Analysis of xx-mith-te3-00124398-base.sdk
Contents
Original Sudoku
level: hard
position: ...4..7....6....32...2.1564..........31..2..86.4..82..31.8.4.2..68.23.4...261.... initial
Autosolve
position: ...4..7....6....32...2.1564..........31..2..86.4..82..31.8.4.2..68.23.4...261.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E4: 5,7,9 => CTR => E4: 4,6 * CNT 1 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E4: 5,7,9 => CTR => E4: 4,6 * STA E4: 4,6 * CNT 1 HDP CHAINS / 54 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction Position
position: ...4.67....6....32...2.1564..........31..2..86.4..82..31.8.4.2..68.23.4...261.... pair_reduction
See section Pair Reduction for the HDP chains leading to this result.
Deep Pair Reduction
Time used: 0:00:20.486709
The following important HDP chains were detected:
* DIS # A1: 1,9 # B2: 7,9 => CTR => B2: 4,5 * DIS # A1: 1,9 + B2: 4,5 # B9: 7,9 => CTR => B9: 4,5 * DIS # A1: 1,9 + B2: 4,5 + B9: 4,5 # A2: 7,9 => CTR => A2: 1,4,5,8 * DIS # A1: 1,9 + B2: 4,5 + B9: 4,5 + A2: 1,4,5,8 # A3: 7,9 => CTR => A3: 8 * PRF # A1: 1,9 + B2: 4,5 + B9: 4,5 + A2: 1,4,5,8 + A3: 8 # C3: 7,9 => SOL * STA # A1: 1,9 + B2: 4,5 + B9: 4,5 + A2: 1,4,5,8 + A3: 8 + C3: 7,9 * CNT 5 HDP CHAINS / 80 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...4..7....6....32...2.1564..........31..2..86.4..82..31.8.4.2..68.23.4...261.... | initial |
| ...4..7....6....32...2.1564..........31..2..86.4..82..31.8.4.2..68.23.4...261.... | autosolve |
| ...4.67....6....32...2.1564..........31..2..86.4..82..31.8.4.2..68.23.4...261.... | pair_reduction |
| 123456789456789132879231564287145396531962478694378215315894627768523941942617853 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (9) I1: 1,9 A4: 2,8 B4: 2,8 D4: 1,3 E5: 4,6 D6: 1,3 G5: 4,6 G7: 6,9 G8: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A2: 1.. / A1 = 1 => 8 pairs (_) / A2 = 1 => 11 pairs (_) D4,D6: 1.. / D4 = 1 => 8 pairs (_) / D6 = 1 => 12 pairs (_) G8,I8: 1.. / G8 = 1 => 10 pairs (_) / I8 = 1 => 12 pairs (_) A2,G2: 1.. / A2 = 1 => 11 pairs (_) / G2 = 1 => 8 pairs (_) A1,B1: 2.. / A1 = 2 => 10 pairs (_) / B1 = 2 => 8 pairs (_) A4,B4: 2.. / A4 = 2 => 8 pairs (_) / B4 = 2 => 10 pairs (_) A1,A4: 2.. / A1 = 2 => 10 pairs (_) / A4 = 2 => 8 pairs (_) B1,B4: 2.. / B1 = 2 => 8 pairs (_) / B4 = 2 => 10 pairs (_) C1,C3: 3.. / C1 = 3 => 12 pairs (_) / C3 = 3 => 11 pairs (_) E1,E3: 3.. / E1 = 3 => 11 pairs (_) / E3 = 3 => 12 pairs (_) D4,D6: 3.. / D4 = 3 => 12 pairs (_) / D6 = 3 => 8 pairs (_) G9,I9: 3.. / G9 = 3 => 14 pairs (_) / I9 = 3 => 5 pairs (_) C1,E1: 3.. / C1 = 3 => 12 pairs (_) / E1 = 3 => 11 pairs (_) C3,E3: 3.. / C3 = 3 => 11 pairs (_) / E3 = 3 => 12 pairs (_) D6,I6: 3.. / D6 = 3 => 8 pairs (_) / I6 = 3 => 12 pairs (_) G4,G9: 3.. / G4 = 3 => 5 pairs (_) / G9 = 3 => 14 pairs (_) A2,B2: 4.. / A2 = 4 => 8 pairs (_) / B2 = 4 => 9 pairs (_) E4,E5: 4.. / E4 = 4 => 7 pairs (_) / E5 = 4 => 13 pairs (_) G4,G5: 4.. / G4 = 4 => 13 pairs (_) / G5 = 4 => 7 pairs (_) A9,B9: 4.. / A9 = 4 => 9 pairs (_) / B9 = 4 => 8 pairs (_) E4,G4: 4.. / E4 = 4 => 7 pairs (_) / G4 = 4 => 13 pairs (_) E5,G5: 4.. / E5 = 4 => 13 pairs (_) / G5 = 4 => 7 pairs (_) A2,A9: 4.. / A2 = 4 => 8 pairs (_) / A9 = 4 => 9 pairs (_) B2,B9: 4.. / B2 = 4 => 9 pairs (_) / B9 = 4 => 8 pairs (_) E1,F1: 6.. / E1 = 6 => 0 pairs (X) / F1 = 6 => 10 pairs (_) G7,I7: 6.. / G7 = 6 => 6 pairs (_) / I7 = 6 => 17 pairs (_) E5,G5: 6.. / E5 = 6 => 7 pairs (_) / G5 = 6 => 13 pairs (_) F1,F4: 6.. / F1 = 6 => 10 pairs (_) / F4 = 6 => 0 pairs (X) I4,I7: 6.. / I4 = 6 => 6 pairs (_) / I7 = 6 => 17 pairs (_) H1,G2: 8.. / H1 = 8 => 5 pairs (_) / G2 = 8 => 15 pairs (_) A4,B4: 8.. / A4 = 8 => 10 pairs (_) / B4 = 8 => 8 pairs (_) G9,H9: 8.. / G9 = 8 => 5 pairs (_) / H9 = 8 => 15 pairs (_) G2,G9: 8.. / G2 = 8 => 15 pairs (_) / G9 = 8 => 5 pairs (_) H1,H9: 8.. / H1 = 8 => 5 pairs (_) / H9 = 8 => 15 pairs (_) * DURATION: 0:00:10.395097 START: 07:34:51.675187 END: 07:35:02.070284 2025-04-05 * CP COUNT: (34) * CLUE FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:20.250991 START: 07:35:16.545035 END: 07:35:36.796026 2025-04-05 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00124398-base-pr-002.dot * REASONING * DIS # A1: 1,9 # B2: 7,9 => CTR => B2: 4,5 * DIS # A1: 1,9 + B2: 4,5 # B9: 7,9 => CTR => B9: 4,5 * DIS # A1: 1,9 + B2: 4,5 + B9: 4,5 # A2: 7,9 => CTR => A2: 1,4,5,8 * DIS # A1: 1,9 + B2: 4,5 + B9: 4,5 + A2: 1,4,5,8 # A3: 7,9 => CTR => A3: 8 * PRF # A1: 1,9 + B2: 4,5 + B9: 4,5 + A2: 1,4,5,8 + A3: 8 # C3: 7,9 => SOL * STA # A1: 1,9 + B2: 4,5 + B9: 4,5 + A2: 1,4,5,8 + A3: 8 + C3: 7,9 * CNT 5 HDP CHAINS / 80 HYP OPENED
Header Info
rating: 32414; r2: 642514; index: 124398
Solution
position: 123456789456789132879231564287145396531962478694378215315894627768523941942617853 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 # H1: 1,9 => UNS * INC # G2: 1,9 => UNS * INC # A1: 1,9 => UNS * INC # A1: 2,5,8 => UNS * INC # I4: 1,9 => UNS * INC # I6: 1,9 => UNS * INC # I8: 1,9 => UNS * INC # A1: 2,8 => UNS * INC # A1: 1,5,9 => UNS * INC # B1: 2,8 => UNS * INC # B1: 5,9 => UNS * INC # G4: 1,3 => UNS * INC # I4: 1,3 => UNS * INC # E4: 4,6 => UNS * DIS # E4: 5,7,9 => CTR => E4: 4,6 * INC # I6: 1,3 => UNS * INC # I6: 5,7,9 => UNS * INC # G4: 4,6 => UNS * INC # G4: 1,3,9 => UNS * INC # I7: 6,9 => UNS * INC # I7: 5,7 => UNS * INC # G4: 6,9 => UNS * INC # G4: 1,3,4 => UNS * INC # I8: 1,9 => UNS * INC # I8: 5,7 => UNS * INC # G2: 1,9 => UNS * INC # G4: 1,9 => UNS * CNT 27 HDP CHAINS / 27 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # H1: 1,9 => UNS * INC # G2: 1,9 => UNS * INC # A1: 1,9 => UNS * INC # A1: 2,5,8 => UNS * INC # I4: 1,9 => UNS * INC # I6: 1,9 => UNS * INC # I8: 1,9 => UNS * INC # A1: 2,8 => UNS * INC # A1: 1,5,9 => UNS * INC # B1: 2,8 => UNS * INC # B1: 5,9 => UNS * INC # G4: 1,3 => UNS * INC # I4: 1,3 => UNS * INC # E4: 4,6 => UNS * DIS # E4: 5,7,9 => CTR => E4: 4,6 * INC E4: 4,6 # I6: 1,3 => UNS * INC E4: 4,6 # I6: 5,7,9 => UNS * INC E4: 4,6 # G4: 4,6 => UNS * INC E4: 4,6 # G4: 1,3,9 => UNS * INC E4: 4,6 # I7: 6,9 => UNS * INC E4: 4,6 # I7: 5,7 => UNS * INC E4: 4,6 # G4: 6,9 => UNS * INC E4: 4,6 # G4: 1,3,4 => UNS * INC E4: 4,6 # I8: 1,9 => UNS * INC E4: 4,6 # I8: 5,7 => UNS * INC E4: 4,6 # G2: 1,9 => UNS * INC E4: 4,6 # G4: 1,9 => UNS * INC E4: 4,6 # H1: 1,9 => UNS * INC E4: 4,6 # G2: 1,9 => UNS * INC E4: 4,6 # A1: 1,9 => UNS * INC E4: 4,6 # A1: 2,5,8 => UNS * INC E4: 4,6 # I4: 1,9 => UNS * INC E4: 4,6 # I6: 1,9 => UNS * INC E4: 4,6 # I8: 1,9 => UNS * INC E4: 4,6 # A1: 2,8 => UNS * INC E4: 4,6 # A1: 1,5,9 => UNS * INC E4: 4,6 # B1: 2,8 => UNS * INC E4: 4,6 # B1: 5,9 => UNS * INC E4: 4,6 # G4: 1,3 => UNS * INC E4: 4,6 # I4: 1,3 => UNS * INC E4: 4,6 # G4: 4,6 => UNS * INC E4: 4,6 # G4: 1,3,9 => UNS * INC E4: 4,6 # I6: 1,3 => UNS * INC E4: 4,6 # I6: 5,7,9 => UNS * INC E4: 4,6 # G4: 4,6 => UNS * INC E4: 4,6 # G4: 1,3,9 => UNS * INC E4: 4,6 # I7: 6,9 => UNS * INC E4: 4,6 # I7: 5,7 => UNS * INC E4: 4,6 # G4: 6,9 => UNS * INC E4: 4,6 # G4: 1,3,4 => UNS * INC E4: 4,6 # I8: 1,9 => UNS * INC E4: 4,6 # I8: 5,7 => UNS * INC E4: 4,6 # G2: 1,9 => UNS * INC E4: 4,6 # G4: 1,9 => UNS * STA E4: 4,6 * CNT 54 HDP CHAINS / 54 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # H1: 1,9 => UNS * INC # G2: 1,9 => UNS * INC # A1: 1,9 => UNS * INC # A1: 2,5,8 => UNS * INC # I4: 1,9 => UNS * INC # I6: 1,9 => UNS * INC # I8: 1,9 => UNS * INC # A1: 2,8 => UNS * INC # A1: 1,5,9 => UNS * INC # B1: 2,8 => UNS * INC # B1: 5,9 => UNS * INC # G4: 1,3 => UNS * INC # I4: 1,3 => UNS * INC # G4: 4,6 => UNS * INC # G4: 1,3,9 => UNS * INC # I6: 1,3 => UNS * INC # I6: 5,7,9 => UNS * INC # G4: 4,6 => UNS * INC # G4: 1,3,9 => UNS * INC # I7: 6,9 => UNS * INC # I7: 5,7 => UNS * INC # G4: 6,9 => UNS * INC # G4: 1,3,4 => UNS * INC # I8: 1,9 => UNS * INC # I8: 5,7 => UNS * INC # G2: 1,9 => UNS * INC # G4: 1,9 => UNS * INC # H1: 1,9 # H4: 1,9 => UNS * INC # H1: 1,9 # H6: 1,9 => UNS * INC # H1: 1,9 # I4: 1,9 => UNS * INC # H1: 1,9 # I6: 1,9 => UNS * INC # H1: 1,9 # I8: 1,9 => UNS * INC # H1: 1,9 # A1: 2,8 => UNS * INC # H1: 1,9 # A1: 5 => UNS * INC # H1: 1,9 # B1: 2,8 => UNS * INC # H1: 1,9 # B1: 5 => UNS * INC # H1: 1,9 # G4: 1,3 => UNS * INC # H1: 1,9 # I4: 1,3 => UNS * INC # H1: 1,9 # G4: 4,6 => UNS * INC # H1: 1,9 # G4: 1,3,9 => UNS * INC # H1: 1,9 # I6: 1,3 => UNS * INC # H1: 1,9 # I6: 9 => UNS * INC # H1: 1,9 # G4: 4,6 => UNS * INC # H1: 1,9 # G4: 1,3,9 => UNS * INC # H1: 1,9 # I7: 6,9 => UNS * INC # H1: 1,9 # I7: 5,7 => UNS * INC # H1: 1,9 # G4: 6,9 => UNS * INC # H1: 1,9 # G4: 1,3,4 => UNS * INC # H1: 1,9 # I8: 1,9 => UNS * INC # H1: 1,9 # I8: 5,7 => UNS * INC # H1: 1,9 # G4: 1,9 => UNS * INC # H1: 1,9 # G4: 3,4,6 => UNS * INC # H1: 1,9 # I9: 3,9 => UNS * INC # H1: 1,9 # I9: 5,7 => UNS * INC # H1: 1,9 # G4: 3,9 => UNS * INC # H1: 1,9 # G4: 1,4,6 => UNS * INC # H1: 1,9 => UNS * INC # G2: 1,9 # A1: 1,9 => UNS * INC # G2: 1,9 # A1: 2,5 => UNS * INC # G2: 1,9 # I8: 1,9 => UNS * INC # G2: 1,9 # I8: 5,7 => UNS * INC # G2: 1,9 # A2: 1,9 => UNS * INC # G2: 1,9 # A2: 4,5,7,8 => UNS * INC # G2: 1,9 # I8: 1,9 => UNS * INC # G2: 1,9 # I8: 5,7 => UNS * INC # G2: 1,9 => UNS * INC # A1: 1,9 # A2: 1,9 => UNS * INC # A1: 1,9 # A2: 4,5,7,8 => UNS * INC # A1: 1,9 # A2: 7,9 => UNS * DIS # A1: 1,9 # B2: 7,9 => CTR => B2: 4,5 * INC # A1: 1,9 + B2: 4,5 # A3: 7,9 => UNS * INC # A1: 1,9 + B2: 4,5 # C3: 7,9 => UNS * INC # A1: 1,9 + B2: 4,5 # E3: 7,9 => UNS * INC # A1: 1,9 + B2: 4,5 # E3: 3,8 => UNS * INC # A1: 1,9 + B2: 4,5 # B6: 7,9 => UNS * DIS # A1: 1,9 + B2: 4,5 # B9: 7,9 => CTR => B9: 4,5 * DIS # A1: 1,9 + B2: 4,5 + B9: 4,5 # A2: 7,9 => CTR => A2: 1,4,5,8 * DIS # A1: 1,9 + B2: 4,5 + B9: 4,5 + A2: 1,4,5,8 # A3: 7,9 => CTR => A3: 8 * PRF # A1: 1,9 + B2: 4,5 + B9: 4,5 + A2: 1,4,5,8 + A3: 8 # C3: 7,9 => SOL * STA # A1: 1,9 + B2: 4,5 + B9: 4,5 + A2: 1,4,5,8 + A3: 8 + C3: 7,9 * CNT 79 HDP CHAINS / 80 HYP OPENED