Analysis of xx-mith-te3-00141082-base.sdk
Contents
Original Sudoku
level: hard
position: .23....8.4...8..3686..7....23.947......83..47...5.1...37...8.246..7......8....67. initial
Autosolve
position: .23....8.4...8..3686..7....23.947......83..47...5.1...37...8.246..7......8....67. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C6: 7,9 => CTR => C6: 4,6,8 * DIS # C6: 4,9 => CTR => C6: 6,7,8 * CNT 2 HDP CHAINS / 20 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C6: 7,9 => CTR => C6: 4,6,8 * STA C6: 4,6,8 * CNT 1 HDP CHAINS / 25 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction Position
position: .23...78.4.7.8..3686..7.4..23.947......83..477..5.1...37...8.246..7......8....67. pair_reduction
See section Pair Reduction for the HDP chains leading to this result.
Deep Pair Reduction
Time used: 0:00:05.571001
The following important HDP chains were detected:
* PRF # D3: 1,2 # I3: 5,9 => SOL * STA # D3: 1,2 + I3: 5,9 * CNT 1 HDP CHAINS / 23 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .23....8.4...8..3686..7....23.947......83..47...5.1...37...8.246..7......8....67. | initial |
| .23....8.4...8..3686..7....23.947......83..47...5.1...37...8.246..7......8....67. | autosolve |
| .23...78.4.7.8..3686..7.4..23.947......83..477..5.1...37...8.246..7......8....67. | pair_reduction |
| 123456789457189236869273415231947568596832147748561392375618924612794853984325671 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (7) D2: 1,2 A6: 7,9 B6: 4,9 F5: 2,6 E6: 2,6 H6: 6,9 D7: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F5,E6: 2.. / F5 = 2 => 11 pairs (_) / E6 = 2 => 12 pairs (_) C8,C9: 2.. / C8 = 2 => 7 pairs (_) / C9 = 2 => 8 pairs (_) F5,G5: 2.. / F5 = 2 => 11 pairs (_) / G5 = 2 => 12 pairs (_) I3,I6: 2.. / I3 = 2 => 7 pairs (_) / I6 = 2 => 0 pairs (*) D3,F3: 3.. / D3 = 3 => 7 pairs (_) / F3 = 3 => 10 pairs (_) G6,I6: 3.. / G6 = 3 => 7 pairs (_) / I6 = 3 => 8 pairs (_) D3,D9: 3.. / D3 = 3 => 7 pairs (_) / D9 = 3 => 10 pairs (_) G6,G8: 3.. / G6 = 3 => 7 pairs (_) / G8 = 3 => 8 pairs (_) G1,G3: 4.. / G1 = 4 => 0 pairs (X) / G3 = 4 => 7 pairs (_) B6,C6: 4.. / B6 = 4 => 8 pairs (_) / C6 = 4 => 0 pairs (X) B6,B8: 4.. / B6 = 4 => 8 pairs (_) / B8 = 4 => 0 pairs (X) F5,E6: 6.. / F5 = 6 => 12 pairs (_) / E6 = 6 => 11 pairs (_) H4,H6: 6.. / H4 = 6 => 9 pairs (_) / H6 = 6 => 12 pairs (_) D7,E7: 6.. / D7 = 6 => 7 pairs (_) / E7 = 6 => 13 pairs (_) C4,H4: 6.. / C4 = 6 => 12 pairs (_) / H4 = 6 => 9 pairs (_) C5,F5: 6.. / C5 = 6 => 11 pairs (_) / F5 = 6 => 12 pairs (_) D1,D7: 6.. / D1 = 6 => 13 pairs (_) / D7 = 6 => 7 pairs (_) F1,F5: 6.. / F1 = 6 => 11 pairs (_) / F5 = 6 => 12 pairs (_) A1,C2: 7.. / A1 = 7 => 0 pairs (X) / C2 = 7 => 6 pairs (_) G1,G2: 7.. / G1 = 7 => 6 pairs (_) / G2 = 7 => 0 pairs (X) A6,C6: 7.. / A6 = 7 => 6 pairs (_) / C6 = 7 => 0 pairs (X) A1,G1: 7.. / A1 = 7 => 0 pairs (X) / G1 = 7 => 6 pairs (_) C2,G2: 7.. / C2 = 7 => 6 pairs (_) / G2 = 7 => 0 pairs (X) A1,A6: 7.. / A1 = 7 => 0 pairs (X) / A6 = 7 => 6 pairs (_) C2,C6: 7.. / C2 = 7 => 6 pairs (_) / C6 = 7 => 0 pairs (X) C4,C6: 8.. / C4 = 8 => 15 pairs (_) / C6 = 8 => 7 pairs (_) G8,I8: 8.. / G8 = 8 => 8 pairs (_) / I8 = 8 => 8 pairs (_) * DURATION: 0:00:06.069964 START: 13:04:30.235544 END: 13:04:36.305508 2025-04-05 * CP COUNT: (27) * SOLUTION FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:05.454564 START: 13:04:42.354599 END: 13:04:47.809163 2025-04-05 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00141082-base-pr-002.dot * REASONING * PRF # D3: 1,2 # I3: 5,9 => SOL * STA # D3: 1,2 + I3: 5,9 * CNT 1 HDP CHAINS / 23 HYP OPENED
Header Info
rating: 37437; r2: 836913; index: 141082
Solution
position: 123456789457189236869273415231947568596832147748561392375618924612794853984325671 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:
* INC # D3: 1,2 => UNS * INC # D3: 3,4 => UNS * INC # G2: 1,2 => UNS * INC # G2: 5,7,9 => UNS * INC # D9: 1,2 => UNS * INC # D9: 3,4 => UNS * DIS # C6: 7,9 => CTR => C6: 4,6,8 * INC # C6: 4,6,8 => UNS * INC # A1: 7,9 => UNS * INC # A1: 1,5 => UNS * DIS # C6: 4,9 => CTR => C6: 6,7,8 * INC # C6: 6,7,8 => UNS * INC # B8: 4,9 => UNS * INC # B8: 1,5 => UNS * INC # C6: 6,9 => UNS * INC # C6: 4,7,8 => UNS * INC # E7: 1,6 => UNS * INC # E7: 5,9 => UNS * INC # D1: 1,6 => UNS * INC # D1: 4 => UNS * CNT 20 HDP CHAINS / 20 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D3: 1,2 => UNS * INC # D3: 3,4 => UNS * INC # G2: 1,2 => UNS * INC # G2: 5,7,9 => UNS * INC # D9: 1,2 => UNS * INC # D9: 3,4 => UNS * DIS # C6: 7,9 => CTR => C6: 4,6,8 * INC C6: 4,6,8 # B8: 4,9 => UNS * INC C6: 4,6,8 # B8: 1,5 => UNS * INC C6: 4,6,8 # E7: 1,6 => UNS * INC C6: 4,6,8 # E7: 5,9 => UNS * INC C6: 4,6,8 # D1: 1,6 => UNS * INC C6: 4,6,8 # D1: 4 => UNS * INC C6: 4,6,8 # D3: 1,2 => UNS * INC C6: 4,6,8 # D3: 3 => UNS * INC C6: 4,6,8 # G2: 1,2 => UNS * INC C6: 4,6,8 # G2: 5,9 => UNS * INC C6: 4,6,8 # D9: 1,2 => UNS * INC C6: 4,6,8 # D9: 3,4 => UNS * INC C6: 4,6,8 # B8: 4,9 => UNS * INC C6: 4,6,8 # B8: 1,5 => UNS * INC C6: 4,6,8 # E7: 1,6 => UNS * INC C6: 4,6,8 # E7: 5,9 => UNS * INC C6: 4,6,8 # D1: 1,6 => UNS * INC C6: 4,6,8 # D1: 4 => UNS * STA C6: 4,6,8 * CNT 25 HDP CHAINS / 25 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # D3: 1,2 => UNS * INC # D3: 3 => UNS * INC # G2: 1,2 => UNS * INC # G2: 5,9 => UNS * INC # D9: 1,2 => UNS * INC # D9: 3,4 => UNS * INC # B8: 4,9 => UNS * INC # B8: 1,5 => UNS * INC # E7: 1,6 => UNS * INC # E7: 5,9 => UNS * INC # D1: 1,6 => UNS * INC # D1: 4 => UNS * INC # D3: 1,2 # G2: 1,2 => UNS * INC # D3: 1,2 # G2: 5,9 => UNS * INC # D3: 1,2 # E1: 5,9 => UNS * INC # D3: 1,2 # F1: 5,9 => UNS * INC # D3: 1,2 # B2: 5,9 => UNS * INC # D3: 1,2 # G2: 5,9 => UNS * INC # D3: 1,2 # F8: 5,9 => UNS * INC # D3: 1,2 # F9: 5,9 => UNS * INC # D3: 1,2 # I3: 1,2 => UNS * PRF # D3: 1,2 # I3: 5,9 => SOL * STA # D3: 1,2 + I3: 5,9 * CNT 22 HDP CHAINS / 23 HYP OPENED