Analysis of xx-mith-te3-00153031-base.sdk
Contents
Original Sudoku
level: hard
position: ..3......45....2.6.89.7..............1.6.25.4....47..15...2..177....145....7.56.2 initial
Autosolve
position: ..3......45....2.6.89.7..............1.6.25.4....47..15...2..177....145....7.56.2 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D3: 3,4 => CTR => D3: 1,2,5 * DIS # C4: 7,8 => CTR => C4: 2,4,5,6 * DIS # A6: 2,6 => CTR => A6: 3,8,9 * DIS # C6: 2,6 => CTR => C6: 5,8 * DIS # C6: 6,8 => CTR => C6: 2,5 * CNT 5 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D3: 3,4 => CTR => D3: 1,2,5 * DIS D3: 1,2,5 # C4: 7,8 => CTR => C4: 2,4,5,6 * DIS D3: 1,2,5 + C4: 2,4,5,6 # A6: 2,6 => CTR => A6: 3,8,9 * DIS D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 # C6: 2,6 => CTR => C6: 5,8 * STA D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 + C6: 5,8 * CNT 4 HDP CHAINS / 39 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction Position
position: ..3......45....2.6.89.7..............1.6.25.4....47..15...2..177....145....7.56.2 pair_reduction
See section Pair Reduction for the HDP chains leading to this result.
Deep Pair Reduction
Time used: 0:00:06.418185
The following important HDP chains were detected:
* PRF # F3: 3,4 # H1: 8,9 => SOL * STA # F3: 3,4 + H1: 8,9 * CNT 1 HDP CHAINS / 25 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..3......45....2.6.89.7..............1.6.25.4....47..15...2..177....145....7.56.2 | initial |
| ..3......45....2.6.89.7..............1.6.25.4....47..15...2..177....145....7.56.2 | autosolve |
| ..3......45....2.6.89.7..............1.6.25.4....47..15...2..177....145....7.56.2 | pair_reduction |
| 123456789457189236689273145274518963318692574965347821596824317732961458841735692 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (8) C2: 1,7 G3: 1,3 H3: 3,4 I3: 3,5 C5: 7,8 H4: 2,6 H6: 2,6 C7: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G1,G3: 1.. / G1 = 1 => 10 pairs (_) / G3 = 1 => 8 pairs (_) D4,E4: 1.. / D4 = 1 => 8 pairs (_) / E4 = 1 => 9 pairs (_) A9,C9: 1.. / A9 = 1 => 16 pairs (_) / C9 = 1 => 21 pairs (_) C2,C9: 1.. / C2 = 1 => 16 pairs (_) / C9 = 1 => 21 pairs (_) D1,D3: 2.. / D1 = 2 => 11 pairs (_) / D3 = 2 => 9 pairs (_) H4,H6: 2.. / H4 = 2 => 6 pairs (_) / H6 = 2 => 6 pairs (_) B8,C8: 2.. / B8 = 2 => 14 pairs (_) / C8 = 2 => 8 pairs (_) A3,D3: 2.. / A3 = 2 => 11 pairs (_) / D3 = 2 => 9 pairs (_) H1,H3: 4.. / H1 = 4 => 10 pairs (_) / H3 = 4 => 8 pairs (_) B4,C4: 4.. / B4 = 4 => 17 pairs (_) / C4 = 4 => 16 pairs (_) B9,C9: 4.. / B9 = 4 => 16 pairs (_) / C9 = 4 => 17 pairs (_) D7,F7: 4.. / D7 = 4 => 8 pairs (_) / F7 = 4 => 0 pairs (*) B4,B9: 4.. / B4 = 4 => 17 pairs (_) / B9 = 4 => 16 pairs (_) C4,C9: 4.. / C4 = 4 => 16 pairs (_) / C9 = 4 => 17 pairs (_) I1,I3: 5.. / I1 = 5 => 10 pairs (_) / I3 = 5 => 8 pairs (_) C4,C6: 5.. / C4 = 5 => 0 pairs (X) / C6 = 5 => 10 pairs (_) D3,I3: 5.. / D3 = 5 => 10 pairs (_) / I3 = 5 => 8 pairs (_) C6,D6: 5.. / C6 = 5 => 10 pairs (_) / D6 = 5 => 0 pairs (X) E1,E4: 5.. / E1 = 5 => 9 pairs (_) / E4 = 5 => 10 pairs (_) H4,H6: 6.. / H4 = 6 => 6 pairs (_) / H6 = 6 => 6 pairs (_) F7,E8: 6.. / F7 = 6 => 0 pairs (X) / E8 = 6 => 9 pairs (_) A3,F3: 6.. / A3 = 6 => 11 pairs (_) / F3 = 6 => 10 pairs (_) E1,E8: 6.. / E1 = 6 => 0 pairs (X) / E8 = 6 => 9 pairs (_) B1,C2: 7.. / B1 = 7 => 16 pairs (_) / C2 = 7 => 21 pairs (_) G4,H5: 7.. / G4 = 7 => 16 pairs (_) / H5 = 7 => 21 pairs (_) C2,H2: 7.. / C2 = 7 => 21 pairs (_) / H2 = 7 => 16 pairs (_) C5,H5: 7.. / C5 = 7 => 16 pairs (_) / H5 = 7 => 21 pairs (_) B1,B4: 7.. / B1 = 7 => 16 pairs (_) / B4 = 7 => 21 pairs (_) G1,G4: 7.. / G1 = 7 => 21 pairs (_) / G4 = 7 => 16 pairs (_) * DURATION: 0:00:08.035027 START: 22:42:31.552305 END: 22:42:39.587332 2025-04-06 * CP COUNT: (29) * SOLUTION FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:06.277963 START: 22:42:50.905363 END: 22:42:57.183326 2025-04-06 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00153031-base-pr-002.dot * REASONING * PRF # F3: 3,4 # H1: 8,9 => SOL * STA # F3: 3,4 + H1: 8,9 * CNT 1 HDP CHAINS / 25 HYP OPENED
Header Info
rating: 42014; r2: 763097; index: 153031
Solution
position: 123456789457189236689273145274518963318692574965347821596824317732961458841735692 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 # D3: 1,3 => UNS * INC # D3: 2,4,5 => UNS * DIS # D3: 3,4 => CTR => D3: 1,2,5 * INC # D3: 1,2,5 => UNS * INC # F3: 3,4 => UNS * INC # D3: 3,5 => UNS * INC # D3: 1,2,4 => UNS * DIS # C4: 7,8 => CTR => C4: 2,4,5,6 * INC # C4: 2,4,5,6 => UNS * INC # H5: 7,8 => UNS * INC # H5: 3,9 => UNS * INC # A4: 2,6 => UNS * INC # B4: 2,6 => UNS * INC # C4: 2,6 => UNS * DIS # A6: 2,6 => CTR => A6: 3,8,9 * INC # A6: 3,8,9 => UNS * INC # B6: 2,6 => UNS * DIS # C6: 2,6 => CTR => C6: 5,8 * INC # C6: 5,8 => UNS * INC # C8: 6,8 => UNS * INC # C8: 2 => UNS * INC # F7: 6,8 => UNS * INC # F7: 3,4,9 => UNS * INC # C4: 6,8 => UNS * DIS # C6: 6,8 => CTR => C6: 2,5 * INC # C6: 2,5 => UNS * CNT 26 HDP CHAINS / 26 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D3: 1,3 => UNS * INC # D3: 2,4,5 => UNS * DIS # D3: 3,4 => CTR => D3: 1,2,5 * INC D3: 1,2,5 # F3: 3,4 => UNS * INC D3: 1,2,5 # F3: 3,4 => UNS * INC D3: 1,2,5 # F3: 6 => UNS * INC D3: 1,2,5 # F3: 3,4 => UNS * INC D3: 1,2,5 # F3: 6 => UNS * DIS D3: 1,2,5 # C4: 7,8 => CTR => C4: 2,4,5,6 * INC D3: 1,2,5 + C4: 2,4,5,6 # H5: 7,8 => UNS * INC D3: 1,2,5 + C4: 2,4,5,6 # H5: 3,9 => UNS * INC D3: 1,2,5 + C4: 2,4,5,6 # A4: 2,6 => UNS * INC D3: 1,2,5 + C4: 2,4,5,6 # B4: 2,6 => UNS * INC D3: 1,2,5 + C4: 2,4,5,6 # C4: 2,6 => UNS * DIS D3: 1,2,5 + C4: 2,4,5,6 # A6: 2,6 => CTR => A6: 3,8,9 * INC D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 # B6: 2,6 => UNS * DIS D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 # C6: 2,6 => CTR => C6: 5,8 * INC D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 + C6: 5,8 # C8: 6,8 => UNS * INC D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 + C6: 5,8 # C8: 2 => UNS * INC D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 + C6: 5,8 # F7: 6,8 => UNS * INC D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 + C6: 5,8 # F7: 3,4,9 => UNS * INC D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 + C6: 5,8 # F3: 3,4 => UNS * INC D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 + C6: 5,8 # F3: 6 => UNS * INC D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 + C6: 5,8 # H5: 7,8 => UNS * INC D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 + C6: 5,8 # H5: 3,9 => UNS * INC D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 + C6: 5,8 # A4: 2,6 => UNS * INC D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 + C6: 5,8 # B4: 2,6 => UNS * INC D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 + C6: 5,8 # C4: 2,6 => UNS * INC D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 + C6: 5,8 # B1: 2,6 => UNS * INC D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 + C6: 5,8 # B8: 2,6 => UNS * INC D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 + C6: 5,8 # D6: 5,8 => UNS * INC D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 + C6: 5,8 # D6: 3,9 => UNS * INC D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 + C6: 5,8 # A4: 2,6 => UNS * INC D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 + C6: 5,8 # B4: 2,6 => UNS * INC D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 + C6: 5,8 # C4: 2,6 => UNS * INC D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 + C6: 5,8 # C8: 6,8 => UNS * INC D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 + C6: 5,8 # C8: 2 => UNS * INC D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 + C6: 5,8 # F7: 6,8 => UNS * INC D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 + C6: 5,8 # F7: 3,4,9 => UNS * STA D3: 1,2,5 + C4: 2,4,5,6 + A6: 3,8,9 + C6: 5,8 * CNT 39 HDP CHAINS / 39 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # F3: 3,4 => UNS * INC # F3: 6 => UNS * INC # H5: 7,8 => UNS * INC # H5: 3,9 => UNS * INC # A4: 2,6 => UNS * INC # B4: 2,6 => UNS * INC # C4: 2,6 => UNS * INC # B1: 2,6 => UNS * INC # B8: 2,6 => UNS * INC # D6: 5,8 => UNS * INC # D6: 3,9 => UNS * INC # A4: 2,6 => UNS * INC # B4: 2,6 => UNS * INC # C4: 2,6 => UNS * INC # C8: 6,8 => UNS * INC # C8: 2 => UNS * INC # F7: 6,8 => UNS * INC # F7: 3,4,9 => UNS * INC # F3: 3,4 # B4: 2,7 => UNS * INC # F3: 3,4 # B4: 3,4,6,9 => UNS * INC # F3: 3,4 # F7: 3,4 => UNS * INC # F3: 3,4 # F7: 6,8,9 => UNS * INC # F3: 3,4 # G1: 8,9 => UNS * PRF # F3: 3,4 # H1: 8,9 => SOL * STA # F3: 3,4 + H1: 8,9 * CNT 24 HDP CHAINS / 25 HYP OPENED