5 |389 89 7 35 4 9 | 8 6 7 | 23 1 25 ------------+------------+------------ 4 123 38 |369 5 136 |289 7 289 9 235 357 | 37 8 34 | 24 6 1 18 6 78 | 79 2 14 |489 5 3 ------------+------------+------------ 35 9 356 | 36 1 8 | 7 2 4 128 13 368 | 4 7 236 | 5 389 89 28 7 4 | 5 9 23 | 1 38 6 "pure bivalue loop" 5 6 29 | 7 3 1 | 29 4 8 247 248 17 | 5 9 48 | 6 3 12 349 348 13 | 48 6 2 | 5 7 19 ---------------+---------------+--------------- 367 9 37 | 2 47 5 | 1 8 467 27 25 4 | 68 1 68 | 3 59 579 16 15 8 | 3 47 9 | 47 2 56 ---------------+---------------+--------------- 1234 7 6 | 9 8 34 | 24 15 245 1349 134 5 | 46 2 3467 | 8 19 479 8 24 29 | 1 5 47 |2479 6 3 "mixed loop" 1 37 8 | 4 2 9 | 5 37 6 36 45 9 | 58 36 7 | 48 1 2 27 45 26 | 1 36 58 | 3478 9 34 ------------------+------------------+------------------ 348 2 135 | 38 9 468 | 16 356 7 347 6 137 | 237 5 24 | 123 8 9 9 378 357 | 2378 1 26 | 236 4 35 ------------------+------------------+------------------ 378 378 2367 | 9 4 125 | 367 23567 135 5 9 237 | 6 8 12 | 347 237 134 26 1 4 | 25 7 3 | 9 256 8 "a Ruud daily nightmare" 2379 6 49 | 5 28 48 | 3789 1 389 259 179 159 | 3 1268 168 | 589 79 4 35 14 8 | 7 9 14 | 2 356 356 ------------------+------------------+------------------ 4 139 7 | 2 1568 1368 | 359 3569 3569 69 5 169 | 146 7 36 | 349 8 2 8 23 26 | 46 56 9 | 1 3456 7 ------------------+------------------+------------------ 59 79 3 | 18 4 2 | 6 579 18 1 249 24569 | 689 36 7 |34589 3459 3589 679 8 469 | 169 136 5 | 3479 2 139 "jeff : bug" "BUG with a cell containing more than 3 candidates" 1 28 3 | 4 5 6 | 7 289 89 4 5 7 | 3 89 29 | 12 6 18 6 28 9 | 7 18 12 | 4 5 3 ---------------+---------------+--------------- 9 7 4 | 5 3 8 | 12 12 6 5 3 6 | 19 2 19 | 8 4 7 8 1 2 | 6 4 7 | 9 3 5 ---------------+---------------+--------------- 27 9 1 | 28 6 3 | 5 78 4 27 6 5 | 28 19 4 | 3 1789 189 3 4 8 | 19 7 5 | 6 19 2 "BUG with three quadrivalue cells" 7 2 69 | 5 3 69 | 8 1 4 89 4689 5 | 1 2 48 | 3 69 7 1 3 48 | 69 7 48 | 5 69 2 ---------------+---------------+--------------- 6 1 2 | 8 4 5 | 9 7 3 5 47 47 | 3 9 1 | 6 2 8 3 89 89 | 7 6 2 | 1 4 5 ---------------+---------------+--------------- 89 6789 6789 | 4 1 3 | 2 5 69 4 69 3 | 2 5 69 | 7 8 1 2 5 1 | 69 8 7 | 4 3 69 "BUG with 30 bivalue and 1 trivalue unassigned cells" 4 78 6 | 3 9 5 | 78 2 1 37 9 25 | 8 1 26 | 57 36 4 38 1 25 | 7 4 26 | 58 9 36 ------------+------------+------------ 2 36 14 | 14 5 8 | 36 7 9 16 78 378 | 16 2 9 | 4 5 38 9 5 48 | 46 3 7 | 2 1 68 ------------+------------+------------ 78 2 78 | 9 6 3 | 1 4 5 5 4 9 | 2 8 1 | 36 36 7 16 36 13 | 5 7 4 | 9 8 2 "most would solve this with an xy-wing or forcing chain" 2 9 8 | 47 567 56 | 3 1 45 7 4 5 | 2 1 3 | 6 9 8 1 3 6 | 48 58 9 | 2 7 45 ------------+------------+------------ 5 1 4 | 6 3 8 | 7 2 9 6 2 9 | 17 57 15 | 8 4 3 8 7 3 | 9 4 2 | 1 5 6 ------------+------------+------------ 4 5 2 | 18 68 16 | 9 3 7 3 8 1 | 5 9 7 | 4 6 2 9 6 7 | 3 2 4 | 5 8 1 "Nick's simple trivalue puzzle" 4 78 6 | 3 9 5 | 78 2 1 37 9 25 | 8 1 26 | 57 36 4 38 1 25 | 7 4 26 | 58 9 36 ------------+------------+------------ 2 36 14 | 14 5 8 | 36 7 9 16 78 378 | 16 2 9 | 4 5 38 9 5 48 | 46 3 7 | 2 1 68 ------------+------------+------------ 78 2 78 | 9 6 3 | 1 4 5 5 4 9 | 2 8 1 | 36 36 7 16 36 13 | 5 7 4 | 9 8 2 "more unsolved poly-valued cells, multi-BUGs are possible" 2 7 3 | 6 8 4 | 19 5 19 9 1 4 | 5 7 3 | 8 2 6 58 6 58 | 9 1 2 | 34 7 34 ---------------+---------------+--------------- 6 38 7 | 4 5 1 | 2 389 389 48 2 9 | 3 6 7 | 5 148 148 45 35 1 | 8 2 9 | 6 34 7 ---------------+---------------+--------------- 1 58 258 | 7 3 6 | 49 489 2489 7 9 6 | 2 4 8 | 13 13 5 3 4 28 | 1 9 5 | 7 6 28 "the biggest BUG I've found so far" 7 49 6 | 5 1 3 | 48 489 2 14 1349 2 | 8 6 49 | 7 5 349 5 349 8 | 7 49 2 | 34 1 6 ---------------+---------------+--------------- 3 6 7 | 9 2 5 | 148 48 14 9 2 5 | 4 8 1 | 36 367 37 48 48 1 | 6 3 7 | 9 2 5 ---------------+---------------+--------------- 6 7 39 | 1 5 49 | 2 34 8 2 5 4 | 3 7 8 | 16 69 19 18 18 39 | 2 49 6 | 5 347 347 "another BUG" 1 36 2 | 58 358 9 | 7 4 56 4 36 9 | 7 35 2 | 68 58 1 8 7 5 | 6 1 4 | 2 9 3 ------------+------------+------------ 9 45 17 | 58 67 36 | 48 13 2 3 45 78 | 2 9 1 |468 58 567 6 2 178 | 4 578 35 | 9 13 57 ------------+------------+------------ 7 1 6 | 3 4 8 | 5 2 9 5 9 4 | 1 2 7 | 3 6 8 2 8 3 | 9 56 56 | 1 7 4 "when I ran into a puzzle, #1394, that generates a bad bug reduction" 69 35 49 |4569 1 2 | 34 7 8 269 38 2489 | 469 7 49 | 34 5 1 7 45 1 | 3 8 45 | 2 9 6 ---------------+---------------+--------------- 8 6 59 | 7 23 35 | 1 4 29 4 2 7 | 8 9 1 | 6 3 5 59 1 3 | 245 24 6 | 7 8 29 ---------------+---------------+--------------- 3 9 6 | 1 5 7 | 8 2 4 25 7 245 | 24 6 8 | 9 1 3 1 48 248 | 249 234 349 | 5 6 7 "#1329, which gets to this state" 7 3 9 | 18 18 2 | 5 6 4 68 16 18 | 5 4 7 | 2 3 9 2 5 4 | 6 9 3 | 8 1 7 ---------------+---------------+--------------- 456 67 23 | 47 23 9 | 1 8 56 56 679 123 | 27 123 8 | 369 4 2356 48 19 1238 | 124 5 6 | 39 7 23 ---------------+---------------+--------------- 1 2 6 | 3 7 5 | 4 9 8 39 4 5 | 89 68 1 | 7 2 36 39 8 7 | 29 26 4 | 36 5 1 "#75" 9 6 8 | 24 7 24 | 3 5 1 57 3 4 | 8 1 56 | 9 2 67 57 1 2 | 56 3 9 | 4 67 8 ---------------+---------------+--------------- 13 28 9 | 247 248 1247 | 6 38 5 4 7 56 | 3 89 56 | 28 1 29 13 28 56 | 56 289 12 | 7 389 4 ---------------+---------------+--------------- 2 59 1 | 79 6 38 | 58 4 37 8 59 3 | 1 24 247 | 25 67 2679 6 4 7 | 29 5 38 | 1 89 239 "#1265" 7 49 6 | 5 1 3 | 48 489 2 14 1349 2 | 8 6 49 | 7 5 349 5 349 8 | 7 49 2 | 34 1 6 ---------------+---------------+--------------- 3 6 7 | 9 2 5 | 148 48 14 9 2 5 | 4 8 1 | 36 367 37 48 48 1 | 6 3 7 | 9 2 5 ---------------+---------------+--------------- 6 7 39 | 1 5 49 | 2 34 8 2 5 4 | 3 7 8 | 16 69 19 18 18 39 | 2 49 6 | 5 347 347 "can this puzzle be advanced with by the BUG principle" 3 79 579 | 1 2 8 | 49 459 6 6 4 25 | 3 7 9 | 8 15 12 8 1 29 | 5 6 4 | 7 39 23 ---------------+---------------+--------------- 9 5 1 | 7 4 3 | 2 6 8 7 3 4 | 2 8 6 | 19 19 5 2 8 6 | 9 1 5 | 3 47 47 ---------------+---------------+--------------- 4 27 3 | 8 5 1 | 6 27 9 1 6 79 | 4 39 2 | 5 8 37 5 29 8 | 6 39 7 | 14 1234 134 "posted this BUG grid here" 569 8 45 | 46 1 59 | 2 3 7 7 46 2 | 3 468 68 | 5 1 9 59 1 3 | 57 79 2 | 6 8 4 ------------+------------+------------ 1 2 7 | 45 34 35 | 9 6 8 48 5 6 | 9 78 1 | 47 2 3 48 3 9 | 67 2 678 | 47 5 1 ------------+------------+------------ 2 9 1 | 8 67 67 | 3 4 5 3 7 8 | 2 5 4 | 1 9 6 56 46 45 | 1 39 39 | 8 7 2 "please consider this BUG (from a puzzle in another thread)" 3 2 56 | 8 7 4 | 1 56 9 68 9 4 | 3 1 56 | 2 7 568 1 7 568 | 2 56 9 | 68 3 4 ------------+------------+------------ 68 4 7 | 59 89 1 | 56 2 3 9 68 2 | 4 56 3 |568 1 7 5 1 3 | 7 2 68 | 4 9 68 ------------+------------+------------ 4 3 18 | 19 89 2 | 7 56 56 7 68 16 | 15 3 58 | 9 4 2 2 5 9 | 6 4 7 | 3 8 1 "a good example posted by TopRank with the following BUG grid" 4 18 7 | 58 6 15 | 3 2 9 6 28 9 | 278 2378 23 | 4 5 1 5 12 3 | 4 12 9 | 6 8 7 ---------------+---------------+--------------- 7 9 5 | 6 13 13 | 2 4 8 8 4 6 | 257 27 25 | 9 1 3 1 3 2 | 9 4 8 | 5 7 6 ---------------+---------------+--------------- 9 6 4 | 1 5 7 | 8 3 2 3 5 1 | 28 28 6 | 7 9 4 2 7 8 | 3 9 4 | 1 6 5 "BUG-reduction with a 4-value square" 4 2 1 | 7 59 3 | 6 59 8 3 7 58 | 89 6 4 | 1 59 2 9 58 6 | 1 28 25 | 7 4 3 ---------------+---------------+--------------- 2 45 3 | 49 59 6 | 8 7 1 1 4568 58 | 48 7 25 | 3 26 9 7 68 9 | 3 28 1 | 5 26 4 ---------------+---------------+--------------- 8 9 4 | 6 3 7 | 2 1 5 6 3 2 | 5 1 9 | 4 8 7 5 1 7 | 2 4 8 | 9 3 6 "is a partially solved board from Susser's sample BUG" 7 25 59 | 1 4 3 | 8 29 6 39 6 8 | 2 7 59 | 35 14 14 239 14 14 | 6 8 59 | 7 29 35 ------------+------------+------------ 8 45 45 | 7 9 6 | 1 3 2 6 9 7 | 3 1 2 | 4 5 8 1 3 2 | 48 5 48 | 6 7 9 ------------+------------+------------ 5 17 6 | 89 2 178 | 39 148 134 29 8 19 | 45 3 14 | 25 6 7 4 127 3 |589 6 178 |259 18 15 "#87 of the top95 " 7 49 6 | 5 1 3 | 48 489 2 14 1349 2 | 8 6 49 | 7 5 349 5 349 8 | 7 49 2 | 34 1 6 ---------------+---------------+--------------- 3 6 7 | 9 2 5 | 148 48 14 9 2 5 | 4 8 1 | 36 367 37 48 48 1 | 6 3 7 | 9 2 5 ---------------+---------------+--------------- 6 7 39 | 1 5 49 | 2 34 8 2 5 4 | 3 7 8 | 16 69 19 18 18 39 | 2 49 6 | 5 347 347 "9 non-BUG candidates" 7 49 6 | 5 1 3 | 48 489 2 14 1349 2 | 8 6 49 | 7 5 349 5 349 8 | 7 49 2 | 34 1 6 ---------------+---------------+--------------- 3 6 7 | 9 2 5 | 148 48 14 9 2 5 | 4 8 1 | 36 367 37 48 48 1 | 6 3 7 | 9 2 5 ---------------+---------------+--------------- 6 7 39 | 1 5 49 | 2 34 8 2 5 4 | 3 7 8 | 16 69 19 18 18 39 | 2 49 6 | 5 347 347 "these same three cells are part of an almost unique rectangle for which we have the AUR grid" 7 49 6 | 5 1 3 | 48 489 2 14 1349 2 | 8 6 49 | 7 5 349 5 349 8 | 7 49 2 | 34 1 6 ---------------+---------------+--------------- 3 6 7 | 9 2 5 | 148 48 14 9 2 5 | 4 8 1 | 36 367 37 48 48 1 | 6 3 7 | 9 2 5 ---------------+---------------+--------------- 6 7 39 | 1 5 49 | 2 34 8 2 5 4 | 3 7 8 | 16 69 19 18 18 39 | 2 49 6 | 5 347 347 "for this BUG grid" 7 49 6 | 5 1 3 | 48 489 2 14 1349 2 | 8 6 49 | 7 5 349 5 349 8 | 7 49 2 | 34 1 6 ---------------+---------------+--------------- 3 6 7 | 9 2 5 | 148 48 14 9 2 5 | 4 8 1 | 36 367 37 48 48 1 | 6 3 7 | 9 2 5 ---------------+---------------+--------------- 6 7 39 | 1 5 49 | 2 34 8 2 5 4 | 3 7 8 | 16 69 19 18 18 39 | 2 49 6 | 5 347 347 "one of my Susser users sent me this interesting BUG" 3 4 7 | 6 1 2 | 8 5 9 9 6 8 | 5 7 3 | 1 2 4 5 12 12 | 4 9 8 | 7 3 6 ------------+------------+------------ 8 9 5 | 12 3 14 | 24 6 7 124 12 6 | 7 24 9 | 5 8 3 7 3 24 | 8 5 6 | 24 9 1 ------------+------------+------------ 6 8 3 | 12 24 7 | 9 14 5 124 7 124 | 9 6 5 | 3 14 8 14 5 9 | 3 8 14 | 6 7 2 "is not really a BUG grid" 3 4 7 | 6 1 2 | 8 5 9 9 6 8 | 5 7 3 | 1 2 4 5 12 12 | 4 9 8 | 7 3 6 ------------+------------+------------ 8 9 5 | 12 3 14 | 24 6 7 124 12 6 | 7 24 9 | 5 8 3 7 3 24 | 8 5 6 | 24 9 1 ------------+------------+------------ 6 8 3 | 12 24 7 | 9 14 5 124 7 124 | 9 6 5 | 3 14 8 14 5 9 | 3 8 14 | 6 7 2 "is a cool one for BUG-Lite" 6 47 3 | 5 1 47 | 2 8 9 8 257 27 | 6 9 3 | 4 57 1 457 1 9 | 28 27 478 | 6 3 57 ------------+------------+------------ 1 8 6 | 9 3 5 | 7 2 4 47 247 5 | 28 6 78 | 1 9 3 9 3 27 | 4 27 1 | 5 6 8 ------------+------------+------------ 25 9 8 | 7 4 6 | 3 1 25 3 57 4 | 1 8 2 | 9 57 6 27 6 1 | 3 5 9 | 8 4 27 "carcul : almost nice loops : ANL" "an ANL can be used inside another nice loop" 57 38 2 | 6 57 4 | 19 19 38 6 9 57 | 1 257 38 | 4 25 38 4 1 38 | 38 25 9 | 256 256 7 ------------------+------------------+------------------ 1279 378 1389 | 238 4 6 | 1279 1279 5 1257 3567 4 | 235 9 235 | 1267 8 16 259 568 89 | 7 1 258 | 3 269 4 ------------------+------------------+------------------ 8 24 567 | 25 3 1 | 567 4567 9 3 24 567 | 9 8 257 | 1567 14567 16 19 57 19 | 4 6 57 | 8 3 2 "example of an almost nice loop" 159 2 7 | 59 4 8 | 19 6 3 4 6 8 | 3 259 1 | 29 7 25 3 59 15 | 7 2569 269 |12489 12458 2458 ------------------+------------------+------------------ 579 8 4 | 1 2359 239 | 6 25 257 2 1 6 | 8 57 47 | 3 45 9 579 59 3 | 459 2569 269 | 1248 12458 24578 ------------------+------------------+------------------ 8 3 12 | 6 17 47 | 5 9 24 15 7 125 | 49 139 39 | 248 248 6 6 4 9 | 2 8 5 | 7 3 1 "almost turbot fish and almost grouped nice loop" 6 47 14 | 8 3 5 | 2 17 9 137 8 9 | 2467 46 2467 | 356 14567 1457 37 5 2 | 1 9 467 | 36 8 47 ------------------+------------------+------------------ 9 2 56 | 456 8 146 | 7 15 3 8 3 567 | 9 16 167 | 4 125 125 4 1 57 | 57 2 3 | 8 9 6 ------------------+------------------+------------------ 257 9 8 | 3 146 1246 | 56 24567 2457 125 46 14 | 246 7 8 | 9 3 245 27 467 3 | 246 5 9 | 1 2467 8 "example of a longer ANL" 5 1 278 | 2678 678 3 | 9 678 4 279 4 278 | 2678 6789 5 | 268 3 1 6 279 3 | 1 4 2789 | 5 78 278 ------------------+------------------+------------------ 8 3 1 | 2567 67 267 | 4 569 69 24 25 9 | 3 1 46 | 7 568 68 47 57 6 | 58 89 489 | 1 2 3 ------------------+------------------+------------------ 3 679 4 | 678 2 1 | 68 6789 5 1 8 27 | 9 5 67 | 3 4 267 279 2679 5 | 4 3 678 | 268 1 26789 "two incompatible nice loops rule" 8 167 4 | 2 5 3 | 9 67 17 26 5 126 | 4 9 7 | 126 8 3 279 3 279 | 18 6 18 | 4 25 57 ------------------+------------------+------------------ 1 8 79 | 379 2 5 | 37 4 6 4 27 257 | 37 1 6 | 357 9 8 3 679 5679 | 789 47 48 | 57 1 2 ------------------+------------------+------------------ 25679 2679 8 | 17 3 14 | 26 25 49 257 4 127 | 6 78 9 | 128 3 157 679 1679 3 | 5 478 2 | 168 67 49 "carcul : almost unique rectangle : AUR" "type 2 AUR" 3 1 9 | 6 7 48 | 248 25 458 6 7 2 | 38 5 348 | 48 1 9 5 8 4 | 2 9 1 | 7 6 3 ---------------+---------------+--------------- 278 4 137 | 9 238 5 | 6 27 18 28 6 35 | 7 1 38 |2348 9 458 9 23 157 | 4 238 6 | 238 57 15 ---------------+---------------+--------------- 4 9 8 | 5 6 2 | 1 3 7 27 23 37 | 1 4 9 | 5 8 6 1 5 6 | 38 38 7 | 9 4 2 "AUR (bennys)" 7 589 59 | 6 259 258 | 3 4 1 18 4 6 | 35 357 18 | 257 9 25 2 1359 1359 | 579 4 15 | 6 8 57 ---------------+---------------+--------------- 19 169 7 | 4 259 3 | 25 256 8 389 389 4 | 259 6 25 | 1 2357 257 5 36 2 | 8 1 7 | 49 36 49 ---------------+---------------+--------------- 169 2 159 | 157 8 46 | 49 57 3 369 7 359 | 235 235 46 | 8 1 49 4 135 8 | 135 357 9 | 257 25 6 "type 2 AUR variation with both candidates in the same cell (ronk)" 368 36 68 | 5 2 1 | 79 4 79 1 4 2 | 3 79 79 | 5 8 6 9 7 5 | 46 48 68 | 3 2 1 ---------------+---------------+--------------- 36 369 4 | 8 679 2 | 79 1 5 2 5 69 | 1 4679 79 | 48 3 4789 7 8 1 | 49 3 5 | 24 6 249 ---------------+---------------+--------------- 5 69 689 | 2 1 4 | 68 7 3 468 1 3 | 7 5 68 |2468 9 248 468 2 7 | 69 89 3 | 1 5 48 "almost unique loop" 389 1 39 | 35 7 25689 | 2689 26 4 389 2 6 | 34 149 189 | 89 5 7 5 47 47 | 69 269 2689 | 2689 1 3 ------------------+------------------+------------------ 679 3 8 | 2 169 1569 | 167 4 59 679 5 1 | 69 8 4 | 3 67 2 4 69 2 | 15 3 7 | 16 8 59 ------------------+------------------+------------------ 26 69 79 | 8 5 3 | 4 27 1 12 47 5 | 147 69 69 | 27 3 8 13 8 347 | 47 124 12 | 5 9 6 "type 1 AUR in cells r2c89/r6c89" 268 2689 1 | 4 5 26 | 79 789 3 356 3569 3456 | 136 7 8 | 2 149 149 7 238 348 | 13 9 12 | 5 148 6 ---------------------+---------------------+--------------------- 68 68 9 | 7 1 3 | 4 5 2 4 13 2 | 9 6 5 | 8 13 7 135 7 35 | 2 8 4 | 6 139 19 ---------------------+---------------------+--------------------- 1268 4 68 | 168 3 9 | 17 267 5 123568 123568 3568 | 168 4 7 | 19 269 89 9 168 7 | 5 2 16 | 3 46 48 "type 2 almost unique rectangle in cells r1c78/r4c78 (top95 #87)" 7 49 6 | 5 1 3 | 48 489 2 14 1349 2 | 8 6 49 | 7 5 349 5 349 8 | 7 49 2 | 34 1 6 ---------------+---------------+--------------- 3 6 7 | 9 2 5 | 148 48 14 9 2 5 | 4 8 1 | 36 367 37 48 48 1 | 6 3 7 | 9 2 5 ---------------+---------------+--------------- 6 7 39 | 1 5 49 | 2 34 8 2 5 4 | 3 7 8 | 16 69 19 18 18 39 | 2 49 6 | 5 347 347 "type 2 AUR in cells r1c6, r1c7, r2c6, and r2c7" 3 1 9 | 6 7 48 | 248 25 458 6 7 2 | 38 5 348 | 48 1 9 5 8 4 | 2 9 1 | 7 6 3 ---------------+---------------+--------------- 278 4 137 | 9 238 5 | 6 27 18 28 6 35 | 7 1 38 |2348 9 458 9 23 157 | 4 238 6 | 238 57 15 ---------------+---------------+--------------- 4 9 8 | 5 6 2 | 1 3 7 27 23 37 | 1 4 9 | 5 8 6 1 5 6 | 38 38 7 | 9 4 2 "type 2 AUR" 3 1 9 | 6 7 48 | 248 25 458 6 7 2 | 38 5 348 | 48 1 9 5 8 4 | 2 9 1 | 7 6 3 ---------------+---------------+--------------- 278 4 137 | 9 238 5 | 6 27 18 28 6 5 | 7 1 38 |2348 9 48 9 23 17 | 4 28 6 | 238 57 15 ---------------+---------------+--------------- 4 9 8 | 5 6 2 | 1 3 7 27 23 37 | 1 4 9 | 5 8 6 1 5 6 | 38 38 7 | 9 4 2 "r4c6<>6" 4 1258 12 | 15 9 7 | 6 158 3 38 158 9 | 6 134 34 | 7 158 2 367 156 1367 | 135 8 2 | 9 15 4 ---------------+---------------+--------------- 9 3 1267 | 17 1246 46 | 8 67 5 2678 268 4 | 9 236 5 | 23 67 1 267 126 5 | 137 1236 8 | 23 4 9 ---------------+---------------+--------------- 2356 7 236 | 4 356 36 | 1 9 8 1 4 8 | 2 7 9 | 5 3 6 356 9 36 | 8 356 1 | 4 2 7 "AUR (45) + 1 at cells r1c26 and r3c26:" 1 245 9 | 6 3 45 | 7 25 8 235 8 35 | 7 1 9 | 25 4 6 6 45 7 | 2 8 45 | 3 1 9 ---------------+---------------+--------------- 345 25 2345 | 45 9 7 | 6 8 1 45 7 1 | 3 6 8 | 245 9 25 9 6 8 | 1 45 2 | 45 3 7 ---------------+---------------+--------------- 245 3 6 | 9 45 1 | 8 7 245 8 1 245 | 45 7 6 | 9 25 3 7 9 45 | 8 2 3 | 1 6 45 "type 3 AUR" 6 2459 124 | 28 149 3 | 245 1458 7 245 2345 7 | 268 14 68 | 9 13458 1458 249 8 1234 | 7 5 19 | 234 6 14 ------------------+------------------+------------------ 3 2479 24 | 59 6 5789 | 1 2489 489 12 269 8 | 3 19 4 | 7 259 569 1479 4679 5 | 89 2 1789 | 46 489 3 ------------------+------------------+------------------ 45 1 346 | 4569 8 2 | 3456 7 4569 2457 23457 9 | 456 37 56 | 8 1345 1456 8 3457 46 | 1 37 569 | 456 3459 2 "type 3 AUR in cells r8c24/r9c246 (angus unlimited077" 45 3 8 |2456 1 7 | 9 56 24 145 7 9 |2456 8 245 |1245 356 1234 6 14 2 | 45 3 9 | 8 57 147 ---------------+---------------+--------------- 9 168 135 | 7 26 25 | 125 4 1238 48 468 57 | 3 2469 1 | 257 579 278 134 2 1357 | 459 49 8 | 157 3579 6 ---------------+---------------+--------------- 2 5 4 | 1 7 3 | 6 8 9 138 189 13 | 89 5 6 | 47 2 47 7 89 6 |2489 249 24 | 3 1 5 "type 2 AUR variant (top1465 #272)" 368 36 68 | 5 2 1 | 79 4 79 1 4 2 | 3 79 79 | 5 8 6 9 7 5 | 46 48 68 | 3 2 1 ---------------+---------------+--------------- 36 369 4 | 8 679 2 | 79 1 5 2 5 69 | 1 4679 79 | 48 3 4789 7 8 1 | 49 3 5 | 24 6 249 ---------------+---------------+--------------- 5 69 689 | 2 1 4 | 68 7 3 468 1 3 | 7 5 68 |2468 9 248 468 2 7 | 69 89 3 | 1 5 48 "barely advances (top1465 #409)" 2 47 5 | 8 19 6 | 3 14 79 134 9 134 |234 7 24 | 8 5 6 8 347 6 | 34 5 19 | 2 14 79 ------------+------------+------------ 147 145 2 | 57 39 349 | 6 8 13 9 8 14 | 24 6 234 | 5 7 13 367 356 37 | 1 8 57 | 9 2 4 ------------+------------+------------ 137 2 137 | 6 13 8 | 4 9 5 5 13 8 | 9 4 13 | 7 6 2 46 46 9 | 57 2 57 | 1 3 8 "(March 8th, 2006, Koalog Collection)" 6 4 58 | 2 9 7 | 18 135 135 7 2 3 | 158 4 15 | 689 569 56 58 1 9 | 58 3 6 | 4 7 2 ------------------+------------------+------------------ 4 35 15 | 7 2 8 | 16 1356 9 9 358 578 | 6 1 4 | 27 235 357 2 6 17 | 9 5 3 | 17 8 4 ------------------+------------------+------------------ 3 57 4 | 15 8 159 |12679 1269 167 158 578 2 | 4 6 159 | 3 19 178 18 9 6 | 3 7 2 | 5 4 18 "rw : uniqueness chains" "a type C chain in action" 2468 568 4568 | 2348 1 9 | 3568 23456 7 246789 3 46789 | 248 78 5 | 1 246 24 2478 578 1 | 6 378 3478 | 358 9 2345 ---------------------+---------------------+--------------------- 1 578 2 | 9 4 378 | 357 357 6 4678 5678 45678 | 38 3678 1 | 3579 2357 2359 3 9 67 | 5 67 2 | 4 1 8 ---------------------+---------------------+--------------------- 789 4 3789 | 38 5 6 | 2 37 1 69 1 369 | 7 2 34 | 3569 8 3459 5 2 3678 | 1 9 348 | 367 3467 34 "the moment the cycle appears" 248 6 45 | 24 1 9 | 358 2345 7 79 3 79 | 24 8 5 | 1 6 24 24 58 1 | 6 3 7 | 58 9 24 ---------------+---------------+--------------- 1 578 2 | 9 4 38 | 357 35 6 48 578 45 | 38 6 1 |3579 235 2359 3 9 6 | 5 7 2 | 4 1 8 ---------------+---------------+--------------- 79 4 789 | 38 5 6 | 2 37 1 6 1 3 | 7 2 4 | 59 8 59 5 2 78 | 1 9 38 | 6 347 34 "(Eppstein) interesting unique chain" 5 2346 2379 | 47 3479 1 | 249 349 8 123479 12348 12379 | 4578 34579 3478 | 6 1349 1249 1349 1348 139 | 48 6 2 | 5 7 149 ---------------------+---------------------+--------------------- 367 9 37 | 2 47 5 | 1 468 467 267 256 4 | 678 1 678 | 3 5689 5679 167 156 8 | 3 47 9 | 47 2 4567 ---------------------+---------------------+--------------------- 1234 7 6 | 9 8 34 | 24 145 1245 12349 1234 5 | 467 2347 3467 | 24789 14689 124679 8 24 29 | 1 2457 467 | 2479 4569 3 "BUG-Lite and Uniqueness patterns" 56 456 8 | 7 1 46 | 2 9 3 37 37 46 | 46 9 2 | 1 8 5 2 1 9 | 3 58 58 | 4 6 7 ---------------+---------------+--------------- 16 456 2 | 46 7 9 | 3 15 8 136 3456 456 | 8 2 46 | 7 15 9 8 9 7 | 5 3 1 | 6 2 4 ---------------+---------------+--------------- 4 58 1 | 2 58 3 | 9 7 6 9 5678 56 | 1 4 578 | 58 3 2 57 2 3 | 9 6 578 | 58 4 1 "a better example of a reverse bug in action" 3589 1289 1235 | 4 7 126 | 12 3689 3689 4 7 123 | 26 9 8 | 12 5 36 89 12 6 | 3 5 12 | 7 489 489 ---------------+---------------+--------------- 6 345 7 | 9 28 23 | 58 348 1 1 35 9 | 568 4 7 | 568 2 368 2 345 8 | 56 1 36 | 569 7 3469 ---------------+---------------+--------------- 389 1289 4 | 128 236 5 | 689 689 7 3578 6 35 | 78 38 9 | 4 1 2 789 1289 12 |1278 268 4 | 3 689 5 "to the theory of this thread, can I validly place r6c7=1?" 8 1 9 | 7 4 6 | 2 5 3 357 345 347 | 2 15 9 | 8 6 14 6 45 2 | 3 15 8 | 9 7 14 ---------------+---------------+--------------- 4 259 17 | 8 6 3 | 15 29 279 79 6 8 | 1 29 5 | 4 3 279 359 2359 13 | 4 29 7 | 15 8 6 ---------------+---------------+--------------- 1 49 5 | 6 3 2 | 7 49 8 39 8 34 | 5 7 1 | 6 249 29 2 7 6 | 9 8 4 | 3 1 5 "uniqueness : a puzzle that can be solved with knowledge of advanced uniqueness chains" 3 1 5 | 9 6 4 | 7 8 2 2 7 9 | 3 8 1 | 5 4 6 48 6 48 | 7 2 5 | 13 9 13 ------------------+------------------+------------------ 4679 259 47 | 15 179 6789 | 2368 236 489 45679 3 1 | 2 579 6789 | 468 56 489 569 8 26 | 4 3 69 | 126 125 7 ------------------+------------------+------------------ 1789 29 78 | 6 1479 237 | 48 123 5 1569 4 26 | 8 159 239 | 1236 7 13 1678 25 3 | 15 147 27 | 9 126 48 "reveals a pair, a x-wing and some other reductions that take us here" 3 1 5 | 9 6 4 | 7 8 2 2 7 9 | 3 8 1 | 5 4 6 48 6 48 | 7 2 5 | 13 9 13 ------------------+------------------+------------------ 4679 259 47 | 15 179 6789 | 3468 236 489 45679 3 1 | 2 579 6789 | 468 56 489 569 8 26 | 4 3 69 | 126 15 7 ------------------+------------------+------------------ 1789 29 78 | 6 1479 237 | 48 123 5 159 4 26 | 8 159 39 | 26 7 13 1678 25 3 | 15 147 27 | 9 126 48 "ruud : uniqueness type 6 meets x-wing" 2 5 1 | 7 4 8 | 9 6 3 3 9 4 | 6 5 2 | 7 18 18 6 7 8 | 1 3 9 | 4 5 2 ------------+------------+------------ 5 26 267 | 9 8 3 | 12 4 17 1 8 3 | 4 2 7 | 5 9 6 9 4 27 | 5 1 6 | 28 3 78 ------------+------------+------------ 8 3 69 | 2 679 4 | 16 17 5 4 26 5 | 8 67 1 | 3 27 9 7 1 269 | 3 69 5 | 68 28 4 "type-6 pattern is like an overlay of an X-wing on a unique rectangle" 2589 78 3 | 1 2678 2678 | 256 569 4 25 14 14 | 9 236 26 |2356 7 8 289 6 79 | 4 2378 5 | 123 39 129 ---------------+---------------+--------------- 89 78 5 | 27 4 3 | 267 1 2679 34 34 6 | 278 1 2789 | 257 59 2579 1 2 79 | 6 5 79 | 8 4 3 ---------------+---------------+--------------- 34 134 148 | 5 9 4678 |1467 2 167 6 9 248 |2378 278 1 |3457 358 57 7 5 1248 | 238 268 2468 | 9 368 16 "rectangle type 3" 247 1 8 | 5 379 6 |3479 2479 34 9 257 256 | 47 8 34 | 1 267 356 3 457 56 | 2 79 1 | 479 8 456 ---------------+---------------+--------------- 5 37 4 | 9 137 8 | 6 17 2 27 6 9 | 147 1257 245 | 478 3 148 8 237 1 | 467 2367 234 | 5 47 9 ---------------+---------------+--------------- 1246 9 25 | 8 1256 7 | 34 146 1346 126 258 3 | 16 4 25 | 89 169 7 146 48 7 | 3 16 9 | 2 5 1468 "rectangle with 2 strong links" 247 1 8 | 5 379 6 |3479 279 34 9 257 256 | 47 8 34 | 1 267 356 3 457 56 | 2 79 1 | 479 8 456 ---------------+---------------+--------------- 5 37 4 | 9 137 8 | 6 17 2 27 6 9 | 147 1257 245 | 478 3 148 8 237 1 | 467 2367 234 | 5 47 9 ---------------+---------------+--------------- 1246 9 25 | 8 1256 7 | 34 146 1346 126 258 3 | 16 4 25 | 89 169 7 146 48 7 | 3 16 9 | 2 5 1468 "rectangle with 1 strong link and diagonal extras" 247 1 8 | 5 379 6 |3479 279 34 9 257 25 | 47 8 34 | 1 267 356 3 457 6 | 2 79 1 | 479 8 45 ---------------+---------------+--------------- 5 37 4 | 9 137 8 | 6 17 2 27 6 9 | 147 1257 245 | 478 3 148 8 237 1 | 467 2367 234 | 5 47 9 ---------------+---------------+--------------- 1246 9 25 | 8 1256 7 | 34 146 1346 126 258 3 | 16 4 25 | 89 169 7 146 48 7 | 3 16 9 | 2 5 1468 "rectangle with 1 strong link not connecting the in-line extras (Mike Barker)" 8 4 39 | 13 5 6 | 7 2 19 7 1 2 | 4 9 8 | 6 5 3 69 36 5 | 7 12 23 | 89 48 149 ------------------+------------------+------------------ 13469 5 8 | 1369 146 349 | 2 16 7 169 67 79 | 1569 126 259 | 4 3 8 1346 2 34 | 8 7 34 | 59 16 59 ------------------+------------------+------------------ 2 78 47 | 56 468 1 | 3 9 45 345 38 6 | 59 48 459 | 1 7 2 45 9 1 | 2 3 7 | 58 48 6 "rectangle with 2 strong links" 8 4 39 | 13 5 6 | 7 2 19 7 1 2 | 4 9 8 | 6 5 3 69 36 5 | 7 12 23 | 89 48 149 ---------------+---------------+--------------- 1349 5 8 |1369 146 349 | 2 16 7 169 67 79 |1569 126 259 | 4 3 8 1346 2 34 | 8 7 34 | 59 16 59 ---------------+---------------+--------------- 2 78 47 | 56 468 1 | 3 9 45 345 38 6 | 59 48 459 | 1 7 2 45 9 1 | 2 3 7 | 58 48 6 "logical use of uniqueness : xy cycles : rw" 12 5 6 | 3 7 12 | 4 89 89 8 3 12 | 1245 9 1245 | 6 7 15 4 7 9 | 15 6 8 | 135 2 135 ------------------+------------------+------------------ 5 6 178 | 9 4 3 | 2 18 178 127 12 4 | 256 8 256 | 1357 1359 13579 9 28 3 | 25 1 7 | 58 4 6 ------------------+------------------+------------------ 36 9 157 | 8 2 16 | 1357 135 4 36 4 178 | 167 5 9 | 1378 138 2 127 128 12578 | 147 3 14 | 9 6 1578 "uniqueness : ANL : another example of an almost turbot fish" 178 2789 3 | 4 158 1578 | 6 12789 129 14678 5 1267 | 167 1368 9 | 2348 12478 1234 14678 4789 1679 | 2 1368 1678 | 3489 14789 5 ------------------+------------------+------------------ 2 6 8 | 59 7 45 | 1 3 49 134 34 15 | 8 149 124 | 2459 6 7 9 47 157 | 3 146 1246 | 2458 2458 24 ------------------+------------------+------------------ 5 2379 2679 | 167 1469 1467 | 2349 1249 8 3678 3789 4 | 167 2 15678 | 359 159 1369 68 1 29 | 59 4589 3 | 7 2459 2469 "uniqueness : ANL : almost unique rectangle and almost almost unique rectangle" 69 4 7 | 269 16 8 | 5 126 3 369 1 39 | 2679 4567 257 | 28 24678 267 2 8 5 | 3 1467 17 | 9 1467 167 ------------------+------------------+------------------ 157 257 6 | 4 8 9 | 3 127 127 137 9 123 | 267 1367 1237 | 4 5 8 48 237 48 | 27 1357 12357 | 6 1279 1279 ------------------+------------------+------------------ 139 36 139 | 8 2 4 | 7 69 5 78 27 28 | 5 9 6 | 1 3 4 459 56 49 | 1 37 37 | 28 2689 269 "uniqueness : ANL : AUR in cells {r3c2|r3c3|r5c2|r5c3}" 15 1579 459 | 18 126 68 | 47 3 29 6 47 2 | 59 3 59 | 8 47 1 3 189 89 | 7 12 4 | 5 29 6 ---------------------+---------------------+--------------------- 45 3 7 | 6 9 1 | 2 45 8 18 189 489 | 3 5 2 | 146 16 7 125 125 6 | 4 8 7 | 9 15 3 ---------------------+---------------------+--------------------- 9 568 58 | 2 167 3 | 167 1678 4 7 2468 1 | 89 46 689 | 3 2689 5 248 2468 3 | 1589 1467 5689 | 167 126789 29 "uniqueness : ANL : two ANLs that set up with the same condition: 75^4" 1256 12 1258 | 1368 7 1236 | 9 4 1236 126 7 1248 | 1368 9 12346 | 2368 136 5 3 1249 12489 | 168 124 5 | 268 7 126 ------------------+------------------+------------------ 259 8 7 | 4 235 2369 | 1 3569 2369 4 6 3 | 159 8 129 | 257 59 279 1259 129 1259 | 3569 235 7 |23456 8 23469 ------------------+------------------+------------------ 8 12349 12469 | 7 1345 1349 | 456 1569 1469 7 1349 146 | 1359 145 1349 | 456 2 8 19 5 149 | 2 6 8 | 347 139 13479 "uniqueness : AUR : type 6 rectangle with 1 strong link not connecting the in-line extras" 56 26 246 | 1458 7 9 | 3 1246 1248 1 9 2467 | 458 3 48 |24578 2467 248 357 37 8 | 145 2 6 | 457 147 9 ------------------+------------------+------------------ 4 2378 1 | 78 5 2378 | 289 239 6 368 5 9 | 468 1468 12348 | 248 234 7 3678 23678 2367 |46789 4689 23478 | 1 5 2348 ------------------+------------------+------------------ 2 178 5 | 3 1489 1478 | 6 1479 14 36789 13678 367 | 2 14689 1478 | 479 13479 5 3679 4 367 | 679 169 5 | 279 8 123 "uniqueness : AUR : type 1 AUR" 167 2 13478 | 468 3489 468 | 5 79 168 156 138 9 | 7 358 2568 | 246 246 1268 567 478 478 |24568 4589 1 | 79 3 268 ------------------+------------------+------------------ 4 15 126 | 13 7 58 | 1236 2568 9 3 59 16 | 458 2 4589 | 16 58 7 8 1579 127 | 13 6 59 | 123 25 4 ------------------+------------------+------------------ 127 6 38 | 9 1458 24578 | 247 247 235 1279 147 147 | 256 15 3 | 8 2679 256 279 38 5 | 2468 48 24678 |24679 1 236 "uniqueness : AUR : type 3 AUR" 1 458 45 | 9 6 3 | 7 58 2 6 3 257 | 1 2578 257 | 9 58 4 78 9 257 | 28 2578 4 | 6 1 3 ---------------+---------------+--------------- 47 247 1 | 3 9 257 | 48 6 58 5 67 8 | 4 17 167 | 2 3 9 9 246 3 | 28 258 256 | 14 7 15 ---------------+---------------+--------------- 2 1 9 | 7 3 8 | 5 4 6 478 4578 457 | 6 12 12 | 3 9 78 3 78 6 | 5 4 9 | 18 2 178 "uniqueness : uniqueness chain : BUG-Lites and Uniqueness patterns" 358 12358 358 | 9 13567 12367 | 2367 123678 4 3489 123489 389 | 12346 1367 123467 | 5 1236789 36789 7 6 359 | 12345 8 1234 | 23 1239 39 ------------------------+------------------------+------------------------ 2 35789 35689 | 34568 356 3468 | 1 34678 3678 368 378 1 | 23468 36 9 | 3467 34678 5 3568 358 4 | 7 1356 1368 | 9 368 2 ------------------------+------------------------+------------------------ 1 3589 35689 | 368 4 3678 | 2367 235679 3679 3469 349 7 | 36 2 5 | 8 3469 1 345689 34589 2 | 1368 13679 13678 | 3467 345679 3679