Analysis of zz-ksudoku-000-base.sdk
Contents
Original Sudoku
level: medium
position: ...2..5..2.9....81.57...9...8...4.....1.2.3.....8...927..56.2.45..9........14.... initial
Autosolve
position: ...2.95..2.9.5..81.57...92..82.941.59.1.253.8..58...9279.56.2145149.2....2.14..59 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D2: 6,7 => CTR => D2: 3,4 * PRF # G2: 6,7 => SOL * PRF # F6: 6,7 => SOL * DIS # I1: 3,6 => CTR => I1: 7 * DIS # A3: 3,6 => CTR => A3: 1,4,8 * PRF # D3: 3,6 => SOL * DIS # I8: 7 => CTR => I8: 3,6 * DIS # A1: 3,6 => CTR => A1: 1,4,8 * DIS # A3: 3,6 => CTR => A3: 1,4,8 * PRF # F6: 6,7 => SOL * PRF # H5: 6,7 => SOL * DIS # D2: 6,7 => CTR => D2: 3,4 * PRF # H5: 6,7 => SOL * PRF # D4: 3 => SOL * DIS # H8: 6,7 => CTR => H8: 3 * DIS # C9: 3,8 => CTR => C9: 6 * DIS # C1: 6 => CTR => C1: 3,8 * DIS # F9: 7 => CTR => F9: 3,8 * DIS # G8: 6 => CTR => G8: 7,8 * DIS # G8: 6 => CTR => G8: 7,8 * CNT 20 HDP CHAINS / 57 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D2: 6,7 => CTR => D2: 3,4 * PRF D2: 3,4 # G2: 6,7 => SOL * STA D2: 3,4 + G2: 6,7 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...2..5..2.9....81.57...9...8...4.....1.2.3.....8...927..56.2.45..9........14.... | initial |
| ...2.95..2.9.5..81.57...92..82.941.59.1.253.8..58...9279.56.2145149.2....2.14..59 | autosolve |
| 168239547239457681457681923682394175941725368375816492793568214514972836826143759 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) F2: 6,7 I3: 3,6 A4: 3,6 D5: 6,7 H4: 6,7 C7: 3,8 F7: 3,8 E8: 7,8 G9: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A3: 1.. / A1 = 1 => 9 pairs (_) / A3 = 1 => 14 pairs (_) E6,F6: 1.. / E6 = 1 => 0 pairs (*) / F6 = 1 => 0 pairs (X) A1,E1: 1.. / A1 = 1 => 9 pairs (_) / E1 = 1 => 14 pairs (_) F3,F6: 1.. / F3 = 1 => 0 pairs (*) / F6 = 1 => 0 pairs (X) D4,E6: 3.. / D4 = 3 => 0 pairs (*) / E6 = 3 => 0 pairs (X) F7,F9: 3.. / F7 = 3 => 17 pairs (_) / F9 = 3 => 14 pairs (_) H8,I8: 3.. / H8 = 3 => 10 pairs (_) / I8 = 3 => 0 pairs (X) B2,D2: 3.. / B2 = 3 => 12 pairs (_) / D2 = 3 => 16 pairs (_) A4,D4: 3.. / A4 = 3 => 16 pairs (_) / D4 = 3 => 0 pairs (*) C7,F7: 3.. / C7 = 3 => 14 pairs (_) / F7 = 3 => 17 pairs (_) H1,H8: 3.. / H1 = 3 => 0 pairs (X) / H8 = 3 => 10 pairs (_) D2,D3: 4.. / D2 = 4 => 0 pairs (*) / D3 = 4 => 0 pairs (X) H1,G2: 4.. / H1 = 4 => 0 pairs (*) / G2 = 4 => 0 pairs (X) H5,G6: 4.. / H5 = 4 => 12 pairs (_) / G6 = 4 => 0 pairs (*) A3,D3: 4.. / A3 = 4 => 0 pairs (*) / D3 = 4 => 0 pairs (X) B5,H5: 4.. / B5 = 4 => 0 pairs (*) / H5 = 4 => 0 pairs (X) G2,G6: 4.. / G2 = 4 => 12 pairs (_) / G6 = 4 => 0 pairs (*) H1,H5: 4.. / H1 = 4 => 0 pairs (*) / H5 = 4 => 0 pairs (X) A9,C9: 6.. / A9 = 6 => 0 pairs (X) / C9 = 6 => 11 pairs (_) C1,C9: 6.. / C1 = 6 => 0 pairs (X) / C9 = 6 => 11 pairs (_) B5,B6: 7.. / B5 = 7 => 13 pairs (_) / B6 = 7 => 16 pairs (_) E8,F9: 7.. / E8 = 7 => 14 pairs (_) / F9 = 7 => 0 pairs (X) D4,H4: 7.. / D4 = 7 => 17 pairs (_) / H4 = 7 => 12 pairs (_) F9,G9: 7.. / F9 = 7 => 0 pairs (X) / G9 = 7 => 14 pairs (_) I1,I8: 7.. / I1 = 7 => 11 pairs (_) / I8 = 7 => 0 pairs (X) G8,G9: 8.. / G8 = 8 => 14 pairs (_) / G9 = 8 => 0 pairs (X) C7,F7: 8.. / C7 = 8 => 17 pairs (_) / F7 = 8 => 14 pairs (_) E8,G8: 8.. / E8 = 8 => 0 pairs (X) / G8 = 8 => 14 pairs (_) * DURATION: 0:00:44.690138 START: 06:29:02.480286 END: 06:29:47.170424 2017-05-01 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,C7,D5,E8,F2,F7,G9,H4,I3) * ...2.95..2.9.5..81.57...92..82.941.59.1.253.8..58...9279.56.2145149.2....2.14..59 * PAIR F2: 6,7 BLK 2 D2: 6,7,3,4 # reduction candidate for 6,7 D2: 6,7 => CTR * 468219537239.5.48115743892668239417597162534834587169279356.2145149.2....2.14..59 D2: 3,4 # 12 pairs * PAIR F2: 6,7 ROW 2 G2: 6,7,4 # reduction candidate for 6,7 G2: 6,7 => SOLVED * 168239547239457681457681923682394175941725368375816492793568214514972836826143759 G2: 4 # 12 pairs * PAIR F2: 6,7 COL F F6: 6,7,1 # reduction candidate for 6,7 F6: 6,7 => SOLVED * 168239547239457681457681923682394175941725368375816492793568214514972836826143759 F6: 1 # 12 pairs * PAIR I3: 3,6 BLK 3 H1: 3,6,4,7 # reduction candidate for 3,6 H1: 3,6 # 14 pairs I1: 3,6,7 # reduction candidate for 3,6 I1: 3,6 => CTR * 8..21957.2.9756481157438926.823941659.1.253.8..58.1.92798563214514982637.2.147859 I1: 7 # 11 pairs * PAIR I3: 3,6 ROW 3 A3: 3,6,1,4,8 # reduction candidate for 3,6 A3: 3,6 => CTR * 1.82395.7239.5.481657481923382.941.59.1.253484.581.692793568214514972836826143759 A3: 1,4,8 # 9 pairs D3: 3,6,4 # reduction candidate for 3,6 D3: 3,6 => SOLVED * 168239547239457681457681923682394175941725368375816492793568214514972836826143759 D3: 4 # 9 pairs * PAIR I3: 3,6 COL I I8: 3,6,7 # reduction candidate for 3,6 I8: 7 => CTR * 8..21957.2.9756481157438926.823941659.1.253.8..58.1.92798563214514982637.2.147859 I8: 3,6 # 11 pairs * PAIR A4: 3,6 BLK 4 A6: 3,6,4 # reduction candidate for 3,6 A6: 3,6 # 19 pairs B6: 3,6,4,7 # reduction candidate for 3,6 B6: 3,6 # 14 pairs * PAIR A4: 3,6 ROW 4 D4: 3,6,7 # reduction candidate for 3,6 D4: 7 # 17 pairs D4: 3,6 # 12 pairs * PAIR A4: 3,6 COL A A1: 3,6,1,4,8 # reduction candidate for 3,6 A1: 3,6 => CTR * .482195672.9.574811574.6923.82.941.59.1.253484.5831692793568214514972836826143759 A1: 1,4,8 # 9 pairs A3: 3,6,1,4,8 # reduction candidate for 3,6 A3: 3,6 => CTR * 1.82395.7239.5.481657481923382.941.59.1.253484.581.692793568214514972836826143759 A3: 1,4,8 # 9 pairs A9: 3,6,8 # reduction candidate for 3,6 A9: 3,6 # 17 pairs * PAIR D5: 6,7 BLK 5 D4: 6,7,3 # reduction candidate for 6,7 D4: 6,7 # 16 pairs F6: 6,7,1 # reduction candidate for 6,7 F6: 6,7 => SOLVED * 168239547239457681457681923682394175941725368375816492793568214514972836826143759 F6: 1 # 12 pairs * PAIR D5: 6,7 ROW 5 B5: 6,7,4 # reduction candidate for 6,7 B5: 6,7 # 12 pairs H5: 6,7,4 # reduction candidate for 6,7 H5: 6,7 => SOLVED * 168239547239457681457681923682394175941725368375816492793568214514972836826143759 H5: 4 # 12 pairs * PAIR D5: 6,7 COL D D2: 6,7,3,4 # reduction candidate for 6,7 D2: 6,7 => CTR * 468219537239.5.48115743892668239417597162534834587169279356.2145149.2....2.14..59 D2: 3,4 # 12 pairs * PAIR H4: 6,7 BLK 6 H5: 6,7,4 # reduction candidate for 6,7 H5: 6,7 => SOLVED * 168239547239457681457681923682394175941725368375816492793568214514972836826143759 H5: 4 # 12 pairs G6: 6,7,4 # reduction candidate for 6,7 G6: 6,7 # 12 pairs * PAIR H4: 6,7 ROW 4 D4: 6,7,3 # reduction candidate for 6,7 D4: 3 => SOLVED * 168239547239457681457681923682394175941725368375816492793568214514972836826143759 D4: 6,7 # 16 pairs * PAIR H4: 6,7 COL H H1: 6,7,3,4 # reduction candidate for 6,7 H1: 6,7 # 14 pairs H8: 6,7,3 # reduction candidate for 6,7 H8: 6,7 => CTR * 468219537239.5648115743892668239417597162534834587169279356.2145149.2.63.2.14..59 H8: 3 # 10 pairs * PAIR C7: 3,8 BLK 7 A9: 3,8,6 # reduction candidate for 3,8 A9: 3,8 # 11 pairs C9: 3,8,6 # reduction candidate for 3,8 C9: 3,8 => CTR * ..62.95..2.9.5.481.574..92.382.941.59.1.253.84.5831.9279.56.2145149.2...62.14..59 C9: 6 # 11 pairs * PAIR C7: 3,8 COL C C1: 3,8,6 # reduction candidate for 3,8 C1: 6 => CTR * ..62.95..2.9.5.481.574..92.382.941.59.1.253.84.5831.9279.56.2145149.2...62.14..59 C1: 3,8 # 11 pairs * PAIR F7: 3,8 BLK 8 F9: 3,8,7 # reduction candidate for 3,8 F9: 7 => CTR * 8..2195..2.9756481157438926.823941759716253484358.1.92798563214514982....2.147859 F9: 3,8 # 14 pairs * PAIR E8: 7,8 BLK 8 F9: 7,8,3 # reduction candidate for 7,8 F9: 7,8 # 17 pairs F9: 3 # 14 pairs * PAIR E8: 7,8 ROW 8 G8: 7,8,6 # reduction candidate for 7,8 G8: 6 => CTR * 8..2195..2.9756481157438926.823941759.1.253.8..58.1.927985632145149826...2.147859 G8: 7,8 # 14 pairs * PAIR E8: 7,8 COL E E1: 7,8,1,3 # reduction candidate for 7,8 E1: 7,8 # 12 pairs E1: 1,3 # 11 pairs * PAIR G9: 7,8 BLK 9 G8: 7,8,6 # reduction candidate for 7,8 G8: 6 => CTR * 8..2195..2.9756481157438926.823941759.1.253.8..58.1.927985632145149826...2.147859 G8: 7,8 # 14 pairs * PAIR G9: 7,8 ROW 9 F9: 7,8,3 # reduction candidate for 7,8 F9: 7,8 # 17 pairs F9: 3 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-ksudoku-000-base-pr-000.dot * REASONING * DIS # D2: 6,7 => CTR => D2: 3,4 * PRF # G2: 6,7 => SOL * PRF # F6: 6,7 => SOL * DIS # I1: 3,6 => CTR => I1: 7 * DIS # A3: 3,6 => CTR => A3: 1,4,8 * PRF # D3: 3,6 => SOL * DIS # I8: 7 => CTR => I8: 3,6 * DIS # A1: 3,6 => CTR => A1: 1,4,8 * DIS # A3: 3,6 => CTR => A3: 1,4,8 * PRF # F6: 6,7 => SOL * PRF # H5: 6,7 => SOL * DIS # D2: 6,7 => CTR => D2: 3,4 * PRF # H5: 6,7 => SOL * PRF # D4: 3 => SOL * DIS # H8: 6,7 => CTR => H8: 3 * DIS # C9: 3,8 => CTR => C9: 6 * DIS # C1: 6 => CTR => C1: 3,8 * DIS # F9: 7 => CTR => F9: 3,8 * DIS # G8: 6 => CTR => G8: 7,8 * DIS # G8: 6 => CTR => G8: 7,8 * CNT 20 HDP CHAINS / 57 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,C7,D5,E8,F2,F7,G9,H4,I3) * ...2.95..2.9.5..81.57...92..82.941.59.1.253.8..58...9279.56.2145149.2....2.14..59 * PAIR F2: 6,7 BLK 2 D2: 6,7,3,4 # reduction candidate for 6,7 D2: 6,7 => CTR * 468219537239.5.48115743892668239417597162534834587169279356.2145149.2....2.14..59 * PAIR F2: 6,7 ROW 2 G2: 6,7,4 # reduction candidate for 6,7 G2: 6,7 => SOLVED * 168239547239457681457681923682394175941725368375816492793568214514972836826143759 * DURATION: 0:00:04.173129 START: 06:30:39.596928 END: 06:30:43.770057 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-ksudoku-000-base-pr-001.dot * REASONING * DIS # D2: 6,7 => CTR => D2: 3,4 * PRF D2: 3,4 # G2: 6,7 => SOL * STA D2: 3,4 + G2: 6,7 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
level: medium * PAIR REDUCTION .. * ROUND 1: ...2.95..2.9.5..81.57...92..82.941.59.1.253.8..58...9279.56.2145149.2....2.14..59 F2: 6,7 D2: 3,4,6,7 # reduction candidate for 6,7 D2: 6,7 => CTR * 468219537239.5.48115743892668239417597162534834587169279356.2145149.2....2.14..59 G2: 4,6,7 # reduction candidate for 6,7 G2: 6,7 => SOLVED * 168239547239457681457681923682394175941725368375816492793568214514972836826143759 * SOLVED! -------------------------------------------------- good |:guess:| -------------------------------------------------- highlight 6,7 D4 := !3 => ... D4,D5,H4: 7,6 + H5: 7,6,4 = > H5 = 4 => CTR => D4 = 3 * AUTO .. * SOLVED! |:step:| 00 -------------------------------------------------- swordfish |:guess:| (highlight 3): * DISABLE VALUE:: E6 != 3 A6,A4,D4,D2,B2,B6: 3 => A1,A3,A9,B1,D3 != 3 # swordfish * AUTO .. * SOLVED! |:step:| 00 -------------------------------------------------- xwing |:guess:| (highlight 3): * DISABLE VALUE:: C1 != 3 C7,F7,F9,C9: 3 => A9 != 9 # xwing C1 = 3 => CTR => A9,C1 != 3 * DISABLE VALUE:: A9 != 3 C7,F7,F9,C9: 3 => C1 != 9 # xwing A9 = 3 => CTR => A9,C1 != 3 |:step:| 00 -------------------------------------------------- swordfish |:guess:| (highlight 4): * DISABLE VALUE:: A1 != 4 D2,G2,G6,A6,A3,D3 => B2,B6 != 4 # swordfish A1 = 4 => CTR => A1 != 4 => B2,B6 != 4
Solution
position: 168239547239457681457681923682394175941725368375816492793568214514972836826143759 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:
* DIS # D2: 6,7 => CTR => D2: 3,4 * INC # D2: 3,4 => UNS * PRF # G2: 6,7 => SOL * INC # G2: 4 => UNS * PRF # F6: 6,7 => SOL * INC # F6: 1 => UNS * INC # H1: 3,6 => UNS * DIS # I1: 3,6 => CTR => I1: 7 * INC # I1: 7 => UNS * DIS # A3: 3,6 => CTR => A3: 1,4,8 * INC # A3: 1,4,8 => UNS * PRF # D3: 3,6 => SOL * INC # D3: 4 => UNS * INC # I8: 3,6 => UNS * DIS # I8: 7 => CTR => I8: 3,6 * INC # A6: 3,6 => UNS * INC # B6: 3,6 => UNS * INC # D4: 3,6 => UNS * INC # D4: 7 => UNS * DIS # A1: 3,6 => CTR => A1: 1,4,8 * INC # A1: 1,4,8 => UNS * DIS # A3: 3,6 => CTR => A3: 1,4,8 * INC # A3: 1,4,8 => UNS * INC # A9: 3,6 => UNS * INC # D4: 6,7 => UNS * PRF # F6: 6,7 => SOL * INC # F6: 1 => UNS * INC # B5: 6,7 => UNS * PRF # H5: 6,7 => SOL * INC # H5: 4 => UNS * DIS # D2: 6,7 => CTR => D2: 3,4 * INC # D2: 3,4 => UNS * PRF # H5: 6,7 => SOL * INC # H5: 4 => UNS * INC # G6: 6,7 => UNS * INC # D4: 6,7 => UNS * PRF # D4: 3 => SOL * INC # H1: 6,7 => UNS * DIS # H8: 6,7 => CTR => H8: 3 * INC # H8: 3 => UNS * INC # A9: 3,8 => UNS * DIS # C9: 3,8 => CTR => C9: 6 * INC # C9: 6 => UNS * INC # C1: 3,8 => UNS * DIS # C1: 6 => CTR => C1: 3,8 * INC # F9: 3,8 => UNS * DIS # F9: 7 => CTR => F9: 3,8 * INC # F9: 7,8 => UNS * INC # F9: 3 => UNS * INC # G8: 7,8 => UNS * DIS # G8: 6 => CTR => G8: 7,8 * INC # E1: 7,8 => UNS * INC # E1: 1,3 => UNS * INC # G8: 7,8 => UNS * DIS # G8: 6 => CTR => G8: 7,8 * INC # F9: 7,8 => UNS * INC # F9: 3 => UNS * CNT 57 HDP CHAINS / 57 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D2: 6,7 => CTR => D2: 3,4 * PRF D2: 3,4 # G2: 6,7 => SOL * STA D2: 3,4 + G2: 6,7 * CNT 2 HDP CHAINS / 2 HYP OPENED