Analysis of xx-mith-te3-00086597-base.sdk
Contents
Original Sudoku
level: hard
position: 12...6.89..6..91.28.9..156....36.......9.2.56....78...5.2...6.8..1......9.......5 initial
Autosolve
position: 12...6.89..6..91.28.9..156....36.......9.2.56....78...5.2...6.8..1......9.......5 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D6: 1 => CTR => D6: 4,5 * DIS # B4: 4,5 => CTR => B4: 1,7,8,9 * 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 # D6: 1 => CTR => D6: 4,5 * DIS D6: 4,5 # C6: 3 => CTR => C6: 4,5 * DIS D6: 4,5 + C6: 4,5 # D9: 1,4 => CTR => D9: 2,6,8 * DIS D6: 4,5 + C6: 4,5 + D9: 2,6,8 # E8: 4,9 => CTR => E8: 2,5,8 * STA D6: 4,5 + C6: 4,5 + D9: 2,6,8 + E8: 2,5,8 * CNT 4 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction Position
position: 12...6.89.56..91.28.9..156.2..36.......912.566...78...5.219.6.8..1......9......15 pair_reduction
See section Pair Reduction for the HDP chains leading to this result.
Deep Pair Reduction
Time used: 0:00:05.483102
The following important HDP chains were detected:
* DIS # C4: 4,5 # A2: 3,7 => CTR => A2: 4 * DIS # C4: 4,5 + A2: 4 # C9: 3,7 => CTR => C9: 8 * PRF # C4: 4,5 + A2: 4 + C9: 8 # G9: 2 => SOL * STA # C4: 4,5 + A2: 4 + C9: 8 + G9: 2 * CNT 3 HDP CHAINS / 14 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 12...6.89..6..91.28.9..156....36.......9.2.56....78...5.2...6.8..1......9.......5 | initial |
| 12...6.89..6..91.28.9..156....36.......9.2.56....78...5.2...6.8..1......9.......5 | autosolve |
| 12...6.89.56..91.28.9..156.2..36.......912.566...78...5.219.6.8..1......9......15 | pair_reduction |
| 123456789456789132879231564215364897387912456694578321542193678761825943938647215 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (3) F4: 4,5 E5: 1,4 D7: 1,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E5,D6: 1.. / E5 = 1 => 6 pairs (_) / D6 = 1 => 0 pairs (X) I4,I6: 1.. / I4 = 1 => 4 pairs (_) / I6 = 1 => 5 pairs (_) H7,H9: 1.. / H7 = 1 => 21 pairs (_) / H9 = 1 => 3 pairs (_) B4,I4: 1.. / B4 = 1 => 5 pairs (_) / I4 = 1 => 4 pairs (_) B5,E5: 1.. / B5 = 1 => 0 pairs (X) / E5 = 1 => 6 pairs (_) D3,E3: 2.. / D3 = 2 => 4 pairs (_) / E3 = 2 => 6 pairs (_) A4,A6: 2.. / A4 = 2 => 3 pairs (_) / A6 = 2 => 0 pairs (X) C1,B2: 5.. / C1 = 5 => 0 pairs (X) / B2 = 5 => 3 pairs (_) F4,D6: 5.. / F4 = 5 => 11 pairs (_) / D6 = 5 => 11 pairs (_) F4,F8: 5.. / F4 = 5 => 11 pairs (_) / F8 = 5 => 11 pairs (_) A6,B6: 6.. / A6 = 6 => 3 pairs (_) / B6 = 6 => 0 pairs (X) D8,D9: 6.. / D8 = 6 => 3 pairs (_) / D9 = 6 => 3 pairs (_) B9,D9: 6.. / B9 = 6 => 3 pairs (_) / D9 = 6 => 3 pairs (_) A6,A8: 6.. / A6 = 6 => 3 pairs (_) / A8 = 6 => 0 pairs (X) D2,E2: 8.. / D2 = 8 => 3 pairs (_) / E2 = 8 => 6 pairs (_) G4,G5: 8.. / G4 = 8 => 3 pairs (_) / G5 = 8 => 5 pairs (_) B4,B6: 9.. / B4 = 9 => 4 pairs (_) / B6 = 9 => 3 pairs (_) E7,E8: 9.. / E7 = 9 => 3 pairs (_) / E8 = 9 => 14 pairs (_) E7,H7: 9.. / E7 = 9 => 3 pairs (_) / H7 = 9 => 14 pairs (_) * DURATION: 0:00:04.717675 START: 12:45:17.566794 END: 12:45:22.284469 2025-04-06 * CP COUNT: (19) * CLUE FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:05.368215 START: 12:45:32.234000 END: 12:45:37.602215 2025-04-06 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00086597-base-pr-002.dot * REASONING * DIS # C4: 4,5 # A2: 3,7 => CTR => A2: 4 * DIS # C4: 4,5 + A2: 4 # C9: 3,7 => CTR => C9: 8 * PRF # C4: 4,5 + A2: 4 + C9: 8 # G9: 2 => SOL * STA # C4: 4,5 + A2: 4 + C9: 8 + G9: 2 * CNT 3 HDP CHAINS / 14 HYP OPENED
Header Info
rating: 21650; r2: 480554; index: 86597
Solution
position: 123456789456789132879231564215364897387912456694578321542193678761825943938647215 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 # D6: 4,5 => UNS * DIS # D6: 1 => CTR => D6: 4,5 * DIS # B4: 4,5 => CTR => B4: 1,7,8,9 * INC # B4: 1,7,8,9 => UNS * INC # C4: 4,5 => UNS * INC # F8: 4,5 => UNS * INC # F8: 3,7 => UNS * INC # D6: 1,4 => UNS * INC # D6: 5 => UNS * INC # B5: 1,4 => UNS * INC # B5: 3,7,8 => UNS * INC # E7: 1,4 => UNS * INC # E9: 1,4 => UNS * INC # E7: 1,4 => UNS * INC # D9: 1,4 => UNS * INC # E9: 1,4 => UNS * INC # H7: 1,4 => UNS * INC # H7: 3,7,9 => UNS * INC # D6: 1,4 => UNS * INC # D6: 5 => UNS * CNT 20 HDP CHAINS / 20 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D6: 4,5 => UNS * DIS # D6: 1 => CTR => D6: 4,5 * INC D6: 4,5 # C4: 4,5 => UNS * INC D6: 4,5 # C4: 7,8 => UNS * INC D6: 4,5 # F8: 4,5 => UNS * INC D6: 4,5 # F8: 3,7 => UNS * INC D6: 4,5 # D9: 1,4 => UNS * INC D6: 4,5 # D9: 2,6,8 => UNS * INC D6: 4,5 # H7: 1,4 => UNS * INC D6: 4,5 # H7: 3,7,9 => UNS * INC D6: 4,5 # C4: 4,5 => UNS * INC D6: 4,5 # C4: 7,8 => UNS * INC D6: 4,5 # F8: 4,5 => UNS * INC D6: 4,5 # F8: 3,7 => UNS * INC D6: 4,5 # C6: 4,5 => UNS * DIS D6: 4,5 # C6: 3 => CTR => C6: 4,5 * INC D6: 4,5 + C6: 4,5 # D1: 4,5 => UNS * INC D6: 4,5 + C6: 4,5 # D8: 4,5 => UNS * INC D6: 4,5 + C6: 4,5 # D1: 4,5 => UNS * INC D6: 4,5 + C6: 4,5 # D8: 4,5 => UNS * DIS D6: 4,5 + C6: 4,5 # D9: 1,4 => CTR => D9: 2,6,8 * DIS D6: 4,5 + C6: 4,5 + D9: 2,6,8 # E8: 4,9 => CTR => E8: 2,5,8 * INC D6: 4,5 + C6: 4,5 + D9: 2,6,8 + E8: 2,5,8 # C4: 4,5 => UNS * INC D6: 4,5 + C6: 4,5 + D9: 2,6,8 + E8: 2,5,8 # C4: 7,8 => UNS * INC D6: 4,5 + C6: 4,5 + D9: 2,6,8 + E8: 2,5,8 # C4: 4,5 => UNS * INC D6: 4,5 + C6: 4,5 + D9: 2,6,8 + E8: 2,5,8 # C4: 7,8 => UNS * INC D6: 4,5 + C6: 4,5 + D9: 2,6,8 + E8: 2,5,8 # F8: 4,5 => UNS * INC D6: 4,5 + C6: 4,5 + D9: 2,6,8 + E8: 2,5,8 # F8: 3,7 => UNS * INC D6: 4,5 + C6: 4,5 + D9: 2,6,8 + E8: 2,5,8 # D1: 4,5 => UNS * INC D6: 4,5 + C6: 4,5 + D9: 2,6,8 + E8: 2,5,8 # D8: 4,5 => UNS * STA D6: 4,5 + C6: 4,5 + D9: 2,6,8 + E8: 2,5,8 * CNT 30 HDP CHAINS / 30 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # C4: 4,5 => UNS * INC # C4: 7,8 => UNS * INC # C4: 4,5 => UNS * INC # C4: 7,8 => UNS * INC # F8: 4,5 => UNS * INC # F8: 3,7 => UNS * INC # D1: 4,5 => UNS * INC # D8: 4,5 => UNS * DIS # C4: 4,5 # A2: 3,7 => CTR => A2: 4 * INC # C4: 4,5 + A2: 4 # C5: 3,7 => UNS * DIS # C4: 4,5 + A2: 4 # C9: 3,7 => CTR => C9: 8 * INC # C4: 4,5 + A2: 4 + C9: 8 # G9: 3,7 => UNS * PRF # C4: 4,5 + A2: 4 + C9: 8 # G9: 2 => SOL * STA # C4: 4,5 + A2: 4 + C9: 8 + G9: 2 * CNT 13 HDP CHAINS / 14 HYP OPENED