Analysis of xx-mith-te3-00029219-base.sdk
Contents
Original Sudoku
level: hard
position: ....56.8....18...66892.3...24....9...36...8.49.8..4..........28.62...4..89....6.3 initial
Autosolve
position: ....56.8....18...66892.3...24....9...36...8.49.8..4..........28.62...4..89....6.3 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D1: 9 => CTR => D1: 4,7 * DIS # E7: 4,7 => CTR => E7: 1,3,6,9 * CNT 2 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D1: 9 => CTR => D1: 4,7 * STA D1: 4,7 * CNT 1 HDP CHAINS / 24 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction Position
position: ....56.89...189..66892.3...24....9...36...8.49.8..4..2.......28.62...49.89....6.3 pair_reduction
See section Pair Reduction for the HDP chains leading to this result.
Deep Pair Reduction
Time used: 0:00:16.979686
The following important HDP chains were detected:
* DIS # C1: 4,7 # D9: 5 => CTR => D9: 4,7 * DIS # C1: 4,7 + D9: 4,7 # G2: 7 => CTR => G2: 2,3 * DIS # D9: 5 # A2: 3,7 => CTR => A2: 4,5 * PRF # D9: 5 + A2: 4,5 # C2: 3,7 => SOL * STA # D9: 5 + A2: 4,5 + C2: 3,7 * CNT 4 HDP CHAINS / 80 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....56.8....18...66892.3...24....9...36...8.49.8..4..........28.62...4..89....6.3 | initial |
| ....56.8....18...66892.3...24....9...36...8.49.8..4..........28.62...4..89....6.3 | autosolve |
| ....56.89...189..66892.3...24....9...36...8.49.8..4..2.......28.62...49.89....6.3 | pair_reduction |
| 123456789457189236689273145245318967736925814918764352374691528562837491891542673 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (2) F2: 7,9 E3: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,B2: 2.. / B1 = 2 => 5 pairs (_) / B2 = 2 => 4 pairs (_) E5,F5: 2.. / E5 = 2 => 4 pairs (_) / F5 = 2 => 2 pairs (_) G6,I6: 2.. / G6 = 2 => 0 pairs (X) / I6 = 2 => 3 pairs (_) E9,F9: 2.. / E9 = 2 => 2 pairs (_) / F9 = 2 => 4 pairs (_) B2,G2: 2.. / B2 = 2 => 4 pairs (_) / G2 = 2 => 5 pairs (_) E5,E9: 2.. / E5 = 2 => 4 pairs (_) / E9 = 2 => 2 pairs (_) F5,F9: 2.. / F5 = 2 => 2 pairs (_) / F9 = 2 => 4 pairs (_) I1,I6: 2.. / I1 = 2 => 0 pairs (X) / I6 = 2 => 3 pairs (_) D1,E3: 4.. / D1 = 4 => 7 pairs (_) / E3 = 4 => 10 pairs (_) H2,H3: 4.. / H2 = 4 => 10 pairs (_) / H3 = 4 => 7 pairs (_) E3,H3: 4.. / E3 = 4 => 10 pairs (_) / H3 = 4 => 7 pairs (_) H4,H6: 6.. / H4 = 6 => 2 pairs (_) / H6 = 6 => 2 pairs (_) D7,E7: 6.. / D7 = 6 => 2 pairs (_) / E7 = 6 => 12 pairs (_) D4,F4: 8.. / D4 = 8 => 4 pairs (_) / F4 = 8 => 2 pairs (_) D8,F8: 8.. / D8 = 8 => 2 pairs (_) / F8 = 8 => 4 pairs (_) D4,D8: 8.. / D4 = 8 => 4 pairs (_) / D8 = 8 => 2 pairs (_) F4,F8: 8.. / F4 = 8 => 2 pairs (_) / F8 = 8 => 4 pairs (_) D1,F2: 9.. / D1 = 9 => 0 pairs (X) / F2 = 9 => 6 pairs (_) I1,H2: 9.. / I1 = 9 => 6 pairs (_) / H2 = 9 => 0 pairs (X) H8,I8: 9.. / H8 = 9 => 6 pairs (_) / I8 = 9 => 0 pairs (X) D1,I1: 9.. / D1 = 9 => 0 pairs (X) / I1 = 9 => 6 pairs (_) F2,H2: 9.. / F2 = 9 => 6 pairs (_) / H2 = 9 => 0 pairs (X) E5,E7: 9.. / E5 = 9 => 3 pairs (_) / E7 = 9 => 4 pairs (_) H2,H8: 9.. / H2 = 9 => 0 pairs (X) / H8 = 9 => 6 pairs (_) I1,I8: 9.. / I1 = 9 => 6 pairs (_) / I8 = 9 => 0 pairs (X) * DURATION: 0:00:05.730992 START: 11:05:04.714559 END: 11:05:10.445551 2025-04-04 * CP COUNT: (25) * CLUE FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:16.787739 START: 11:05:16.807489 END: 11:05:33.595228 2025-04-04 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00029219-base-pr-002.dot * REASONING * DIS # C1: 4,7 # D9: 5 => CTR => D9: 4,7 * DIS # C1: 4,7 + D9: 4,7 # G2: 7 => CTR => G2: 2,3 * DIS # D9: 5 # A2: 3,7 => CTR => A2: 4,5 * PRF # D9: 5 + A2: 4,5 # C2: 3,7 => SOL * STA # D9: 5 + A2: 4,5 + C2: 3,7 * CNT 4 HDP CHAINS / 80 HYP OPENED
Header Info
rating: 5969; r2: 144837; index: 29219
Solution
position: 123456789457189236689273145245318967736925814918764352374691528562837491891542673 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 # D1: 7,9 => UNS * INC # D1: 4 => UNS * INC # H2: 7,9 => UNS * INC # H2: 3,4 => UNS * INC # F5: 7,9 => UNS * INC # F7: 7,9 => UNS * INC # D1: 4,7 => UNS * DIS # D1: 9 => CTR => D1: 4,7 * INC # H3: 4,7 => UNS * INC # H3: 1,5 => UNS * DIS # E7: 4,7 => CTR => E7: 1,3,6,9 * INC # E7: 1,3,6,9 => UNS * INC # E9: 4,7 => UNS * CNT 13 HDP CHAINS / 13 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D1: 7,9 => UNS * INC # D1: 4 => UNS * INC # H2: 7,9 => UNS * INC # H2: 3,4 => UNS * INC # F5: 7,9 => UNS * INC # F7: 7,9 => UNS * INC # D1: 4,7 => UNS * DIS # D1: 9 => CTR => D1: 4,7 * INC D1: 4,7 # H3: 4,7 => UNS * INC D1: 4,7 # H3: 1,5 => UNS * INC D1: 4,7 # E9: 4,7 => UNS * INC D1: 4,7 # E9: 1,2 => UNS * INC D1: 4,7 # A1: 4,7 => UNS * INC D1: 4,7 # C1: 4,7 => UNS * INC D1: 4,7 # D9: 4,7 => UNS * INC D1: 4,7 # D9: 5 => UNS * INC D1: 4,7 # H3: 4,7 => UNS * INC D1: 4,7 # H3: 1,5 => UNS * INC D1: 4,7 # E9: 4,7 => UNS * INC D1: 4,7 # E9: 1,2 => UNS * INC D1: 4,7 # A1: 3,4 => UNS * INC D1: 4,7 # A2: 3,4 => UNS * INC D1: 4,7 # C1: 3,4 => UNS * INC D1: 4,7 # C2: 3,4 => UNS * STA D1: 4,7 * CNT 24 HDP CHAINS / 24 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 4,7 => UNS * INC # C1: 4,7 => UNS * INC # D9: 4,7 => UNS * INC # D9: 5 => UNS * INC # H3: 4,7 => UNS * INC # H3: 1,5 => UNS * INC # E9: 4,7 => UNS * INC # E9: 1,2 => UNS * INC # A1: 3,4 => UNS * INC # A2: 3,4 => UNS * INC # C1: 3,4 => UNS * INC # C2: 3,4 => UNS * INC # A1: 4,7 # A2: 4,7 => UNS * INC # A1: 4,7 # C2: 4,7 => UNS * INC # A1: 4,7 # D9: 4,7 => UNS * INC # A1: 4,7 # D9: 5 => UNS * INC # A1: 4,7 # H3: 4,7 => UNS * INC # A1: 4,7 # H3: 1,5 => UNS * INC # A1: 4,7 # E9: 4,7 => UNS * INC # A1: 4,7 # E9: 1,2 => UNS * INC # A1: 4,7 # G2: 2,3 => UNS * INC # A1: 4,7 # G2: 7 => UNS * INC # A1: 4,7 # A2: 3,4 => UNS * INC # A1: 4,7 # A2: 5,7 => UNS * INC # A1: 4,7 # C2: 3,4 => UNS * INC # A1: 4,7 # C2: 5,7 => UNS * INC # A1: 4,7 => UNS * INC # C1: 4,7 # A2: 4,7 => UNS * INC # C1: 4,7 # C2: 4,7 => UNS * INC # C1: 4,7 # D9: 4,7 => UNS * DIS # C1: 4,7 # D9: 5 => CTR => D9: 4,7 * INC # C1: 4,7 + D9: 4,7 # H3: 4,7 => UNS * INC # C1: 4,7 + D9: 4,7 # H3: 1,5 => UNS * INC # C1: 4,7 + D9: 4,7 # E9: 4,7 => UNS * INC # C1: 4,7 + D9: 4,7 # E9: 1,2 => UNS * INC # C1: 4,7 + D9: 4,7 # G2: 2,3 => UNS * DIS # C1: 4,7 + D9: 4,7 # G2: 7 => CTR => G2: 2,3 * INC # C1: 4,7 + D9: 4,7 + G2: 2,3 # A2: 3,4 => UNS * INC # C1: 4,7 + D9: 4,7 + G2: 2,3 # A2: 5,7 => UNS * INC # C1: 4,7 + D9: 4,7 + G2: 2,3 # C2: 3,4 => UNS * INC # C1: 4,7 + D9: 4,7 + G2: 2,3 # C2: 5,7 => UNS * INC # C1: 4,7 + D9: 4,7 + G2: 2,3 # A2: 4,7 => UNS * INC # C1: 4,7 + D9: 4,7 + G2: 2,3 # C2: 4,7 => UNS * INC # C1: 4,7 + D9: 4,7 + G2: 2,3 # H3: 4,7 => UNS * INC # C1: 4,7 + D9: 4,7 + G2: 2,3 # H3: 1,5 => UNS * INC # C1: 4,7 + D9: 4,7 + G2: 2,3 # E9: 4,7 => UNS * INC # C1: 4,7 + D9: 4,7 + G2: 2,3 # E9: 1,2 => UNS * INC # C1: 4,7 + D9: 4,7 + G2: 2,3 # H3: 4,7 => UNS * INC # C1: 4,7 + D9: 4,7 + G2: 2,3 # H3: 1,5 => UNS * INC # C1: 4,7 + D9: 4,7 + G2: 2,3 # A2: 4,7 => UNS * INC # C1: 4,7 + D9: 4,7 + G2: 2,3 # C2: 4,7 => UNS * INC # C1: 4,7 + D9: 4,7 + G2: 2,3 # D4: 3,6 => UNS * INC # C1: 4,7 + D9: 4,7 + G2: 2,3 # E4: 3,6 => UNS * INC # C1: 4,7 + D9: 4,7 + G2: 2,3 # D6: 3,6 => UNS * INC # C1: 4,7 + D9: 4,7 + G2: 2,3 # E6: 3,6 => UNS * INC # C1: 4,7 + D9: 4,7 + G2: 2,3 # A2: 3,4 => UNS * INC # C1: 4,7 + D9: 4,7 + G2: 2,3 # A2: 5,7 => UNS * INC # C1: 4,7 + D9: 4,7 + G2: 2,3 # C2: 3,4 => UNS * INC # C1: 4,7 + D9: 4,7 + G2: 2,3 # C2: 5,7 => UNS * INC # C1: 4,7 + D9: 4,7 + G2: 2,3 # E9: 4,7 => UNS * INC # C1: 4,7 + D9: 4,7 + G2: 2,3 # E9: 1,2 => UNS * INC # C1: 4,7 + D9: 4,7 + G2: 2,3 => UNS * INC # D9: 4,7 # A1: 4,7 => UNS * INC # D9: 4,7 # C1: 4,7 => UNS * INC # D9: 4,7 # H3: 4,7 => UNS * INC # D9: 4,7 # H3: 1,5 => UNS * INC # D9: 4,7 # E9: 4,7 => UNS * INC # D9: 4,7 # E9: 1,2 => UNS * INC # D9: 4,7 # A1: 3,4 => UNS * INC # D9: 4,7 # A2: 3,4 => UNS * INC # D9: 4,7 # C1: 3,4 => UNS * INC # D9: 4,7 # C2: 3,4 => UNS * INC # D9: 4,7 # E9: 4,7 => UNS * INC # D9: 4,7 # E9: 1,2 => UNS * INC # D9: 4,7 => UNS * INC # D9: 5 # G1: 3,7 => UNS * INC # D9: 5 # G2: 3,7 => UNS * DIS # D9: 5 # A2: 3,7 => CTR => A2: 4,5 * PRF # D9: 5 + A2: 4,5 # C2: 3,7 => SOL * STA # D9: 5 + A2: 4,5 + C2: 3,7 * CNT 79 HDP CHAINS / 80 HYP OPENED