Analysis of xx-mith-te3-00116706-base.sdk
Contents
Original Sudoku
level: medium
position: 1.3.567...5718....68.3..5.........7.5..76....7.8.13.6.371...85.....3..9......134. initial
Autosolve
position: 1.3.567...5718....68.3..5....6....7.5..76....7.8.13.6.371...85.....3..9......134. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # I4: 2,4,5,8,9 => SOL * PRF # F8: 2,7 => SOL * PRF # G8: 2,6 => SOL * DIS # I8: 2,6 => CTR => I8: 1,7 * PRF # I2: 2,6 => SOL * CNT 5 HDP CHAINS / 31 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # I4: 2,4,5,8,9 => SOL * STA I4: 2,4,5,8,9 * CNT 1 HDP CHAINS / 14 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.3.567...5718....68.3..5.........7.5..76....7.8.13.6.371...85.....3..9......134. | initial |
| 1.3.567...5718....68.3..5....6....7.5..76....7.8.13.6.371...85.....3..9......134. | autosolve |
| 123456789457189236689372514236945178514768923798213465371694852842537691965821347 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) H1: 2,8 H2: 2,3 H3: 1,2 B4: 1,3 B5: 1,3 E9: 2,7 I7: 2,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H3,I3: 1.. / H3 = 1 => 6 pairs (_) / I3 = 1 => 9 pairs (_) B4,B5: 1.. / B4 = 1 => 10 pairs (_) / B5 = 1 => 4 pairs (_) G8,I8: 1.. / G8 = 1 => 11 pairs (_) / I8 = 1 => 0 pairs (*) H3,H5: 1.. / H3 = 1 => 6 pairs (_) / H5 = 1 => 9 pairs (_) H2,I2: 3.. / H2 = 3 => 6 pairs (_) / I2 = 3 => 9 pairs (_) B4,B5: 3.. / B4 = 3 => 4 pairs (_) / B5 = 3 => 10 pairs (_) B4,I4: 3.. / B4 = 3 => 4 pairs (_) / I4 = 3 => 10 pairs (_) H2,H5: 3.. / H2 = 3 => 6 pairs (_) / H5 = 3 => 9 pairs (_) I4,I6: 5.. / I4 = 5 => 0 pairs (X) / I6 = 5 => 7 pairs (_) C8,C9: 5.. / C8 = 5 => 9 pairs (_) / C9 = 5 => 8 pairs (_) D6,I6: 5.. / D6 = 5 => 0 pairs (X) / I6 = 5 => 7 pairs (_) C9,D9: 5.. / C9 = 5 => 8 pairs (_) / D9 = 5 => 9 pairs (_) F4,F8: 5.. / F4 = 5 => 7 pairs (_) / F8 = 5 => 9 pairs (_) G2,I2: 6.. / G2 = 6 => 9 pairs (_) / I2 = 6 => 0 pairs (*) B8,B9: 6.. / B8 = 6 => 10 pairs (_) / B9 = 6 => 13 pairs (_) D7,I7: 6.. / D7 = 6 => 10 pairs (_) / I7 = 6 => 12 pairs (_) G2,G8: 6.. / G2 = 6 => 9 pairs (_) / G8 = 6 => 0 pairs (*) E3,F3: 7.. / E3 = 7 => 0 pairs (*) / F3 = 7 => 0 pairs (X) F8,E9: 7.. / F8 = 7 => 0 pairs (*) / E9 = 7 => 0 pairs (X) I8,I9: 7.. / I8 = 7 => 11 pairs (_) / I9 = 7 => 0 pairs (*) F8,I8: 7.. / F8 = 7 => 0 pairs (*) / I8 = 7 => 0 pairs (X) E9,I9: 7.. / E9 = 7 => 11 pairs (_) / I9 = 7 => 0 pairs (*) E3,E9: 7.. / E3 = 7 => 0 pairs (*) / E9 = 7 => 0 pairs (X) F3,F8: 7.. / F3 = 7 => 11 pairs (_) / F8 = 7 => 0 pairs (*) H1,I1: 8.. / H1 = 8 => 6 pairs (_) / I1 = 8 => 13 pairs (_) A8,A9: 8.. / A8 = 8 => 9 pairs (_) / A9 = 8 => 8 pairs (_) A9,D9: 8.. / A9 = 8 => 8 pairs (_) / D9 = 8 => 9 pairs (_) H1,H5: 8.. / H1 = 8 => 6 pairs (_) / H5 = 8 => 13 pairs (_) * DURATION: 0:00:08.931480 START: 06:00:06.805143 END: 06:00:15.736623 2025-04-05 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B5,E9,H1,H2,H3,I7) * 1.3.567...5718....68.3..5....6....7.5..76....7.8.13.6.371...85.....3..9......134. * PAIR H1: 2,8 BLK 3 I1: 2,8,4,9 # reduction candidate for 2,8 I1: 2,8 # 10 pairs I1: 4,9 # 7 pairs * PAIR H1: 2,8 COL H H5: 2,8,1,3 # reduction candidate for 2,8 H5: 1,3 # 8 pairs H5: 2,8 # 6 pairs * PAIR H2: 2,3 BLK 3 I2: 2,3,4,6,9 # reduction candidate for 2,3 I2: 2,3 # 13 pairs I2: 4,6,9 # 6 pairs * PAIR H2: 2,3 COL H H5: 2,3,1,8 # reduction candidate for 2,3 H5: 1,8 # 7 pairs H5: 2,3 # 6 pairs * PAIR H3: 1,2 BLK 3 I3: 1,2,4,9 # reduction candidate for 1,2 I3: 1,2 # 13 pairs I3: 4,9 # 7 pairs * PAIR H3: 1,2 COL H H5: 1,2,3,8 # reduction candidate for 1,2 H5: 1,2 # 9 pairs H5: 3,8 # 8 pairs * PAIR B4: 1,3 ROW 4 I4: 1,3,2,4,5,8,9 # reduction candidate for 1,3 I4: 2,4,5,8,9 => SOLVED * 123456789457189236689372514236945178514768923798213465371694852842537691965821347 I4: 1,3 # 11 pairs * PAIR B5: 1,3 ROW 5 H5: 1,3,2,8 # reduction candidate for 1,3 H5: 1,3 # 8 pairs I5: 1,3,2,4,8,9 # reduction candidate for 1,3 I5: 1,3 # 7 pairs * PAIR E9: 2,7 BLK 8 F8: 2,7,5,8 # reduction candidate for 2,7 F8: 2,7 => SOLVED * 123456789457189236689372514236945178514768923798213465371694852842537691965821347 F8: 5,8 # 11 pairs * PAIR E9: 2,7 ROW 9 I9: 2,7,6 # reduction candidate for 2,7 I9: 6 # 14 pairs I9: 2,7 # 12 pairs * PAIR E9: 2,7 COL E E3: 2,7,4,9 # reduction candidate for 2,7 E3: 4,9 # 12 pairs E3: 2,7 # 10 pairs * PAIR I7: 2,6 BLK 9 G8: 2,6,1 # reduction candidate for 2,6 G8: 2,6 => SOLVED * 123456789457189236689372514236945178514768923798213465371694852842537691965821347 G8: 1 # 11 pairs I8: 2,6,1,7 # reduction candidate for 2,6 I8: 2,6 => CTR * 1.3.5678..5718.6..68.37.5....6..5.785..768...7.8.13.653716..852....37196.6..21347 I8: 1,7 # 8 pairs I9: 2,6,7 # reduction candidate for 2,6 I9: 2,6 # 11 pairs * PAIR I7: 2,6 ROW 7 D7: 2,6,4,9 # reduction candidate for 2,6 D7: 4,9 # 13 pairs D7: 2,6 # 10 pairs * PAIR I7: 2,6 COL I I2: 2,6,3,4,9 # reduction candidate for 2,6 I2: 2,6 => SOLVED * 123456789457189236689372514236945178514768923798213465371694852842537691965821347 I2: 3,4,9 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-mith-te3-00116706-base-pr-000.dot * REASONING * PRF # I4: 2,4,5,8,9 => SOL * PRF # F8: 2,7 => SOL * PRF # G8: 2,6 => SOL * DIS # I8: 2,6 => CTR => I8: 1,7 * PRF # I2: 2,6 => SOL * CNT 5 HDP CHAINS / 31 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B5,E9,H1,H2,H3,I7) * 1.3.567...5718....68.3..5....6....7.5..76....7.8.13.6.371...85.....3..9......134. * PAIR H1: 2,8 BLK 3 I1: 2,8,4,9 # reduction candidate for 2,8 I1: 2,8 # 10 pairs I1: 4,9 # 7 pairs * PAIR H1: 2,8 COL H H5: 2,8,1,3 # reduction candidate for 2,8 H5: 1,3 # 8 pairs H5: 2,8 # 6 pairs * PAIR H2: 2,3 BLK 3 I2: 2,3,4,6,9 # reduction candidate for 2,3 I2: 2,3 # 13 pairs I2: 4,6,9 # 6 pairs * PAIR H2: 2,3 COL H H5: 2,3,1,8 # reduction candidate for 2,3 H5: 1,8 # 7 pairs H5: 2,3 # 6 pairs * PAIR H3: 1,2 BLK 3 I3: 1,2,4,9 # reduction candidate for 1,2 I3: 1,2 # 13 pairs I3: 4,9 # 7 pairs * PAIR H3: 1,2 COL H H5: 1,2,3,8 # reduction candidate for 1,2 H5: 1,2 # 9 pairs H5: 3,8 # 8 pairs * PAIR B4: 1,3 ROW 4 I4: 1,3,2,4,5,8,9 # reduction candidate for 1,3 I4: 2,4,5,8,9 => SOLVED * 123456789457189236689372514236945178514768923798213465371694852842537691965821347 * DURATION: 0:00:02.376899 START: 06:00:21.240939 END: 06:00:23.617838 2025-04-05 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00116706-base-pr-001.dot * REASONING * PRF # I4: 2,4,5,8,9 => SOL * STA I4: 2,4,5,8,9 * CNT 1 HDP CHAINS / 14 HYP OPENED
Header Info
rating: 29864; r2: 568142; index: 116706
Solution
position: 123456789457189236689372514236945178514768923798213465371694852842537691965821347 solved
See section 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 # I1: 2,8 => UNS * INC # I1: 4,9 => UNS * INC # H5: 2,8 => UNS * INC # H5: 1,3 => UNS * INC # I2: 2,3 => UNS * INC # I2: 4,6,9 => UNS * INC # H5: 2,3 => UNS * INC # H5: 1,8 => UNS * INC # I3: 1,2 => UNS * INC # I3: 4,9 => UNS * INC # H5: 1,2 => UNS * INC # H5: 3,8 => UNS * INC # I4: 1,3 => UNS * PRF # I4: 2,4,5,8,9 => SOL * INC # H5: 1,3 => UNS * INC # I5: 1,3 => UNS * PRF # F8: 2,7 => SOL * INC # F8: 5,8 => UNS * INC # I9: 2,7 => UNS * INC # I9: 6 => UNS * INC # E3: 2,7 => UNS * INC # E3: 4,9 => UNS * PRF # G8: 2,6 => SOL * INC # G8: 1 => UNS * DIS # I8: 2,6 => CTR => I8: 1,7 * INC # I8: 1,7 => UNS * INC # I9: 2,6 => UNS * INC # D7: 2,6 => UNS * INC # D7: 4,9 => UNS * PRF # I2: 2,6 => SOL * INC # I2: 3,4,9 => UNS * CNT 31 HDP CHAINS / 31 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # I1: 2,8 => UNS * INC # I1: 4,9 => UNS * INC # H5: 2,8 => UNS * INC # H5: 1,3 => UNS * INC # I2: 2,3 => UNS * INC # I2: 4,6,9 => UNS * INC # H5: 2,3 => UNS * INC # H5: 1,8 => UNS * INC # I3: 1,2 => UNS * INC # I3: 4,9 => UNS * INC # H5: 1,2 => UNS * INC # H5: 3,8 => UNS * INC # I4: 1,3 => UNS * PRF # I4: 2,4,5,8,9 => SOL * STA I4: 2,4,5,8,9 * CNT 14 HDP CHAINS / 14 HYP OPENED