The New Sudoku Players' Forum

by **yzfwsf** » Mon Jan 08, 2024 3:48 am

The first column is the possible elimination quantity of potential Blossom Loops, and the second column is the puzzle string. This is an Library Format string compatible with Hodoku.

Code: Select all: 17 :0000:x:2....7.6..5..2.1....93.....3...9.+7.66+71+4+38.2.9..7..3.......1.....2...6..8..5...7.:415 924 626 432 435 636 437 439 548 568 569 672 573 486 496:: 17 :0000:x:..3.7..4..7.4...3.5....8+7....6.92...2..8...7..51...2....+79...5......51.7..+5.1...9:911 614 921 132 232 632 452 872 375 483:: 17 :0000:x:..2...+54....57...65...+4.3..+1+27.9...5.39.+57.1..+5.1......4...+5.9.2....84+5...5.1...8:811 821 823 833 454 466 691:: 16 :0000:x:2.+3...4..76......3..53...6.4.217.....3...6.9..+7+6..5...+32..8.9....7..1.3.6..2.....:814 225 528 235 474 779:: 16 :0000:x:..4..6..37..+49..8..9...84...5.....1.....1.2..2..9....5.2...4.6.6..7.+9..4..9+63....:526 627 534 235 239 643 245 745 845 649 852 659 662 363 663 763 765 865 571 173 874 577 597:: 16 :0000:x:5....4..1..8.........2.1.3.3..8..7...6.45...........2.7.6...8..2..3...7....1....4:913 618 527 528 529 635 442 148 648 948 153 953 356 956 462 367 369 579 979 885 895 995 597 697 997 998:: 16 :0000:x:+9+24.....71..5.+92.....2...9..1.+9....3..9+7.6.4.8..1....+9..1.9...63+9...7.8..8.3..9..:115 633 733 537 539 465 476 577 485 495 496:: 16 :0000:x:5..4....1.8...72....7.6.....5.943.....4.+7....7....13...+7.8+2.9...6.+73+4.5+22....9..7:912 913 321 431 932 534 438 439 643 951 157 963 192 193 197 198 498:: 16 :0000:x:..4..7..3+71+9+38.4....+859+4.1..8......4..5..3.7.9....15..8...+3.6...9.4.+8.....37....8:217 218 518 618 229 947 259 659:: 16 :0000:x:.2...9.1...3.2...8...1..3..6....7.3.+2+3....7..+7845.......2.9.1..5......4..4...5..7:615 635 947 949 958 959 165:: 16 :0000:x:.1..7...2..59..........39..1.......9.2.....8......47....3.6.5+1+8.8...1.3+75.+18+3..+96:611 613 414 417 617 621 821 825 427 434 634 642 544 644 545 546 247 447 951 953 155 457 159 559 564 565 965 471 274 485:: ; Anti-phase AIC: r4c2 <> 3 16 :0000:x:...+8962......3..8.8..2....77....8.5.......3....195...6.16.+8...2..2.6..4.3.....5+6.:119 722 723 129 266 386 496 796:: 16 :0000:x:...+1+394..8..5+4..3..3..7...1.....17.+42..4...6..+4..6..+15.5..1...3..6..41..+1..9...4.:719 229 929 931 837 838 941 942 943 952 353 953 361 967 971 789:: 16 :0000:x:..34..6..6....8....4.2+6..5.1.+4..5.+69..69..1...9.+14+6.32..8.3..9+6.6...94.....6....7:711 129 552 858 272 772 183 292 897:: 15 :0000:x:4....8.+3...3.6...5.7.3.4....4.1..5....5..9...1...4+5..3..9..2.64.2+45...9.7..+4+9.8+5+2:919 127 341 646 749 651 851 355 757 767 786:: 15 :0000:x:2..3...8..9..1+82....3..2..9..7.3...2.5+28...1....+25.4...6.9........78+6..4......69.:415 421 431 435 455 476 378 578 382 192 494 496:: 15 :0000:x:.....6.1..5.+1.+7..3..1.8.7..2....41.......5..2...8+2+167......3.9.5+387....+1..2.1+83..:912 514 217 519 428 631 234 934 238 539 343 943 548 351 451 353 574 579 994 599:: 15 :0000:x:..4.5.3...1.....7.9....1..6.4.+6+98.2....1+23..4..27+4+5....6...2..82..5.......3.6..5.:916 732 335:: 15 :0000:x:1...8..4..5.2....7..7..46...2...6...5...7...3..85...6...+5.418...1......53......9.:139 672 781 981 692:: 15 :0000:x:4..6+28.3.....1.....2.4....8.8.+26.+37...2+7.9+8..7...+8.5.2.4.8....3....7.1....6..2.8.:324 628 629 536 638 362 576 677 586 595 995:: 15 :0000:x:1..4..7....7.....6.9..8..3......5.4.......67..8.2....52.+9..4..1..1...9.+7.7..9..5.:216 819 124 125 228 236 144 847 154 156 461 166 491 493 297 897 899:: 15 :0000:x:.1.9+7.6....4....7.7.......2.5...+9.3....2.8..7....432..3..8....5.4..9..6...6..78..:813 221 322 625 226 829 149 952 169 969 273 276 178 291 595:: 15 :0000:x:..3..96..5...1.....7.4....3..2.....798....1.......6.3..5.2...9.....9...2....715..:633 235 237 344 544 844 345 346 753 555 356 556 564 764 864 492:: 15 :0000:x:+1.5.......6.51.3.......2.1...2.8.+1.6+9.8+1+642...1+6+25..9...4.2...16.....9...9.....7.:712 914 916 219 926 732 934 674 376 776 386:: 15 :0000:x:.2..9..+5.1....3.....81...2.2+96.4.5.....9..6...7...1..9...57.4..4......3+5..5.....8:717 622 531 737 552 158 159 976 183 284 285 685 686 886 187 987 391 392::

by **totuan** » Tue Jan 09, 2024 8:01 am

Just checked for highest ER’s rates

#02 ER-9.2

Hidden Text: Show

Code: Select all: 17 :0000:x:..3.7..4..7.4...3.5....8+7....6.92...2..8...7..51...2....+79...5......51.7..+5.1...9:911 614 921 132 232 632 452 872 375 483:: *-----------------------------------------------------------------------------* | 1689 12689 3 | 1256 7 169 | 5689 4 12568 | | 1689 7 289 | 4 256 169 | 5689 3 12568 | | 5 *49-126 *24-9 | 1236 236 8 | 7 126+9 126 | |-------------------------+-------------------------+-------------------------| | 478-3 48-3 6 | 1357 9 2 | 3458 18 13458 | | 2 +3-49 *49 | 8 456-3 146-3 | 4569-3 7 1456-3 | | 4789-3 5 1 | 367 346 3467 | 2 689 3468 | |-------------------------+-------------------------+-------------------------| | 13468 12468-3 7 | 9 23468 346 | 3468 5 23468 | | 34689 24689-3 289-4 | 236 23468 5 | 1 268 7 | | 3468 2468-3 5 | 2367 1 3467 | 3468 268 9 | *-----------------------------------------------------------------------------*

AUR(49)r35c23 => (3)r5c2=(9)r3c8 ER-9.2 => ER-9.0
(3)r5c2==(9)r3c8-r6c8=(49)r5c37-(49=3)r5c2 => loop

Code: Select all: Raw Rank = 0 (linksets - sets) 7 Sets = {9R35 9C8 5N23 4B1 9B6} 7 Links = {3r5 3c2 49c3 3n2 34b4} 1 AUR = (94)R53C32 AUR points {aur 4r3c2 9r3c2 9r3c3 9r5c2 4r5c3 } 17 Eliminations, 1 Assignment --> [5N2*3r5*3c2*3b4] => r5c2=3, (3n2) => r3c2<>1, (3n2) => r3c2<>2, (3n2) => r3c2<>6, (9R3*9c3) => r3c3<>9, (3b4) => r4c1<>3, (3c2*3b4) => r4c2<>3, (5N2*4b4) => r5c2<>4, (9R5*5N2) => r5c2<>9, (3r5) => r5c5<>3, (3r5) => r5c6<>3, (3r5) => r5c7<>3, (3r5) => r5c9<>3, (3b4) => r6c1<>3, (3c2) => r7c2<>3, (3c2) => r8c2<>3, (4c3) => r8c3<>4, (3c2) => r9c2<>3

#24 ER-9.2

Hidden Text: Show

Code: Select all: 15 :0000:x:+1.5.......6.51.3.......2.1...2.8.+1.6+9.8+1+642...1+6+25..9...4.2...16.....9...9.....7.:712 914 916 219 926 732 934 674 376 776 386:: *-----------------------------------------------------------------------------* | 1 23478 5 | 347-68 3479 3678 | 478-6 2468 24789 | | 2478 6 79 | 5 1 78 | 3 248 24789 | | 3478 3478 379 | 3467-8 3479 2 | 45678 1 45789 | |-------------------------+-------------------------+-------------------------| | 3457 3457 2 | 379 8 379 | 1 345 6 | | 9 357 8 | 1 6 4 | 2 35 357 | | 347 1 6 | 2 5 37 | 478 9 3478 | |-------------------------+-------------------------+-------------------------| | 3578 3578 4 | 379-68 2 35679-8 | 568 36-58 1 | | 6 258-37 137 | 3478 347 15-378 | 9 23458 23458 | | 258-3 9 13 | 3468 34 156-3 | 4568 7 23458 | *-----------------------------------------------------------------------------*

On trying to present as diagram: ER-9.2 => ER-8.9

Code: Select all: --------------------------(3)r7c46 | || (13=7)r89c3-r7c12=(379)r7c46,r46c6---| (3)r7c12 => loop | || -(78=6)r12c6-r1c8=(6)r7c8-(3)r7c8

Code: Select all: Raw Rank = 0 (linksets - sets) 11 Sets = {6R3 39R7 6C8 89N3 1246N6 7B8} 11 Links = {6r1 7r8 3789c6 7n48 8b2 13b7} 17 Eliminations --> (6r1) => r1c4<>6, (8b2) => r1c4<>8, (6r1) => r1c7<>6, (8b2) => r3c4<>8, (7n4) => r7c4<>6, (7n4) => r7c4<>8, (8c6) => r7c6<>8, (7n8) => r7c8<>5, (7n8) => r7c8<>8, (3b7) => r8c2<>3, (7r8) => r8c2<>7, (3c6) => r8c6<>3, (7B8*7c6*7r8) => r8c6<>7, (8c6) => r8c6<>8, (3b7) => r9c1<>3, (3c6) => r9c6<>3, (8c6) => r9c6<>8

#16 ER-9.1

Hidden Text: Show

Code: Select all: 15 :0000:x:2..3...8..9..1+82....3..2..9..7.3...2.5+28...1....+25.4...6.9........78+6..4......69.:415 421 431 435 455 476 378 578 382 192 494 496:: *-----------------------------------------------------------------------------* | 2 147 1456 | 3 679 4579 | 157 8 156-7 | | 4567 9 456 | 456 1 8 | 2 3467-5 3567 | | 14568-7 1478 3 | 456 67 2 | 157 46-57 9 | |-------------------------+-------------------------+-------------------------| | 14689 148 7 | 146 3 149 | 589 56 2 | | 3469 5 2 | 8 679 479 | 379 1 367 | | 13689 138 1689 | 2 5 179 | 4 367 3678 | |-------------------------+-------------------------+-------------------------| | 134578 6 1458 | 9 24 135 | 78-135 27-35 1578-3 | | 159-3 12-3 159 | 7 8 6 | 135 235 4 | | 134578 27-1348 1458 | 15 24 135 | 6 9 1578-3 | *-----------------------------------------------------------------------------*

On trying to present as diagram: ER-9.1 => ER-7.3

Code: Select all: ------------------------(5)r4c7=r4c8-(5)r8c8 | || (3=157)r138c7--| (3)r8c8 => loop | || --(7)r2c89=r2c1-r79c1=(7-2)r9c2=r8c2-(2)r8c8

Code: Select all: Raw Rank = 1 (linksets - sets) 8 Sets = {7R2 138N7 8N8 5B6 27B7} 9 Links = {23r8 1c7 5c78 7c1 9n2 3b9 7b3} 18 Eliminations --> (7b3) => r1c9<>7, (5c8) => r2c8<>5, (7c1) => r3c1<>7, (5c8) => r3c8<>5, (7b3) => r3c8<>7, (1c7) => r7c7<>1, (3b9) => r7c7<>3, (5c7) => r7c7<>5, (3b9) => r7c8<>3, (5c8) => r7c8<>5, (3b9) => r7c9<>3, (3r8) => r8c1<>3, (3r8) => r8c2<>3, (9n2) => r9c2<>1, (9n2) => r9c2<>3, (9n2) => r9c2<>4, (9n2) => r9c2<>8, (3b9) => r9c9<>3

I’m not sure above moves is Blossom Loops.
Thanks for your puzzles!
totuan

by **yzfwsf** » Tue Jan 09, 2024 12:11 pm

Hi totuan:
The solution path for #24 #16 is similar to the path of the solver. #2 is not because the solver does not use AUR in the logic.

yzfwsf

by **totuan** » Tue Jan 09, 2024 5:19 pm

yzfwsf wrote:Hi totuan:
The solution path for #24 #16 is similar to the path of the solver. #2 is not because the solver does not use AUR in the logic.

Yes, maybe this one for #2:

Hidden Text: Show

totuan

by **yzfwsf** » Wed Jan 10, 2024 4:05 am

Cell Type Blossom Loop: 346r7c6 => r4c9 <> 1, r9c246,r7c2 <> 3, r7c25,r9c26 <> 4, r569c6,r8c1 <> 6, r4c179,r8c1 <> 8
Burring Loop: 4r7c6 - r8c5 = r8c12 - (4=1368)r1279c1 - r6c1 = r6c89 - (8=1)r4c8 - r4c4 = r5c6 - (1=96)r12c6 - 6r7c6
Burr Branch 1: 3r7c6 - r8c45 = 3r8c12

Region Type Blossom Loop: 3r7c1248 => r9c16,r8c2 <> 3, r7c8 <> 5, r1c47 <> 6, r8c26 <> 7, r7c468,r13c4,r89c6 <> 8
Burring Loop: (3-9)r7c4 = r7c6 - (9=3786)r1246c6 - r1c8 = (6-3)r7c8
Burr Branch 1: 3r7c1 - (3=17)r89c3 - r7c12 = 7r7c4

Cell Type Blossom Loop: 235r8c8 => r6c2,r7c7 <> 1, r7c79,r8c1,r9c9 <> 3, r9c2 <> 4, r23c8,r7c7 <> 5, r3c18,r1c9 <> 7, r69c2 <> 8
Burring Loop: 2r8c8 - (2=1)r8c2 - (1=487)r134c2 - r2c1 = r2c89 - (7=153)r138c7 - 3r8c8
Burr Branch 1: 5r8c8 - r4c8 = 5r4c7

by **yzfwsf** » Wed Jan 17, 2024 12:00 am

Post solver's solution path:
#01

Code: Select all: ,--------------------,------------------,-----------------------, | 2 1348 348 | 189 158 7 | 4589 6 34589 | | 47 5 34678 | 68 2 49 | 1 3489 34789 | | 147 168 9 | 3 1568 45 | 258 458 2578 | :--------------------+------------------+-----------------------: | 3 248 458 | 12 9 25 | 7 148 6 | | 6 7 1 | 4 3 8 | 59 2 59 | | 9 248 458 | 7 156 256 | 3 148 148 | :--------------------+------------------+-----------------------: | 457 349 3467 | 2689 4678 1 | 24589 34589 234589 | | 1457 1349 2 | 89 478 39 | 6 134589 134589 | | 8 13469 346 | 5 46 2369 | 249 7 12349 | '--------------------'------------------'-----------------------'

Blossom Loop: 249r9c7 => r7c7 <> 2, r7c3 <> 3, r2c389,r9c239,r7c3 <> 4, r3c9 <> 5, r9c6 <> 6, r3c9 <> 8, r2789c9,r7c7 <> 9; Anti-phase AIC: r9c6 <> 9
Burring Loop: 2r9c7 - r3c7 = (2-7)r3c9 = r3c1 - r2c3 = (7-6)r7c3 = r7c45 - (6=4)r9c5 - 4r9c7
Burr Branch 1: 9r9c7 - r78c8 = r2c8 - (9=4)r2c6 - (4=7)r2c1

#03

Code: Select all: ,-------------------,---------------------,---------------------, | 3679 16789 2 | 3689 368 1369 | 5 4 179 | | 349 189 134 | 5 7 1239 | 1289 28 6 | | 5 16789 16 | 2689 4 1269 | 3 278 1279 | :-------------------+---------------------+---------------------: | 1 2 7 | 3468 9 346 | 68 368 5 | | 468 3 9 | 268 5 7 | 268 1 24 | | 468 5 468 | 1 2368 236 | 26789 23678 23479 | :-------------------+---------------------+---------------------: | 3678 4 1368 | 2367 236 5 | 1267 9 1237 | | 2 1679 136 | 3679 36 8 | 4 5 137 | | 379 679 5 | 234679 1 23469 | 267 2367 8 | '-------------------'---------------------'---------------------'

Region Type Blossom Loop: 6r1389c2 => r2c3 <> 1, r267c7 <> 2, r8c4 <> 3, r9c46,r1c1,r6c7,r8c4 <> 6, b9p138 <> 7, r6c78,r2c7,r4c8 <> 8
Burring Loop: 6r8c2 - (6=137)r8c359 - (7=286)r459c7 - r7c7 = r9c78 - 6r9c2
Burr Branch 1: 6r1c2 - (6=1)r3c3 - r123c2 = 1r8c2

#04

Code: Select all: ,------------------,-------------------,----------------------, | 2 189 3 | 5679 1569 789 | 4 1578 15789 | | 7 6 1489 | 4589 1459 2489 | 1258 128 3 | | 189 1489 5 | 3 149 24789 | 1278 6 12789 | :------------------+-------------------+----------------------: | 4 589 2 | 1 7 389 | 3568 58 568 | | 158 3 18 | 48 24 6 | 12578 9 124578 | | 189 7 6 | 489 2349 5 | 1238 1248 1248 | :------------------+-------------------+----------------------: | 3 2 14 | 567 8 47 | 9 1457 1456 | | 589 4589 7 | 4569 4569 1 | 2568 3 24568 | | 6 14589 1489 | 2 3459 3479 | 1578 14578 14578 | '------------------'-------------------'----------------------'

Region Type Blossom Loop: 5r24589c7 => r1c5 <> 1, r589c9,r9c8 <> 5, r8c9 <> 6, r4c267,r6c789,r5c79 <> 8, r1c45 <> 9
Burring Loop: 5r2c7 - (5=1897)r1c2689 - r1c4 = (7-6)r7c4 = r7c9 - (6=85)r4c89 - 5r5c7
Burr Branch 1: 5r8c7 - r7c89 = 5r7c4

#05

Code: Select all: ,--------------------,---------------,-------------------, | 158 18 4 | 125 257 6 | 1579 2579 3 | | 7 136 12356 | 4 9 123 | 15 8 126 | | 135 9 12356 | 123 57 8 | 4 257 167 | :--------------------+---------------+-------------------: | 3489 5 378 | 238 46 237 | 36789 1 789 | | 3489 3467 3678 | 358 1 357 | 2 3479 789 | | 2 13478 18 | 9 46 37 | 3678 347 5 | :--------------------+---------------+-------------------: | 138 2 3578 | 15 58 4 | 13789 6 1789 | | 6 138 1358 | 7 258 9 | 1358 235 4 | | 1458 1478 9 | 6 3 125 | 178 257 1278 | '--------------------'---------------'-------------------'

Region Type Blossom Loop: 8r6c237 => r29c2,r7c7 <> 1, r8c3 <> 3, r467c7,r379c9,r56c8 <> 7, r47c7,r9c2 <> 8
Burring Loop: 8r6c2 - (8=13)r18c2 - r7c13 = (3-9)r7c7 = r7c9 - (9=78)r45c9 - 8r6c7
Burr Branch 1: (8-1)r6c3 = 1r6c2

#06

Code: Select all: ,---------------------,---------------------,-------------------, | 5 2379 237 | 679 36789 4 | 269 89 1 | | 1469 123479 8 | 5679 3679 35679 | 2469 469 2679 | | 469 479 479 | 2 789 1 | 4569 3 56789 | :---------------------+---------------------+-------------------: | 3 1259 12459 | 8 1269 269 | 7 45 569 | | 189 6 27 | 4 5 27 | 139 189 389 | | 1489 15789 14579 | 679 13679 3679 | 14569 2 5689 | :---------------------+---------------------+-------------------: | 7 13459 6 | 59 249 259 | 8 159 23 | | 2 14589 1459 | 3 469 5689 | 1569 7 569 | | 89 3589 359 | 1 267 256789 | 23 56 4 | '---------------------'---------------------'-------------------'

Region Type Blossom Loop: 5r479c8 => r2c2,r6c3 <> 4, r7c2 <> 5, r2c9,r8c6 <> 6, r3c5 <> 7, r3c1579,r2c129,r89c6,r1c2 <> 9
Burring Loop: 5r7c8 - (5=2496)b8p1235 - r8c79 = (6-5)r9c8
Burr Branch 1: (5-4)r4c8 = r4c3 - r6c1 = r23c1 - (4=97)r3c23 - r3c9 = (7-2)r2c9 = 2r7c9

#07

Code: Select all: ,---------------------,------------------,-------------------, | 9 2 4 | 68 368 138 | 13568 1356 7 | | 1 367 3678 | 5 34678 9 | 2 36 48 | | 567 3567 358 | 2 134678 1348 | 13468 9 148 | :---------------------+------------------+-------------------: | 24567 1 2567 | 9 2458 2458 | 5678 2567 3 | | 25 35 9 | 7 2358 6 | 158 4 1258 | | 8 34567 23567 | 1 235 2345 | 567 2567 9 | :---------------------+------------------+-------------------: | 2457 457 1 | 48 9 258 | 347 2357 6 | | 3 9 256 | 46 1256 7 | 145 8 1245 | | 24567 8 2567 | 3 1256 125 | 9 1257 1245 | '---------------------'------------------'-------------------'

Region Type Blossom Loop: 7r9c138 => r13c7 <> 1, r9c18,r4c1 <> 2, r6c2 <> 3, r8c9 <> 4, r9c18,r4c1,r6c2 <> 5, r2c3 <> 6, r2c3 <> 7, r13c7,r5c9 <> 8
Burring Loop: (7-4)r9c1 = r9c9 - (4=81)r23c9 - r1c8 = (1-7)r9c8
Burr Branch 1: 7r9c3 - (7=2356)b4p3459 - r89c3 = 6r9c1

#08

Code: Select all: ,------------------,----------------,--------------------, | 5 23 236 | 4 89 28 | 678 36789 1 | | 1469 8 1369 | 135 159 7 | 2 3469 34569 | | 139 1234 7 | 123 6 258 | 458 389 3589 | :------------------+----------------+--------------------: | 168 5 128 | 9 4 3 | 1678 12678 68 | | 1368 1239 4 | 256 7 2568 | 568 12689 5689 | | 7 29 268 | 256 58 1 | 3 24689 45689 | :------------------+----------------+--------------------: | 134 7 135 | 8 2 56 | 9 1346 346 | | 189 6 189 | 7 3 4 | 18 5 2 | | 2 34 358 | 156 15 9 | 468 368 7 | '------------------'----------------'--------------------'

Cell Type Blossom Loop: 268r6c3 => r25c1 <> 1, r56c2,r1c3 <> 2, r3c2 <> 3, r4c78 <> 6, r14c78,r6c89,r3c6 <> 8, r2c1 <> 9
Burring Loop: 6r6c3 - r45c1 = (6-4)r2c1 = (4-2)r3c2 = r3c46 - (2=8)r1c6 - r1c5 = r6c5 - 8r6c3
Burr Branch 1: 2r6c3 - (2=681)r4c139 - r5c2 = 1r3c2

#09

Code: Select all: ,--------------------,------------------,-------------------, | 256 256 4 | 126 126 7 | 89 89 3 | | 7 1 9 | 3 8 26 | 4 256 56 | | 236 236 8 | 5 9 4 | 27 1 267 | :--------------------+------------------+-------------------: | 1236 8 1267 | 269 2567 2569 | 123 2369 4 | | 1246 246 5 | 2689 246 3 | 1289 7 19 | | 9 23467 267 | 268 2467 1 | 5 2368 26 | :--------------------+------------------+-------------------: | 8 2457 127 | 129 3 259 | 6 2459 12579 | | 1256 9 1267 | 4 1256 8 | 1237 235 1257 | | 12456 2456 3 | 7 1256 2569 | 129 2459 8 | '--------------------'------------------'-------------------'

Region Type Blossom Loop: 5r7c2689 => r8c7 <> 1, r7c289,r6c25,r8c79,r4c5 <> 2, r4c8 <> 3, r8c9,r9c6 <> 5, r6c25,r4c5 <> 6, r7c8 <> 9
Burring Loop: (5-7)r7c2 = (7-3)r6c2 = r6c8 - r8c8 = (3-7)r8c7 = r3c7 - (7=265)r236c9 - 5r7c9
Burr Branch 1: 5r7c6 - r4c6 = (5-7)r4c5 = (7-4)r6c5 = 4r6c2
Burr Branch 2: (5-4)r7c8 = 4r7c2

#10

Code: Select all: ,--------------------,---------------------,--------------------, | 48 2 5678 | 34678 34578 9 | 456 1 456 | | 149 15679 3 | 467 2 46 | 4569 5679 8 | | 489 5679 56789 | 1 4578 468 | 3 25679 24569 | :--------------------+---------------------+--------------------: | 6 159 159 | 2489 148 7 | 2458 3 1245 | | 2 3 159 | 4689 1468 1468 | 7 568 1456 | | 7 8 4 | 5 36 1236 | 269 269 1269 | :--------------------+---------------------+--------------------: | 38 67 2 | 34678 9 3468 | 1 568 356 | | 5 1679 16789 | 23678 13678 12368 | 2689 4 2369 | | 1389 4 1689 | 2368 1368 5 | 2689 2689 7 | '--------------------'---------------------'--------------------'

Region Type Blossom Loop: 9r368c9 => r45c5,r8c6 <> 1, r68c9 <> 2, r7c4 <> 3, r2c1 <> 4, r68c69 <> 6, r8c6,r9c1 <> 8, r3c238 <> 9
Burring Loop: 9r3c9 - (9=483)r137c1 - (3=4681)r2357c6 - r6c6 = (1-9)r6c9
Burr Branch 1: (9-3)r8c9 = 3r7c9

#11

Code: Select all: ,--------------------,--------------------,-----------------, | 3489 1 489 | 56 7 568 | 38 456 2 | | 2347 3467 5 | 9 124 268 | 1368 467 134 | | 24678 467 24678 | 125 12458 3 | 9 4567 145 | :--------------------+--------------------+-----------------: | 1 3457 4678 | 237 28 2678 | 36 2456 9 | | 3467 2 467 | 13567 59 5679 | 136 8 34 | | 3689 3569 689 | 1236 128 4 | 7 256 135 | :--------------------+--------------------+-----------------: | 279 479 3 | 47 6 279 | 5 1 8 | | 2469 8 2469 | 245 259 1 | 24 3 7 | | 5 47 1 | 8 3 27 | 24 9 6 | '--------------------'--------------------'-----------------'

Cell Type Blossom Loop: 2678r4c6 => r2c17,r5c7 <> 3, r4c2 <> 4, r3c45,r1c8 <> 5, r3c13,r4c38,r6c2 <> 6, r4c2,r5c6 <> 7, r7c1 <> 9; Anti-phase AIC: r4c2 <> 3
Burring Loop: 6r4c6 - (6=3)r4c7 - r1c7 = r1c1 - (3=4679)r2379c2 - (9=27)r79c6 - 7r4c6
Burr Branch 1: 8r4c6 - (8=562)b2p136

#12

Code: Select all: ,----------------------,-------------------,------------------, | 145 3457 3457 | 8 9 6 | 2 13 345 | | 124569 24569 459 | 1457 3 1457 | 1469 8 459 | | 8 34569 3459 | 2 14 145 | 1469 139 7 | :----------------------+-------------------+------------------: | 7 23469 349 | 1346 124 8 | 149 5 149 | | 24569 245689 4589 | 1467 1247 1247 | 3 1279 1489 | | 24 2348 1 | 9 5 347 | 478 27 6 | :----------------------+-------------------+------------------: | 459 1 6 | 3457 8 34579 | 79 379 2 | | 59 5789 2 | 1357 6 1579 | 1789 4 1389 | | 3 4789 4789 | 147 1247 129 | 5 6 189 | '----------------------'-------------------'------------------'

Region Type Blossom Loop: 9r9c2369 => r9c6 <> 1, r5c125,r6c2 <> 2, r3c8 <> 3, r25c1 <> 4, r25c1 <> 5, r7c46,r8c7 <> 7, r8c279 <> 9
Burring Loop: 9r9c3 - (9=451)r178c1 - (1=3)r1c8 - (3=79)r7c78 - 9r9c9
Burr Branch 1: (9-2)r9c6 = r9c5 - r4c5 = r4c2 - (2=4)r6c1

#13

Code: Select all: ,-------------------,--------------------,-------------------, | 567 267 257 | 1 3 9 | 4 2578 268 | | 8 12679 1279 | 5 4 26 | 269 3 67 | | 456 3 2459 | 268 7 268 | 2569 259 1 | :-------------------+--------------------+-------------------: | 356 68 358 | 238 2589 1 | 7 289 4 | | 2 178 1578 | 4 589 3578 | 389 6 89 | | 79 4 3789 | 2378 6 2378 | 238 1 5 | :-------------------+--------------------+-------------------: | 47 5 24789 | 2678 1 2678 | 2689 2789 3 | | 379 2789 6 | 2378 258 4 | 1 25789 289 | | 1 278 2378 | 9 258 235678 | 2568 4 2678 | '-------------------'--------------------'-------------------'

Region Type Blossom Loop: 2r7c34678 => r8c48,r9c67,r1c8 <> 2, r3c3,r4c5 <> 5, r2c2 <> 6, r2c23,r1c8,r7c3 <> 7, r4c5,r7c3 <> 8, r5c7,r8c8 <> 9
Burring Loop: (2-9)r7c3 = r7c78 - r8c9 = r5c9 - r5c5 = (9-2)r4c5 = r89c5 - 2r7c4
Burr Branch 1: 2r7c7 - r89c9 = r1c9 - (2=5674)b1p1237 - r3c3 = 4r7c3

#14

Code: Select all: ,---------------------,------------------,------------------, | 2589 12578 3 | 4 1579 17 | 6 1278 18 | | 6 1257 12579 | 357 1579 8 | 2379 1247 34 | | 789 4 179 | 2 6 137 | 3789 5 138 | :---------------------+------------------+------------------: | 1 2378 4 | 378 278 5 | 78 6 9 | | 23578 2378 6 | 9 278 237 | 1 47 458 | | 578 9 57 | 1 4 6 | 578 3 2 | :---------------------+------------------+------------------: | 2457 15 8 | 57 3 1247 | 25 9 6 | | 2357 6 257 | 578 12578 9 | 4 128 1358 | | 23459 135 1259 | 6 1258 124 | 235 128 7 | '---------------------'------------------'------------------'

Region Type Blossom Loop: 7r3c1367 => r1c258 <> 1, r2c3457,r5c16,r1c5,r7c6 <> 7, r1c18,r5c19,r3c7 <> 8
Burring Loop: 7r3c3 - r12c2 = r45c2 - r6c13 = (7-8)r6c7 = r6c1 - r3c1 = r3c79 - (8=1)r1c9 - (1=7)r1c6 - 7r3c6
Burr Branch 1: 7r3c7 - (7=85)r46c7

#15

Code: Select all: ,-------------------,-----------------,--------------------, | 4 1569 126 | 279 1257 8 | 12679 3 167 | | 289 189 3 | 279 6 17 | 2479 12478 5 | | 25689 7 1268 | 3 125 4 | 1269 128 1689 | :-------------------+-----------------+--------------------: | 2689 4 2678 | 1 2378 37 | 5 278 689 | | 23 368 5 | 2678 278 9 | 1246 12478 1678 | | 1 689 2678 | 2678 4 5 | 269 278 3 | :-------------------+-----------------+--------------------: | 358 1358 9 | 78 1378 2 | 137 6 4 | | 368 2 4 | 5 1378 136 | 137 9 17 | | 7 136 16 | 4 9 136 | 8 5 2 | '-------------------'-----------------'--------------------'

Region Type Blossom Loop: 2r2345c1 => r235c8,r56c7 <> 2, r7c2,r8c6 <> 3, r6c3 <> 6, b5p27 <> 7, r3c18,r4c19,r5c8 <> 8
Burring Loop: 2r2c1 - (2=168)r139c3 - r3c9 = r45c9 - (8=27)r46c8 - r5c89 = r5c45 - (7=3)r4c6 - r9c6 = r9c2 - r5c2 = (3-2)r5c1
Burr Branch 1: 2r4c1 - (2=3786)r4c3568

#17

Code: Select all: ,---------------------,----------------,-----------------, | 34789 2478 3479 | 2349 3459 6 | 4589 1 489 | | 4689 5 469 | 1 49 7 | 2489 268 3 | | 349 2469 1 | 345 8 29 | 7 456 469 | :---------------------+----------------+-----------------: | 2 6789 567 | 369 3679 4 | 1 38 589 | | 16789 146789 4679 | 369 3679 5 | 489 348 2 | | 349 49 3459 | 8 2 1 | 6 7 459 | :---------------------+----------------+-----------------: | 1467 1467 467 | 246 456 3 | 2458 9 4678 | | 5 3 8 | 7 469 29 | 24 246 1 | | 4679 4679 2 | 456 1 8 | 3 456 467 | '---------------------'----------------'-----------------'

Region Type Blossom Loop: 9r3c1269 => r1c1 <> 3, r3679c9,r5c23,r3c4,r6c3,r7c7 <> 4, r125c1,r45c2 <> 9
Burring Loop: 9r3c2 - r12c3 = r56c3 - (9=43)r6c12 - r3c1 = (3-5)r3c4 = r3c8 - (5=246)b9p458 - r23c8 = (6-9)r3c9
Burr Branch 1: (9-2)r3c6 = 2r8c6
#18

Code: Select all: ,-------------------,------------------,--------------------, | 678 278 4 | 289 5 67 | 3 189 129 | | 3568 1 568 | 23489 38 469 | 24589 7 259 | | 9 2358 578 | 2348 78 1 | 2458 48 6 | :-------------------+------------------+--------------------: | 1357 4 157 | 6 9 8 | 157 2 1357 | | 5678 5789 56789 | 1 2 3 | 56789 689 4 | | 1368 389 2 | 7 4 5 | 1689 13689 139 | :-------------------+------------------+--------------------: | 1457 6 1579 | 349 137 2 | 1479 1349 8 | | 2 789 1789 | 5 1378 479 | 14679 13469 1379 | | 1478 789 3 | 489 6 479 | 12479 5 1279 | '-------------------'------------------'--------------------'

Region Type Blossom Loop: 7r7c1357 => r4c9 <> 1, r2c4,r6c1 <> 3, r2c7 <> 5, r8c357,r9c17 <> 7, r135c2,r2c47 <> 8, r5c2 <> 9
Burring Loop: 7r7c5 - (7=8)r3c5 - (8=23496)b2p14567 - (6=385)r2c135 - r2c9 = (5-7)r4c9 = r89c9 - 7r7c7
Burr Branch 1: 7r7c1 - (7=893)r689c2 - r4c1 = 3r4c9

#19

Code: Select all: ,------------------,--------------------,--------------------, | 1 369 2369 | 3679 8 3579 | 2359 4 29 | | 4689 5 3469 | 2 1369 39 | 139 138 7 | | 289 389 7 | 139 1359 4 | 6 12358 289 | :------------------+--------------------+--------------------: | 479 2 1349 | 13489 139 6 | 14579 1578 1489 | | 5 469 1469 | 1489 7 289 | 1249 128 3 | | 479 3479 8 | 5 1239 239 | 12479 6 1249 | :------------------+--------------------+--------------------: | 2679 79 5 | 3679 4 1 | 8 237 26 | | 2468 1 2469 | 36789 2369 23789 | 2347 237 5 | | 3 478 246 | 678 256 2578 | 1247 9 1246 | '------------------'--------------------'--------------------'

Region Type Blossom Loop: 6r278c1 => r69c9,r8c1 <> 2, r45c3 <> 4, r7c4 <> 6, r7c48,r9c2 <> 7, r3c8 <> 8, r2c17,r46c9,r1c7 <> 9
Burring Loop: (6-4)r2c1 = r2c3 - (4=2796)b7p1269 - 6r8c1
Burr Branch 1: 6r7c1 - (6=298)r137c9 - r2c8 = 8r2c1

#20

Code: Select all: ,---------------------,----------------,--------------------, | 4 1579 1579 | 6 2 8 | 79 3 1579 | | 35689 35679 35789 | 59 1 357 | 24679 2459 4579 | | 13569 2 13579 | 4 359 37 | 679 159 8 | :---------------------+----------------+--------------------: | 159 8 1459 | 2 6 145 | 3 7 149 | | 1356 1356 2 | 7 345 9 | 8 146 146 | | 7 169 1349 | 13 8 134 | 5 1469 2 | :---------------------+----------------+--------------------: | 1259 4 1579 | 8 59 16 | 279 2569 3 | | 23589 359 3589 | 359 7 346 | 1 24569 4569 | | 1359 13579 6 | 1359 34 2 | 479 8 4579 | '---------------------'----------------'--------------------'

Region Type Blossom Loop: 6r2c127 => r5c12,r4c9,r6c8 <> 1, r7c8 <> 2, r28c1 <> 3, r9c9 <> 4, r28c1 <> 5, r5c2 <> 6, r2c7 <> 7, r2c17,r8c1 <> 9
Burring Loop: (6-8)r2c1 = (8-2)r8c1 = r8c8 - r2c8 = (2-6)r2c7
Burr Branch 1: 6r2c2 - r6c2 = r6c8 - (6=14)r5c89 - r5c5 = r9c5 - r9c7 = 4r2c7

#21

Code: Select all: ,---------------------,---------------------,------------------, | 1 2356 23568 | 4 2356 369 | 7 289 29 | | 3458 2345 7 | 359 235 1239 | 12458 189 6 | | 456 9 2456 | 1567 8 167 | 1245 3 24 | :---------------------+---------------------+------------------: | 3679 1236 236 | 36789 1367 5 | 123 4 2389 | | 3459 12345 2345 | 389 134 389 | 6 7 2389 | | 3679 8 346 | 2 13467 3679 | 13 19 5 | :---------------------+---------------------+------------------: | 2 356 9 | 35678 3567 4 | 38 68 1 | | 34568 3456 1 | 3568 2356 2368 | 9 268 7 | | 368 7 368 | 1368 9 12368 | 34 5 234 | '---------------------'---------------------'------------------'

Region Type Blossom Loop: 6r1478c2 => r2c7 <> 1, r1c3,r2c7 <> 2, r45c2,r9c46 <> 3, r5c2 <> 4, r3c4,r5c2 <> 5, r1c3,r8c1 <> 6, r9c46,r8c1 <> 8
Burring Loop: 6r4c2 - (6=345792)b4p134679 - r3c3 = r3c79 - r1c8 = r8c8 - (2=3486)r9c1379 - 6r8c2
Burr Branch 1: 6r1c2 - (6=23591)b2p23456 - r2c8 = (1-9)r6c8 = r12c8 - (9=2)r1c9

#22

Code: Select all: ,--------------------,--------------------,--------------------, | 258 1 235 | 9 7 245 | 6 458 348 | | 5689 2689 4 | 1356 12358 156 | 1359 7 139 | | 7 3689 3589 | 13456 13568 1456 | 13459 14589 2 | :--------------------+--------------------+--------------------: | 12468 5 1278 | 167 16 9 | 14 3 468 | | 1469 36 139 | 2 156 8 | 1459 1459 7 | | 1689 6789 1789 | 1567 4 3 | 2 1589 68 | :--------------------+--------------------+--------------------: | 3 279 179 | 8 126 146 | 1479 249 5 | | 1258 4 12578 | 135 9 125 | 137 6 13 | | 159 29 6 | 1345 123 7 | 8 1249 1349 | '--------------------'--------------------'--------------------'

Cell Type Blossom Loop: 139r5c3 => r468c3,r239c5,r6c8,r8c7 <> 1, r9c5 <> 2, r2c9,r3c3 <> 3, r3c5 <> 6, r6c8 <> 8, r59c1 <> 9
Burring Loop: 1r5c3 - (1=297)b7p238 - r7c7 = (7-3)r8c7 = r23c7 - r1c9 = r1c3 - 3r5c3
Burr Branch 1: 9r5c3 - r5c78 = (9-5)r6c8 = r6c4 - (5=162)r457c5 - r2c5 = 2r2c2

#23

Code: Select all: ,---------------------,------------------,---------------------, | 1248 124 3 | 578 258 9 | 6 124578 1458 | | 5 2469 4689 | 3678 1 2378 | 24789 2478 489 | | 1268 7 189 | 4 568 258 | 89 1258 3 | :---------------------+------------------+---------------------: | 1346 1346 2 | 19 458 458 | 489 4568 7 | | 9 8 456 | 357 234 247 | 1 2456 456 | | 147 14 1457 | 19 2458 6 | 2489 3 4589 | :---------------------+------------------+---------------------: | 134678 5 14678 | 2 3468 348 | 3478 9 1468 | | 134678 1346 14678 | 3568 9 3458 | 3478 14678 2 | | 23468 2369 4689 | 368 7 1 | 5 468 468 | '---------------------'------------------'---------------------'

Cell Type Blossom Loop: 357r5c4 => r2c6 <> 2, r8c4 <> 3, r4c128,r9c1 <> 4, r6c5 <> 5, r9c12 <> 6, r2c6,r4c8,r9c1 <> 8, r2c37,r6c7 <> 9
Burring Loop: 3r5c4 - (3=4689)r9c3489 - r3c3 = r3c7 - (9=485)r4c567 - 5r5c4
Burr Branch 1: 7r5c4 - r5c6 = (7-3)r2c6 = 3r2c4

#25

Code: Select all: ,------------------,--------------------,--------------------, | 367 2 347 | 4678 9 4678 | 138 5 13467 | | 1 45 479 | 24678 2568 3 | 789 46789 467 | | 3679 3456 8 | 1 56 4567 | 39 2 3467 | :------------------+--------------------+--------------------: | 2 9 6 | 378 4 78 | 5 178 137 | | 358 1348 134 | 9 2358 2578 | 6 478 2347 | | 358 7 34 | 2368 23568 1 | 238 48 9 | :------------------+--------------------+--------------------: | 3689 1368 1239 | 5 7 268 | 4 169 126 | | 4 168 279 | 68 18 29 | 27 3 5 | | 679 16 5 | 2346 1236 2469 | 1279 1679 8 | '------------------'--------------------'--------------------'

Region Type Blossom Loop: 8r2568c5 => r9c8 <> 1, r6c5 <> 2, r6c15,r1c7 <> 3, r129c4,r7c12,r3c2,r9c1 <> 6, r5c68,r2c4 <> 8
Burring Loop: 8r2c5 - r1c46 = (8-1)r1c7 = r9c7 - r9c5 = (1-8)r8c5
Burr Branch 1: 8r5c5 - r5c12 = r6c1 - (8=2346)r6c3478 - r8c4 = r8c2 - (6=1)r9c2

The New Sudoku Players' Forum

Blossom Loop Practice 25 Puzzles

Blossom Loop Practice 25 Puzzles

Re: Blossom Loop Practice 25 Puzzles

Re: Blossom Loop Practice 25 Puzzles

Re: Blossom Loop Practice 25 Puzzles

Re: Blossom Loop Practice 25 Puzzles

Re: Blossom Loop Practice 25 Puzzles