Analysis of zz-www.sudokuwiki.org-0126-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=126
level: medium
position: .....2..4.7.1...9.6.1.5.2...86...7......9......9...36...2.6.5.1.6...9.2.5..7..... initial
Autosolve
position: .....2..427.1...9.6.1.5.2...862..7.9....9......9...36...2.6.5.1.6.5.9.2.5..72.9.6 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D5: 4,8 => CTR => D5: 3,6 * DIS # F5: 4,8 => CTR => F5: 1,3,5,6,7 * DIS # D3: 4,8 => CTR => D3: 3,9 * DIS # H7: 4,8 => CTR => H7: 3,7 * PRF # C8: 4,8 => SOL * DIS # E8: 4,8 => CTR => E8: 1,3 * CNT 6 HDP CHAINS / 23 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D5: 4,8 => CTR => D5: 3,6 * DIS D5: 3,6 # F5: 4,8 => CTR => F5: 1,3,5,6,7 * DIS D5: 3,6 + F5: 1,3,5,6,7 # D3: 4,8 => CTR => D3: 3,9 * DIS D5: 3,6 + F5: 1,3,5,6,7 + D3: 3,9 # D7: 3 => CTR => D7: 4,8 * DIS D5: 3,6 + F5: 1,3,5,6,7 + D3: 3,9 + D7: 4,8 # H7: 4,8 => CTR => H7: 3,7 * DIS D5: 3,6 + F5: 1,3,5,6,7 + D3: 3,9 + D7: 4,8 + H7: 3,7 # H9: 3 => CTR => H9: 4,8 * PRF D5: 3,6 + F5: 1,3,5,6,7 + D3: 3,9 + D7: 4,8 + H7: 3,7 + H9: 4,8 # C8: 4,8 => SOL * STA D5: 3,6 + F5: 1,3,5,6,7 + D3: 3,9 + D7: 4,8 + H7: 3,7 + H9: 4,8 + C8: 4,8 * CNT 7 HDP CHAINS / 20 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....2..4.7.1...9.6.1.5.2...86...7......9......9...36...2.6.5.1.6...9.2.5..7..... | initial |
| .....2..427.1...9.6.1.5.2...862..7.9....9......9...36...2.6.5.1.6.5.9.2.5..72.9.6 | autosolve |
| 895372614273146895641958237486231759327695148159487362932864571768519423514723986 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (3) G2: 6,8 D6: 4,8 G8: 4,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G1,H1: 1.. / G1 = 1 => 5 pairs (_) / H1 = 1 => 14 pairs (_) A8,B9: 1.. / A8 = 1 => 0 pairs (X) / B9 = 1 => 4 pairs (_) E8,F9: 1.. / E8 = 1 => 4 pairs (_) / F9 = 1 => 0 pairs (X) A8,E8: 1.. / A8 = 1 => 0 pairs (X) / E8 = 1 => 4 pairs (_) B9,F9: 1.. / B9 = 1 => 4 pairs (_) / F9 = 1 => 0 pairs (X) G1,G5: 1.. / G1 = 1 => 5 pairs (_) / G5 = 1 => 14 pairs (_) B5,B6: 2.. / B5 = 2 => 4 pairs (_) / B6 = 2 => 4 pairs (_) I5,I6: 2.. / I5 = 2 => 4 pairs (_) / I6 = 2 => 4 pairs (_) B5,I5: 2.. / B5 = 2 => 4 pairs (_) / I5 = 2 => 4 pairs (_) B6,I6: 2.. / B6 = 2 => 4 pairs (_) / I6 = 2 => 4 pairs (_) C2,B3: 4.. / C2 = 4 => 15 pairs (_) / B3 = 4 => 5 pairs (_) G5,G8: 4.. / G5 = 4 => 0 pairs (X) / G8 = 4 => 5 pairs (_) H1,I2: 5.. / H1 = 5 => 0 pairs (X) / I2 = 5 => 8 pairs (_) C2,I2: 5.. / C2 = 5 => 0 pairs (X) / I2 = 5 => 8 pairs (_) F4,H4: 5.. / F4 = 5 => 6 pairs (_) / H4 = 5 => 10 pairs (_) D1,F2: 6.. / D1 = 6 => 5 pairs (_) / F2 = 6 => 14 pairs (_) G1,G2: 6.. / G1 = 6 => 14 pairs (_) / G2 = 6 => 5 pairs (_) D5,F5: 6.. / D5 = 6 => 14 pairs (_) / F5 = 6 => 5 pairs (_) D1,G1: 6.. / D1 = 6 => 5 pairs (_) / G1 = 6 => 14 pairs (_) F2,G2: 6.. / F2 = 6 => 14 pairs (_) / G2 = 6 => 5 pairs (_) D1,D5: 6.. / D1 = 6 => 5 pairs (_) / D5 = 6 => 14 pairs (_) F2,F5: 6.. / F2 = 6 => 14 pairs (_) / F5 = 6 => 5 pairs (_) E1,F3: 7.. / E1 = 7 => 3 pairs (_) / F3 = 7 => 0 pairs (X) H7,I8: 7.. / H7 = 7 => 5 pairs (_) / I8 = 7 => 0 pairs (X) E1,H1: 7.. / E1 = 7 => 3 pairs (_) / H1 = 7 => 0 pairs (X) A7,H7: 7.. / A7 = 7 => 0 pairs (X) / H7 = 7 => 5 pairs (_) C5,C8: 7.. / C5 = 7 => 10 pairs (_) / C8 = 7 => 5 pairs (_) E1,E6: 7.. / E1 = 7 => 3 pairs (_) / E6 = 7 => 0 pairs (X) I3,I8: 7.. / I3 = 7 => 5 pairs (_) / I8 = 7 => 0 pairs (X) D1,D3: 9.. / D1 = 9 => 0 pairs (X) / D3 = 9 => 4 pairs (_) A7,B7: 9.. / A7 = 9 => 7 pairs (_) / B7 = 9 => 6 pairs (_) B3,D3: 9.. / B3 = 9 => 0 pairs (X) / D3 = 9 => 4 pairs (_) A1,A7: 9.. / A1 = 9 => 6 pairs (_) / A7 = 9 => 7 pairs (_) * DURATION: 0:00:41.799690 START: 05:50:16.717043 END: 05:50:58.516733 2017-05-01 * CP COUNT: (33) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D6,G2,G8) * .....2..427.1...9.6.1.5.2...862..7.9....9......9...36...2.6.5.1.6.5.9.2.5..72.9.6 * PAIR G2: 6,8 BLK 3 G1: 6,8,1 # reduction candidate for 6,8 G1: 6,8 # 14 pairs G1: 1 # 5 pairs * PAIR G2: 6,8 ROW 2 F2: 6,8,3,4 # reduction candidate for 6,8 F2: 6,8 # 8 pairs F2: 3,4 # 6 pairs * PAIR D6: 4,8 BLK 5 D5: 4,8,3,6 # reduction candidate for 4,8 D5: 4,8 => CTR * 9..6821742781436956419572...8623.7.9....96.1...9.7.36.79236.5.186.519427514728936 D5: 3,6 # 4 pairs F5: 4,8,1,3,5,6,7 # reduction candidate for 4,8 F5: 4,8 => CTR * ....7261427.1.68956.1.5.2...862.5749...69.15..59..7362..2.6.5.1.6.5.942.51.72.9.6 F5: 1,3,5,6,7 # 3 pairs E6: 4,8,1,7 # reduction candidate for 4,8 E6: 4,8 # 8 pairs F6: 4,8,1,5,7 # reduction candidate for 4,8 F6: 4,8 # 10 pairs * PAIR D6: 4,8 COL D D3: 4,8,3,9 # reduction candidate for 4,8 D3: 4,8 => CTR * ...972614274136895691.5.237.862..7.9...69.1....9...36.942368571.6.5194235137249.6 D3: 3,9 # 4 pairs D7: 4,8,3 # reduction candidate for 4,8 D7: 4,8 # 6 pairs * PAIR G8: 4,8 BLK 9 H7: 4,8,3,7 # reduction candidate for 4,8 H7: 4,8 => CTR * 93..72154275184693641953278.862..7.9..7.9.8....9..736.792.6.581863519427514728936 H7: 3,7 # 4 pairs H9: 4,8,3 # reduction candidate for 4,8 H9: 4,8 # 6 pairs * PAIR G8: 4,8 ROW 8 A8: 4,8,1,3,7 # reduction candidate for 4,8 A8: 4,8 # 7 pairs C8: 4,8,3,7 # reduction candidate for 4,8 C8: 4,8 => SOLVED * 895372614273146895641958237486231759327695148159487362932864571768519423514723986 C8: 3,7 # 4 pairs E8: 4,8,1,3 # reduction candidate for 4,8 E8: 4,8 => CTR * .5..72..427.1.68956.1.5.2374862137593.5697...719..5362..236.571167589423534721986 E8: 1,3 # 4 pairs * PAIR G8: 4,8 COL G G5: 4,8,1 # reduction candidate for 4,8 G5: 1 # 14 pairs G5: 4,8 # 5 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0126-base-pr-000.dot * REASONING * DIS # D5: 4,8 => CTR => D5: 3,6 * DIS # F5: 4,8 => CTR => F5: 1,3,5,6,7 * DIS # D3: 4,8 => CTR => D3: 3,9 * DIS # H7: 4,8 => CTR => H7: 3,7 * PRF # C8: 4,8 => SOL * DIS # E8: 4,8 => CTR => E8: 1,3 * CNT 6 HDP CHAINS / 23 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D6,G2,G8) * .....2..427.1...9.6.1.5.2...862..7.9....9......9...36...2.6.5.1.6.5.9.2.5..72.9.6 * PAIR G2: 6,8 BLK 3 G1: 6,8,1 # reduction candidate for 6,8 G1: 6,8 # 14 pairs G1: 1 # 5 pairs * PAIR G2: 6,8 ROW 2 F2: 6,8,3,4 # reduction candidate for 6,8 F2: 6,8 # 8 pairs F2: 3,4 # 6 pairs * PAIR D6: 4,8 BLK 5 D5: 4,8,3,6 # reduction candidate for 4,8 D5: 4,8 => CTR * 9..6821742781436956419572...8623.7.9....96.1...9.7.36.79236.5.186.519427514728936 F5: 4,8,1,3,5,6,7 # reduction candidate for 4,8 F5: 4,8 => CTR * ....7261427.1.68956.1.5.2...862.5749...69.15..59..7362..2.6.5.1.6.5.942.51.72.9.6 E6: 4,8,1,7 # reduction candidate for 4,8 E6: 4,8 # 8 pairs F6: 4,8,1,5,7 # reduction candidate for 4,8 F6: 4,8 # 10 pairs * PAIR D6: 4,8 COL D D3: 4,8,3,9 # reduction candidate for 4,8 D3: 4,8 => CTR * ...972614274136895691.5.237.862..7.9.2.69.1.8..9...362942368571.6.5194235137249.6 D7: 4,8,3 # reduction candidate for 4,8 D7: 4,8 # 7 pairs * RESTART * PAIR D6: 4,8 COL D D7: 4,8,3 # reduction candidate for 4,8 D7: 3 => CTR * ...8.26142781...9.6.1.5.2...862..7.9....9......94..36...236.5.1.6.5.9.2.5..72.9.6 * PAIR RESTART * PAIR D6: 4,8 BLK 5 E6: 4,8,1,7 # reduction candidate for 4,8 E6: 4,8 # 10 pairs F6: 4,8,1,5,7 # reduction candidate for 4,8 F6: 4,8 # 12 pairs * PAIR G8: 4,8 BLK 9 H7: 4,8,3,7 # reduction candidate for 4,8 H7: 4,8 => CTR * 9....2..427.1...9.64195728..862..7.9..7.9......9...36.792.635.1863519427514728936 H9: 4,8,3 # reduction candidate for 4,8 H9: 4,8 # 10 pairs * RESTART * PAIR G8: 4,8 BLK 9 H9: 4,8,3 # reduction candidate for 4,8 H9: 3 => CTR * ....721542751..693641953287.862.57.9...3968....9..736...2.6.571.6.53942851.72.936 * PAIR G8: 4,8 ROW 8 A8: 4,8,1,3,7 # reduction candidate for 4,8 A8: 4,8 # 13 pairs C8: 4,8,3,7 # reduction candidate for 4,8 C8: 4,8 => SOLVED * 895372614273146895641958237486231759327695148159487362932864571768519423514723986 * DURATION: 0:00:16.570022 START: 05:51:15.677942 END: 05:51:32.247964 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0126-base-pr-001.dot * REASONING * DIS # D5: 4,8 => CTR => D5: 3,6 * DIS D5: 3,6 # F5: 4,8 => CTR => F5: 1,3,5,6,7 * DIS D5: 3,6 + F5: 1,3,5,6,7 # D3: 4,8 => CTR => D3: 3,9 * DIS D5: 3,6 + F5: 1,3,5,6,7 + D3: 3,9 # D7: 3 => CTR => D7: 4,8 * DIS D5: 3,6 + F5: 1,3,5,6,7 + D3: 3,9 + D7: 4,8 # H7: 4,8 => CTR => H7: 3,7 * DIS D5: 3,6 + F5: 1,3,5,6,7 + D3: 3,9 + D7: 4,8 + H7: 3,7 # H9: 3 => CTR => H9: 4,8 * PRF D5: 3,6 + F5: 1,3,5,6,7 + D3: 3,9 + D7: 4,8 + H7: 3,7 + H9: 4,8 # C8: 4,8 => SOL * STA D5: 3,6 + F5: 1,3,5,6,7 + D3: 3,9 + D7: 4,8 + H7: 3,7 + H9: 4,8 + C8: 4,8 * CNT 7 HDP CHAINS / 20 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=126
Solution
position: 895372614273146895641958237486231759327695148159487362932864571768519423514723986 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 # G1: 6,8 => UNS * INC # G1: 1 => UNS * INC # F2: 6,8 => UNS * INC # F2: 3,4 => UNS * DIS # D5: 4,8 => CTR => D5: 3,6 * INC # D5: 3,6 => UNS * DIS # F5: 4,8 => CTR => F5: 1,3,5,6,7 * INC # F5: 1,3,5,6,7 => UNS * INC # E6: 4,8 => UNS * INC # F6: 4,8 => UNS * DIS # D3: 4,8 => CTR => D3: 3,9 * INC # D3: 3,9 => UNS * INC # D7: 4,8 => UNS * DIS # H7: 4,8 => CTR => H7: 3,7 * INC # H7: 3,7 => UNS * INC # H9: 4,8 => UNS * INC # A8: 4,8 => UNS * PRF # C8: 4,8 => SOL * INC # C8: 3,7 => UNS * DIS # E8: 4,8 => CTR => E8: 1,3 * INC # E8: 1,3 => UNS * INC # G5: 4,8 => UNS * INC # G5: 1 => UNS * CNT 23 HDP CHAINS / 23 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G1: 6,8 => UNS * INC # G1: 1 => UNS * INC # F2: 6,8 => UNS * INC # F2: 3,4 => UNS * DIS # D5: 4,8 => CTR => D5: 3,6 * DIS D5: 3,6 # F5: 4,8 => CTR => F5: 1,3,5,6,7 * INC D5: 3,6 + F5: 1,3,5,6,7 # E6: 4,8 => UNS * INC D5: 3,6 + F5: 1,3,5,6,7 # F6: 4,8 => UNS * DIS D5: 3,6 + F5: 1,3,5,6,7 # D3: 4,8 => CTR => D3: 3,9 * INC D5: 3,6 + F5: 1,3,5,6,7 + D3: 3,9 # D7: 4,8 => UNS * INC D5: 3,6 + F5: 1,3,5,6,7 + D3: 3,9 # D7: 4,8 => UNS * DIS D5: 3,6 + F5: 1,3,5,6,7 + D3: 3,9 # D7: 3 => CTR => D7: 4,8 * INC D5: 3,6 + F5: 1,3,5,6,7 + D3: 3,9 + D7: 4,8 # E6: 4,8 => UNS * INC D5: 3,6 + F5: 1,3,5,6,7 + D3: 3,9 + D7: 4,8 # F6: 4,8 => UNS * DIS D5: 3,6 + F5: 1,3,5,6,7 + D3: 3,9 + D7: 4,8 # H7: 4,8 => CTR => H7: 3,7 * INC D5: 3,6 + F5: 1,3,5,6,7 + D3: 3,9 + D7: 4,8 + H7: 3,7 # H9: 4,8 => UNS * INC D5: 3,6 + F5: 1,3,5,6,7 + D3: 3,9 + D7: 4,8 + H7: 3,7 # H9: 4,8 => UNS * DIS D5: 3,6 + F5: 1,3,5,6,7 + D3: 3,9 + D7: 4,8 + H7: 3,7 # H9: 3 => CTR => H9: 4,8 * INC D5: 3,6 + F5: 1,3,5,6,7 + D3: 3,9 + D7: 4,8 + H7: 3,7 + H9: 4,8 # A8: 4,8 => UNS * PRF D5: 3,6 + F5: 1,3,5,6,7 + D3: 3,9 + D7: 4,8 + H7: 3,7 + H9: 4,8 # C8: 4,8 => SOL * STA D5: 3,6 + F5: 1,3,5,6,7 + D3: 3,9 + D7: 4,8 + H7: 3,7 + H9: 4,8 + C8: 4,8 * CNT 20 HDP CHAINS / 20 HYP OPENED