The New Sudoku Players' Forum

by **Mike Barker** » Sun Apr 13, 2008 4:59 am

I've tried to go back and status the 21 puzzles. I couldn't find pencil marks for 1-5. Going through the posts it looks like Obi-wahn solved #6, 12, 15, 19, 20 with broken wings, Danny solved #6 with Dual Kraken Xwings, Ron solved #7, 10, 11 with Remote Gardian Broken Wings (Broken Wings with an extra chain), Myth solved #7-11 with what he called Broken fish, and Wapati solved #8 with Dual Mutant Jellyfish. #21 is solvable with an Endofin Mutant Starfish and #14 is solvable by a mutant starfish which performs eliminations on two digits.

Code: Select all: ........29.2.....4.6.3..98..1...8.6....13.....3...74....8......6..24.31.....7...5 #1 ....1.85.87.....32..............7......82...7..96.4..8..59...7.4.....1.6....8.52. #2 ..5....7.1......6..43...2....6..2..53...7...........2..5.8...9....9.48....7.26.3. #3 ..72....62...4..758.....1..1.4.6.8...2.8....3.....9....3...4..14..6..2.....7..... #4 ..4..8......2..1.....5.134.9.....8.64.8...71.751.....383...4........6..75.7...... #5 1......2...84.6..1..4....7.....79...3.761...4.........69...1.58.8....7...31.....9 #6 BW, Dual Kraken Xwing | 1 56 3 | 8 9 7 | 4 2 56 | | 25 7 8 | 4 235 6 | 59 39 1 | | 9 256 4 | 1 235 25 | 8 7 356| :------------+------------+------------: | 258 4 6 | 25 7 9 | 1 38 35 | | 3 25 7 | 6 1 258| 259 89 4 | | 258 1 9 | 3 8-5 4 | 25 6 7 | :------------+------------+------------: | 6 9 2 | 7 4 1 | 3 5 8 | | 4 8 5 | 9 6 3 | 7 1 2 | | 7 3 1 | 25 258 258| 6 4 9 | .8.64........9..4......7.....9..62.........7.46..73..5.784....95....9.86.3....... #7 Remote BW, Broken Swordfish | 123 8 57 | 6 4 125 | 9 1-2 237 | | 6 12 57 | 358 9 1258 | 157 4 2378 | | 123 9 4 | 1358 12358 7 | 15 6 238 | :------------------+------------------+------------------: | 7 15 9 | 158 158 6 | 2 3 4 | | 8 25 3 | 9 25 4 | 6 7 1 | | 4 6 12 | 12 7 3 | 8 9 5 | :------------------+------------------+------------------: | 12 7 8 | 4 6 125 | 3 125 9 | | 5 4 12 | 1237 13 9 | 17 8 6 | | 9 3 6 | 1578 1258 1258 | 4 125 7-2 | ..8..53.6.7..3......21.....8..5......6......7..7...14.71......9..9..4...6...9.574 #8 Broken Swordfish, Dual Mutant Jellyfish | 14 9 8 | 247 247 5 | 3 12 6 | | 15 7 6 | 289 3 289 | 4 59 12 | | 345 345 2 | 1 46 69 | 7 59 8 | :------------------+------------------+------------------: | 8 234 1 | 5 24 7 | 9 6 23 | | 2349 6 5 | 2349 1 239 | 28 238 7 | | 239 3-2 7 | 23689 268 23689| 1 4 5 | :------------------+------------------+------------------: | 7 1 4 | 2368 5 2368 | 268 238 9 | | 25 258 9 | 23678 2678 4 | 268 1238 13 | | 6 28 3 | 28 9 1 | 5 7 4 | ...54..3.....6.9...25....6.5.1..92...4..76.5....4...9..3.9.......2..1..4..8.3.... #9 Broken Xwing | 6789 16789 679 | 5 4 78 | 178 3 2 | | 34 178 34 | 178 6 2 | 9 178 5 | | 78 2 5 | 178 9 3 | 4 6 178 | :------------------+------------------+------------------: | 5 67 1 | 3 8 9 | 2 4 67 | | 389 4 39 | 2 7 6 | 18 5 138 | | 2 678 367 | 4 1 5 | 678 9 3678 | :------------------+------------------+------------------: | 1467 3 467 | 9 2 478 | 5 178 1678 | | 679 79 2 | 678 5 1 | 3 78 4 | | 1467 5 8 | 6-7 3 47 | 167 2 9 | .2..1...5..9......1347........54......6...7.8.15..3.9....1......6.3..41.....9...2 #10 Remote BW, Broken Swordfish | 678 2 78 | 468 1 9 | 3 47 5 | | 5678 578 9 | 2 3 468 | 68 47 1 | | 1 3 4 | 7 568 568 | 689 2 69 | :------------------+------------------+------------------: | 2789 789 278 | 5 4 7-8 | 1 6 3 | | 3 4 6 | 9 2 1 | 7 5 8 | | 7-8 1 5 | 68 678 3 | 2 9 4 | :------------------+------------------+------------------: | 24 579 3 | 1 567 24 | 569 8 679 | | 25789 6 278 | 3 578 2578 | 4 1 79 | | 4578 578 1 | 468 9 45678| 56 3 2 | .3..9.1.7..96..3....12...8......95.....31.......56.723..6.......17...8...2..3..5. #11 Remote BW, Broken Swordfish | 2-48 3 25 | 48 9 458 | 1 6 7 | | 578 578 9 | 6 57-8 1 | 3 4 2 | | 467 467 1 | 2 7-4 3 | 9 8 5 | :------------------+------------------+------------------: | 24678 4678 3 | 478 248 9 | 5 1 68 | | 2678 5678 25 | 3 1 27 | 46 9 468 | | 1 9 48 | 5 6 48 | 7 2 3 | :------------------+------------------+------------------: | 3 458 6 | 19 458 458 | 2 7 19 | | 459 1 7 | 49 245 26 | 8 3 469 | | 489 2 48 | 14789 3 67 | 46 5 1469 | ...7....9.9...2.7.....3.61.1......4.3.7..48..9....63......589....89...2..1....... #12 BW | 246 2346 2345| 7 46 1 | 245 8 9 | | 6-4 9 1 | 456 8 2 | 45 7 3 | | 8 7 245 | 45 3 9 | 6 1 245 | :---------------+---------------+---------------: | 1 8 6 | 3 9 5 | 27 4 27 | | 3 5 7 | 2 1 4 | 8 9 6 | | 9 24 24 | 8 7 6 | 3 5 1 | :---------------+---------------+---------------: | 2467 2346 234 | 1 5 8 | 9 36 47 | | 457 36 8 | 9 46 37 | 1 2 457 | | 4567 1 9 | 46 2 37 | 457 36 8 | .9......481......7..648....3..7.......9..61.....8..9...5.1....8...6.751.2........ #13 | 5 9 23 | 23 7 1 | 68 68 4 | | 8 1 4 | 9 6 23 | 23 5 7 | | 7 23 6 | 4 8 5 | 23 9 1 | :---------------+---------------+---------------: | 3 268 258 | 7 1 9 | 48 248 256 | | 4 78 9 | 235 235 6 | 1 78 235 | | 1 267 257 | 8 345 234 | 9 27-3 2356| :---------------+---------------+---------------: | 6 5 37 | 1 9 234 | 47 234 8 | | 9 348 38 | 6 234 7 | 5 1 2-3 | | 2 347 1 | 35 345 8 | 467 346 9 | 5...4.2...1..2.7....21......7..1...62...3...4..6....7...4.7.69.3.........9.3.1..2 #14 Mutant Starfish Mutant Starfish (r57c59b9/r6c28b38, fins=r3c5|r89c7): => r3c7<>58 +--------------------+-----------------------+--------------------+ | 5 368 3789 | 6789 4 36789 | 2 1368 189* | | 4689 1 389 | 5689 2 35689 | 7 34568 589* | | 46789 3468 2 | 1 5689# 356789 | 4-58 34568 589* | +--------------------+-----------------------+--------------------+ | 489 7 3589 | 4589 1 4589 | 358 2 6 | | 2 58* 1 | 67 3 67 | 9 58* 4 | | 489 3458 6 | 24589 589* 24589 | 1358 7 158* | +--------------------+-----------------------+--------------------+ | 1 258* 4 | 258* 7 258* | 6 9 3 | | 3 26 58 | 2469 69 2469 | 158# 158* 7 | | 678 9 578 | 3 568* 1 | 458# 458* 2 | +--------------------+-----------------------+--------------------+ ...8.7....1.3..6.....45...89.4.....7.............4.1...2.....7.453......7....2.39 #15 BW | 25 4 256 | 8 16 7 | 3 9 12 | | 8 1 7 | 3 2 9 | 6 5 4 | | 3 9 26 | 4 5 16 | 7 12 8 | :---------------+---------------+---------------: | 9 36 4 | 126 8 13 | 5 26 7 | | 1256 368 18 | 26 7 356 | 9 4 23-6| | 256 7 25 | 9 4 356 | 1 8 236 | :---------------+---------------+---------------: | 16 2 9 | 16 3 4 | 8 7 5 | | 4 5 3 | 7 9 8 | 2 16 16 | | 7 68 18 | 5 16 2 | 4 3 9 | .1.53.4..4.5.....38.........3......95...86.4....4...........6....81...921.6.4.3.5 #16 | 279 1 279 | 5 3 279 | 4 6 8 | | 4 2679 5 | 2679 1279 8 | 129 27 3 | | 8 2679 3 | 269 129 4 | 1259 257 17 | :---------------+---------------+---------------: | 6 3 4 | 2-7 257 1 | 8 257 9 | | 5 279 1279| 3 8 6 | 12 4 17 | | 27 8 127 | 4 2579 279 | 125 3 6 | :---------------+---------------+---------------: | 279 5 279 | 8 279 3 | 6 1 4 | | 3 4 8 | 1 6 5 | 7 9 2 | | 1 279 6 | 279 4 279 | 3 8 5 | 3........6.1.8..43...14...68...7.1..2..4.9..7.7.....2.1...927......5..8..2....... #17 | 3 4 7 | 56 2 56 | 9 1 8 | | 6 5 1 | 9 8 7 | 2 4 3 | | 9 8 2 | 1 4 3 | 5 7 6 | :------------------+------------------+------------------: | 8 9-6 34569| 2 7 56 | 1 356 459 | | 2 1 356 | 4 36 9 | 8 356 7 | | 45 7 3569 | 356 1 8 | 46 2 59 | :------------------+------------------+------------------: | 1 36 48 | 368 9 2 | 7 56 45 | | 47 369 9-6 | 367 5 1 | 346 8 2 | | 57 2 58 | 78 36 4 | 36 9 1 | 1.........48.9....7..5..2...5..219.4.6.94.5....9.3..8.9....48.........6..7......5 #18 | 1 23 2356 | 4 78 2367 | 367 359 3689 | | 2356 4 8 | 123 9 2367 | 1367 135 136 | | 7 9 36 | 5 18 36 | 2 4 18 | :------------------+------------------+------------------: | 8 5 37 | 6 2 1 | 9 37 4 | | 23 6 1237 | 9 4 8 | 5 1237 1237 | | 4 12 9 | 7 3 5 | 16 8 126 | :------------------+------------------+------------------: | 9 123 56 | 123 56 4 | 8 1237 1237 | | 235 8 12345| 123 157 2379 | 134 6 1239 | | 236 7 12346| 8 6-1 239 | 134 1239 5 | .2....65.....3......6.29..88.......5...4...62.79..3.....831..7..........3...78.4. #19 BW | 79 2 3 | 8 4 1 | 6 5 79 | | 1579 8 157 | 567 3 56 | 24 29 479 | | 457 45 6 | 57 2 9 | 3 1 8 | :------------------+------------------+------------------: | 8 46 24 | 1 9 26 | 7 3 5 | | 15 3 15 | 4 8 7 | 9 6 2 | | 26 7 9 | 256 56 3 | 14 8 14 | :------------------+------------------+------------------: | 2456 4569 8 | 3 1 2456 | 25 7 69 | | 24567 1 2457 | 2569 56 2456 | 8 9-2 3 | | 3 569 25 | 2569 7 8 | 125 4 169 | ....97.5.1.......9....2.1.4..34.8....8...2...9...7..2.....4.7......6..48.29..36.. #20 BW | 38 34 248 | 1 9 7 | 23 5 6 | | 1 357 2567| 368 35 4 | 23 78 9 | | 3567 9 567 | 368 2 56 | 1 78 4 | :---------------+---------------+---------------: | 2 6 3 | 4 1 8 | 5 9 7 | | 57 8 157 | 9 35 2 | 4 6 13 | | 9 45 145 | 36 7 56 | 8 2 13 | :---------------+---------------+---------------: | 68 1 68 | 5 4 9 | 7 3 2 | | 357 357 7-5 | 2 6 1 | 9 4 8 | | 4 2 9 | 7 8 3 | 6 1 5 | .......39.5....6....68...4129.5.3.7...5..74....1.......7.16..9.6...85...1........ #21 Endofin Mutant Starfish Endofin Mutant Starfish (r27c7b26/r1c3986, fins=r789c7): => r8c98<>2 +-----------------+------------------+-------------------+ | 48 1 278 | 247* 2457* 6 | 257* 3 9 | | 49 5 27* | 349 349 1 | 6 28* 278* | | 39 23 6 | 8 57 29* | 57 4 1 | +-----------------+------------------+-------------------+ | 2 9 48 | 5 14 3 | 18 7 6 | | 38 368 5 | 269 129 7 | 4 128* 238* | | 7 346 1 | 246 24 8 | 9 5 23* | +-----------------+------------------+-------------------+ | 5 7 234* | 1 6 24* | 238# 9 248* | | 6 24 2349 | 2379 8 5 | 1237# 1-2 47-2 | | 1 248 23489 | 2379 2379 249 | 237# 6 5 | +-----------------+------------------+-------------------+

by **daj95376** » Sun Apr 13, 2008 7:52 am

Code: Select all: ........29.2.....4.6.3..98..1...8.6....13.....3...74....8......6..24.31.....7...5 #1 +--------------------------------------------------------------+ | 137 78 1347 | 4679 689 149 | 16 5 2 | | 9 578 2 | 567 568 15 | 16 3 4 | | 145 6 145 | 3 25 1245 | 9 8 7 | |--------------------+--------------------+--------------------| | 247 1 479 | 49 29 8 | 5 6 3 | | 245 245 6 | 1 3 245 | 8 7 9 | | 8 3 59 | 569 569 7 | 4 2 1 | |--------------------+--------------------+--------------------| | 245 25 8 | 59 1 3 | 7 49 6 | | 6 579 57 | 2 4 59 | 3 1 8 | | 13 49 13 | 8 7 6 | 2 49 5 | +--------------------------------------------------------------+ Templates (A: 1) <> 5 [r3c5]

Code: Select all: ....1.85.87.....32..............7......82...7..96.4..8..59...7.4.....1.6....8.52. #2 +--------------------------------------------------------------+ | 2369 236 36 | 7 1 2369 | 8 5 4 | | 8 7 1 | 5 4 69 | 69 3 2 | | 3569 456 2346 | 23 39 8 | 7 69 1 | |--------------------+--------------------+--------------------| | 236 2346 8 | 1 39 7 | 236 469 5 | | 15 15 346 | 8 2 39 | 369 469 7 | | 7 23 9 | 6 5 4 | 23 1 8 | |--------------------+--------------------+--------------------| | 12 8 5 | 9 6 12 | 4 7 3 | | 4 9 23 | 23 7 5 | 1 8 6 | | 136 136 7 | 4 8 13 | 5 2 9 | +--------------------------------------------------------------+ Templates (A: 1) <> 3 [r1c2]

Code: Select all: ..5....7.1......6..43...2....6..2..53...7...........2..5.8...9....9.48....7.26.3. #3 +--------------------------------------------------------------+ | 2 6 5 | 34 1489 1389 | 49 7 189 | | 1 7 89 | 2 489 5 | 349 6 389 | | 89 4 3 | 7 6 189 | 2 5 189 | |--------------------+--------------------+--------------------| | 7 189 6 | 34 1489 2 | 139 48 5 | | 3 2 489 | 5 7 189 | 19 48 6 | | 5 189 489 | 6 1489 1389 | 7 2 39 | |--------------------+--------------------+--------------------| | 4 5 1 | 8 3 7 | 6 9 2 | | 6 3 2 | 9 5 4 | 8 1 7 | | 89 89 7 | 1 2 6 | 5 3 4 | +--------------------------------------------------------------+ Templates (A: 1) <> 9 [r1c7]

Code: Select all: ..72....62...4..758.....1..1.4.6.8...2.8....3.....9....3...4..14..6..2.....7..... #4 +--------------------------------------------------------------------------------+ | 359 1 7 | 2 359 35 | 4 8 6 | | 2 69 369 | 1 4 8 | 39 7 5 | | 8 4 359 | 359 7 6 | 1 239 29 | |--------------------------+--------------------------+--------------------------| | 1 59 4 | 35 6 2357 | 8 259 279 | | 5679 2 569 | 8 15 157 | 569 4 3 | | 3567 568 3568 | 4 25 9 | 56 1 27 | |--------------------------+--------------------------+--------------------------| | 56 3 28 | 59 28 4 | 7 569 1 | | 4 7 159 | 6 1359 135 | 2 359 8 | | 569 5689 125689 | 7 12358 1235 | 359 3569 4 | +--------------------------------------------------------------------------------+ Templates (A: 1) <> 5 [r4c8],[r9c7] Templates (A: 1) <> 9 [r9c38] *** not necessary

Code: Select all: ..4..8......2..1.....5.134.9.....8.64.8...71.751.....383...4........6..75.7...... #5 +--------------------------------------------------------------+ | 1236 179 4 | 369 3679 8 | 29 67 5 | | 36 789 5 | 2 4 39 | 1 67 89 | | 26 789 29 | 5 679 1 | 3 4 289 | |--------------------+--------------------+--------------------| | 9 2 3 | 4 1 7 | 8 5 6 | | 4 6 8 | 39 239 5 | 7 1 29 | | 7 5 1 | 68 68 29 | 4 29 3 | |--------------------+--------------------+--------------------| | 8 3 6 | 7 5 4 | 29 29 1 | | 12 4 29 | 1389 389 6 | 5 38 7 | | 5 19 7 | 1389 2389 239 | 6 38 4 | +--------------------------------------------------------------+ Templates (A: 1) <> 9 [r3c3],[r8c45],[r9c2]

by **Mike Barker** » Sun Apr 13, 2008 11:56 pm

It looks possible to apply Danny's Dual Kraken X-wing to NoFish1. The difference here is that one of the fins for each Xwing directly link to the target cell while the others link indirectly through the other X-wing.

Code: Select all: Xwing:c36\r38+fin:r2c6 =5= r5c6|r6c3 -5- r5c1|r6c4 =5= Xwing:c14\r37+fin:r2c4 => r3c5<>5 +-----------------------------+ | | | | | 5 | 5@ 5 5*| | | 5@ 5*| -5 5*| | |---------+----------+--------| | | | | | 5x 5 | 5#| | | 5#| 5x 5 | | |---------+----------+--------| | 5@ 5 | 5@ | | | 5 5*| 5*| | | | | | +-----------------------------+

NoFish2 requires a Kraken finned Xwing and a Kraken column:

Code: Select all: Xwing:c16\r19+fin:r3c1 =3= r4c1|r5c6 -3- r4c5=3=r3c5 -3- r3c4=3=r8c4 -3- r8c3 =3= r1c3c => r1c2<>3 | | + -3- r5c3 =3==================================+ +--------------------------------+ | 3* -3 3A | 3*| | | | | | | 3* 3A | 3a 3A | | |-----------+----------+---------| | 3# 3 | 3a | 3 | | 3a | 3#| 3 | | 3 | | 3 | |-----------+----------+---------| | | | | | 3a | 3A | | | 3* 3 | 3*| | +--------------------------------+

NoFish3 takes a Kraken finned X-wing and a Kraken finned (sashimi) Swordfish:

Code: Select all: Xwing:r25c37+fin:r2c9 =9= r2c5|r5c6 -3- r3c6|r4c5 =3= Swordfish:r349\c127+fin:r3c9 => r1c7<>9 +-------------------------------------+ | | 9 9 | -9 9 | | 9* | 9# | 9* 9* | | 9@ | 9x | 9@ | |-----------+------------+------------| | 9@ | 9x | 9@ | | 9* | 9# | 9* | | 9 9 | 9 9 | 9 | |-----------+------------+------------| | | | | | | | | | 9@ 9@ | | | +-------------------------------------+

NoFish4 has an added twist with additional fins. In this case the starting point is a Kraken finned (sashimi) Swordfish which links with both an empty rectangle and a Kraken row:

Code: Select all: + -5- r7c1 =5================+ | | Swordfish: r158\c567+fin:r8c8 =5= r1c1|r8c3 -5- r3c3=5=r3c4 -5- r7c4=5=r7c8 => r4c8,r9c7<>5 | + =5= r5c13 -5- r46c2=5=r9c2 -5- r9c78=5=r78c8 +-------------------------------------+ | 5# | 5* 5* | | | | | | | 5a | 5A | | |------------+------------+-----------| | 5b | 5 5 | -5 | | 5# 5# | 5* 5* | 5* | | 5 5b 5 | 5 | 5 | |------------+------------+-----------| | 5a | 5a | 5AB | | 5# | 5* 5* | 5*B | | 5 5B 5 | 5 5 |-5b 5b | +-------------------------------------+

NoFish5 again uses a finned Xwing, direct links of one fin, and the other fins linked via a Kraken row. The difference here is that the fish does not directly link to the target cell, but links through a grouped strong link.

Code: Select all: r8c3=9=r8c45 -9- Xwing:r15c45+fin:r1c2 =9= r1c7 -9- r7c7=9=r7c8 -9- r6c8=9=r6c6 -9- r2c6=9=r2c2 | | + =9= r5c9 -9- ----------------+ => r3c3<>9 => r9c2<>9 => r8c45<>9 +--------------------------------------+ | 9# | 9* 9* | 9# | | 9B | 9b | 9b | | 9 -9 | 9 | 9 | |------------+------------+------------| | | | | | | 9* 9* | 9# | | | 9B | 9b | |------------+------------+------------| | | | 9b 9B | | 9A | 9a 9a | | | 9 | 9 9 9 | | +--------------------------------------+

NoFish17 is a Kraken finned (sashimi) Xwing with a Kraken Row:

Code: Select all: + -6- r5c8 =6= ==============+ | | Xwing:r67c34+fin:r7c2 =6= r6c7|r7c8 -6- r9c7=6=r9c5 -6- r5c5=6=r5c3 => r4c2,r8c3<>6 +------------------------------------+ | | 6 6 | | | | | | | | | | :-----------+------------+-----------: | -6 6 | 6 | 6 | | 6A | 6a | 6a | | 6* | 6* | 6# | :-----------+------------+-----------: | 6# | 6* | 6# | | 6 -6 | 6 | 6 | | | 6A | 6a | +------------------------------------+

NoFish18 is a Kraken Xwing/Kraken Column pattern, but with an additional link in the column:

Code: Select all: + -9- r5c8 =9= ==========+ += r9c8 | | | Xwing:r89c47 =5= r5c3|r6c7 -9- r6c2=9=r7c2 -9- r7c8 =9= r2c8 -9- r2c4=9=r3c5 => r9c5<>9 +-------------------------------------+ | | | | | | 1b | 1 1B 1 | | | 1B | 1 | :------------+------------+-----------: | | | | | 1#| | 1a 1 | | 1a | | 1# 1 | :------------+------------+-----------: | 1A | 1 | 1a 1 | | 1*| 1 1 | 1* 1 | | 1*| -1 | 1* 1A | +-------------------------------------+

NoFish20 reverts back to the Dual Kraken Xwing configuration:

Code: Select all: Xwing:r35c13 =5= r3c6|r5c5 -9- r2c5|r6c6 =9= Xwing:r26c23 => r8c3<>5 +-------------------------------+ | | | | | 5@ 5@| 5x | | | 5* 5*| 5#| | :----------+----------+---------: | | | | | 5* 5*| 5# | | | 5@ 5@| 5x| | :----------+----------+---------: | | | | | 5 5 -5 | | | | | | | +-------------------------------+

Enough - I'll leave #13 and #16 for others. It does look like all of the NoFish are really fish after all.

by **ronk** » Mon Apr 14, 2008 1:46 am

For these broken wings: If all the guardian cells('G') were false, we would have an illegal turbot fish('*') with five conjugate links. Therefore, at least one of the guardian cells must be true.

Code: Select all: NoFish1 ........29.2.....4.6.3..98..1...8.6....13.....3...74....8......6..24.31.....7...5 After SSTS: . . . | . . . | . . . . 5 . | G5 5 5 | . . . G5 . 5 | . -5 5 | . . . ---------+----------+---------- . . . | . . . | . . . *5 G5 . | . . 5 | . . . . . *5 | *5 G5 . | . . . ---------+----------+---------- *5 G5 . | *5 . . | . . . . 5 5 | . . 5 | . . . . . . | . . . | . . .

Except for r57c2, r3c5 sees all the guardians. But r3c5 indirectly sees r57c2 via the empty rectangle in b1. Therefore r3c5<>5.

Code: Select all: NoFish3 ..5....7.1......6..43...2....6..2..53...7...........2..5.8...9....9.48....7.26.3. After SSTS: . . . | . 9 G9 | -9 . 9 . . *9 | . 9 . | 9 . 9 *9 . . | . . *9 | . . G9 ---------+----------+---------- . 9 . | . 9 . | 9 . . . . *9 | . . *9 | G9 . . . 9 G9 | . 9 G9 | . . 9 ---------+----------+---------- . . . | . . . | . . . . . . | . . . | . . . 9 9 . | . . . | . . .

Except for r6c36, r1c7 sees all the guardians. But r1c7 indirectly sees r6c36 via the empty rectangle in b6. Therefore r1c7<>9.

Code: Select all: NoFish5 ..4..8......2..1.....5.134.9.....8.64.8...71.751.....383...4........6..75.7...... After SSTS: . 9 . | 9 9 . | 9 . . . G9 . | . . *9 | . . *9 . 9 -9 | . 9 . | . . G9 ---------+----------+---------- . . . | . . . | . . . . . . | 9 9 . | . . *9 . . . | . . *9 | . *9 . ---------+----------+---------- . . . | 9 9 . | 9 9 . . . 9 | 9 9 . | 9 . . . 9 . | 9 9 G9 | . . .

Except for r9c6, r3c3 sees all the guardians. But r3c3 indirectly sees r9c6 via the grouped strong link in c2. Therefore r3c3<>9.

Code: Select all: NoFish17 3........6.1.8..43...14...68...7.1..2..4.9..7.7.....2.1...927......5..8..2....... After SSTS: . . . | 6 . 6 | . . . . . . | . . . | . . . . . . | . . . | . . . ---------+----------+---------- . -6 6 | . . G6 | . 6 . . . 6 | . *6 . | . 6 . . . G6 | *6 . . | *6 . . ---------+----------+---------- . 6 . | 6 . . | . 6 . . 6 6 | 6 . . | G6 . . . . . | . *6 . | *6 . .

Except for r8c7, r4c2 sees all the guardians. But r4c2 indirectly sees r8c7 via the empty rectangle in b7. Therefore r4c2<>6.

Code: Select all: NoFish18 1.........48.9....7..5..2...5..219.4.6.94.5....9.3..8.9....48.........6..7......5 . . . | . . . | . . . . . . | 1 . . | 1 G1 1 . . . | . 1 . | . . 1 ---------+----------+---------- . . . | . . . | . . . . . *1 | . . . | . *1 G1 . 1 . | . . . | 1 . 1 ---------+----------+---------- . *1 . | G1 . . | . *1 G1 . . *1 | 1 1 . | 1 . 1 . . G1 | . -1 . | 1 G1 .

Except for r2c8 and r57c9, r9c5 sees all the guardians. But r9c5 indirectly sees r2c8 (and r57c9) via the empty rectangle(s) in b2 (and b3). Therefore r9c5<>1.

Code: Select all: NoFish20 ....97.5.1.......9....2.1.4..34.8....8...2...9...7..2.....4.7......6..48.29..36..

Obi-Wahn's broken-wing elimination is here.

Mike Barker wrote:It does look like all of the NoFish are really fish after all.

Fish are constraint set problems that do not require chains. All your so-called fish include chains.

by **daj95376** » Mon Apr 14, 2008 4:01 am

A complete failure in a Colors chain will provide the necessary invalid pattern.

Code: Select all: NoFish2 +-----------------------------------+ | G3 -3 G3 | . . G3 | . . . | | . . . | . . . | . 3 . | | G3 . G3 | 3 3 . | . . . | |-----------+-----------+-----------| | B3 3 . | . B3 . | 3 . . | | . . A3 | . . A3 | 3 . . | | . 3 . | . . . | 3 . . | |-----------+-----------+-----------| | . . . | . . . | . . 3 | | . . B3 | 3 . . | . . . | | A3 G3 . | . . B3 | . . . | +-----------------------------------+

Without the Guardian cells, there would be two Blue cells in [r4] and two Amber cells in [r5].

FWIW, a complete failure in a Colors chain is how I cracked all of the NoFish puzzles that I recently reviewed. I have not tried this approach with all of the NoFish puzzles, yet.

by **daj95376** » Mon Apr 14, 2008 4:35 pm

For NoFish13, there are two eliminations that are jointly linked true or false.

Code: Select all: [r6c8]=3=[r56c9]-3-[r8c9] [r6c8]-3-[r56c9]=3=[r8c9]

Code: Select all: NoFish13 +-----------------------------------+ | . . 3 | 3 . . | . . . | | . . . | . . B3 | A3 . . | | . A3 . | . . . | B3 . . | |-----------+-----------+-----------| | 3 . . | . . . | . . . | | . . . | 3 3 . | . . 3 | | . . . | . 3 G3 | . -3 3 | |-----------+-----------+-----------| | . . A3 | . . ?3 | . G3 . | | . G3 G3 | . 3 . | . . -3 | | . B3 . | 3 3 . | . 3 . | +-----------------------------------+

Without the Guardian cells, cell [r7c6] must be Blue in [r7] and Amber in [c6]. The guardian cells prevent either [r6c8] or [r8c9] from being true.

For NoFish16, there is one elimination and a link. It also gets complicated!

Code: Select all: [r5c9]=7=[r4c8]-7-[r4c4]

Code: Select all: NoFish16 +-----------------------------------+ | A7 . A7 | . . B7 | . . . | | . B7 . | 7 7 . | . 7 . | | . B7 . | . . . | . 7 7 | |-----------+-----------+-----------| | . . . | -7 7 . | . 7 . | | . G7 7 | . . . | . . 7 | | 7 . 7 | . 7 G7 | . . . | |-----------+-----------+-----------| | A7 . A7 | . 7 . | . . . | | . . . | . . . | 7 . . | | . B7 . | G7 . A7 | . . . | +-----------------------------------+

Without the Guardian cells, a grouped Colors results in either a contradiction for Blue in [c2] or an Amber X-Wing r17\c13 that eliminates the candidate in [b4]. Two of the guardian cells see [r4c4] directly. The other guardian cell prevents [r5c9] from being true.

by **ronk** » Mon Apr 14, 2008 5:24 pm

Mike Barker wrote:I'll leave #13 and #16 for others.

Looks like I came up with the same -- or essentially the same -- broken wings as daj95376.

For these broken wings, if all the guardian cells (G) were false, we would have illegal [edit: loops]] (*) with seven conjugate links. Therefore, at least one of the guardian cells must be true.

Code: Select all: NoFish13 .9......481......7..648....3..7.......9..61.....8..9...5.1....8...6.751.2........ After SSTS: . . *3 | *3 . . | . . . . . . | . . *3 | 3 . . . *3 . | . . . | 3 . . ---------+----------+---------- . . . | . . . | . . . . . . | 3 3 . | . . 3 . . . | . 3 G3 | . 3 3 ---------+----------+---------- . . *3 | . . *3 | . G3 . . G3 G3 | . 3 . | . . -3 . *3 . | 3 3 . | . 3 .

Except for r6c6, r8c9 sees all the guardians. But r8c9 indirectly sees r6c6 via the empty rectangle in b6. Therefore r8c9<>3.

Code: Select all: NoFish16 .1.53.4..4.5.....38.........3......95...86.4....4...........6....81...921.6.4.3.5 After SSTS: *7 . *7 | . . *7 | . . . . *7 . | 7 7 . | . 7 . . *7 . | 7 7 . | . 7 7 ---------+----------+---------- . . . | -7 7 . | . 7 . . G7 7 | . . . | . . 7 7 . 7 | . 7 G7 | . . . ---------+----------+---------- *7 . *7 | . *7 . | . . . . . . | . . . | . . . . *7 . | G7 . *7 | . . .

Except for r5c2, r4c4 sees all the guardians. But r4c4 indirectly sees r5c2 via the strong link in b6. Therefore r4c4<>7. The unusual thing here is that two of the conjugate links are due to two empty rectangles.

by **daj95376** » Mon Apr 14, 2008 6:47 pm

ronk: For me, your illegal chains are easier to understand if I think of them as invalid (possibly grouped) loops. What do you think?

Yes, our slightly different approaches lead to similar results. I start by assuming the elimination cell(s) is/are true and also perform any Naked Singles that result. After that, the Colors contradiction is easy to locate. The guardian cells become obvious during this process.

I guess it's possible to find a contradiction first and then surmise the guardian cells and the elimination, but I seriously doubt anyone would do so.

by **ronk** » Mon Apr 14, 2008 7:09 pm

daj95376 wrote:For me, your illegal chains are easier to understand if I think of them as invalid (possibly grouped) loops. What do you think?

Yes, I should have said loop rather than chain. Did you mean something else as well?

by **daj95376** » Mon Apr 14, 2008 10:05 pm

ronk wrote:Did you mean something else as well?

No, I was just thinking that your illegal loops were a smarter way to go than my more complicated Colors approach. I was trying to get both colors to produce a contradiction, and then realized (from your solutions) that a contradiction for just one color was sufficient under the right circumstances. Nice!

Website · by **denis_berthier** » Sat Apr 19, 2008 11:07 am

NRCZ CHAINS SUBSUME BROKEN WINGS

I already posted this in the fully supersymmetric chains thread, but participants in the Broken Wings discussion may have missed it.

When re'born asked me (at the bottom of this page: http://forum.enjoysudoku.com/viewtopic.php?t=5591&postdays=0&postorder=asc&start=45) whether there was "a nice way of either subsuming broken wings into nrczt-chains, or melding them into a even slightly bigger theory", I concentrated on Rod Hagglund's definition of Broken Wings (here: http://forum.enjoysudoku.com/viewtopic.php?t=2666&highlight=) and I noticed the logic for justifying the eliminations was very different from the logic of the nrczt-chain rules.
But, recently I was again asked the same question by a friend. As I looked at Broken Wings again, instead of reading the proof, I tried to translate them into my approach.
The result is obvious and I don't understand how I can have missed this in my answer to re'born:
nrcz-chains subsume broken wings. What Rod Haglund calls guardian cells can be understood as mere additional z-candidates in my approach.
There's no need of the t-extension.

Even without the t-extension, nrcz-chains are much more general than broken wings (and each of the following reasons may have misled me the first time I looked at them = in addition to the different logic involved):
- there's no need for a closed loop
- there`s no need for all links to be conjugacy links (modulo the guardians): the constraint bears only on even links;
- the length of the `loop` can be odd or even, no matter (this is a consequence of the previous point);
- the number of additional z-candidates in any link is completely irrelevant.

I wish this may help users of Broken Wings generalise this technique and widen their arsenal of techniques.

by **hobiwan** » Fri Jun 27, 2008 1:26 pm

I found the following puzzle in the latest pattern game:

Code: Select all: 100002003020010040005600000003000007040080090900000500000004900080090070600700001 # 114 10.3/10.3/10.0 - Mauricio

After an initial brute force move (r5c6=6), some ALS and a finned franken jellyfish my solver arrives at:

Code: Select all: .---------------------.---------------------.---------------------. | 1 79 4689 | 4589 457 2 | 678 568 3 | | 378 2 689 | 3589 1 3579 | 678 4 5689 | | 3478 379 5 | 6 347 3789 | 12 12 89 | :---------------------+---------------------+---------------------: | 28 156 3 | 12459 245 159 | 1468 168 7 | | 57 4 17 | 135 8 6 | 13 9 2 | | 9 16 28 | 1234 2347 137 | 5 1368 46 | :---------------------+---------------------+---------------------: | 2357 1357 127 | 12358 6 4 | 9 2358 58 | | 2345 8 124 | 1235 9 135 | 2346 7 456 | | 6 359 249 | 7 235 358 | 2348 235 1 | '---------------------'---------------------'---------------------' Template Delete: => r2c3<>8

I can't find a fish for that elimination. Can you?

by **DanG** » Sun Jul 06, 2008 4:05 am

Hi hobiwan,

Actually there are about 8 Broken Wings (BW) on your diagram among the cells marked with "T"(Turbots).

Code: Select all: Filter 8 . . 8 | T8 . . | T8 8 . 8 . -8 | 8 . . | 8 . 8 ← 8 . . | . . T8 | . . T8 ---------+----------+--------- +8 . . | . . . | 8 8 . . . . | . 8 . | . . . . . 8 | . . . | . +8 . ---------+----------+--------- . . . | T8 . . | . 8 T8 . 8 . | . . . | . . . . . . | . . T8 | T8 . . ↑ T - turbot or BW cells ↑← mark the corridors

T cells also form what I called a SoPT.
Now a solution which start with your template cell r2c3=8 => r4c1=8 => r6c8=8
and all 8-candidates are canceled except the "T" marked cells which form an impossible patern (impossible jelly fish).. therefore r2c3≠8

This is an ordinary 4 box SoPT (b2,b3,b8,b9). I am looking forward to finding a puzzle with a 6 box SoPT.. Maybe somebody will find one and post it here..

by **hobiwan** » Mon Jul 07, 2008 9:34 am

DanG, thanks for the links. I don't have time to work through them carefully right now, but I will.

by **daj95376** » Tue Jul 08, 2008 10:46 pm

???

Code: Select all: +--------------------------------------------------------------+ | 2 7 6 | 148 3 148 | 9 18 5 | | 3 8 1 | 2 5 9 | 6 7 4 | | 9 5 4 | 1678 178 167 | 18 2 3 | |--------------------+--------------------+--------------------| | 5 6 27 | 3 4789 478 | 248 489 1 | | 48 9 38 | 16 2 16 | 348 5 7 | | 478 1 23 | 478 4789 5 | 23 489 6 | |--------------------+--------------------+--------------------| | 6 3 78 | 1478 1478 2 | 5 14 9 | | 178 4 9 | 5 6 78 | 17 3 2 | | 17 2 5 | 9 147 3 | 147 6 8 | +--------------------------------------------------------------+ Templates (A: 1) <> 7 [r3c5]

Code: Select all: +--------------------------------------------------------------+ | 9 137 2 | 4 8 6 | 5 137 137 | | 4 8 6 | 5 37 137 | 39 1379 2 | | 137 5 137 | 9 2 137 | 6 8 4 | |--------------------+--------------------+--------------------| | 5 6 8 | 2 13 9 | 7 4 13 | | 137 1379 4 | 36 136 5 | 2 139 8 | | 2 39 13 | 7 4 8 | 139 5 6 | |--------------------+--------------------+--------------------| | 6 137 9 | 8 5 37 | 4 2 137 | | 37 4 5 | 1 367 2 | 8 367 9 | | 8 2 137 | 36 9 4 | 13 1367 5 | +--------------------------------------------------------------+ Templates (A: 1) <> 3 [r2c8],[r5c5],[r9c38]

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