Analysis of xx-mith-te3-00094080-base.sdk
Contents
Original Sudoku
level: medium
position: .2..567...5718.2..6.82.7.......7.194......62.....21.73.168.2.5....7.....8....5... initial
Autosolve
position: .2..567...5718.2..6.82.7.......7.194......62.....21.73.168.2.5....7.....8....5... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I9: 6,9 => CTR => I9: 1,2,7 * PRF # I9: 1,6 => SOL * DIS # I9: 7,9 => CTR => I9: 1,2,6 * CNT 3 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 # I9: 6,9 => CTR => I9: 1,2,7 * PRF I9: 1,2,7 # H9: 3,4 => SOL * STA I9: 1,2,7 + H9: 3,4 * CNT 2 HDP CHAINS / 16 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2..567...5718.2..6.82.7.......7.194......62.....21.73.168.2.5....7.....8....5... | initial |
| .2..567...5718.2..6.82.7.......7.194......62.....21.73.168.2.5....7.....8....5... | autosolve |
| 123456789457189236698237415265378194731594628984621573316842957549713862872965341 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) I1: 8,9 I2: 6,9 F4: 3,8 I5: 5,8 G6: 5,8 E8: 1,6 E9: 1,6 I7: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,C1: 1.. / A1 = 1 => 8 pairs (_) / C1 = 1 => 0 pairs (X) H3,I3: 1.. / H3 = 1 => 10 pairs (_) / I3 = 1 => 13 pairs (_) A5,C5: 1.. / A5 = 1 => 0 pairs (X) / C5 = 1 => 8 pairs (_) E8,E9: 1.. / E8 = 1 => 6 pairs (_) / E9 = 1 => 6 pairs (_) A1,A5: 1.. / A1 = 1 => 8 pairs (_) / A5 = 1 => 0 pairs (X) C1,C5: 1.. / C1 = 1 => 0 pairs (X) / C5 = 1 => 8 pairs (_) A4,C4: 2.. / A4 = 2 => 9 pairs (_) / C4 = 2 => 10 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 => 9 pairs (_) / A8 = 2 => 10 pairs (_) G3,I3: 5.. / G3 = 5 => 12 pairs (_) / I3 = 5 => 0 pairs (*) I5,G6: 5.. / I5 = 5 => 12 pairs (_) / G6 = 5 => 0 pairs (*) A8,C8: 5.. / A8 = 5 => 10 pairs (_) / C8 = 5 => 10 pairs (_) G3,G6: 5.. / G3 = 5 => 12 pairs (_) / G6 = 5 => 0 pairs (*) I3,I5: 5.. / I3 = 5 => 0 pairs (*) / I5 = 5 => 0 pairs (X) H2,I2: 6.. / H2 = 6 => 10 pairs (_) / I2 = 6 => 8 pairs (_) B4,B6: 6.. / B4 = 6 => 8 pairs (_) / B6 = 6 => 17 pairs (_) D4,D6: 6.. / D4 = 6 => 17 pairs (_) / D6 = 6 => 8 pairs (_) E8,E9: 6.. / E8 = 6 => 6 pairs (_) / E9 = 6 => 6 pairs (_) B4,D4: 6.. / B4 = 6 => 8 pairs (_) / D4 = 6 => 17 pairs (_) B6,D6: 6.. / B6 = 6 => 17 pairs (_) / D6 = 6 => 8 pairs (_) A5,B5: 7.. / A5 = 7 => 7 pairs (_) / B5 = 7 => 0 pairs (X) A7,B9: 7.. / A7 = 7 => 0 pairs (X) / B9 = 7 => 7 pairs (_) I7,I9: 7.. / I7 = 7 => 7 pairs (_) / I9 = 7 => 0 pairs (X) A7,I7: 7.. / A7 = 7 => 0 pairs (X) / I7 = 7 => 7 pairs (_) B9,I9: 7.. / B9 = 7 => 7 pairs (_) / I9 = 7 => 0 pairs (X) A5,A7: 7.. / A5 = 7 => 7 pairs (_) / A7 = 7 => 0 pairs (X) B5,B9: 7.. / B5 = 7 => 0 pairs (X) / B9 = 7 => 7 pairs (_) H1,I1: 8.. / H1 = 8 => 10 pairs (_) / I1 = 8 => 13 pairs (_) F4,F5: 8.. / F4 = 8 => 8 pairs (_) / F5 = 8 => 20 pairs (_) I5,G6: 8.. / I5 = 8 => 0 pairs (*) / G6 = 8 => 0 pairs (X) B4,F4: 8.. / B4 = 8 => 20 pairs (_) / F4 = 8 => 8 pairs (_) B6,G6: 8.. / B6 = 8 => 0 pairs (*) / G6 = 8 => 0 pairs (X) G6,G8: 8.. / G6 = 8 => 12 pairs (_) / G8 = 8 => 0 pairs (*) H1,H8: 8.. / H1 = 8 => 10 pairs (_) / H8 = 8 => 13 pairs (_) * DURATION: 0:00:09.924667 START: 23:57:09.222127 END: 23:57:19.146794 2025-04-04 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (E8,E9,F4,G6,I1,I2,I5,I7) * .2..567...5718.2..6.82.7.......7.194......62.....21.73.168.2.5....7.....8....5... * PAIR I1: 8,9 COL I I8: 8,9,1,2,6 # reduction candidate for 8,9 I8: 8,9 # 14 pairs I8: 1,2,6 # 8 pairs * PAIR I2: 6,9 COL I I8: 6,9,1,2,8 # reduction candidate for 6,9 I8: 6,9 # 10 pairs I9: 6,9,1,2,7 # reduction candidate for 6,9 I9: 6,9 => CTR * .2..567...5718.2..6.82.7..12...7.1947.1...625....21873.168.2.57...7...82872..5.16 I9: 1,2,7 # 8 pairs * PAIR F4: 3,8 BLK 5 F5: 3,8,4,9 # reduction candidate for 3,8 F5: 3,8 # 13 pairs F5: 4,9 # 9 pairs * PAIR F4: 3,8 ROW 4 B4: 3,8,6 # reduction candidate for 3,8 B4: 3,8 # 17 pairs B4: 6 # 8 pairs * PAIR E8: 1,6 ROW 8 H8: 1,6,3,4,8 # reduction candidate for 1,6 H8: 1,6 # 12 pairs I8: 1,6,2,8,9 # reduction candidate for 1,6 I8: 1,6 # 11 pairs * PAIR E9: 1,6 ROW 9 H9: 1,6,3,4 # reduction candidate for 1,6 H9: 1,6 # 9 pairs I9: 1,6,2,7,9 # reduction candidate for 1,6 I9: 1,6 => SOLVED * 123456789457189236698237415265378194731594628984621573316842957549713862872965341 I9: 2,7,9 # 9 pairs * PAIR I7: 7,9 BLK 9 I9: 7,9,1,2,6 # reduction candidate for 7,9 I9: 7,9 => CTR * .2..567...5718.2.66.82.7..12...7.194......625....21873.168.2.5....7...828.2..5... I9: 1,2,6 # 7 pairs * PAIR I7: 7,9 ROW 7 A7: 7,9,3,4 # reduction candidate for 7,9 A7: 7,9 # 11 pairs A7: 3,4 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-mith-te3-00094080-base-pr-000.dot * REASONING * DIS # I9: 6,9 => CTR => I9: 1,2,7 * PRF # I9: 1,6 => SOL * DIS # I9: 7,9 => CTR => I9: 1,2,6 * CNT 3 HDP CHAINS / 18 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (E8,E9,F4,G6,I1,I2,I5,I7) * .2..567...5718.2..6.82.7.......7.194......62.....21.73.168.2.5....7.....8....5... * PAIR I1: 8,9 COL I I8: 8,9,1,2,6 # reduction candidate for 8,9 I8: 8,9 # 14 pairs I8: 1,2,6 # 8 pairs * PAIR I2: 6,9 COL I I8: 6,9,1,2,8 # reduction candidate for 6,9 I8: 6,9 # 10 pairs I9: 6,9,1,2,7 # reduction candidate for 6,9 I9: 6,9 => CTR * .2..567...5718.2..6.82.7..12...7.1947.1...625....21873.168.2.57...7...82872..5.16 * RESTART * PAIR I2: 6,9 COL I I8: 6,9,1,2,8 # reduction candidate for 6,9 I8: 6,9 # 10 pairs I8: 1,2,8 # 8 pairs * PAIR RESTART * PAIR I2: 6,9 COL I I8: 6,9,1,2,8 # reduction candidate for 6,9 I8: 6,9 # 10 pairs I8: 1,2,8 # 8 pairs * PAIR F4: 3,8 BLK 5 F5: 3,8,4,9 # reduction candidate for 3,8 F5: 3,8 # 13 pairs F5: 4,9 # 9 pairs * PAIR F4: 3,8 ROW 4 B4: 3,8,6 # reduction candidate for 3,8 B4: 3,8 # 17 pairs B4: 6 # 8 pairs * PAIR E8: 1,6 ROW 8 H8: 1,6,3,4,8 # reduction candidate for 1,6 H8: 1,6 # 12 pairs I8: 1,6,2,8,9 # reduction candidate for 1,6 I8: 1,6 # 11 pairs * PAIR E9: 1,6 ROW 9 H9: 1,6,3,4 # reduction candidate for 1,6 H9: 3,4 => SOLVED * 123456789457189236698237415265378194731594628984621573316842957549713862872965341 * DURATION: 0:00:02.729537 START: 23:57:21.979931 END: 23:57:24.709468 2025-04-04 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00094080-base-pr-001.dot * REASONING * DIS # I9: 6,9 => CTR => I9: 1,2,7 * PRF I9: 1,2,7 # H9: 3,4 => SOL * STA I9: 1,2,7 + H9: 3,4 * CNT 2 HDP CHAINS / 16 HYP OPENED
Header Info
rating: 23839; r2: 528086; index: 94080
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 # I8: 8,9 => UNS * INC # I8: 1,2,6 => UNS * INC # I8: 6,9 => UNS * DIS # I9: 6,9 => CTR => I9: 1,2,7 * INC # I9: 1,2,7 => UNS * INC # F5: 3,8 => UNS * INC # F5: 4,9 => UNS * INC # B4: 3,8 => UNS * INC # B4: 6 => UNS * INC # H8: 1,6 => UNS * INC # I8: 1,6 => UNS * INC # H9: 1,6 => UNS * PRF # I9: 1,6 => SOL * INC # I9: 2,7,9 => UNS * DIS # I9: 7,9 => CTR => I9: 1,2,6 * INC # I9: 1,2,6 => UNS * INC # A7: 7,9 => UNS * INC # A7: 3,4 => UNS * CNT 18 HDP CHAINS / 18 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # I8: 8,9 => UNS * INC # I8: 1,2,6 => UNS * INC # I8: 6,9 => UNS * DIS # I9: 6,9 => CTR => I9: 1,2,7 * INC I9: 1,2,7 # I8: 6,9 => UNS * INC I9: 1,2,7 # I8: 1,2,8 => UNS * INC I9: 1,2,7 # I8: 6,9 => UNS * INC I9: 1,2,7 # I8: 1,2,8 => UNS * INC I9: 1,2,7 # F5: 3,8 => UNS * INC I9: 1,2,7 # F5: 4,9 => UNS * INC I9: 1,2,7 # B4: 3,8 => UNS * INC I9: 1,2,7 # B4: 6 => UNS * INC I9: 1,2,7 # H8: 1,6 => UNS * INC I9: 1,2,7 # I8: 1,6 => UNS * INC I9: 1,2,7 # H9: 1,6 => UNS * PRF I9: 1,2,7 # H9: 3,4 => SOL * STA I9: 1,2,7 + H9: 3,4 * CNT 16 HDP CHAINS / 16 HYP OPENED