Analysis of xx-mith-te3-00153396-base.sdk
Contents
Original Sudoku
level: hard
position: .23.56......18.......7.2.....5..49...6....45..94....235.2.9.36..36....949........ initial
Autosolve
position: .23.56......18.......7.2.....5..49...6....45..94....235.2.9.36..36....949........ autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H3: 1,8 => CTR => H3: 3,4 * DIS # D9: 4,8 => CTR => D9: 2,3,5,6 * CNT 2 HDP CHAINS / 18 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H3: 1,8 => CTR => H3: 3,4 * DIS H3: 3,4 # D9: 4,8 => CTR => D9: 2,3,5,6 * STA H3: 3,4 + D9: 2,3,5,6 * CNT 2 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction Position
position: .23.56......18.......7.2.....5..49...6....45..94....235.2.9.36..36....949........ pair_reduction
See section Pair Reduction for the HDP chains leading to this result.
Deep Pair Reduction
Time used: 0:00:22.134144
The following important HDP chains were detected:
* DIS # F5: 1,7,8 # G1: 1,8 => CTR => G1: 7 * PRF # F5: 1,7,8 + G1: 7 # A6: 1,8 => SOL * STA # F5: 1,7,8 + G1: 7 + A6: 1,8 * CNT 2 HDP CHAINS / 107 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .23.56......18.......7.2.....5..49...6....45..94....235.2.9.36..36....949........ | initial |
| .23.56......18.......7.2.....5..49...6....45..94....235.2.9.36..36....949........ | autosolve |
| .23.56......18.......7.2.....5..49...6....45..94....235.2.9.36..36....949........ | pair_reduction |
| 123456789457189236689732145275364918361928457894571623542897361736215894918643572 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (8) B2: 5,7 C2: 7,9 D1: 4,9 F2: 3,9 E3: 3,4 A4: 2,3 A5: 2,3 D7: 4,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G2,I2: 2.. / G2 = 2 => 8 pairs (_) / I2 = 2 => 8 pairs (_) A4,A5: 2.. / A4 = 2 => 6 pairs (_) / A5 = 2 => 6 pairs (_) I2,I9: 2.. / I2 = 2 => 8 pairs (_) / I9 = 2 => 8 pairs (_) F2,E3: 3.. / F2 = 3 => 11 pairs (_) / E3 = 3 => 11 pairs (_) H2,H3: 3.. / H2 = 3 => 11 pairs (_) / H3 = 3 => 11 pairs (_) A4,A5: 3.. / A4 = 3 => 6 pairs (_) / A5 = 3 => 6 pairs (_) F2,H2: 3.. / F2 = 3 => 11 pairs (_) / H2 = 3 => 11 pairs (_) E3,H3: 3.. / E3 = 3 => 11 pairs (_) / H3 = 3 => 11 pairs (_) D1,E3: 4.. / D1 = 4 => 11 pairs (_) / E3 = 4 => 11 pairs (_) B7,B9: 4.. / B7 = 4 => 11 pairs (_) / B9 = 4 => 11 pairs (_) A2,H2: 4.. / A2 = 4 => 12 pairs (_) / H2 = 4 => 10 pairs (_) B7,D7: 4.. / B7 = 4 => 11 pairs (_) / D7 = 4 => 11 pairs (_) E3,E9: 4.. / E3 = 4 => 11 pairs (_) / E9 = 4 => 11 pairs (_) B2,B3: 5.. / B2 = 5 => 8 pairs (_) / B3 = 5 => 11 pairs (_) D6,F6: 5.. / D6 = 5 => 9 pairs (_) / F6 = 5 => 9 pairs (_) A2,A3: 6.. / A2 = 6 => 10 pairs (_) / A3 = 6 => 12 pairs (_) I4,G6: 6.. / I4 = 6 => 8 pairs (_) / G6 = 6 => 10 pairs (_) D9,E9: 6.. / D9 = 6 => 10 pairs (_) / E9 = 6 => 13 pairs (_) C2,C3: 9.. / C2 = 9 => 11 pairs (_) / C3 = 9 => 12 pairs (_) D1,F2: 9.. / D1 = 9 => 11 pairs (_) / F2 = 9 => 11 pairs (_) D5,F5: 9.. / D5 = 9 => 11 pairs (_) / F5 = 9 => 11 pairs (_) D1,I1: 9.. / D1 = 9 => 11 pairs (_) / I1 = 9 => 11 pairs (_) C3,I3: 9.. / C3 = 9 => 12 pairs (_) / I3 = 9 => 11 pairs (_) D1,D5: 9.. / D1 = 9 => 11 pairs (_) / D5 = 9 => 11 pairs (_) F2,F5: 9.. / F2 = 9 => 11 pairs (_) / F5 = 9 => 11 pairs (_) * DURATION: 0:00:07.216987 START: 22:54:05.196178 END: 22:54:12.413165 2025-04-06 * CP COUNT: (25) * INCONCLUSIVE * DEEP PAIR REDUCTION * DURATION: 0:00:21.881474 START: 22:54:21.300301 END: 22:54:43.181775 2025-04-06 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00153396-base-pr-002.dot * REASONING * DIS # F5: 1,7,8 # G1: 1,8 => CTR => G1: 7 * PRF # F5: 1,7,8 + G1: 7 # A6: 1,8 => SOL * STA # F5: 1,7,8 + G1: 7 + A6: 1,8 * CNT 2 HDP CHAINS / 107 HYP OPENED
Header Info
rating: 42226; r2: 762852; index: 153396
Solution
position: 123456789457189236689732145275364918361928457894571623542897361736215894918643572 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 # G2: 5,7 => UNS * INC # I2: 5,7 => UNS * INC # I2: 7,9 => UNS * INC # I2: 2,5,6 => UNS * INC # F5: 3,9 => UNS * INC # F5: 1,7,8 => UNS * INC # H3: 3,4 => UNS * DIS # H3: 1,8 => CTR => H3: 3,4 * INC # E9: 3,4 => UNS * INC # E9: 1,2,6,7 => UNS * INC # D4: 2,3 => UNS * INC # E4: 2,3 => UNS * INC # D5: 2,3 => UNS * INC # E5: 2,3 => UNS * DIS # D9: 4,8 => CTR => D9: 2,3,5,6 * INC # D9: 2,3,5,6 => UNS * INC # B7: 4,8 => UNS * INC # B7: 1,7 => UNS * CNT 18 HDP CHAINS / 18 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G2: 5,7 => UNS * INC # I2: 5,7 => UNS * INC # I2: 7,9 => UNS * INC # I2: 2,5,6 => UNS * INC # F5: 3,9 => UNS * INC # F5: 1,7,8 => UNS * INC # H3: 3,4 => UNS * DIS # H3: 1,8 => CTR => H3: 3,4 * INC H3: 3,4 # E9: 3,4 => UNS * INC H3: 3,4 # E9: 1,2,6,7 => UNS * INC H3: 3,4 # E9: 3,4 => UNS * INC H3: 3,4 # E9: 1,2,6,7 => UNS * INC H3: 3,4 # D4: 2,3 => UNS * INC H3: 3,4 # E4: 2,3 => UNS * INC H3: 3,4 # D5: 2,3 => UNS * INC H3: 3,4 # E5: 2,3 => UNS * DIS H3: 3,4 # D9: 4,8 => CTR => D9: 2,3,5,6 * INC H3: 3,4 + D9: 2,3,5,6 # B7: 4,8 => UNS * INC H3: 3,4 + D9: 2,3,5,6 # B7: 1,7 => UNS * INC H3: 3,4 + D9: 2,3,5,6 # G2: 5,7 => UNS * INC H3: 3,4 + D9: 2,3,5,6 # I2: 5,7 => UNS * INC H3: 3,4 + D9: 2,3,5,6 # I2: 7,9 => UNS * INC H3: 3,4 + D9: 2,3,5,6 # I2: 2,5,6 => UNS * INC H3: 3,4 + D9: 2,3,5,6 # F5: 3,9 => UNS * INC H3: 3,4 + D9: 2,3,5,6 # F5: 1,7,8 => UNS * INC H3: 3,4 + D9: 2,3,5,6 # E9: 3,4 => UNS * INC H3: 3,4 + D9: 2,3,5,6 # E9: 1,2,6,7 => UNS * INC H3: 3,4 + D9: 2,3,5,6 # H2: 3,4 => UNS * INC H3: 3,4 + D9: 2,3,5,6 # H2: 7 => UNS * INC H3: 3,4 + D9: 2,3,5,6 # D4: 2,3 => UNS * INC H3: 3,4 + D9: 2,3,5,6 # E4: 2,3 => UNS * INC H3: 3,4 + D9: 2,3,5,6 # D5: 2,3 => UNS * INC H3: 3,4 + D9: 2,3,5,6 # E5: 2,3 => UNS * INC H3: 3,4 + D9: 2,3,5,6 # B7: 4,8 => UNS * INC H3: 3,4 + D9: 2,3,5,6 # B7: 1,7 => UNS * STA H3: 3,4 + D9: 2,3,5,6 * CNT 35 HDP CHAINS / 35 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # G2: 5,7 => UNS * INC # I2: 5,7 => UNS * INC # I2: 7,9 => UNS * INC # I2: 2,5,6 => UNS * INC # F5: 3,9 => UNS * INC # F5: 1,7,8 => UNS * INC # E9: 3,4 => UNS * INC # E9: 1,2,6,7 => UNS * INC # H2: 3,4 => UNS * INC # H2: 7 => UNS * INC # D4: 2,3 => UNS * INC # E4: 2,3 => UNS * INC # D5: 2,3 => UNS * INC # E5: 2,3 => UNS * INC # B7: 4,8 => UNS * INC # B7: 1,7 => UNS * INC # G2: 5,7 # A6: 1,8 => UNS * INC # G2: 5,7 # A8: 1,8 => UNS * INC # G2: 5,7 # C5: 1,8 => UNS * INC # G2: 5,7 # C9: 1,8 => UNS * INC # G2: 5,7 # D4: 2,3 => UNS * INC # G2: 5,7 # E4: 2,3 => UNS * INC # G2: 5,7 # C5: 1,8 => UNS * INC # G2: 5,7 # A6: 1,8 => UNS * INC # G2: 5,7 # H4: 1,8 => UNS * INC # G2: 5,7 # H4: 7 => UNS * INC # G2: 5,7 # D5: 2,3 => UNS * INC # G2: 5,7 # E5: 2,3 => UNS * INC # G2: 5,7 # A8: 1,8 => UNS * INC # G2: 5,7 # C9: 1,8 => UNS * INC # G2: 5,7 # F7: 1,8 => UNS * INC # G2: 5,7 # I7: 1,8 => UNS * INC # G2: 5,7 => UNS * INC # I2: 5,7 # A6: 1,8 => UNS * INC # I2: 5,7 # A8: 1,8 => UNS * INC # I2: 5,7 # C5: 1,8 => UNS * INC # I2: 5,7 # C9: 1,8 => UNS * INC # I2: 5,7 # D4: 2,3 => UNS * INC # I2: 5,7 # E4: 2,3 => UNS * INC # I2: 5,7 # C5: 1,8 => UNS * INC # I2: 5,7 # A6: 1,8 => UNS * INC # I2: 5,7 # H4: 1,8 => UNS * INC # I2: 5,7 # H4: 7 => UNS * INC # I2: 5,7 # D5: 2,3 => UNS * INC # I2: 5,7 # E5: 2,3 => UNS * INC # I2: 5,7 # A8: 1,8 => UNS * INC # I2: 5,7 # C9: 1,8 => UNS * INC # I2: 5,7 # F7: 1,8 => UNS * INC # I2: 5,7 # I7: 1,8 => UNS * INC # I2: 5,7 => UNS * INC # I2: 7,9 # A6: 1,8 => UNS * INC # I2: 7,9 # A8: 1,8 => UNS * INC # I2: 7,9 # B4: 1,8 => UNS * INC # I2: 7,9 # B7: 1,8 => UNS * INC # I2: 7,9 # D4: 2,3 => UNS * INC # I2: 7,9 # E4: 2,3 => UNS * INC # I2: 7,9 # D5: 2,3 => UNS * INC # I2: 7,9 # E5: 2,3 => UNS * INC # I2: 7,9 # B4: 1,8 => UNS * INC # I2: 7,9 # A6: 1,8 => UNS * INC # I2: 7,9 # I5: 1,8 => UNS * INC # I2: 7,9 # I5: 7 => UNS * INC # I2: 7,9 # B7: 1,8 => UNS * INC # I2: 7,9 # A8: 1,8 => UNS * INC # I2: 7,9 # F9: 1,8 => UNS * INC # I2: 7,9 # G9: 1,8 => UNS * INC # I2: 7,9 # H9: 1,8 => UNS * INC # I2: 7,9 => UNS * INC # I2: 2,5,6 # G2: 5,7 => UNS * INC # I2: 2,5,6 # G2: 2,6 => UNS * INC # I2: 2,5,6 # F5: 3,9 => UNS * INC # I2: 2,5,6 # F5: 1,7,8 => UNS * INC # I2: 2,5,6 # E9: 3,4 => UNS * INC # I2: 2,5,6 # E9: 1,2,6,7 => UNS * INC # I2: 2,5,6 # H2: 3,4 => UNS * INC # I2: 2,5,6 # H2: 7 => UNS * INC # I2: 2,5,6 # D4: 2,3 => UNS * INC # I2: 2,5,6 # E4: 2,3 => UNS * INC # I2: 2,5,6 # D5: 2,3 => UNS * INC # I2: 2,5,6 # E5: 2,3 => UNS * INC # I2: 2,5,6 # B7: 4,8 => UNS * INC # I2: 2,5,6 # B7: 1,7 => UNS * INC # I2: 2,5,6 => UNS * INC # F5: 3,9 # A2: 4,7 => UNS * INC # F5: 3,9 # A2: 6 => UNS * INC # F5: 3,9 # H1: 4,7 => UNS * INC # F5: 3,9 # H1: 1,8 => UNS * INC # F5: 3,9 # H1: 4,7 => UNS * INC # F5: 3,9 # H1: 1,8 => UNS * INC # F5: 3,9 # A2: 4,7 => UNS * INC # F5: 3,9 # A2: 6 => UNS * INC # F5: 3,9 # G2: 5,6 => UNS * INC # F5: 3,9 # G2: 2 => UNS * INC # F5: 3,9 # I2: 5,9 => UNS * INC # F5: 3,9 # I2: 2 => UNS * INC # F5: 3,9 # D4: 2,3 => UNS * INC # F5: 3,9 # E4: 2,3 => UNS * INC # F5: 3,9 # D5: 2,3 => UNS * INC # F5: 3,9 # E5: 2,3 => UNS * INC # F5: 3,9 # G9: 2,5 => UNS * INC # F5: 3,9 # G9: 1,7,8 => UNS * INC # F5: 3,9 # I2: 2,5 => UNS * INC # F5: 3,9 # I2: 9 => UNS * INC # F5: 3,9 => UNS * DIS # F5: 1,7,8 # G1: 1,8 => CTR => G1: 7 * PRF # F5: 1,7,8 + G1: 7 # A6: 1,8 => SOL * STA # F5: 1,7,8 + G1: 7 + A6: 1,8 * CNT 106 HDP CHAINS / 107 HYP OPENED