Help for Multi Sector Locked Sets
 

MSLS's

This technique took off with the following thread from David Bird: Sharks - a Truth Balancing Method. Look there for the logic. However, there are many examples here to illustrate the method.

Base 4: 4X4

The first 2 ("Cigarette", "Easter Monster") are vanilla 4x4 MSLSs. Others require "truth balancing" by having extra nodes or solved cells in grid or box links.

12.3.....34....1....5......6.24..5......6..7......8..6..42..3......7...9.....9.8. : Base 6789; c5689 r1247 : 16 links: 89c5, 67c6, 69c8, 78c9, 45r1, 25r2, 13r4, 15r7
1.......2.9.4...5...6...7...5.9.3.......7.......85..4.7.....6...3...9.8...2.....1 : Base 1267; c1379 r2468 : 16 links: 26c1, 17c3, 12c7, 67c9, 38r2, 48r4, 39r6, 45r8
98.7.....6..89......5..4...7...3.9....6...7....2....51.6..8.3.......1.4.........2 : Base 1245; c3689 r1247 : 16 links: 14c3, 25c6, 21c8, 45c9, 36r1, 37r2, 68r4, 79r7
.....6..94...8.2.....7...1.2.9...8....4.3.9...6.....5.3.8.4.......5......7...1... : Base 1567; c2468 r2457 : 16 links: 15c2, 16c4, 57c6, 67c8, 39r2, 34r4, 28r5, 29r7
98.7..6..7..6..85...4.5....8..9..7.......3..2.......3.1...97....9...61....81..... : Base 2345; r3569 c1247 +r9c5 r9c6 : 17 links: 23r3, 45r5, 245r6, 2345r9, 6c1, 167c2, 8c4, 9c7
98.76....75..4.8....3..8....7.8..4....9.7..3........2..6...75.....65...2...4....1 : Base 4568; r1247 c3689 +r8c6 r9c6 : 17 links: 45r1, 6r2, 56r4, 48r7, 12c3, 1239c6, 19c8, 39c9
...1....9.......85..9.5..6...5.3...6.7...2...1..4.......3.8..9..2...73..4........ : Base 1247; r5689 c3589: 16 Links; 14r5 27r6 14r8 127r9; 68c3 69c5 5c8 8c9; 3b6;
........9.....1.35..3.9..6...5.3...6.7...2...1..4.......9.8..5..2.7.....4.....8.. : Base 1247; r5689 c3589: 16 Links; 14r5 27r6 14r8 127r9; 68c3 56c5 9c8 3c9; 8b6;
1....5....6.2...4...3...7...4.69........8..6.......2.4..7...1...8.9...2.5.......3 : Base 1357; c1379 r2458 : 16 links: 37c1, 15c3, 35c7, 157c9, 89r2, 8r4, 9r5, 46r8, 2b4
..1...5...2.4...6.3....7....6.28........9..2.......4.65.....1...9.8...4...7.....3 : Base 1357; c1379 r2458 : 16 links: 17c1, 35c3, 37c7, 157c9, 89r2, 9r4, 8r5, 26r8, 4b4
1......8...7..92...6..3.........4..5..9...4.7...92.....3.6.......4..25..8...1.... : Base 1368; c1245 r2458 : 16 links: 36c1, 18c2, 138c4, 68c5, 45r2, 7r4, 5r5, 79r8, 2b4
1.......2..94...5..6....7.....89..4....3.6.....8.4.....2....1..7.......6..5.8..3. : Base 1267; r1378 c3458 : 15 links: 67r1, 12r3, 67r7, 12r8, 34c3, 59c4, 3c5, 89c8
1...56..9...7.........3.56...8...4...7.2.....6....3.1.3...9..5...2.......4....8.. : Base 2478; c2347 r1367 : 15 links: 28c2, 47c3, 48c4, 27c7, 3r1, 19r3, 59r6, 16r7
....5.7.....1.9.6.........52....8.16.......2..3....4.7.7..4......19.2...9.86..... : Base 3457; c2579 r2489 : 15 links: 45c2, 37c5, 35c7, 34c9, 28r2, 9r4, 68r8, 12r9

Base 4: 5X4

1......8......92....6.3...52....8.....5.7.....6.5....4..47...........91..3..6...7 : Base 1289; r1248 c23459 : 20 links: 29r1, 18r2, 19r4, 28r8, 457c2, 37c3, 346c4, 45c5, 36c9
..34..7...5...9.......3..6.........8..4.7..2.91...........6.2....23...4.8..2.5..1 : Base 1589; r2469 c34578 : 19 links: 18r2, 159r4, 58r6, 9r9, 67c3, 76c4, 24c5, 346c7, 37c8
98.7.....6...5.9....5....6.5...4..3..7...2..1..6...4....3.9..4....1....2.....8... : Base 1278; r1589 c13578 : 19 links: 12r1, 8r5, 78r8, 127r9, 34c1, 49c3, 36c5, 356c7, 59c8
..34..........9..6.9..7..1...4...8...7..6..2.5.....3......9...28..5.7....1...2.7. : Base 3458; r1468 c25689 : 19 links: 58r1, 35r4, 48r6, 34r8, 26c2, 12c5, 61c6, 69c8, 179c9
.2...6.....71....6....3..5...86......1...8..75...4......1..2..8....9..4.9..8..3.. : Base 3459; r3689 c23469 : 19 links: 49r3, 39r6, 35r8, 45r9, 678c2, 26c3, 27c4, 17c6, 12c9
1...5..8...7.....6.9.2.........13....7.9..4..8..5......4.6..9.......5.3...2...6.7 : Base 1358; r1468 c23479 : 19 links: 3r1, 58r4, 13r6, 18r8, 26c2, 469c3, 47c4, 27c7, 249c9
98.7..6....7....5.....4....8.........6...3.2...16..7..6..9..1...1...4..5....2...3 : Base 1789; r1467 c25689 + r2c2 r3c2 : 20 links: 1r1, 179r4, 89r6, 78r7, 2345c2, 35c5, 25c6, 34c8, 24c9

Base 4: 4x5

5.......9.2.1...7...8...3...4.6.........5.......2.7.1...3...8...6...4.2.9.......5 : Base 3589; r13579 c2468 : 20 links: 38r1, 59r3, 389r5, 59r7, 38r9, 17c2, 47c4, 126c6, 46c8
98.7.....6.....98...5.....7.4..3..6..3...2..1..96.......85..7......1...3.....4.2. : Base 1234; r34589 c1347 +r3c2 r3c8 : 20 links: 1234r3, 12r4, 4r5, 24r8, 13r9, 578c1, 7c3, 89c4, 568c7

Base 4: 4x3

98.76....7..5..9....4..9...6...9.3...2.....4...8......3....65.....35..94....7...1 : Base 1248; r3561 c457 : 12 links: 128r3, 18r5, 124r6, 5c1, 6c4, 3c5, 7c7
98.76....7..5..9....4..9...6...9.3...2.....4...8......3....65.....37..91....5...4 : Base 1248; r3561 c457 : 12 links: 128r3, 18r5, 124r6, 5c1, 6c4, 3c5, 7c7

Base 3: 3X3

98.76.5..7...5.8....4......8...7.9...3.2............1.5.......9.7..9..85...6..7.. : Base 589; r247 c348 + r1c3 r8c3 r8c4 r1c8 r9c8 : 14 links: 9r2, 5r4, 8r7, 1236c3, 134c4, 2346c8
98.7..6..7..9..5...4..83...5..6..9...2.....4...4.1..5..5.4.......7..64......97... : Base 679; r489 c248 + r2c2 r3c4 r5c4 r6c4 r1c8 r2c8 : 14 links: 7r4, 9r8, 6r9, 13c2, 12358c4, 1238c8
98.7..6..7..9..5...4..83...5..6..7...2.....4...4.1..5..5.4.......9..64......79... : Base 679; r489 c248 + r2c2 r3c4 r5c4 r6c4 r1c8 r2c8 : 14 links: 9r4, 7r8, 6r9, 13c2, 12358c4, 1238c8
98.7..6..7......98..5.....43...2.....7.9...6......1....9.8....6..1.3.7.......5.4. : Base 678; r257 c356 + r1c3 r1c5 r1c6 : 12 links: 6r2, 8r5, 7r7, 234c3, 145c5, 234c6
98.7..6..5...9......7..4...3......7...84..5.......5..8.7...2.1...98..4....59..8.. : Base 789; r347 c579 +r3c1 r3c2 r3c4 r4c3 r4c4 r7c3 r7c4 : 16 links: 12356r3, 1246r4, 3456r7, 8c5, 9c7, 9c9
98.7..6..7..5..4...3.....8.5...9...4...4....6....579..4..9..7....9.7...2.....1... : Base 457; r359 c357 +r1c3 r3c1 r3c4 r5c1 r5c6 r9c1 r9c4 : 16 links: 126r3, 1238r5, 2368r9, 457c3, 4c5, 5c7
98.7..6....7.5..9...4......37.8....9..2...83......1...2...9...7.9.6...8......7..6 : Base 689; r469 c358 +r1c3 r8c3 r1c5 r8c5 r1c8 r3c8 r7c8 : 15 links: 6r4, 6r6, 8r9, 135c3, 1234c5, 12457c8
98.7.......7.65.........7..74..8......96..8.........433....2.1...89..6..........2 : Base 789; r458 c689 +r1c6 r1c8 r3c8 r1c9 r3c9 : 14 links: 9r4, 7r5, 7r8, 134c6, 2356c8, 1456c9
98.7..6....7.5..9........7886.9....7..4.6.........3...72.6...8......12..........6 : Base 678; r369 c356 +r1c3 r4c3 r7c3 r1c5 r4c5 r7c5 r1c6 r4c6 r7c6 : 17 links: 6r3, 8r6, 8r9, 12359c3, 12349c5, 2459c6
98.76.5..7..8..9....6......8..5..7....4.7.........3.2.1......59.5.9...87..8...1.. : Base 579; r245 c368 +r1c3 r8c3 r1c6 r7c6 r8c6 r1c8 r9c8 : 15 links: 5r2, 9r4, 9r5, 123c3, 12468c6, 1346c8
98.7..6..7...5......4..9.3.4.......2.9...348...3.....63....794..4......7....1.... : Base 379; r458 c135 +r4c8 r3c1 r6c1 r9c1 r1c3 r2c3 r7c3 r3c5 r7c5 : 17 links: 79r4, 7r5, 9r8, 12568c1, 12568c3, 268c5

Base 2: 3x3

98.7.....6..5..4....3.6..8.3...9..6..9....5....24....1.3..8..2......9..8.....73.6 : Base 89; r457 c347 +r1c3 r2c3 r8c3 r8c4 r9c4 r3c7 r8c7 : 15 links: 8r4, 8r5, 9r7, 14567c3, 1236c4, 127c7
98.7..6..5.4.8........3....76.8...9.......8.6........727.9....8..5...........192. : Base 69; r578 c358 +r1c3 r4c3 r1c5 r4c5 r1c8 r2c8 r6c8 : 15 links: 9r5, 6r7, 6r8, 123c3, 1245c5, 13457c8