Analysis of xx-mith-te3-00052230-base.sdk
Contents
Original Sudoku
level: hard
position: ..3......45...9...6.9..35.4..47.1.......9.42.9.5842...3...2.94.5.....6.2....6...3 initial
Autosolve
position: ..3......45...9...6.9..35.4..47.1.......9.42.9.5842...3.6.2.94.5.....6.2....6...3 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D1: 1,2 => CTR => D1: 4,5,6 * DIS # B4: 2,8 => CTR => B4: 3,6 * CNT 2 HDP CHAINS / 33 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D1: 1,2 => CTR => D1: 4,5,6 * DIS D1: 4,5,6 # B4: 2,8 => CTR => B4: 3,6 * STA D1: 4,5,6 + B4: 3,6 * CNT 2 HDP CHAINS / 55 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction Position
position: ..3......45...9...6.9..35.42.47.1.......9.42.9.5842...3.6.2.94.5.....6.2..2.6...3 pair_reduction
See section Pair Reduction for the HDP chains leading to this result.
Deep Pair Reduction
Time used: 0:00:06.356222
The following important HDP chains were detected:
* PRF # D2: 1,2 # C2: 7,8 => SOL * STA # D2: 1,2 + C2: 7,8 * CNT 1 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..3......45...9...6.9..35.4..47.1.......9.42.9.5842...3...2.94.5.....6.2....6...3 | initial |
| ..3......45...9...6.9..35.4..47.1.......9.42.9.5842...3.6.2.94.5.....6.2....6...3 | autosolve |
| ..3......45...9...6.9..35.42.47.1.......9.42.9.5842...3.6.2.94.5.....6.2..2.6...3 | pair_reduction |
| 123456789457189236689273514264731895831695427975842361316527948598314672742968153 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (8) D3: 1,2 A4: 2,8 E4: 3,5 F5: 5,6 G4: 3,8 B8: 4,9 B9: 4,9 D7: 1,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G1,G2: 2.. / G1 = 2 => 8 pairs (_) / G2 = 2 => 9 pairs (_) A4,B4: 2.. / A4 = 2 => 7 pairs (_) / B4 = 2 => 0 pairs (X) A9,C9: 2.. / A9 = 2 => 0 pairs (X) / C9 = 2 => 8 pairs (_) B3,D3: 2.. / B3 = 2 => 16 pairs (_) / D3 = 2 => 8 pairs (_) C2,C9: 2.. / C2 = 2 => 0 pairs (X) / C9 = 2 => 8 pairs (_) G2,H2: 3.. / G2 = 3 => 15 pairs (_) / H2 = 3 => 8 pairs (_) E4,D5: 3.. / E4 = 3 => 9 pairs (_) / D5 = 3 => 10 pairs (_) D8,E8: 3.. / D8 = 3 => 9 pairs (_) / E8 = 3 => 10 pairs (_) B5,D5: 3.. / B5 = 3 => 9 pairs (_) / D5 = 3 => 10 pairs (_) D5,D8: 3.. / D5 = 3 => 10 pairs (_) / D8 = 3 => 9 pairs (_) E4,E8: 3.. / E4 = 3 => 9 pairs (_) / E8 = 3 => 10 pairs (_) D1,F1: 4.. / D1 = 4 => 8 pairs (_) / F1 = 4 => 13 pairs (_) B8,B9: 4.. / B8 = 4 => 10 pairs (_) / B9 = 4 => 6 pairs (_) I7,H9: 5.. / I7 = 5 => 12 pairs (_) / H9 = 5 => 8 pairs (_) E1,E4: 5.. / E1 = 5 => 9 pairs (_) / E4 = 5 => 10 pairs (_) H4,H9: 5.. / H4 = 5 => 12 pairs (_) / H9 = 5 => 8 pairs (_) B4,B6: 6.. / B4 = 6 => 7 pairs (_) / B6 = 6 => 13 pairs (_) D5,F5: 6.. / D5 = 6 => 14 pairs (_) / F5 = 6 => 8 pairs (_) F1,F5: 6.. / F1 = 6 => 14 pairs (_) / F5 = 6 => 8 pairs (_) H1,I1: 9.. / H1 = 9 => 8 pairs (_) / I1 = 9 => 8 pairs (_) H4,I4: 9.. / H4 = 9 => 8 pairs (_) / I4 = 9 => 8 pairs (_) B8,B9: 9.. / B8 = 9 => 6 pairs (_) / B9 = 9 => 10 pairs (_) D8,D9: 9.. / D8 = 9 => 10 pairs (_) / D9 = 9 => 6 pairs (_) B8,D8: 9.. / B8 = 9 => 6 pairs (_) / D8 = 9 => 10 pairs (_) B9,D9: 9.. / B9 = 9 => 10 pairs (_) / D9 = 9 => 6 pairs (_) H1,H4: 9.. / H1 = 9 => 8 pairs (_) / H4 = 9 => 8 pairs (_) I1,I4: 9.. / I1 = 9 => 8 pairs (_) / I4 = 9 => 8 pairs (_) * DURATION: 0:00:08.021893 START: 08:53:15.760178 END: 08:53:23.782071 2025-04-06 * CP COUNT: (27) * CLUE FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:06.215745 START: 08:53:39.516456 END: 08:53:45.732201 2025-04-06 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00052230-base-pr-002.dot * REASONING * PRF # D2: 1,2 # C2: 7,8 => SOL * STA # D2: 1,2 + C2: 7,8 * CNT 1 HDP CHAINS / 30 HYP OPENED
Header Info
rating: 10660; r2: 345229; index: 52230
Solution
position: 123456789457189236689273514264731895831695427975842361316527948598314672742968153 solved
See section Deep 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 # D1: 1,2 => CTR => D1: 4,5,6 * INC # D1: 4,5,6 => UNS * INC # D2: 1,2 => UNS * INC # B3: 1,2 => UNS * INC # B3: 7,8 => UNS * DIS # B4: 2,8 => CTR => B4: 3,6 * INC # B4: 3,6 => UNS * INC # A1: 2,8 => UNS * INC # A9: 2,8 => UNS * INC # D5: 3,5 => UNS * INC # D5: 6 => UNS * INC # H4: 3,5 => UNS * INC # H4: 6,8,9 => UNS * INC # D5: 5,6 => UNS * INC # D5: 3 => UNS * INC # F1: 5,6 => UNS * INC # F1: 4,7,8 => UNS * INC # H4: 3,8 => UNS * INC # H4: 5,6,9 => UNS * INC # B4: 3,8 => UNS * INC # B4: 2,6 => UNS * INC # G2: 3,8 => UNS * INC # G2: 1,2,7 => UNS * INC # D8: 4,9 => UNS * INC # D8: 1,3 => UNS * INC # D9: 4,9 => UNS * INC # D9: 1,5 => UNS * INC # D9: 1,5 => UNS * INC # D9: 4,9 => UNS * INC # I7: 1,5 => UNS * INC # I7: 7,8 => UNS * INC # D1: 1,5 => UNS * INC # D1: 2,4,6 => UNS * CNT 33 HDP CHAINS / 33 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D1: 1,2 => CTR => D1: 4,5,6 * INC D1: 4,5,6 # D2: 1,2 => UNS * INC D1: 4,5,6 # D2: 1,2 => UNS * INC D1: 4,5,6 # D2: 6 => UNS * INC D1: 4,5,6 # B3: 1,2 => UNS * INC D1: 4,5,6 # B3: 7,8 => UNS * DIS D1: 4,5,6 # B4: 2,8 => CTR => B4: 3,6 * INC D1: 4,5,6 + B4: 3,6 # D5: 3,5 => UNS * INC D1: 4,5,6 + B4: 3,6 # D5: 6 => UNS * INC D1: 4,5,6 + B4: 3,6 # H4: 3,5 => UNS * INC D1: 4,5,6 + B4: 3,6 # H4: 6,8,9 => UNS * INC D1: 4,5,6 + B4: 3,6 # D5: 5,6 => UNS * INC D1: 4,5,6 + B4: 3,6 # D5: 3 => UNS * INC D1: 4,5,6 + B4: 3,6 # F1: 5,6 => UNS * INC D1: 4,5,6 + B4: 3,6 # F1: 4,7,8 => UNS * INC D1: 4,5,6 + B4: 3,6 # H4: 3,8 => UNS * INC D1: 4,5,6 + B4: 3,6 # H4: 5,6,9 => UNS * INC D1: 4,5,6 + B4: 3,6 # G2: 3,8 => UNS * INC D1: 4,5,6 + B4: 3,6 # G2: 1,2,7 => UNS * INC D1: 4,5,6 + B4: 3,6 # D8: 4,9 => UNS * INC D1: 4,5,6 + B4: 3,6 # D8: 1,3 => UNS * INC D1: 4,5,6 + B4: 3,6 # D9: 4,9 => UNS * INC D1: 4,5,6 + B4: 3,6 # D9: 1,5 => UNS * INC D1: 4,5,6 + B4: 3,6 # D9: 1,5 => UNS * INC D1: 4,5,6 + B4: 3,6 # D9: 4,9 => UNS * INC D1: 4,5,6 + B4: 3,6 # I7: 1,5 => UNS * INC D1: 4,5,6 + B4: 3,6 # I7: 7,8 => UNS * INC D1: 4,5,6 + B4: 3,6 # D2: 1,2 => UNS * INC D1: 4,5,6 + B4: 3,6 # D2: 6 => UNS * INC D1: 4,5,6 + B4: 3,6 # B3: 1,2 => UNS * INC D1: 4,5,6 + B4: 3,6 # B3: 7,8 => UNS * INC D1: 4,5,6 + B4: 3,6 # B6: 3,6 => UNS * INC D1: 4,5,6 + B4: 3,6 # B6: 1,7 => UNS * INC D1: 4,5,6 + B4: 3,6 # H4: 3,6 => UNS * INC D1: 4,5,6 + B4: 3,6 # H4: 5,8,9 => UNS * INC D1: 4,5,6 + B4: 3,6 # D5: 3,5 => UNS * INC D1: 4,5,6 + B4: 3,6 # D5: 6 => UNS * INC D1: 4,5,6 + B4: 3,6 # H4: 3,5 => UNS * INC D1: 4,5,6 + B4: 3,6 # H4: 6,8,9 => UNS * INC D1: 4,5,6 + B4: 3,6 # D5: 5,6 => UNS * INC D1: 4,5,6 + B4: 3,6 # D5: 3 => UNS * INC D1: 4,5,6 + B4: 3,6 # F1: 5,6 => UNS * INC D1: 4,5,6 + B4: 3,6 # F1: 4,7,8 => UNS * INC D1: 4,5,6 + B4: 3,6 # H4: 3,8 => UNS * INC D1: 4,5,6 + B4: 3,6 # H4: 5,6,9 => UNS * INC D1: 4,5,6 + B4: 3,6 # G2: 3,8 => UNS * INC D1: 4,5,6 + B4: 3,6 # G2: 1,2,7 => UNS * INC D1: 4,5,6 + B4: 3,6 # D8: 4,9 => UNS * INC D1: 4,5,6 + B4: 3,6 # D8: 1,3 => UNS * INC D1: 4,5,6 + B4: 3,6 # D9: 4,9 => UNS * INC D1: 4,5,6 + B4: 3,6 # D9: 1,5 => UNS * INC D1: 4,5,6 + B4: 3,6 # D9: 1,5 => UNS * INC D1: 4,5,6 + B4: 3,6 # D9: 4,9 => UNS * INC D1: 4,5,6 + B4: 3,6 # I7: 1,5 => UNS * INC D1: 4,5,6 + B4: 3,6 # I7: 7,8 => UNS * STA D1: 4,5,6 + B4: 3,6 * CNT 55 HDP CHAINS / 55 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # D2: 1,2 => UNS * INC # D2: 6 => UNS * INC # B3: 1,2 => UNS * INC # B3: 7,8 => UNS * INC # B6: 3,6 => UNS * INC # B6: 1,7 => UNS * INC # H4: 3,6 => UNS * INC # H4: 5,8,9 => UNS * INC # D5: 3,5 => UNS * INC # D5: 6 => UNS * INC # H4: 3,5 => UNS * INC # H4: 6,8,9 => UNS * INC # D5: 5,6 => UNS * INC # D5: 3 => UNS * INC # F1: 5,6 => UNS * INC # F1: 4,7,8 => UNS * INC # H4: 3,8 => UNS * INC # H4: 5,6,9 => UNS * INC # G2: 3,8 => UNS * INC # G2: 1,2,7 => UNS * INC # D8: 4,9 => UNS * INC # D8: 1,3 => UNS * INC # D9: 4,9 => UNS * INC # D9: 1,5 => UNS * INC # D9: 1,5 => UNS * INC # D9: 4,9 => UNS * INC # I7: 1,5 => UNS * INC # I7: 7,8 => UNS * PRF # D2: 1,2 # C2: 7,8 => SOL * STA # D2: 1,2 + C2: 7,8 * CNT 29 HDP CHAINS / 30 HYP OPENED