Analysis of zz-handy-001-base.sdk
Contents
Original Sudoku
level: medium
position: ....5..6.7.9..1....4....8...5...3.91.........21.7...3...5....7....2..4.3.8..6.... initial
Autosolve
position: ....5..6.7.9..1...54....8...5...3.91.........21.7...3...5....7....2..4.3.8..6.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 2,3 => CTR => B2: 6 * DIS # G1: 2,3 => CTR => G1: 1,7,9 * DIS # B7: 9 => CTR => B7: 2,3 * DIS # C3: 3,6 => CTR => C3: 1,2 * CNT 4 HDP CHAINS / 19 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 2,3 => CTR => B2: 6 * DIS B2: 6 # G1: 2,3 => CTR => G1: 1,7,9 * DIS B2: 6 + G1: 1,7,9 # B7: 9 => CTR => B7: 2,3 * DIS B2: 6 + G1: 1,7,9 + B7: 2,3 # C3: 3 => CTR => C3: 1,2 * DIS B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 # C9: 1,2 => CTR => C9: 3,4,7 * DIS B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 + C9: 3,4,7 # E2: 4,8 => CTR => E2: 2 * DIS B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 + C9: 3,4,7 + E2: 2 # H9: 5 => CTR => H9: 1,2 * PRF B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 + C9: 3,4,7 + E2: 2 + H9: 1,2 # G5: 5,6 => SOL * STA B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 + C9: 3,4,7 + E2: 2 + H9: 1,2 + G5: 5,6 * CNT 8 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....5..6.7.9..1....4....8...5...3.91.........21.7...3...5....7....2..4.3.8..6.... | initial |
| ....5..6.7.9..1...54....8...5...3.91.........21.7...3...5....7....2..4.3.8..6.... | autosolve |
| 138954762769821354542376819457683291893512647216749538925438176671295483384167925 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (3) B1: 2,3 H3: 1,2 G6: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G1,H3: 1.. / G1 = 1 => 18 pairs (_) / H3 = 1 => 6 pairs (_) D5,E5: 1.. / D5 = 1 => 0 pairs (X) / E5 = 1 => 3 pairs (_) C3,H3: 1.. / C3 = 1 => 18 pairs (_) / H3 = 1 => 6 pairs (_) B7,C9: 2.. / B7 = 2 => 9 pairs (_) / C9 = 2 => 0 pairs (X) E4,G4: 2.. / E4 = 2 => 4 pairs (_) / G4 = 2 => 7 pairs (_) G1,G2: 3.. / G1 = 3 => 0 pairs (X) / G2 = 3 => 4 pairs (_) H2,H5: 4.. / H2 = 4 => 5 pairs (_) / H5 = 4 => 5 pairs (_) F8,H8: 5.. / F8 = 5 => 4 pairs (_) / H8 = 5 => 0 pairs (X) D5,D9: 5.. / D5 = 5 => 3 pairs (_) / D9 = 5 => 0 pairs (X) B2,C3: 6.. / B2 = 6 => 4 pairs (_) / C3 = 6 => 0 pairs (X) G7,I7: 6.. / G7 = 6 => 8 pairs (_) / I7 = 6 => 5 pairs (_) B2,D2: 6.. / B2 = 6 => 4 pairs (_) / D2 = 6 => 0 pairs (X) C4,G4: 7.. / C4 = 7 => 6 pairs (_) / G4 = 7 => 5 pairs (_) C9,F9: 7.. / C9 = 7 => 0 pairs (X) / F9 = 7 => 4 pairs (_) B5,B8: 7.. / B5 = 7 => 7 pairs (_) / B8 = 7 => 5 pairs (_) E3,E8: 7.. / E3 = 7 => 4 pairs (_) / E8 = 7 => 0 pairs (X) A1,C1: 8.. / A1 = 8 => 5 pairs (_) / C1 = 8 => 5 pairs (_) D2,E2: 8.. / D2 = 8 => 5 pairs (_) / E2 = 8 => 7 pairs (_) I7,H8: 8.. / I7 = 8 => 0 pairs (X) / H8 = 8 => 5 pairs (_) H5,H8: 8.. / H5 = 8 => 0 pairs (X) / H8 = 8 => 5 pairs (_) A5,B5: 9.. / A5 = 9 => 4 pairs (_) / B5 = 9 => 6 pairs (_) E6,F6: 9.. / E6 = 9 => 3 pairs (_) / F6 = 9 => 5 pairs (_) * DURATION: 0:00:25.286557 START: 06:25:11.341799 END: 06:25:36.628356 2017-05-01 * CP COUNT: (22) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,G6,H3) * ....5..6.7.9..1...54....8...5...3.91.........21.7...3...5....7....2..4.3.8..6.... * PAIR B1: 2,3 BLK 1 C1: 2,3,1,8 # reduction candidate for 2,3 C1: 2,3 # 18 pairs B2: 2,3,6 # reduction candidate for 2,3 B2: 2,3 => CTR * ....5.9677.96813.55469..81..5...3.919.3......21.7...3..95....7....29.4.3.82.67.59 B2: 6 # 4 pairs C3: 2,3,1,6 # reduction candidate for 2,3 C3: 2,3 # 8 pairs * PAIR B1: 2,3 ROW 1 G1: 2,3,1,7,9 # reduction candidate for 2,3 G1: 2,3 => CTR * .3..5.26.769.213..542...81..5...3.91...512.4821.7..53..25....76...2.5483.8..6.... G1: 1,7,9 # 4 pairs * PAIR B1: 2,3 COL B B7: 2,3,9 # reduction candidate for 2,3 B7: 9 => CTR * .2..54.677698213..54..768...5.6.329193.51274.21.7.953.495138672671295483382467... B7: 2,3 # 6 pairs * PAIR H3: 1,2 BLK 3 G1: 1,2,3,7,9 # reduction candidate for 1,2 G1: 1,2 # 13 pairs G1: 3,7,9 # 6 pairs * PAIR H3: 1,2 ROW 3 C3: 1,2,3,6 # reduction candidate for 1,2 C3: 3,6 => CTR * ....5.9677.9..13.554..7.812.5...3.91...51..2.21.7..53...5.3.276...2.5483382467159 C3: 1,2 # 8 pairs * PAIR H3: 1,2 COL H H9: 1,2,5 # reduction candidate for 1,2 H9: 5 # 6 pairs H9: 1,2 # 6 pairs * PAIR G6: 5,6 BLK 6 G5: 5,6,2,7 # reduction candidate for 5,6 G5: 5,6 # 7 pairs I5: 5,6,2,4,7,8 # reduction candidate for 5,6 I5: 5,6 # 9 pairs I6: 5,6,4,8 # reduction candidate for 5,6 I6: 5,6 # 11 pairs * PAIR G6: 5,6 ROW 6 F6: 5,6,4,8,9 # reduction candidate for 5,6 F6: 5,6 # 6 pairs F6: 4,8,9 # 3 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-handy-001-base-pr-000.dot * REASONING * DIS # B2: 2,3 => CTR => B2: 6 * DIS # G1: 2,3 => CTR => G1: 1,7,9 * DIS # B7: 9 => CTR => B7: 2,3 * DIS # C3: 3,6 => CTR => C3: 1,2 * CNT 4 HDP CHAINS / 19 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,G6,H3) * ....5..6.7.9..1...54....8...5...3.91.........21.7...3...5....7....2..4.3.8..6.... * PAIR B1: 2,3 BLK 1 C1: 2,3,1,8 # reduction candidate for 2,3 C1: 2,3 # 18 pairs B2: 2,3,6 # reduction candidate for 2,3 B2: 2,3 => CTR * ....5.9677.96813.55469..81..5...3.919.3......21.7...3..95....7....29.4.3.82.67.59 C3: 2,3,1 # reduction candidate for 2,3 C3: 2,3 # 8 pairs * PAIR B1: 2,3 ROW 1 G1: 2,3,1,7,9 # reduction candidate for 2,3 G1: 2,3 => CTR * .3..5.26.769.213..542...81..5...3.91...512.4821.7..53..25....76...2.5483.8..6.... * PAIR B1: 2,3 COL B B7: 2,3,9 # reduction candidate for 2,3 B7: 9 => CTR * 12835..6.7698.13..54397681285.6.3.9193.512.4821.789.3.49513827667129548338246715. * PAIR RESTART * PAIR B1: 2,3 BLK 1 C1: 2,3,1,8 # reduction candidate for 2,3 C1: 2,3 # 18 pairs C3: 2,3,1 # reduction candidate for 2,3 C3: 2,3 # 12 pairs * PAIR H3: 1,2 ROW 3 C3: 1,2,3 # reduction candidate for 1,2 C3: 3 => CTR * ....5..6.769..13..543...81..5...3.9139.......21.7...3..35....7..7.2..4.3.82367.59 * PAIR H3: 1,2 COL H H9: 1,2,5 # reduction candidate for 1,2 H9: 1,2 # 13 pairs H9: 5 # 12 pairs * PAIR RESTART * PAIR H3: 1,2 COL H H9: 1,2,5 # reduction candidate for 1,2 H9: 1,2 # 13 pairs H9: 5 # 12 pairs * PAIR G6: 5,6 BLK 6 G5: 5,6,2,7 # reduction candidate for 5,6 G5: 5,6 # 15 pairs I5: 5,6,2,4,7,8 # reduction candidate for 5,6 I5: 5,6 # 16 pairs I6: 5,6,4,8 # reduction candidate for 5,6 I6: 5,6 # 18 pairs * PAIR G6: 5,6 ROW 6 F6: 5,6,4,8,9 # reduction candidate for 5,6 F6: 5,6 # 14 pairs F6: 4,8,9 # 10 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (B1,B5,B7,B8,C3,D1,D2,G6,H3,I3) * ....5..6.769..13..54....8...5...3.91.........21.7...3...5....7....2..4.3.8..6.... * PAIR B1: 2,3 BLK 1 C1: 2,3,1,8 # reduction candidate for 2,3 C1: 2,3 # 18 pairs C1: 1,8 # 11 pairs * PAIR C3: 1,2 BLK 1 C1: 1,2,3,8 # reduction candidate for 1,2 C1: 3,8 # 11 pairs C1: 1,2 # 11 pairs * PAIR C3: 1,2 COL C C9: 1,2,3,4,7 # reduction candidate for 1,2 C9: 1,2 => CTR * .3.95..6.7698.13..54.3768.9.5.6.3.91..351....21.7..53.425139678...2854133814679.. * PAIR RESTART * PAIR C3: 1,2 BLK 1 C1: 1,2,8 # reduction candidate for 1,2 C1: 8 # 12 pairs C1: 1,2 # 11 pairs * PAIR D1: 4,9 BLK 2 F1: 4,9,2,7 # reduction candidate for 4,9 F1: 4,9 # 17 pairs F1: 2,7 # 10 pairs * PAIR D1: 4,9 ROW 1 I1: 4,9,2,7 # reduction candidate for 4,9 I1: 2,7 # 17 pairs I1: 4,9 # 14 pairs * PAIR D1: 4,9 COL D D7: 4,9,1,3,8 # reduction candidate for 4,9 D7: 4,9 # 19 pairs D9: 4,9,1,3,5 # reduction candidate for 4,9 D9: 4,9 # 15 pairs * PAIR D2: 4,8 BLK 2 E2: 4,8,2 # reduction candidate for 4,8 E2: 4,8 => CTR * .389527647694813..5423768198576.3.91.9.51824721.7..538.2583..76.7.295483.8.1679.. * PAIR H3: 1,2 COL H H9: 1,2,5 # reduction candidate for 1,2 H9: 5 => CTR * .32.5.167769821345541376829.576.3291.9.51278.2187.9536.25.3.678.762..413.8..67.52 * PAIR RESTART * PAIR G6: 5,6 BLK 6 G5: 5,6,7 # reduction candidate for 5,6 G5: 5,6 => SOLVED * 138954762769821354542376819457683291893512647216749538925438176671295483384167925 * DURATION: 0:00:33.478204 START: 06:25:49.184918 END: 06:26:22.663122 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-handy-001-base-pr-001.dot * REASONING * DIS # B2: 2,3 => CTR => B2: 6 * DIS B2: 6 # G1: 2,3 => CTR => G1: 1,7,9 * DIS B2: 6 + G1: 1,7,9 # B7: 9 => CTR => B7: 2,3 * DIS B2: 6 + G1: 1,7,9 + B7: 2,3 # C3: 3 => CTR => C3: 1,2 * DIS B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 # C9: 1,2 => CTR => C9: 3,4,7 * DIS B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 + C9: 3,4,7 # E2: 4,8 => CTR => E2: 2 * DIS B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 + C9: 3,4,7 + E2: 2 # H9: 5 => CTR => H9: 1,2 * PRF B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 + C9: 3,4,7 + E2: 2 + H9: 1,2 # G5: 5,6 => SOL * STA B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 + C9: 3,4,7 + E2: 2 + H9: 1,2 + G5: 5,6 * CNT 8 HDP CHAINS / 36 HYP OPENED
Header Info
|:info:| zz-handy-001-step-0 strictly solvable by pair-reduction, 2 iterations * PAIR REDUCTION .. * ROUND 1: ....5..6.7.9..1...54....8...5...3.91.........21.7...3...5....7....2..4.3.8..6.... B1: 2,3 C1: 1,2,3,8 # reduction candidate for 2,3 B2: 2,3,6 # reduction candidate for 2,3 B2: 2,3 => CTR * ....5.9677.96813.55469..81..5...3.919.3......21.7...3..95....7....29.4.3.82.67.59 C3: 1,2,3 # reduction candidate for 2,3 G1: 1,2,3,7,9 # reduction candidate for 2,3 G1: 2,3 => CTR * .3..5.26.769.213..542...81..5...3.91...512.4821.7..53..25....76...2.5483.8..6.... B7: 2,3,9 # reduction candidate for 2,3 B7: 9 => CTR * 12835..6.7698.13..54397681285.6.3.9193.512.4821.789.3.49513827667129548338246715. H3: 1,2 C3: 1,2,3 # reduction candidate for 1,2 C3: 3 => CTR * ....5..6.769..13..543...81..5...3.9139.......21.7...3..35....7..7.2..4.3.82367.59 H9: 1,2,5 # reduction candidate for 1,2 G6: 5,6 G5: 2,5,6,7 # reduction candidate for 5,6 I5: 2,4,5,6,7,8 # reduction candidate for 5,6 I6: 4,5,6,8 # reduction candidate for 5,6 F6: 4,5,6,8,9 # reduction candidate for 5,6 * ROUND 2: ....5..6.769..13..54....8...5...3.91.........21.7...3...5....7....2..4.3.8..6.... B1: 2,3 C1: 1,2,3,8 # reduction candidate for 2,3 C3: 1,2 C1: 1,2,3,8 # reduction candidate for 1,2 C9: 1,2,3,4,7 # reduction candidate for 1,2 C9: 1,2 => CTR * .3.95..6.7698.13..54.3768.9.5.6.3.91..351....21.7..53.425139678...2854133814679.. D1: 4,9 F1: 2,4,7,9 # reduction candidate for 4,9 I1: 2,4,7,9 # reduction candidate for 4,9 D7: 1,3,4,8,9 # reduction candidate for 4,9 D9: 1,3,4,5,9 # reduction candidate for 4,9 D2: 4,8 E2: 2,4,8 # reduction candidate for 4,8 E2: 4,8 => CTR * .389527647694813..5423768198576.3.91.9.51824721.7..538.2583..76.7.295483.8.1679.. H3: 1,2 H9: 1,2,5 # reduction candidate for 1,2 H9: 5 => CTR * .32.5.167769821345541376829.576.3291.9.51278.2187.9536.25.3.678.762..413.8..67.52 G6: 5,6 G5: 5,6,7 # reduction candidate for 5,6 G5: 5,6 => SOLVED * 138954762769821354542376819457683291893512647216749538925438176671295483384167925 * SOLVED! * PAIRS (3) B1: 2,3 H3: 1,2 G6: 5,6 * AUTO .. A3 = 5 # set value Q1: 8.. = A1,C1: 8.. => D1,F1 != 8 Q4: 9.. = A5,B5: 9.. => D5,E5,F5 != 9 Q9: 6.. = G7,I7: 6.. => A7,B7 != 6 pair quad strategy 2,3 1,2 4,8 4,8 4,9 1,9 |:step:| 00 -------------------------------------------------- B1: 2,3 B2: 2,3,6 * DISABLE VALUE:: B2 != 6 * AUTO .. E3 = 3,7 => CTR => B2 = 6 |:step:| 01 -------------------------------------------------- B1: 2,3 G1: 1,2,3,7,9 * DISABLE VALUE:: G1 != 1 * DISABLE VALUE:: G1 != 7 * DISABLE VALUE:: G1 != 9 * AUTO .. I6 = 0 => CTR => G1 = 1,7,9 |:step:| 02 -------------------------------------------------- C3 != 1,2 => C3 = 3 => CTR => C3 != 3 E2 !=2 => CTR => E2 = 2 * DISABLE:: A5 != 3 * DISABLE:: A5 != 6 * DISABLE:: A5 != 9 AUTO .. * SOLVED! |:step:| 03 -------------------------------------------------- ??? |:check:| D2: 4,8 E2: 2,4,8 * DISABLE VALUE:: E2 != 2 => D2,E4: 4,8 * DISABLE VALUE:: D1 != 4 * DISABLE VALUE:: F1 != 4 * DISABLE VALUE:: H2 != 4 * DISABLE VALUE:: I2 != 4 H2: 2,5 I2: 2,5 * DISABLE VALUE:: I3 != 2 * DISABLE VALUE:: H3 != 2 H3: 1 # naked single * DISABLE VALUE:: I1 != 2 * AUTO .. H3 = 1 # set value I1: 4.. # hidden single H5: 4.. # hidden single I1 = 4 # set value H5 = 4 # set value H8: 8.. # hidden single H8 = 8 # set value F8: 5.. # hidden single F8 = 5 # set value D5: 5.. # hidden single D5 = 5 # set value E5: 1.. # hidden single E5 = 1 # set value Q8,Q9: 1.. => A7,A9,C9 != 1 H2: 2,5 I2: 2,5 H9: 2,5 I9: 2,5,9 * FORCE VALUE:: I9 = 9 I9 = 9 # set value I3: 7 # naked single G1: 9.. # hidden single * AUTO .. G1 = 9 # set value D1: 3 # naked single I3 = 7 # set value F1: 7.. # hidden single E8: 7.. # hidden single D1 = 3 # set value B1: 2 # naked single F1 = 7 # set value F9: 4 # naked single E8 = 7 # set value B8: 9 # naked single F9 = 4 # set value D9: 1 # naked single A9: 3 # naked single C3: 3.. # hidden single A7: 4.. # hidden single C9: 7.. # hidden single E7: 3.. # hidden single B5: 7.. # hidden single B1 = 2 # set value C3: 3 # naked single C3 = 3 # set value B5 = 7 # set value A7 = 4 # set value E7 = 3 # set value B7: 9 # naked single B8 = 9 # set value B7 = 0 => CTR => E2 != 4,8 * DISABLE VALUE:: E2 != 4 * DISABLE VALUE:: E2 != 8 => E2 = 2 E2: 2 # naked single * AUTO .. E2 = 2 # set value D2: 8.. # hidden single F5: 2.. # hidden single G4: 2.. # hidden single D2 = 8 # set value G4 = 2 # set value F5 = 2 # set value C4: 7.. # hidden single C4 = 7 # set value B8: 7.. # hidden single F9: 7.. # hidden single B8 = 7 # set value F9 = 7 # set value E3: 7.. # hidden single E3 = 7 # set value E7: 3.. # hidden single E7 = 3 # set value Q2: 4.. = D1,F1: 4.. => I1 != 4 D4: 6 # naked single Q2,Q8: 4.. => D4,D5,F6 != 4 D4 = 6 # set value F3: 6.. # hidden single F3 = 6 # set value |:step:| 03 -------------------------------------------------- I3: 2,9 I1: 2,7,9 * DISABLE VALUE:: I1 != 7 * DISABLE VALUE:: I9 != 2 * DISABLE VALUE:: I9 != 9 I9: 5 # naked single * DISABLE VALUE:: I7 != 9 * DISABLE VALUE:: I7 != 2 * DISABLE VALUE:: G1 != 9 * AUTO .. * SOLVED! I9 = 5 # set value I2: 4 # naked single H2: 5.. # hidden single G1: 7.. # hidden single F8: 5.. # hidden single H9: 2.. # hidden single B7: 2.. # hidden single D5: 5.. # hidden single I5: 7.. # hidden single G1 = 7 # set value H2 = 5 # set value I2 = 4 # set value D5 = 5 # set value G5: 6 # naked single G5 = 6 # set value G6: 5 # naked single I6: 8 # naked single I5 = 7 # set value G6 = 5 # set value I6 = 8 # set value H5: 4 # naked single I7: 6 # naked single F6: 9 # naked single B7 = 2 # set value B1: 3 # naked single I7 = 6 # set value F8 = 5 # set value H9 = 2 # set value H3: 1 # naked single C6: 6.. # hidden single E5: 1.. # hidden single H8: 8.. # hidden single F7: 8.. # hidden single A8: 6.. # hidden single B5: 9.. # hidden single B1 = 3 # set value B5: 9 # naked single H3 = 1 # set value H8: 8 # naked single C3: 2 # naked single B5 = 9 # set value E5 = 1 # set value H5 = 4 # set value C6 = 6 # set value C8: 1 # naked single F6 = 9 # set value E6: 4 # naked single F1: 4 # naked single F7 = 8 # set value E8: 9 # naked single A8 = 6 # set value C8 = 1 # set value E8 = 9 # set value H8 = 8 # set value A1: 1.. # hidden single D3: 3.. # hidden single A4: 4.. # hidden single E4: 8.. # hidden single C9: 4.. # hidden single A1 = 1 # set value F1 = 4 # set value D1: 9 # naked single C3 = 2 # set value C1: 8 # naked single I3: 9 # naked single D3 = 3 # set value I3 = 9 # set value I1: 2 # naked single A4 = 4 # set value A7: 9 # naked single E4: 8 # naked single E4 = 8 # set value E6 = 4 # set value A7 = 9 # set value A9: 3 # naked single G7: 1 # naked single G7 = 1 # set value G9: 9 # naked single D7: 4 # naked single A9 = 3 # set value C9: 4 # naked single A5: 8 # naked single C9 = 4 # set value D9: 1 # naked single D9 = 1 # set value G9 = 9 # set value C5: 3.. # hidden single C1 = 8 # set value C5: 3 # naked single D1 = 9 # set value I1 = 2 # set value A5 = 8 # set value C5 = 3 # set value D7 = 4 # set value |:step:| 04 -------------------------------------------------- alternate solution G6: 5,6 G5: 5,6,7 * DISABLE VALUE:: G5 != 7 => G5,G6: 5,6 * DISABLE VALUE:: H5 != 5 * DISABLE VALUE:: I5 != 5 * DISABLE VALUE:: I5 != 6 * DISABLE VALUE:: I6 != 5 * DISABLE VALUE:: I6 != 6 * DISABLE VALUE:: G7 != 6 * DISABLE VALUE:: G9 != 5 * NEW PAIR G7: 1,9 G9: 1,9 * DISABLE VALUE:: G1 != 1 * DISABLE VALUE:: G1 != 9 G1: 7 # naked single * AUTO .. * SOLVED! G1 = 7 # set value H3: 1.. # hidden single I5: 7.. # hidden single I7: 6.. # hidden single H3 = 1 # set value I5 = 7 # set value I7 = 6 # set value H8: 8.. # hidden single B7: 2.. # hidden single F7: 8.. # hidden single H9: 2.. # hidden single I6: 8.. # hidden single I6 = 8 # set value H5: 4 # naked single B7 = 2 # set value B1: 3 # naked single F7 = 8 # set value H8 = 8 # set value H9 = 2 # set value I9: 5.. # hidden single F8: 5.. # hidden single B5: 9.. # hidden single F1: 4.. # hidden single H2: 5.. # hidden single I2: 4.. # hidden single B1 = 3 # set value C3: 2 # naked single B5: 9 # naked single F1 = 4 # set value D1: 9 # naked single H2 = 5 # set value I2: 4 # naked single I2 = 4 # set value C3 = 2 # set value I3: 9 # naked single I3 = 9 # set value I1: 2 # naked single I9: 5 # naked single D3: 3 # naked single B5 = 9 # set value H5 = 4 # set value F8 = 5 # set value F6: 9 # naked single I9 = 5 # set value D5: 5.. # hidden single G6: 5.. # hidden single D1 = 9 # set value I1 = 2 # set value D3 = 3 # set value D5 = 5 # set value G5: 6 # naked single G5 = 6 # set value G6: 5 # naked single F6 = 9 # set value E6: 4 # naked single G6 = 5 # set value C6: 6.. # hidden single E5: 1.. # hidden single E8: 9.. # hidden single A8: 6.. # hidden single E5 = 1 # set value E8: 9 # naked single C6 = 6 # set value C8: 1 # naked single E6 = 4 # set value E4: 8 # naked single A8 = 6 # set value C8 = 1 # set value C1: 8 # naked single E8 = 9 # set value A1: 1.. # hidden single A4: 4.. # hidden single C9: 4.. # hidden single A1 = 1 # set value C1 = 8 # set value C5: 3 # naked single A4 = 4 # set value A7: 9 # naked single E4 = 8 # set value C5 = 3 # set value A5: 8 # naked single C9: 4 # naked single A7 = 9 # set value A9: 3 # naked single G7: 1 # naked single G7 = 1 # set value G9: 9 # naked single D7: 4 # naked single A9 = 3 # set value C9 = 4 # set value D9: 1 # naked single D9 = 1 # set value G9 = 9 # set value A5 = 8 # set value D7 = 4 # set value |:step:| 10 -------------------------------------------------- |:info:| old .. Q9: 6.. = G7,I7: 6.. => A7,B7 != 6 Q1: 8.. = A1,C1: 8.. => D1,F1 != 8 Q4: 9.. = A5,B5: 9.. => D5,E5,F5 != 9 F8 != 5 => CTR => F8 = 5 B2 != 6 => CTR => B2 = 6 C3 = 1 => CTR => C3 != 1 F5 != 2 => CTR => F5 = 2 G2 != 3 => CTR => G2 = 3 C3 = 3 => CTR => C3 != 3 D1 != 9 => CTR => D1 = 9 I9,H9: 2,5 => ... ? C4 != 7 => A4,C4,C6 = 4,6,8 + A4,C4,D4 = 4,6,8 => Q4\A4,C4,C6 != 4,6,8 + E4,G4 != 4,6,8 => E4 = 2 ? B5 != 3 =>
Solution
position: 138954762769821354542376819457683291893512647216749538925438176671295483384167925 solved
See section Pair Reduction for the HDP chains leading to this result.
Appendix: Full HDP Chains
A1. Pair Reduction Analysis
Full list of HDP chains traversed:
* INC # C1: 2,3 => UNS * DIS # B2: 2,3 => CTR => B2: 6 * INC # B2: 6 => UNS * INC # C3: 2,3 => UNS * DIS # G1: 2,3 => CTR => G1: 1,7,9 * INC # G1: 1,7,9 => UNS * INC # B7: 2,3 => UNS * DIS # B7: 9 => CTR => B7: 2,3 * INC # G1: 1,2 => UNS * INC # G1: 3,7,9 => UNS * INC # C3: 1,2 => UNS * DIS # C3: 3,6 => CTR => C3: 1,2 * INC # H9: 1,2 => UNS * INC # H9: 5 => UNS * INC # G5: 5,6 => UNS * INC # I5: 5,6 => UNS * INC # I6: 5,6 => UNS * INC # F6: 5,6 => UNS * INC # F6: 4,8,9 => UNS * CNT 19 HDP CHAINS / 19 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 2,3 => UNS * DIS # B2: 2,3 => CTR => B2: 6 * INC B2: 6 # C3: 2,3 => UNS * DIS B2: 6 # G1: 2,3 => CTR => G1: 1,7,9 * INC B2: 6 + G1: 1,7,9 # B7: 2,3 => UNS * DIS B2: 6 + G1: 1,7,9 # B7: 9 => CTR => B7: 2,3 * INC B2: 6 + G1: 1,7,9 + B7: 2,3 # C1: 2,3 => UNS * INC B2: 6 + G1: 1,7,9 + B7: 2,3 # C3: 2,3 => UNS * INC B2: 6 + G1: 1,7,9 + B7: 2,3 # C3: 1,2 => UNS * DIS B2: 6 + G1: 1,7,9 + B7: 2,3 # C3: 3 => CTR => C3: 1,2 * INC B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 # H9: 1,2 => UNS * INC B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 # H9: 5 => UNS * INC B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 # H9: 1,2 => UNS * INC B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 # H9: 5 => UNS * INC B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 # G5: 5,6 => UNS * INC B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 # I5: 5,6 => UNS * INC B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 # I6: 5,6 => UNS * INC B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 # F6: 5,6 => UNS * INC B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 # F6: 4,8,9 => UNS * INC B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 # C1: 2,3 => UNS * INC B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 # C1: 1,8 => UNS * INC B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 # C1: 1,2 => UNS * INC B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 # C1: 3,8 => UNS * DIS B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 # C9: 1,2 => CTR => C9: 3,4,7 * INC B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 + C9: 3,4,7 # C1: 1,2 => UNS * INC B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 + C9: 3,4,7 # C1: 8 => UNS * INC B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 + C9: 3,4,7 # F1: 4,9 => UNS * INC B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 + C9: 3,4,7 # F1: 2,7 => UNS * INC B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 + C9: 3,4,7 # I1: 4,9 => UNS * INC B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 + C9: 3,4,7 # I1: 2,7 => UNS * INC B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 + C9: 3,4,7 # D7: 4,9 => UNS * INC B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 + C9: 3,4,7 # D9: 4,9 => UNS * DIS B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 + C9: 3,4,7 # E2: 4,8 => CTR => E2: 2 * INC B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 + C9: 3,4,7 + E2: 2 # H9: 1,2 => UNS * DIS B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 + C9: 3,4,7 + E2: 2 # H9: 5 => CTR => H9: 1,2 * PRF B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 + C9: 3,4,7 + E2: 2 + H9: 1,2 # G5: 5,6 => SOL * STA B2: 6 + G1: 1,7,9 + B7: 2,3 + C3: 1,2 + C9: 3,4,7 + E2: 2 + H9: 1,2 + G5: 5,6 * CNT 36 HDP CHAINS / 36 HYP OPENED