Analysis of zz-sudoku-de-702316-base.sdk
Contents
Original Sudoku
level: medium
position: ..4....8.63.....54..97..63.4...36.9.....7.....2.98...5.41..25..78.....46.6....9.. initial
Autosolve
position: .746.3.8963.1..754..97..63.4...36.97.96.7.....2798..65941.6257.78.....46.6...79.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 1,5 => CTR => A3: 2,8 * DIS # A3: 1,5 => CTR => A3: 2,8 * DIS # E3: 2,5 => CTR => E3: 4 * PRF # E3: 4 => SOL * DIS # A1: 2,5 => CTR => A1: 1 * PRF # A1: 1 => SOL * DIS # A1: 5 => CTR => A1: 1,2 * DIS # G4: 1,2 => CTR => G4: 8 * PRF # G4: 8 => SOL * DIS # G5: 1,2 => CTR => G5: 3,4,8 * PRF # G8: 1,2 => SOL * DIS # G8: 3 => CTR => G8: 1,2 * PRF # A3: 1,2 => SOL * PRF # I5: 1,2 => SOL * DIS # I5: 3 => CTR => I5: 1,2 * DIS # I9: 1,2 => CTR => I9: 3,8 * PRF # I9: 3,8 => SOL * DIS # A5: 1,5 => CTR => A5: 3,8 * DIS # A5: 1,3 => CTR => A5: 5,8 * DIS # A5: 1,3 => CTR => A5: 5,8 * DIS # G6: 1,3 => CTR => G6: 4 * PRF # D5: 2,5 => SOL * DIS # D5: 4 => CTR => D5: 2,5 * PRF # F5: 1,4 => SOL * DIS # F5: 5 => CTR => F5: 1,4 * DIS # G6: 3 => CTR => G6: 1,4 * DIS # G4: 1,2 => CTR => G4: 8 * PRF # G4: 8 => SOL * DIS # G5: 1,2 => CTR => G5: 3,4,8 * PRF # I5: 1,2 => SOL * DIS # I5: 3 => CTR => I5: 1,2 * DIS # C9: 2,5 => CTR => C9: 3 * DIS # A1: 2,5 => CTR => A1: 1 * PRF # A1: 1 => SOL * PRF # A3: 2,5 => SOL * DIS # D9: 3,8 => CTR => D9: 4,5 * PRF # D9: 4,5 => SOL * DIS # D9: 3,5 => CTR => D9: 4,8 * DIS # C8: 3,5 => CTR => C8: 2 * PRF # C8: 2 => SOL * PRF # E8: 5,9 => SOL * DIS # E8: 1 => CTR => E8: 5,9 * PRF # I9: 3,8 => SOL * DIS # I9: 1,2 => CTR => I9: 3,8 * PRF # G8: 1,2 => SOL * DIS # G8: 3 => CTR => G8: 1,2 * DIS # I9: 1,2 => CTR => I9: 3,8 * PRF # I9: 3,8 => SOL * CNT 48 HDP CHAINS / 64 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 1,5 => CTR => A3: 2,8 * DIS A3: 2,8 # E3: 2,5 => CTR => E3: 4 * PRF A3: 2,8 + E3: 4 => SOL * STA A3: 2,8 + E3: 4 * CNT 3 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..4....8.63.....54..97..63.4...36.9.....7.....2.98...5.41..25..78.....46.6....9.. | initial |
| .746.3.8963.1..754..97..63.4...36.97.96.7.....2798..65941.6257.78.....46.6...79.. | autosolve |
| 174653289638129754259748631415236897896574312327981465941862573782395146563417928 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) C2: 2,8 B3: 1,5 E1: 2,5 E2: 2,9 F2: 8,9 G1: 1,2 I3: 1,2 B4: 1,5 C4: 5,8 A6: 1,3 D4: 2,5 F6: 1,4 H5: 1,2 A9: 2,5 D7: 3,8 D8: 3,5 F8: 5,9 I7: 3,8 H9: 1,2 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G1,I3: 1.. / G1 = 1 => 0 pairs (X) / I3 = 1 => 0 pairs (_) F5,F6: 1.. / F5 = 1 => 0 pairs (X) / F6 = 1 => 18 pairs (_) E8,E9: 1.. / E8 = 1 => 0 pairs (X) / E9 = 1 => 0 pairs (_) A1,G1: 1.. / A1 = 1 => 0 pairs (*) / G1 = 1 => 0 pairs (X) B4,G4: 1.. / B4 = 1 => 23 pairs (_) / G4 = 1 => 0 pairs (X) E8,G8: 1.. / E8 = 1 => 0 pairs (X) / G8 = 1 => 0 pairs (_) B3,B4: 1.. / B3 = 1 => 0 pairs (X) / B4 = 1 => 23 pairs (_) H5,H9: 1.. / H5 = 1 => 0 pairs (*) / H9 = 1 => 0 pairs (X) G1,I3: 2.. / G1 = 2 => 0 pairs (*) / I3 = 2 => 0 pairs (X) D4,D5: 2.. / D4 = 2 => 20 pairs (_) / D5 = 2 => 0 pairs (X) C2,E2: 2.. / C2 = 2 => 0 pairs (X) / E2 = 2 => 0 pairs (_) D4,G4: 2.. / D4 = 2 => 20 pairs (_) / G4 = 2 => 0 pairs (X) C8,G8: 2.. / C8 = 2 => 0 pairs (*) / G8 = 2 => 0 pairs (X) H5,H9: 2.. / H5 = 2 => 0 pairs (X) / H9 = 2 => 0 pairs (_) A5,A6: 3.. / A5 = 3 => 0 pairs (X) / A6 = 3 => 19 pairs (_) C8,C9: 3.. / C8 = 3 => 0 pairs (X) / C9 = 3 => 20 pairs (_) A6,G6: 3.. / A6 = 3 => 19 pairs (_) / G6 = 3 => 0 pairs (X) D7,I7: 3.. / D7 = 3 => 0 pairs (X) / I7 = 3 => 0 pairs (_) E3,F3: 4.. / E3 = 4 => 0 pairs (*) / F3 = 4 => 0 pairs (X) G5,G6: 4.. / G5 = 4 => 0 pairs (X) / G6 = 4 => 18 pairs (_) D9,E9: 4.. / D9 = 4 => 0 pairs (*) / E9 = 4 => 0 pairs (X) F6,G6: 4.. / F6 = 4 => 0 pairs (X) / G6 = 4 => 18 pairs (_) D5,D9: 4.. / D5 = 4 => 0 pairs (X) / D9 = 4 => 0 pairs (_) E3,E9: 4.. / E3 = 4 => 0 pairs (*) / E9 = 4 => 0 pairs (X) A1,E1: 5.. / A1 = 5 => 0 pairs (X) / E1 = 5 => 23 pairs (_) B3,B4: 5.. / B3 = 5 => 23 pairs (_) / B4 = 5 => 0 pairs (X) C2,A3: 8.. / C2 = 8 => 0 pairs (*) / A3 = 8 => 0 pairs (X) F2,F3: 8.. / F2 = 8 => 0 pairs (X) / F3 = 8 => 0 pairs (_) C4,A5: 8.. / C4 = 8 => 0 pairs (X) / A5 = 8 => 0 pairs (_) G4,G5: 8.. / G4 = 8 => 0 pairs (*) / G5 = 8 => 0 pairs (X) D7,D9: 8.. / D7 = 8 => 0 pairs (*) / D9 = 8 => 0 pairs (X) I7,I9: 8.. / I7 = 8 => 0 pairs (X) / I9 = 8 => 0 pairs (_) C2,F2: 8.. / C2 = 8 => 0 pairs (*) / F2 = 8 => 0 pairs (X) A3,F3: 8.. / A3 = 8 => 0 pairs (X) / F3 = 8 => 0 pairs (_) C4,G4: 8.. / C4 = 8 => 0 pairs (X) / G4 = 8 => 0 pairs (_) A5,G5: 8.. / A5 = 8 => 0 pairs (*) / G5 = 8 => 0 pairs (X) D7,I7: 8.. / D7 = 8 => 0 pairs (*) / I7 = 8 => 0 pairs (X) D9,I9: 8.. / D9 = 8 => 0 pairs (X) / I9 = 8 => 0 pairs (_) A3,A5: 8.. / A3 = 8 => 0 pairs (X) / A5 = 8 => 0 pairs (_) C2,C4: 8.. / C2 = 8 => 0 pairs (*) / C4 = 8 => 0 pairs (X) E2,F2: 9.. / E2 = 9 => 0 pairs (X) / F2 = 9 => 0 pairs (_) E8,F8: 9.. / E8 = 9 => 0 pairs (*) / F8 = 9 => 0 pairs (X) E2,E8: 9.. / E2 = 9 => 0 pairs (X) / E8 = 9 => 0 pairs (_) F2,F8: 9.. / F2 = 9 => 0 pairs (*) / F8 = 9 => 0 pairs (X) * DURATION: 0:01:13.423098 START: 07:57:17.128012 END: 07:58:30.551110 2017-05-01 * CP COUNT: (44) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A9,B3,B4,C2,C4,D4,D7,D8,E1,E2,F2,F6,F8,G1,H5,H9,I3,I7) * .746.3.8963.1..754..97..63.4...36.97.96.7.....2798..65941.6257.78.....46.6...79.. * PAIR C2: 2,8 BLK 1 A3: 2,8,1,5 # reduction candidate for 2,8 A3: 1,5 => CTR * .746.3.89638129754..97.86324.5236897896.7....32798..65941.6257.78..95146.6...79.. A3: 2,8 # 21 pairs * PAIR B3: 1,5 BLK 1 A1: 1,5,2 # reduction candidate for 1,5 A1: 1,5 # 21 pairs A3: 1,5,2,8 # reduction candidate for 1,5 A3: 1,5 => CTR * .746.3.89638129754..97.86324.5236897896.7....32798..65941.6257.78..95146.6...79.. A3: 2,8 # 21 pairs * PAIR E1: 2,5 BLK 2 E3: 2,5,4 # reduction candidate for 2,5 E3: 2,5 => CTR * .746.3.8963.1.87548.97.463.4.823619719647582332798146594136257878.519346.6..479.. E3: 4 => SOLVED * 174653289638129754259748631415236897896574312327981465941862573782395146563417928 * PAIR E1: 2,5 ROW 1 A1: 2,5,1 # reduction candidate for 2,5 A1: 2,5 => CTR * .746.318963.198754..97..63241..36.97.96.7....327981465941.6257.78..19.46.6...79.. A1: 1 => SOLVED * 174653289638129754259748631415236897896574312327981465941862573782395146563417928 * PAIR G1: 1,2 ROW 1 A1: 1,2,5 # reduction candidate for 1,2 A1: 5 => CTR * 5746231896321987548197..63.4...36.97.96.7.....2798..65941.6257.78.....46.6...79.. A1: 1,2 # 23 pairs * PAIR G1: 1,2 COL G G4: 1,2,8 # reduction candidate for 1,2 G4: 1,2 => CTR * .746.3.8963.1..754..97..63.4.8.36.97.96.7.8...2798.465941.6257.78....346.63..79.. G4: 8 => SOLVED * 174653289638129754259748631415236897896574312327981465941862573782395146563417928 G5: 1,2,3,4,8 # reduction candidate for 1,2 G5: 1,2 => CTR * .746.3.8963.1..754..97..63.4...36897896.7...332798.46594136257878.5.9346.638479.. G5: 3,4,8 # 19 pairs G8: 1,2,3 # reduction candidate for 1,2 G8: 1,2 => SOLVED * 174653289638129754259748631415236897896574312327981465941862573782395146563417928 G8: 3 => CTR * .746.3.8963.1..754..97..63.4...36.97.96.7.....2798..65941.6257.782.19346563.479.. * PAIR I3: 1,2 ROW 3 A3: 1,2,5,8 # reduction candidate for 1,2 A3: 1,2 => SOLVED * 174653289638129754259748631415236897896574312327981465941862573782395146563417928 A3: 5,8 # 20 pairs * PAIR I3: 1,2 COL I I5: 1,2,3 # reduction candidate for 1,2 I5: 1,2 => SOLVED * 174653289638129754259748631415236897896574312327981465941862573782395146563417928 I5: 3 => CTR * .746.3.8963.1987548.97.463.4...36.97.96.7...332798..6594136257878.5.9346.638479.. I9: 1,2,3,8 # reduction candidate for 1,2 I9: 1,2 => CTR * .746.3.8963.1..754..97.463.4...36.97.9647...33279814659413625787825193465638479.. I9: 3,8 => SOLVED * 174653289638129754259748631415236897896574312327981465941862573782395146563417928 * PAIR B4: 1,5 BLK 4 A5: 1,5,3,8 # reduction candidate for 1,5 A5: 1,5 => CTR * .746.3.8963.1..7548.97..63.4.8.36.97.96.7.8.332798.46594136257878.5.9346.6...79.. A5: 3,8 # 21 pairs * PAIR C4: 5,8 BLK 4 A5: 5,8,1,3 # reduction candidate for 5,8 A5: 1,3 => CTR * .746.3.8963.1..7548.97..63.4.8.36.97.96.7.8...2798.465941.6257.78....346.63..79.. A5: 5,8 # 23 pairs * PAIR A6: 1,3 BLK 4 A5: 1,3,5,8 # reduction candidate for 1,3 A5: 1,3 => CTR * .746.3.8963.1..7548.97..63.4.8.36.97.96.7.8...2798.465941.6257.78....346.63..79.. A5: 5,8 # 23 pairs * PAIR A6: 1,3 ROW 6 G6: 1,3,4 # reduction candidate for 1,3 G6: 1,3 => CTR * .746.3.8963.1..754..974.63.4...36897896.71423.27984.65941.6257.78.....46.6.4.79.8 G6: 4 # 18 pairs * PAIR D4: 2,5 BLK 5 D5: 2,5,4 # reduction candidate for 2,5 D5: 2,5 => SOLVED * 174653289638129754259748631415236897896574312327981465941862573782395146563417928 D5: 4 => CTR * .746.3.8963.1987548.97.463.4.823619719647582332798146594136257878.519346.6..479.. * PAIR F6: 1,4 BLK 5 F5: 1,4,5 # reduction candidate for 1,4 F5: 1,4 => SOLVED * 174653289638129754259748631415236897896574312327981465941862573782395146563417928 F5: 5 => CTR * .746.3.8963.1987548.97.463.4.823619719647582332798146594136257878.519346.6...79.. * PAIR F6: 1,4 ROW 6 G6: 1,4,3 # reduction candidate for 1,4 G6: 3 => CTR * .746.3.8963.1..754..97..63.4...36.97.96.7.4...27984365941.6257.78.....46.6.4.79.8 G6: 1,4 # 19 pairs * PAIR H5: 1,2 BLK 6 G4: 1,2,8 # reduction candidate for 1,2 G4: 1,2 => CTR * .746.3.8963.1..754..97..63.4.8.36.97.96.7.8...2798.465941.6257.78....346.63..79.. G4: 8 => SOLVED * 174653289638129754259748631415236897896574312327981465941862573782395146563417928 G5: 1,2,3,4,8 # reduction candidate for 1,2 G5: 1,2 => CTR * .746.3.8963.1..754..97..63.4...36897896.7...332798.46594136257878.5.9346.638479.. G5: 3,4,8 # 19 pairs I5: 1,2,3 # reduction candidate for 1,2 I5: 1,2 => SOLVED * 174653289638129754259748631415236897896574312327981465941862573782395146563417928 I5: 3 => CTR * .746.3.8963.1987548.97.463.4...36.97.96.7...332798..6594136257878.5.9346.638479.. * PAIR A9: 2,5 BLK 7 C8: 2,5,3 # reduction candidate for 2,5 C8: 2,5 # 20 pairs C9: 2,5,3 # reduction candidate for 2,5 C9: 2,5 => CTR * .746.318963.1987548197..632458.36.97.96.7.....2798..65941.6257.7835.9246.6...791. C9: 3 # 20 pairs * PAIR A9: 2,5 COL A A1: 2,5,1 # reduction candidate for 2,5 A1: 2,5 => CTR * .746.318963.198754..97..63241..36.97.96.7....327981465941.6257.78..19.46.6...79.. A1: 1 => SOLVED * 174653289638129754259748631415236897896574312327981465941862573782395146563417928 A3: 2,5,1,8 # reduction candidate for 2,5 A3: 2,5 => SOLVED * 174653289638129754259748631415236897896574312327981465941862573782395146563417928 A3: 1,8 # 20 pairs * PAIR D7: 3,8 BLK 8 D9: 3,8,4,5 # reduction candidate for 3,8 D9: 3,8 => CTR * .746.3.8963.1987548.97.463.4.823619719647582332798146594136257878.519346.6..479.. D9: 4,5 => SOLVED * 174653289638129754259748631415236897896574312327981465941862573782395146563417928 * PAIR D8: 3,5 BLK 8 D9: 3,5,4,8 # reduction candidate for 3,5 D9: 3,5 => CTR * .746.318963.198754819754632458236.97.964753..32798146594186257378..19246.6..47918 D9: 4,8 # 20 pairs * PAIR D8: 3,5 ROW 8 C8: 3,5,2 # reduction candidate for 3,5 C8: 3,5 => CTR * .746.31896381..754..97..63241.236897896.7..21327981465941.6257.78..19246.6...791. C8: 2 => SOLVED * 174653289638129754259748631415236897896574312327981465941862573782395146563417928 * PAIR F8: 5,9 BLK 8 E8: 5,9,1 # reduction candidate for 5,9 E8: 5,9 => SOLVED * 174653289638129754259748631415236897896574312327981465941862573782395146563417928 E8: 1 => CTR * .746.3.8963.1987548.97..63.4.8.36.97.96.7.8...2798.465941.6257.78..19346.63..79.. * PAIR I7: 3,8 BLK 9 I9: 3,8,1,2 # reduction candidate for 3,8 I9: 3,8 => SOLVED * 174653289638129754259748631415236897896574312327981465941862573782395146563417928 I9: 1,2 => CTR * .746.3.8963.1..754..97.463.4...36.97.9647...33279814659413625787825193465638479.. * PAIR H9: 1,2 BLK 9 G8: 1,2,3 # reduction candidate for 1,2 G8: 1,2 => SOLVED * 174653289638129754259748631415236897896574312327981465941862573782395146563417928 G8: 3 => CTR * .746.3.8963.1..754..97..63.4...36.97.96.7.....2798..65941.6257.782.19346563.479.. I9: 1,2,3,8 # reduction candidate for 1,2 I9: 1,2 => CTR * .746.3.8963.1..754..97.463.4...36.97.9647...33279814659413625787825193465638479.. I9: 3,8 => SOLVED * 174653289638129754259748631415236897896574312327981465941862573782395146563417928 * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-702316-base-pr-000.dot * REASONING * DIS # A3: 1,5 => CTR => A3: 2,8 * DIS # A3: 1,5 => CTR => A3: 2,8 * DIS # E3: 2,5 => CTR => E3: 4 * PRF # E3: 4 => SOL * DIS # A1: 2,5 => CTR => A1: 1 * PRF # A1: 1 => SOL * DIS # A1: 5 => CTR => A1: 1,2 * DIS # G4: 1,2 => CTR => G4: 8 * PRF # G4: 8 => SOL * DIS # G5: 1,2 => CTR => G5: 3,4,8 * PRF # G8: 1,2 => SOL * DIS # G8: 3 => CTR => G8: 1,2 * PRF # A3: 1,2 => SOL * PRF # I5: 1,2 => SOL * DIS # I5: 3 => CTR => I5: 1,2 * DIS # I9: 1,2 => CTR => I9: 3,8 * PRF # I9: 3,8 => SOL * DIS # A5: 1,5 => CTR => A5: 3,8 * DIS # A5: 1,3 => CTR => A5: 5,8 * DIS # A5: 1,3 => CTR => A5: 5,8 * DIS # G6: 1,3 => CTR => G6: 4 * PRF # D5: 2,5 => SOL * DIS # D5: 4 => CTR => D5: 2,5 * PRF # F5: 1,4 => SOL * DIS # F5: 5 => CTR => F5: 1,4 * DIS # G6: 3 => CTR => G6: 1,4 * DIS # G4: 1,2 => CTR => G4: 8 * PRF # G4: 8 => SOL * DIS # G5: 1,2 => CTR => G5: 3,4,8 * PRF # I5: 1,2 => SOL * DIS # I5: 3 => CTR => I5: 1,2 * DIS # C9: 2,5 => CTR => C9: 3 * DIS # A1: 2,5 => CTR => A1: 1 * PRF # A1: 1 => SOL * PRF # A3: 2,5 => SOL * DIS # D9: 3,8 => CTR => D9: 4,5 * PRF # D9: 4,5 => SOL * DIS # D9: 3,5 => CTR => D9: 4,8 * DIS # C8: 3,5 => CTR => C8: 2 * PRF # C8: 2 => SOL * PRF # E8: 5,9 => SOL * DIS # E8: 1 => CTR => E8: 5,9 * PRF # I9: 3,8 => SOL * DIS # I9: 1,2 => CTR => I9: 3,8 * PRF # G8: 1,2 => SOL * DIS # G8: 3 => CTR => G8: 1,2 * DIS # I9: 1,2 => CTR => I9: 3,8 * PRF # I9: 3,8 => SOL * CNT 48 HDP CHAINS / 64 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A9,B3,B4,C2,C4,D4,D7,D8,E1,E2,F2,F6,F8,G1,H5,H9,I3,I7) * .746.3.8963.1..754..97..63.4...36.97.96.7.....2798..65941.6257.78.....46.6...79.. * PAIR C2: 2,8 BLK 1 A3: 2,8,1,5 # reduction candidate for 2,8 A3: 1,5 => CTR * .746.3.89638129754..97.86324.5236897896.7....32798..65941.6257.78..95146.6...79.. * PAIR E1: 2,5 BLK 2 E3: 2,5,4 # reduction candidate for 2,5 E3: 2,5 => CTR * .746.3.8963.1.87548.97.463.4.823619719647582332798146594136257878.51934626..479.. E3: 4 => SOLVED * 174653289638129754259748631415236897896574312327981465941862573782395146563417928 * DURATION: 0:00:05.895447 START: 07:59:36.582639 END: 07:59:42.478086 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-702316-base-pr-001.dot * REASONING * DIS # A3: 1,5 => CTR => A3: 2,8 * DIS A3: 2,8 # E3: 2,5 => CTR => E3: 4 * PRF A3: 2,8 + E3: 4 => SOL * STA A3: 2,8 + E3: 4 * CNT 3 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokus.de/702316.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: .746.3.8963.1..754..97..63.4...36.97.96.7.....2798..65941.6257.78.....46.6...79.. C2: 2,8 A3: 1,2,5,8 # reduction candidate for 2,8 A3: 1,5 => CTR * .746.3.89638129754..97.86324.5236897896.7....32798..65941.6257.78..95146.6...79.. B3: 1,5 E1: 2,5 E3: 2,4,5 # reduction candidate for 2,5 E3: 2,5 => CTR * .746.3.8963.1.87548.97.463.4.823619719647582332798146594136257878.51934626..479.. E3: 4 => SOLVED * 174653289638129754259748631415236897896574312327981465941862573782395146563417928 * SOLVED! -------------------------------------------------- -------------------------------------------------- * AUTO .. Q1,Q3: 1.. => E1,E3,F3 != 1 Q4: 3.. = A5,A6: 3.. => A9 != 3 Q5: 2.. = D4,D5: 2.. => D2 != 2 Q8: 8.. = D7,D9: 8.. => D2 != 8 Q9: 8.. = I7,I9: 8.. => I5 != 8 Q5: 1.. = F5,F6: 1.. => F8 != 1 * UNSOLVED! |:step:| 00 -------------------------------------------------- swordfish |:guess:| highlight 1 I3 != 1 => A1,G1,G4,B4,B3,A3: 1.. => A5,A6,G5,G6,G8 != 1 # swordfish * DISABLE VALUE:: I3 != 1 I3: 2 # naked single * DISABLE VALUE:: A5 != 1 * DISABLE VALUE:: A6 != 1 A6: 3 # naked single * DISABLE VALUE:: G5 != 1 * DISABLE VALUE:: G6 != 1 * DISABLE VALUE:: G8 != 1 * AUTO .. I3 = 2 # set value G1: 1 # naked single A6 = 3 # set value G6: 4 # naked single G6 = 4 # set value F6: 1 # naked single B4: 1.. # hidden single E8: 1.. # hidden single G1 = 1 # set value B4 = 1 # set value B3: 5 # naked single F6 = 1 # set value E8 = 1 # set value A3: 1.. # hidden single F8: 9.. # hidden single E2: 9.. # hidden single E2 = 9 # set value F2: 8 # naked single F2 = 8 # set value C2: 2 # naked single A3 = 1 # set value B3 = 5 # set value A1: 2 # naked single E3: 4 # naked single F3: 4 # naked single E3 = 4 # set value F3 = 0 => CTR * CTR! => I3 = 1 * FORCE VALUE:: I3 = 1 I3 = 1 # set value G1: 2 # naked single B3: 5 # naked single A1: 1.. # hidden single B4: 1.. # hidden single |:step:| 01 -------------------------------------------------- * AUTO .. A1 = 1 # set value A6: 3 # naked single G1 = 2 # set value E1: 5 # naked single B3 = 5 # set value B4: 1 # naked single B4 = 1 # set value G4: 8 # naked single G4 = 8 # set value C4: 5 # naked single A6 = 3 # set value A5: 8.. # hidden single D4: 2.. # hidden single C8: 2.. # hidden single C2: 8.. # hidden single E1 = 5 # set value C2 = 8 # set value A3: 2 # naked single F2: 9 # naked single F2 = 9 # set value E2: 2 # naked single F8: 5 # naked single A3 = 2 # set value A9: 5 # naked single E3: 4 # naked single E3 = 4 # set value F3: 8 # naked single E9: 1 # naked single F3 = 8 # set value C4 = 5 # set value A5: 8 # naked single D4: 2 # naked single D4 = 2 # set value A5 = 8 # set value C8 = 2 # set value C9: 3 # naked single F8 = 5 # set value D8: 3 # naked single A9 = 5 # set value C9 = 3 # set value E9 = 1 # set value E8: 9 # naked single H9: 2 # naked single H9 = 2 # set value I9: 8 # naked single H5: 1 # naked single I9 = 8 # set value I7: 3 # naked single D9: 4 # naked single D5: 5.. # hidden single I5: 2.. # hidden single D7: 8.. # hidden single G8: 1.. # hidden single E2 = 2 # set value D5 = 5 # set value H5 = 1 # set value G6: 4 # naked single F5: 4 # naked single I5 = 2 # set value G6 = 4 # set value G5: 3 # naked single F6: 1 # naked single D7 = 8 # set value I7 = 3 # set value G8: 1 # naked single D8 = 3 # set value E8 = 9 # set value G8 = 1 # set value D9 = 4 # set value F5 = 4 # set value G5 = 3 # set value F6 = 1 # set value * SOLVED! |:step:| 02 --------------------------------------------------
Solution
position: 174653289638129754259748631415236897896574312327981465941862573782395146563417928 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 # A3: 2,8 => UNS * DIS # A3: 1,5 => CTR => A3: 2,8 * INC # A1: 1,5 => UNS * DIS # A3: 1,5 => CTR => A3: 2,8 * INC # A3: 2,8 => UNS * DIS # E3: 2,5 => CTR => E3: 4 * PRF # E3: 4 => SOL * DIS # A1: 2,5 => CTR => A1: 1 * PRF # A1: 1 => SOL * INC # A1: 1,2 => UNS * DIS # A1: 5 => CTR => A1: 1,2 * DIS # G4: 1,2 => CTR => G4: 8 * PRF # G4: 8 => SOL * DIS # G5: 1,2 => CTR => G5: 3,4,8 * INC # G5: 3,4,8 => UNS * PRF # G8: 1,2 => SOL * DIS # G8: 3 => CTR => G8: 1,2 * PRF # A3: 1,2 => SOL * INC # A3: 5,8 => UNS * PRF # I5: 1,2 => SOL * DIS # I5: 3 => CTR => I5: 1,2 * DIS # I9: 1,2 => CTR => I9: 3,8 * PRF # I9: 3,8 => SOL * DIS # A5: 1,5 => CTR => A5: 3,8 * INC # A5: 3,8 => UNS * INC # A5: 5,8 => UNS * DIS # A5: 1,3 => CTR => A5: 5,8 * DIS # A5: 1,3 => CTR => A5: 5,8 * INC # A5: 5,8 => UNS * DIS # G6: 1,3 => CTR => G6: 4 * INC # G6: 4 => UNS * PRF # D5: 2,5 => SOL * DIS # D5: 4 => CTR => D5: 2,5 * PRF # F5: 1,4 => SOL * DIS # F5: 5 => CTR => F5: 1,4 * INC # G6: 1,4 => UNS * DIS # G6: 3 => CTR => G6: 1,4 * DIS # G4: 1,2 => CTR => G4: 8 * PRF # G4: 8 => SOL * DIS # G5: 1,2 => CTR => G5: 3,4,8 * INC # G5: 3,4,8 => UNS * PRF # I5: 1,2 => SOL * DIS # I5: 3 => CTR => I5: 1,2 * INC # C8: 2,5 => UNS * DIS # C9: 2,5 => CTR => C9: 3 * INC # C9: 3 => UNS * DIS # A1: 2,5 => CTR => A1: 1 * PRF # A1: 1 => SOL * PRF # A3: 2,5 => SOL * INC # A3: 1,8 => UNS * DIS # D9: 3,8 => CTR => D9: 4,5 * PRF # D9: 4,5 => SOL * DIS # D9: 3,5 => CTR => D9: 4,8 * INC # D9: 4,8 => UNS * DIS # C8: 3,5 => CTR => C8: 2 * PRF # C8: 2 => SOL * PRF # E8: 5,9 => SOL * DIS # E8: 1 => CTR => E8: 5,9 * PRF # I9: 3,8 => SOL * DIS # I9: 1,2 => CTR => I9: 3,8 * PRF # G8: 1,2 => SOL * DIS # G8: 3 => CTR => G8: 1,2 * DIS # I9: 1,2 => CTR => I9: 3,8 * PRF # I9: 3,8 => SOL * CNT 64 HDP CHAINS / 64 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 2,8 => UNS * DIS # A3: 1,5 => CTR => A3: 2,8 * DIS A3: 2,8 # E3: 2,5 => CTR => E3: 4 * PRF A3: 2,8 + E3: 4 => SOL * STA A3: 2,8 + E3: 4 * CNT 4 HDP CHAINS / 3 HYP OPENED