Analysis of xx-mith-te3-00094079-base.sdk
Contents
Original Sudoku
level: medium
position: .2..567...5718.2..6.82.7.......78194......62.....21..3.16..2.5..........87...5... initial
Autosolve
position: .2..567...5718.2..6.82.7.......78194......62.....21..3.16..2.5..........87...5... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I9: 6,9 => CTR => I9: 1,2 * PRF # I9: 1,6 => SOL * CNT 2 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I9: 6,9 => CTR => I9: 1,2 * PRF I9: 1,2 # H9: 3,4 => SOL * STA I9: 1,2 + H9: 3,4 * CNT 2 HDP CHAINS / 24 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2..567...5718.2..6.82.7.......78194......62.....21..3.16..2.5..........87...5... | initial |
| .2..567...5718.2..6.82.7.......78194......62.....21..3.16..2.5..........87...5... | autosolve |
| 123456789457189236698237415265378194731594628984621573316842957549713862872965341 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) I1: 8,9 I2: 6,9 B4: 3,6 G6: 5,8 H6: 7,8 D7: 7,8 D8: 7,8 E8: 1,6 E9: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,C1: 1.. / A1 = 1 => 9 pairs (_) / C1 = 1 => 15 pairs (_) H3,I3: 1.. / H3 = 1 => 12 pairs (_) / I3 = 1 => 14 pairs (_) A5,C5: 1.. / A5 = 1 => 15 pairs (_) / C5 = 1 => 9 pairs (_) E8,E9: 1.. / E8 = 1 => 7 pairs (_) / E9 = 1 => 7 pairs (_) A1,A5: 1.. / A1 = 1 => 9 pairs (_) / A5 = 1 => 15 pairs (_) C1,C5: 1.. / C1 = 1 => 15 pairs (_) / C5 = 1 => 9 pairs (_) A4,C4: 2.. / A4 = 2 => 10 pairs (_) / C4 = 2 => 12 pairs (_) I8,I9: 2.. / I8 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) C9,I9: 2.. / C9 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) A4,A8: 2.. / A4 = 2 => 10 pairs (_) / A8 = 2 => 12 pairs (_) G3,I3: 5.. / G3 = 5 => 14 pairs (_) / I3 = 5 => 13 pairs (_) I5,G6: 5.. / I5 = 5 => 14 pairs (_) / G6 = 5 => 13 pairs (_) A8,C8: 5.. / A8 = 5 => 10 pairs (_) / C8 = 5 => 11 pairs (_) G3,G6: 5.. / G3 = 5 => 14 pairs (_) / G6 = 5 => 13 pairs (_) I3,I5: 5.. / I3 = 5 => 13 pairs (_) / I5 = 5 => 14 pairs (_) H2,I2: 6.. / H2 = 6 => 9 pairs (_) / I2 = 6 => 9 pairs (_) B4,B6: 6.. / B4 = 6 => 10 pairs (_) / B6 = 6 => 15 pairs (_) D4,D6: 6.. / D4 = 6 => 15 pairs (_) / D6 = 6 => 10 pairs (_) E8,E9: 6.. / E8 = 6 => 7 pairs (_) / E9 = 6 => 7 pairs (_) B4,D4: 6.. / B4 = 6 => 10 pairs (_) / D4 = 6 => 15 pairs (_) B6,D6: 6.. / B6 = 6 => 15 pairs (_) / D6 = 6 => 10 pairs (_) A5,A6: 7.. / A5 = 7 => 9 pairs (_) / A6 = 7 => 14 pairs (_) I5,H6: 7.. / I5 = 7 => 14 pairs (_) / H6 = 7 => 9 pairs (_) D7,D8: 7.. / D7 = 7 => 15 pairs (_) / D8 = 7 => 7 pairs (_) A5,I5: 7.. / A5 = 7 => 9 pairs (_) / I5 = 7 => 14 pairs (_) A6,H6: 7.. / A6 = 7 => 14 pairs (_) / H6 = 7 => 9 pairs (_) D7,I7: 7.. / D7 = 7 => 15 pairs (_) / I7 = 7 => 7 pairs (_) H6,H8: 7.. / H6 = 7 => 9 pairs (_) / H8 = 7 => 14 pairs (_) H1,I1: 8.. / H1 = 8 => 13 pairs (_) / I1 = 8 => 17 pairs (_) B5,B6: 8.. / B5 = 8 => 10 pairs (_) / B6 = 8 => 0 pairs (*) D7,D8: 8.. / D7 = 8 => 7 pairs (_) / D8 = 8 => 15 pairs (_) B5,I5: 8.. / B5 = 8 => 10 pairs (_) / I5 = 8 => 0 pairs (*) * DURATION: 0:00:09.927075 START: 14:40:40.989765 END: 14:40:50.916840 2025-04-06 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,D7,D8,E8,E9,G6,H6,I1,I2) * .2..567...5718.2..6.82.7.......78194......62.....21..3.16..2.5..........87...5... * PAIR I1: 8,9 COL I I7: 8,9,7 # reduction candidate for 8,9 I7: 8,9 # 15 pairs I8: 8,9,1,2,6,7 # reduction candidate for 8,9 I8: 8,9 # 13 pairs * PAIR I2: 6,9 COL I I8: 6,9,1,2,7,8 # reduction candidate for 6,9 I8: 6,9 # 9 pairs I9: 6,9,1,2 # reduction candidate for 6,9 I9: 6,9 => CTR * .2..567...5718.2..6.82.7..12...78194......625....21873.16..2.57...7...82872..5.16 I9: 1,2 # 10 pairs * PAIR B4: 3,6 ROW 4 D4: 3,6,5 # reduction candidate for 3,6 D4: 3,6 # 14 pairs D4: 5 # 13 pairs * PAIR G6: 5,8 BLK 6 I5: 5,8,7 # reduction candidate for 5,8 I5: 7 # 14 pairs I5: 5,8 # 9 pairs * PAIR H6: 7,8 BLK 6 I5: 7,8,5 # reduction candidate for 7,8 I5: 5 # 14 pairs I5: 7,8 # 13 pairs * PAIR H6: 7,8 COL H H8: 7,8,1,3,4,6 # reduction candidate for 7,8 H8: 7,8 # 17 pairs H8: 1,3,4,6 # 13 pairs * PAIR D7: 7,8 ROW 7 I7: 7,8,9 # reduction candidate for 7,8 I7: 9 # 14 pairs I7: 7,8 # 10 pairs * PAIR D8: 7,8 ROW 8 H8: 7,8,1,3,4,6 # reduction candidate for 7,8 H8: 7,8 # 17 pairs I8: 7,8,1,2,6,9 # reduction candidate for 7,8 I8: 7,8 # 17 pairs * PAIR E8: 1,6 ROW 8 H8: 1,6,3,4,7,8 # reduction candidate for 1,6 H8: 1,6 # 14 pairs I8: 1,6,2,7,8,9 # reduction candidate for 1,6 I8: 1,6 # 13 pairs * PAIR E9: 1,6 ROW 9 H9: 1,6,3,4 # reduction candidate for 1,6 H9: 1,6 # 11 pairs I9: 1,6,2,9 # reduction candidate for 1,6 I9: 1,6 => SOLVED * 123456789457189236698237415265378194731594628984621573316842957549713862872965341 I9: 2,9 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-mith-te3-00094079-base-pr-000.dot * REASONING * DIS # I9: 6,9 => CTR => I9: 1,2 * PRF # I9: 1,6 => SOL * CNT 2 HDP CHAINS / 22 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,D7,D8,E8,E9,G6,H6,I1,I2) * .2..567...5718.2..6.82.7.......78194......62.....21..3.16..2.5..........87...5... * PAIR I1: 8,9 COL I I7: 8,9,7 # reduction candidate for 8,9 I7: 8,9 # 15 pairs I8: 8,9,1,2,6,7 # reduction candidate for 8,9 I8: 8,9 # 13 pairs * PAIR I2: 6,9 COL I I8: 6,9,1,2,7,8 # reduction candidate for 6,9 I8: 6,9 # 9 pairs I9: 6,9,1,2 # reduction candidate for 6,9 I9: 6,9 => CTR * .2..567...5718.2..6.82.7..12...78194......625....21873.16..2.57...7...82872..5.16 * RESTART * PAIR I2: 6,9 COL I I8: 6,9,1,2,7,8 # reduction candidate for 6,9 I8: 1,2,7,8 # 10 pairs I8: 6,9 # 9 pairs * PAIR RESTART * PAIR I2: 6,9 COL I I8: 6,9,1,2,7,8 # reduction candidate for 6,9 I8: 1,2,7,8 # 10 pairs I8: 6,9 # 9 pairs * PAIR B4: 3,6 ROW 4 D4: 3,6,5 # reduction candidate for 3,6 D4: 3,6 # 15 pairs D4: 5 # 14 pairs * PAIR G6: 5,8 BLK 6 I5: 5,8,7 # reduction candidate for 5,8 I5: 7 # 14 pairs I5: 5,8 # 10 pairs * PAIR H6: 7,8 BLK 6 I5: 7,8,5 # reduction candidate for 7,8 I5: 5 # 14 pairs I5: 7,8 # 13 pairs * PAIR H6: 7,8 COL H H8: 7,8,1,3,4,6 # reduction candidate for 7,8 H8: 7,8 # 17 pairs H8: 1,3,4,6 # 13 pairs * PAIR D7: 7,8 ROW 7 I7: 7,8,9 # reduction candidate for 7,8 I7: 9 # 14 pairs I7: 7,8 # 11 pairs * PAIR D8: 7,8 ROW 8 H8: 7,8,1,3,4,6 # reduction candidate for 7,8 H8: 7,8 # 17 pairs I8: 7,8,1,2,6,9 # reduction candidate for 7,8 I8: 7,8 # 17 pairs * PAIR E8: 1,6 ROW 8 H8: 1,6,3,4,7,8 # reduction candidate for 1,6 H8: 1,6 # 14 pairs I8: 1,6,2,7,8,9 # reduction candidate for 1,6 I8: 1,6 # 13 pairs * PAIR E9: 1,6 ROW 9 H9: 1,6,3,4 # reduction candidate for 1,6 H9: 3,4 => SOLVED * 123456789457189236698237415265378194731594628984621573316842957549713862872965341 * DURATION: 0:00:04.457767 START: 14:40:54.955405 END: 14:40:59.413172 2025-04-06 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00094079-base-pr-001.dot * REASONING * DIS # I9: 6,9 => CTR => I9: 1,2 * PRF I9: 1,2 # H9: 3,4 => SOL * STA I9: 1,2 + H9: 3,4 * CNT 2 HDP CHAINS / 24 HYP OPENED
Header Info
rating: 23839; r2: 533598; index: 94079
Solution
position: 123456789457189236698237415265378194731594628984621573316842957549713862872965341 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 # I7: 8,9 => UNS * INC # I8: 8,9 => UNS * INC # I8: 6,9 => UNS * DIS # I9: 6,9 => CTR => I9: 1,2 * INC # I9: 1,2 => UNS * INC # D4: 3,6 => UNS * INC # D4: 5 => UNS * INC # I5: 5,8 => UNS * INC # I5: 7 => UNS * INC # I5: 7,8 => UNS * INC # I5: 5 => UNS * INC # H8: 7,8 => UNS * INC # H8: 1,3,4,6 => UNS * INC # I7: 7,8 => UNS * INC # I7: 9 => UNS * INC # H8: 7,8 => UNS * INC # I8: 7,8 => UNS * INC # H8: 1,6 => UNS * INC # I8: 1,6 => UNS * INC # H9: 1,6 => UNS * PRF # I9: 1,6 => SOL * INC # I9: 2,9 => UNS * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # I7: 8,9 => UNS * INC # I8: 8,9 => UNS * INC # I8: 6,9 => UNS * DIS # I9: 6,9 => CTR => I9: 1,2 * INC I9: 1,2 # I8: 6,9 => UNS * INC I9: 1,2 # I8: 1,2,7,8 => UNS * INC I9: 1,2 # I8: 6,9 => UNS * INC I9: 1,2 # I8: 1,2,7,8 => UNS * INC I9: 1,2 # D4: 3,6 => UNS * INC I9: 1,2 # D4: 5 => UNS * INC I9: 1,2 # I5: 5,8 => UNS * INC I9: 1,2 # I5: 7 => UNS * INC I9: 1,2 # I5: 7,8 => UNS * INC I9: 1,2 # I5: 5 => UNS * INC I9: 1,2 # H8: 7,8 => UNS * INC I9: 1,2 # H8: 1,3,4,6 => UNS * INC I9: 1,2 # I7: 7,8 => UNS * INC I9: 1,2 # I7: 9 => UNS * INC I9: 1,2 # H8: 7,8 => UNS * INC I9: 1,2 # I8: 7,8 => UNS * INC I9: 1,2 # H8: 1,6 => UNS * INC I9: 1,2 # I8: 1,6 => UNS * INC I9: 1,2 # H9: 1,6 => UNS * PRF I9: 1,2 # H9: 3,4 => SOL * STA I9: 1,2 + H9: 3,4 * CNT 24 HDP CHAINS / 24 HYP OPENED