Analysis of xx-mith-te3-00018455-base.sdk
Contents
Original Sudoku
level: hard
position: ...4.678....18.2......72.1..8..4..71......42.74..216.85.4.....7..1.64...93.....4. initial
Autosolve
position: ...4.678....18.2......72.1..8.64..71......42.74..216.85.4.....7..1.64...93.....4. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D8: 7,8 => CTR => D8: 2,3,5,9 * DIS # C9: 7,8 => CTR => C9: 2,6 * PRF # C9: 2,8 => SOL * PRF # C9: 2,7 => SOL * CNT 4 HDP CHAINS / 21 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D8: 7,8 => CTR => D8: 2,3,5,9 * DIS D8: 2,3,5,9 # C9: 8 => CTR => C9: 2,6 * STA D8: 2,3,5,9 + C9: 2,6 * CNT 2 HDP CHAINS / 24 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction Position
position: ...4.678...718.2....8.72.1..8.64..71......42.74..216.85.4.....7871.64...93.....4. pair_reduction
See section Pair Reduction for the HDP chains leading to this result.
Deep Pair Reduction
Time used: 0:00:20.953701
The following important HDP chains were detected:
* DIS # C4: 2,3 # C1: 5,9 => CTR => C1: 2,3 * DIS # C4: 5,9 # B5: 5,9 => CTR => B5: 1,6 * PRF # C4: 5,9 + B5: 1,6 # A5: 3 => SOL * STA # C4: 5,9 + B5: 1,6 + A5: 3 * CNT 3 HDP CHAINS / 83 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...4.678....18.2......72.1..8..4..71......42.74..216.85.4.....7..1.64...93.....4. | initial |
| ...4.678....18.2......72.1..8.64..71......42.74..216.85.4.....7..1.64...93.....4. | autosolve |
| ...4.678...718.2....8.72.1..8.64..71......42.74..216.85.4.....7871.64...93.....4. | pair_reduction |
| 123456789457189263698372514285643971316897425749521638564238197871964352932715846 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (7) A4: 2,3 D5: 7,8 F5: 7,8 B7: 2,6 A8: 2,8 B8: 2,7 E9: 1,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,B1: 1.. / A1 = 1 => 9 pairs (_) / B1 = 1 => 14 pairs (_) A5,B5: 1.. / A5 = 1 => 14 pairs (_) / B5 = 1 => 9 pairs (_) E7,E9: 1.. / E7 = 1 => 11 pairs (_) / E9 = 1 => 9 pairs (_) G7,G9: 1.. / G7 = 1 => 9 pairs (_) / G9 = 1 => 11 pairs (_) E7,G7: 1.. / E7 = 1 => 11 pairs (_) / G7 = 1 => 9 pairs (_) E9,G9: 1.. / E9 = 1 => 9 pairs (_) / G9 = 1 => 11 pairs (_) A1,A5: 1.. / A1 = 1 => 9 pairs (_) / A5 = 1 => 14 pairs (_) B1,B5: 1.. / B1 = 1 => 14 pairs (_) / B5 = 1 => 9 pairs (_) A4,C4: 2.. / A4 = 2 => 8 pairs (_) / C4 = 2 => 13 pairs (_) I8,I9: 2.. / I8 = 2 => 10 pairs (_) / I9 = 2 => 11 pairs (_) B7,D7: 2.. / B7 = 2 => 13 pairs (_) / D7 = 2 => 0 pairs (*) A2,A3: 4.. / A2 = 4 => 7 pairs (_) / A3 = 4 => 9 pairs (_) I2,I3: 4.. / I2 = 4 => 9 pairs (_) / I3 = 4 => 7 pairs (_) A2,I2: 4.. / A2 = 4 => 7 pairs (_) / I2 = 4 => 9 pairs (_) A3,I3: 4.. / A3 = 4 => 9 pairs (_) / I3 = 4 => 7 pairs (_) B7,C9: 6.. / B7 = 6 => 0 pairs (*) / C9 = 6 => 0 pairs (X) H7,I9: 6.. / H7 = 6 => 13 pairs (_) / I9 = 6 => 0 pairs (*) B7,H7: 6.. / B7 = 6 => 0 pairs (*) / H7 = 6 => 0 pairs (X) C9,I9: 6.. / C9 = 6 => 13 pairs (_) / I9 = 6 => 0 pairs (*) H2,H7: 6.. / H2 = 6 => 0 pairs (*) / H7 = 6 => 0 pairs (X) B2,C2: 7.. / B2 = 7 => 0 pairs (X) / C2 = 7 => 6 pairs (_) D5,F5: 7.. / D5 = 7 => 5 pairs (_) / F5 = 7 => 9 pairs (_) B8,C9: 7.. / B8 = 7 => 6 pairs (_) / C9 = 7 => 0 pairs (X) B8,D8: 7.. / B8 = 7 => 6 pairs (_) / D8 = 7 => 0 pairs (X) B2,B8: 7.. / B2 = 7 => 0 pairs (X) / B8 = 7 => 6 pairs (_) C2,C9: 7.. / C2 = 7 => 6 pairs (_) / C9 = 7 => 0 pairs (X) F5,F9: 7.. / F5 = 7 => 9 pairs (_) / F9 = 7 => 5 pairs (_) A3,C3: 8.. / A3 = 8 => 0 pairs (X) / C3 = 8 => 8 pairs (_) D5,F5: 8.. / D5 = 8 => 9 pairs (_) / F5 = 8 => 5 pairs (_) A8,C9: 8.. / A8 = 8 => 8 pairs (_) / C9 = 8 => 0 pairs (X) A3,A8: 8.. / A3 = 8 => 0 pairs (X) / A8 = 8 => 8 pairs (_) C3,C9: 8.. / C3 = 8 => 8 pairs (_) / C9 = 8 => 0 pairs (X) * DURATION: 0:00:09.027571 START: 05:49:15.732252 END: 05:49:24.759823 2025-04-06 * CP COUNT: (32) * SOLUTION FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:20.753863 START: 05:49:33.014706 END: 05:49:53.768569 2025-04-06 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00018455-base-pr-002.dot * REASONING * DIS # C4: 2,3 # C1: 5,9 => CTR => C1: 2,3 * DIS # C4: 5,9 # B5: 5,9 => CTR => B5: 1,6 * PRF # C4: 5,9 + B5: 1,6 # A5: 3 => SOL * STA # C4: 5,9 + B5: 1,6 + A5: 3 * CNT 3 HDP CHAINS / 83 HYP OPENED
Header Info
rating: 3911; r2: 142158; index: 18455
Solution
position: 123456789457189263698372514285643971316897425749521638564238197871964352932715846 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 # C4: 2,3 => UNS * INC # C4: 5,9 => UNS * INC # A1: 2,3 => UNS * INC # A1: 1 => UNS * DIS # D8: 7,8 => CTR => D8: 2,3,5,9 * INC # D8: 2,3,5,9 => UNS * INC # D9: 7,8 => UNS * INC # F9: 7,8 => UNS * INC # F9: 5 => UNS * INC # C9: 2,6 => UNS * DIS # C9: 7,8 => CTR => C9: 2,6 * PRF # C9: 2,8 => SOL * INC # C9: 6,7 => UNS * INC # D8: 2,8 => UNS * INC # D8: 3,5,7,9 => UNS * PRF # C9: 2,7 => SOL * INC # C9: 6,8 => UNS * INC # D8: 2,7 => UNS * INC # D8: 3,5,8,9 => UNS * INC # G9: 1,5 => UNS * INC # G9: 8 => UNS * CNT 21 HDP CHAINS / 21 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C4: 2,3 => UNS * INC # C4: 5,9 => UNS * INC # A1: 2,3 => UNS * INC # A1: 1 => UNS * DIS # D8: 7,8 => CTR => D8: 2,3,5,9 * INC D8: 2,3,5,9 # D9: 7,8 => UNS * INC D8: 2,3,5,9 # D9: 7,8 => UNS * INC D8: 2,3,5,9 # D9: 2,5 => UNS * INC D8: 2,3,5,9 # D9: 7,8 => UNS * INC D8: 2,3,5,9 # D9: 2,5 => UNS * INC D8: 2,3,5,9 # F9: 7,8 => UNS * INC D8: 2,3,5,9 # F9: 5 => UNS * INC D8: 2,3,5,9 # C9: 2,6 => UNS * DIS D8: 2,3,5,9 # C9: 8 => CTR => C9: 2,6 * INC D8: 2,3,5,9 + C9: 2,6 # C4: 2,3 => UNS * INC D8: 2,3,5,9 + C9: 2,6 # C4: 5,9 => UNS * INC D8: 2,3,5,9 + C9: 2,6 # A1: 2,3 => UNS * INC D8: 2,3,5,9 + C9: 2,6 # A1: 1 => UNS * INC D8: 2,3,5,9 + C9: 2,6 # D9: 7,8 => UNS * INC D8: 2,3,5,9 + C9: 2,6 # D9: 2,5 => UNS * INC D8: 2,3,5,9 + C9: 2,6 # F9: 7,8 => UNS * INC D8: 2,3,5,9 + C9: 2,6 # F9: 5 => UNS * INC D8: 2,3,5,9 + C9: 2,6 # I9: 2,6 => UNS * INC D8: 2,3,5,9 + C9: 2,6 # I9: 5 => UNS * STA D8: 2,3,5,9 + C9: 2,6 * CNT 24 HDP CHAINS / 24 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # C4: 2,3 => UNS * INC # C4: 5,9 => UNS * INC # A1: 2,3 => UNS * INC # A1: 1 => UNS * INC # D9: 7,8 => UNS * INC # D9: 2,5 => UNS * INC # F9: 7,8 => UNS * INC # F9: 5 => UNS * INC # I9: 2,6 => UNS * INC # I9: 5 => UNS * INC # C4: 2,3 # A1: 2,3 => UNS * INC # C4: 2,3 # A1: 1 => UNS * INC # C4: 2,3 # C1: 2,3 => UNS * DIS # C4: 2,3 # C1: 5,9 => CTR => C1: 2,3 * INC # C4: 2,3 + C1: 2,3 # D6: 5,9 => UNS * INC # C4: 2,3 + C1: 2,3 # H6: 5,9 => UNS * INC # C4: 2,3 + C1: 2,3 # E5: 5,9 => UNS * INC # C4: 2,3 + C1: 2,3 # D6: 5,9 => UNS * INC # C4: 2,3 + C1: 2,3 # F2: 5,9 => UNS * INC # C4: 2,3 + C1: 2,3 # F2: 3 => UNS * INC # C4: 2,3 + C1: 2,3 # D9: 7,8 => UNS * INC # C4: 2,3 + C1: 2,3 # D9: 2,5 => UNS * INC # C4: 2,3 + C1: 2,3 # F9: 7,8 => UNS * INC # C4: 2,3 + C1: 2,3 # F9: 5 => UNS * INC # C4: 2,3 + C1: 2,3 # I5: 5,9 => UNS * INC # C4: 2,3 + C1: 2,3 # H6: 5,9 => UNS * INC # C4: 2,3 + C1: 2,3 # G3: 5,9 => UNS * INC # C4: 2,3 + C1: 2,3 # G8: 5,9 => UNS * INC # C4: 2,3 + C1: 2,3 # A1: 2,3 => UNS * INC # C4: 2,3 + C1: 2,3 # A1: 1 => UNS * INC # C4: 2,3 + C1: 2,3 # A2: 4,6 => UNS * INC # C4: 2,3 + C1: 2,3 # A2: 3 => UNS * INC # C4: 2,3 + C1: 2,3 # A3: 4,6 => UNS * INC # C4: 2,3 + C1: 2,3 # A3: 3 => UNS * INC # C4: 2,3 + C1: 2,3 # A1: 2,3 => UNS * INC # C4: 2,3 + C1: 2,3 # A1: 1 => UNS * INC # C4: 2,3 + C1: 2,3 # E5: 5,9 => UNS * INC # C4: 2,3 + C1: 2,3 # I5: 5,9 => UNS * INC # C4: 2,3 + C1: 2,3 # D6: 5,9 => UNS * INC # C4: 2,3 + C1: 2,3 # H6: 5,9 => UNS * INC # C4: 2,3 + C1: 2,3 # E5: 5,9 => UNS * INC # C4: 2,3 + C1: 2,3 # D6: 5,9 => UNS * INC # C4: 2,3 + C1: 2,3 # F2: 5,9 => UNS * INC # C4: 2,3 + C1: 2,3 # F2: 3 => UNS * INC # C4: 2,3 + C1: 2,3 # D9: 7,8 => UNS * INC # C4: 2,3 + C1: 2,3 # D9: 2,5 => UNS * INC # C4: 2,3 + C1: 2,3 # F9: 7,8 => UNS * INC # C4: 2,3 + C1: 2,3 # F9: 5 => UNS * INC # C4: 2,3 + C1: 2,3 # I5: 5,9 => UNS * INC # C4: 2,3 + C1: 2,3 # H6: 5,9 => UNS * INC # C4: 2,3 + C1: 2,3 # G3: 5,9 => UNS * INC # C4: 2,3 + C1: 2,3 # G8: 5,9 => UNS * INC # C4: 2,3 + C1: 2,3 # D9: 2,5 => UNS * INC # C4: 2,3 + C1: 2,3 # D9: 7,8 => UNS * INC # C4: 2,3 + C1: 2,3 # I8: 2,5 => UNS * INC # C4: 2,3 + C1: 2,3 # I8: 3,9 => UNS * INC # C4: 2,3 + C1: 2,3 # I8: 2,5 => UNS * INC # C4: 2,3 + C1: 2,3 # I8: 3,9 => UNS * INC # C4: 2,3 + C1: 2,3 # D9: 2,5 => UNS * INC # C4: 2,3 + C1: 2,3 # D9: 7,8 => UNS * INC # C4: 2,3 + C1: 2,3 => UNS * INC # C4: 5,9 # A5: 1,3 => UNS * INC # C4: 5,9 # A5: 6 => UNS * DIS # C4: 5,9 # B5: 5,9 => CTR => B5: 1,6 * INC # C4: 5,9 + B5: 1,6 # C5: 5,9 => UNS * INC # C4: 5,9 + B5: 1,6 # C6: 5,9 => UNS * INC # C4: 5,9 + B5: 1,6 # F4: 5,9 => UNS * INC # C4: 5,9 + B5: 1,6 # G4: 5,9 => UNS * INC # C4: 5,9 + B5: 1,6 # D9: 7,8 => UNS * INC # C4: 5,9 + B5: 1,6 # D9: 2,5 => UNS * INC # C4: 5,9 + B5: 1,6 # F9: 7,8 => UNS * INC # C4: 5,9 + B5: 1,6 # F9: 5 => UNS * INC # C4: 5,9 + B5: 1,6 # I9: 2,6 => UNS * INC # C4: 5,9 + B5: 1,6 # I9: 5 => UNS * INC # C4: 5,9 + B5: 1,6 # A5: 1,3 => UNS * INC # C4: 5,9 + B5: 1,6 # A5: 6 => UNS * INC # C4: 5,9 + B5: 1,6 # C5: 5,9 => UNS * INC # C4: 5,9 + B5: 1,6 # C6: 5,9 => UNS * INC # C4: 5,9 + B5: 1,6 # F4: 5,9 => UNS * INC # C4: 5,9 + B5: 1,6 # G4: 5,9 => UNS * INC # C4: 5,9 + B5: 1,6 # A5: 1,6 => UNS * PRF # C4: 5,9 + B5: 1,6 # A5: 3 => SOL * STA # C4: 5,9 + B5: 1,6 + A5: 3 * CNT 82 HDP CHAINS / 83 HYP OPENED