Analysis of xx-mith-te3-00004484-base.sdk
Contents
Original Sudoku
level: medium
position: ......78.4.......6....3.1542.439...569..45..2.356.2...34..6..9.5.9.2.......9..... initial
Autosolve
position: ......78.4.......6....3.1542.439...569..45..2.356.2...34..6..9.5.9.2.......9..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D1: 1,5 => CTR => D1: 2,4 * PRF # G2: 2 => SOL * DIS # G9: 6,8 => CTR => G9: 2,3,4,5 * DIS # G9: 3,8 => CTR => G9: 2,4,5,6 * CNT 4 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D1: 1,5 => CTR => D1: 2,4 * PRF D1: 2,4 # G2: 2 => SOL * STA D1: 2,4 + G2: 2 * CNT 2 HDP CHAINS / 11 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ......78.4.......6....3.1542.439...569..45..2.356.2...34..6..9.5.9.2.......9..... | initial |
| ......78.4.......6....3.1542.439...569..45..2.356.2...34..6..9.5.9.2.......9..... | autosolve |
| 123456789457189236986237154214398675698745312735612948342561897579823461861974523 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) A1: 1,9 E1: 1,5 I1: 3,9 H2: 2,3 G4: 6,8 G5: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,D3: 2.. / D1 = 2 => 0 pairs (X) / D3 = 2 => 6 pairs (_) G2,H2: 2.. / G2 = 2 => 0 pairs (*) / H2 = 2 => 0 pairs (X) C7,G7: 2.. / C7 = 2 => 7 pairs (_) / G7 = 2 => 6 pairs (_) H2,H9: 2.. / H2 = 2 => 8 pairs (_) / H9 = 2 => 0 pairs (*) C1,C2: 3.. / C1 = 3 => 9 pairs (_) / C2 = 3 => 13 pairs (_) G5,H5: 3.. / G5 = 3 => 7 pairs (_) / H5 = 3 => 11 pairs (_) F8,F9: 3.. / F8 = 3 => 6 pairs (_) / F9 = 3 => 8 pairs (_) C1,I1: 3.. / C1 = 3 => 9 pairs (_) / I1 = 3 => 13 pairs (_) D1,F1: 4.. / D1 = 4 => 8 pairs (_) / F1 = 4 => 0 pairs (X) G6,H6: 4.. / G6 = 4 => 14 pairs (_) / H6 = 4 => 7 pairs (_) D1,D8: 4.. / D1 = 4 => 8 pairs (_) / D8 = 4 => 0 pairs (X) B1,B2: 5.. / B1 = 5 => 14 pairs (_) / B2 = 5 => 6 pairs (_) D7,E9: 5.. / D7 = 5 => 7 pairs (_) / E9 = 5 => 0 pairs (X) G7,G9: 5.. / G7 = 5 => 0 pairs (X) / G9 = 5 => 7 pairs (_) D7,G7: 5.. / D7 = 5 => 7 pairs (_) / G7 = 5 => 0 pairs (X) E9,G9: 5.. / E9 = 5 => 0 pairs (X) / G9 = 5 => 7 pairs (_) F1,F3: 6.. / F1 = 6 => 8 pairs (_) / F3 = 6 => 10 pairs (_) G4,H4: 6.. / G4 = 6 => 6 pairs (_) / H4 = 6 => 11 pairs (_) A1,A3: 9.. / A1 = 9 => 12 pairs (_) / A3 = 9 => 9 pairs (_) I1,G2: 9.. / I1 = 9 => 9 pairs (_) / G2 = 9 => 13 pairs (_) G6,I6: 9.. / G6 = 9 => 9 pairs (_) / I6 = 9 => 13 pairs (_) F2,G2: 9.. / F2 = 9 => 9 pairs (_) / G2 = 9 => 13 pairs (_) A3,F3: 9.. / A3 = 9 => 9 pairs (_) / F3 = 9 => 12 pairs (_) G2,G6: 9.. / G2 = 9 => 13 pairs (_) / G6 = 9 => 9 pairs (_) I1,I6: 9.. / I1 = 9 => 9 pairs (_) / I6 = 9 => 13 pairs (_) * DURATION: 0:00:06.412401 START: 05:41:17.752731 END: 05:41:24.165132 2025-04-04 * CP COUNT: (25) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,E1,G4,G5,H2,I1) * ......78.4.......6....3.1542.439...569..45..2.356.2...34..6..9.5.9.2.......9..... * PAIR A1: 1,9 ROW 1 F1: 1,9,4,6 # reduction candidate for 1,9 F1: 1,9 # 14 pairs F1: 4,6 # 7 pairs * PAIR E1: 1,5 BLK 2 D1: 1,5,2,4 # reduction candidate for 1,5 D1: 1,5 => CTR * 1..5.478.4....9..69..2361542.439...569..45..2.356.294.34..6..9.5.942.......9..4.. D1: 2,4 # 7 pairs D2: 1,5,7,8 # reduction candidate for 1,5 D2: 1,5 # 9 pairs E2: 1,5,7,8 # reduction candidate for 1,5 E2: 1,5 # 12 pairs * PAIR E1: 1,5 ROW 1 B1: 1,5,2,6 # reduction candidate for 1,5 B1: 1,5 # 13 pairs B1: 2,6 # 7 pairs * PAIR E1: 1,5 COL E E9: 1,5,7,8 # reduction candidate for 1,5 E9: 1,5 # 9 pairs E9: 7,8 # 8 pairs * PAIR I1: 3,9 BLK 3 G2: 3,9,2 # reduction candidate for 3,9 G2: 2 => SOLVED * 123456789457189236986237154214398675698745312735612948342561897579823461861974523 G2: 3,9 # 8 pairs * PAIR H2: 2,3 BLK 3 G2: 2,3,9 # reduction candidate for 2,3 G2: 9 # 13 pairs G2: 2,3 # 9 pairs * PAIR H2: 2,3 COL H H9: 2,3,1,4,6,7 # reduction candidate for 2,3 H9: 2,3 # 8 pairs H9: 1,4,6,7 # 8 pairs * PAIR G4: 6,8 COL G G8: 6,8,3,4 # reduction candidate for 6,8 G8: 6,8 # 10 pairs G9: 6,8,2,3,4,5 # reduction candidate for 6,8 G9: 6,8 => CTR * ....1.78.4.....236....3.1542.439...569..453.2.356.294.342.6.59.5.9.2.4.....954.23 G9: 2,3,4,5 # 6 pairs * PAIR G5: 3,8 COL G G8: 3,8,4,6 # reduction candidate for 3,8 G8: 3,8 # 12 pairs G9: 3,8,2,4,5,6 # reduction candidate for 3,8 G9: 3,8 => CTR * ....1.78.4.....236....3.1542.439...569..453.2.356.294.342.6.59.5.9.2.46....954823 G9: 2,4,5,6 # 6 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-mith-te3-00004484-base-pr-000.dot * REASONING * DIS # D1: 1,5 => CTR => D1: 2,4 * PRF # G2: 2 => SOL * DIS # G9: 6,8 => CTR => G9: 2,3,4,5 * DIS # G9: 3,8 => CTR => G9: 2,4,5,6 * CNT 4 HDP CHAINS / 22 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,E1,G4,G5,H2,I1) * ......78.4.......6....3.1542.439...569..45..2.356.2...34..6..9.5.9.2.......9..... * PAIR A1: 1,9 ROW 1 F1: 1,9,4,6 # reduction candidate for 1,9 F1: 1,9 # 14 pairs F1: 4,6 # 7 pairs * PAIR E1: 1,5 BLK 2 D1: 1,5,2,4 # reduction candidate for 1,5 D1: 1,5 => CTR * 1..5.478.4....9..69..2361542.439...569..45..2.356.294.34..6..9.5.942.......9..4.. D2: 1,5,7,8 # reduction candidate for 1,5 D2: 1,5 # 9 pairs E2: 1,5,7,8 # reduction candidate for 1,5 E2: 1,5 # 12 pairs * PAIR E1: 1,5 ROW 1 B1: 1,5,2,6 # reduction candidate for 1,5 B1: 1,5 # 13 pairs B1: 2,6 # 8 pairs * PAIR E1: 1,5 COL E E9: 1,5,7,8 # reduction candidate for 1,5 E9: 1,5 # 10 pairs E9: 7,8 # 9 pairs * PAIR I1: 3,9 BLK 3 G2: 3,9,2 # reduction candidate for 3,9 G2: 2 => SOLVED * 123456789457189236986237154214398675698745312735612948342561897579823461861974523 * DURATION: 0:00:01.772711 START: 05:41:27.205176 END: 05:41:28.977887 2025-04-04 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00004484-base-pr-001.dot * REASONING * DIS # D1: 1,5 => CTR => D1: 2,4 * PRF D1: 2,4 # G2: 2 => SOL * STA D1: 2,4 + G2: 2 * CNT 2 HDP CHAINS / 11 HYP OPENED
Header Info
rating: 769; r2: 23309; index: 4484
Solution
position: 123456789457189236986237154214398675698745312735612948342561897579823461861974523 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 # F1: 1,9 => UNS * INC # F1: 4,6 => UNS * DIS # D1: 1,5 => CTR => D1: 2,4 * INC # D1: 2,4 => UNS * INC # D2: 1,5 => UNS * INC # E2: 1,5 => UNS * INC # B1: 1,5 => UNS * INC # B1: 2,6 => UNS * INC # E9: 1,5 => UNS * INC # E9: 7,8 => UNS * INC # G2: 3,9 => UNS * PRF # G2: 2 => SOL * INC # G2: 2,3 => UNS * INC # G2: 9 => UNS * INC # H9: 2,3 => UNS * INC # H9: 1,4,6,7 => UNS * INC # G8: 6,8 => UNS * DIS # G9: 6,8 => CTR => G9: 2,3,4,5 * INC # G9: 2,3,4,5 => UNS * INC # G8: 3,8 => UNS * DIS # G9: 3,8 => CTR => G9: 2,4,5,6 * INC # G9: 2,4,5,6 => UNS * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F1: 1,9 => UNS * INC # F1: 4,6 => UNS * DIS # D1: 1,5 => CTR => D1: 2,4 * INC D1: 2,4 # D2: 1,5 => UNS * INC D1: 2,4 # E2: 1,5 => UNS * INC D1: 2,4 # B1: 1,5 => UNS * INC D1: 2,4 # B1: 2,6 => UNS * INC D1: 2,4 # E9: 1,5 => UNS * INC D1: 2,4 # E9: 7,8 => UNS * INC D1: 2,4 # G2: 3,9 => UNS * PRF D1: 2,4 # G2: 2 => SOL * STA D1: 2,4 + G2: 2 * CNT 11 HDP CHAINS / 11 HYP OPENED