Analysis of xx-mith-te3-00069919-base.sdk
Contents
Original Sudoku
level: medium
position: 12....78..........7.9....6.2176.........128.....3.5.2..71.2.69.6.2.9..1889..6.2.. initial
Autosolve
position: 12....78..........7.9....6.2176.........128.....3.5.2..71.2.69.6.2.9..1889..6.2.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F1: 4,9 => CTR => F1: 6 * DIS # D2: 4,9 => CTR => D2: 1,2,7,8 * DIS # D5: 7 => CTR => D5: 4,9 * PRF # F4: 4,8 => SOL * PRF # D5: 9 => SOL * DIS # I6: 4,7 => CTR => I6: 1,6,9 * DIS # I5: 4,7 => CTR => I5: 6,9 * DIS # I6: 4,7 => CTR => I6: 1,6,9 * PRF # D5: 9 => SOL * CNT 9 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:
* DIS # F1: 4,9 => CTR => F1: 6 * DIS F1: 6 # D2: 4,9 => CTR => D2: 1,2,7,8 * DIS F1: 6 + D2: 1,2,7,8 # D5: 7 => CTR => D5: 4,9 * DIS F1: 6 + D2: 1,2,7,8 + D5: 4,9 # I5: 4,7 => CTR => I5: 6,9 * PRF F1: 6 + D2: 1,2,7,8 + D5: 4,9 + I5: 6,9 # G6: 4 => SOL * STA F1: 6 + D2: 1,2,7,8 + D5: 4,9 + I5: 6,9 + G6: 4 * CNT 5 HDP CHAINS / 28 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 12....78..........7.9....6.2176.........128.....3.5.2..71.2.69.6.2.9..1889..6.2.. | initial |
| 12....78..........7.9....6.2176.........128.....3.5.2..71.2.69.6.2.9..1889..6.2.. | autosolve |
| 123456789456789132789231564217648953534912876968375421371824695642597318895163247 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) D1: 4,9 A6: 4,9 E4: 4,8 E6: 4,7 H5: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G6,I6: 1.. / G6 = 1 => 7 pairs (_) / I6 = 1 => 15 pairs (_) D9,F9: 1.. / D9 = 1 => 6 pairs (_) / F9 = 1 => 10 pairs (_) D2,D3: 2.. / D2 = 2 => 5 pairs (_) / D3 = 2 => 5 pairs (_) I2,I3: 2.. / I2 = 2 => 5 pairs (_) / I3 = 2 => 5 pairs (_) D2,I2: 2.. / D2 = 2 => 5 pairs (_) / I2 = 2 => 5 pairs (_) D3,I3: 2.. / D3 = 2 => 5 pairs (_) / I3 = 2 => 5 pairs (_) F1,F2: 6.. / F1 = 6 => 5 pairs (_) / F2 = 6 => 0 pairs (X) I5,I6: 6.. / I5 = 6 => 7 pairs (_) / I6 = 6 => 12 pairs (_) C1,F1: 6.. / C1 = 6 => 0 pairs (X) / F1 = 6 => 5 pairs (_) D5,E6: 7.. / D5 = 7 => 0 pairs (X) / E6 = 7 => 11 pairs (_) D8,F8: 7.. / D8 = 7 => 12 pairs (_) / F8 = 7 => 6 pairs (_) H9,I9: 7.. / H9 = 7 => 0 pairs (X) / I9 = 7 => 10 pairs (_) E6,I6: 7.. / E6 = 7 => 11 pairs (_) / I6 = 7 => 0 pairs (X) E2,E6: 7.. / E2 = 7 => 0 pairs (X) / E6 = 7 => 11 pairs (_) F2,F8: 7.. / F2 = 7 => 12 pairs (_) / F8 = 7 => 6 pairs (_) H5,H9: 7.. / H5 = 7 => 10 pairs (_) / H9 = 7 => 0 pairs (X) B6,C6: 8.. / B6 = 8 => 6 pairs (_) / C6 = 8 => 6 pairs (_) E4,F4: 8.. / E4 = 8 => 5 pairs (_) / F4 = 8 => 0 pairs (*) D7,F7: 8.. / D7 = 8 => 6 pairs (_) / F7 = 8 => 10 pairs (_) C2,C6: 8.. / C2 = 8 => 6 pairs (_) / C6 = 8 => 6 pairs (_) A5,A6: 9.. / A5 = 9 => 17 pairs (_) / A6 = 9 => 5 pairs (_) F4,D5: 9.. / F4 = 9 => 12 pairs (_) / D5 = 9 => 0 pairs (*) * DURATION: 0:00:05.914594 START: 19:08:22.802110 END: 19:08:28.716704 2025-04-04 * CP COUNT: (22) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,D1,E4,E6,H5) * 12....78..........7.9....6.2176.........128.....3.5.2..71.2.69.6.2.9..1889..6.2.. * PAIR D1: 4,9 BLK 2 F1: 4,9,6 # reduction candidate for 4,9 F1: 4,9 => CTR * 126...78.....76...7.9....6.2176........71284....345.27.71.2.69.6.2.97.1889..6.27. F1: 6 # 5 pairs D2: 4,9,1,2,7,8 # reduction candidate for 4,9 D2: 4,9 => CTR * 12....78.....7...27.92...6.2176........71284....345.27.7182.69.6.2597.1889.16.27. D2: 1,2,7,8 # 5 pairs F2: 4,9,1,6,7,8 # reduction candidate for 4,9 F2: 4,9 # 11 pairs * PAIR D1: 4,9 ROW 1 I1: 4,9,3,5 # reduction candidate for 4,9 I1: 4,9 # 8 pairs I1: 3,5 # 6 pairs * PAIR D1: 4,9 COL D D5: 4,9,7 # reduction candidate for 4,9 D5: 7 => CTR * 12....78..........7.9....6.2176.9......71284....345.2..71.2.69.6.2.9..1889..6.2.. D5: 4,9 # 11 pairs * PAIR A6: 4,9 BLK 4 A5: 4,9,3,5 # reduction candidate for 4,9 A5: 4,9 # 12 pairs A5: 3,5 # 6 pairs * PAIR A6: 4,9 ROW 6 G6: 4,9,1 # reduction candidate for 4,9 G6: 4,9 # 15 pairs I6: 4,9,1,6,7 # reduction candidate for 4,9 I6: 4,9 # 15 pairs * PAIR E4: 4,8 BLK 5 F4: 4,8,9 # reduction candidate for 4,8 F4: 4,8 => SOLVED * 123456789456789132789231564217648953534912876968375421371824695642597318895163247 F4: 9 # 12 pairs * PAIR E4: 4,8 COL E E2: 4,8,3,5,7 # reduction candidate for 4,8 E2: 4,8 # 14 pairs E3: 4,8,3,5 # reduction candidate for 4,8 E3: 4,8 # 16 pairs * PAIR E6: 4,7 BLK 5 D5: 4,7,9 # reduction candidate for 4,7 D5: 9 => SOLVED * 123456789456789132789231564217648953534912876968375421371824695642597318895163247 D5: 4,7 # 12 pairs * PAIR E6: 4,7 ROW 6 I6: 4,7,1,6,9 # reduction candidate for 4,7 I6: 4,7 => CTR * 12.4..78.........17.92.1.6.217648......9128769..375124.7182.69.6.2597.1889.16.2.7 I6: 1,6,9 # 11 pairs * PAIR E6: 4,7 COL E E2: 4,7,3,5,8 # reduction candidate for 4,7 E2: 3,5,8 # 11 pairs E2: 4,7 # 8 pairs * PAIR H5: 4,7 BLK 6 I5: 4,7,6,9 # reduction candidate for 4,7 I5: 4,7 => CTR * 12.4..78.........17.92.1.6.217648......9128..9..375126.7182.69.6.2597.1889.16.2.. I5: 6,9 # 6 pairs I6: 4,7,1,6,9 # reduction candidate for 4,7 I6: 4,7 => CTR * 12.4..78.........17.92.1.6.217648......9128769..375124.7182.69.6.2597.1889.16.2.7 I6: 1,6,9 # 11 pairs * PAIR H5: 4,7 ROW 5 D5: 4,7,9 # reduction candidate for 4,7 D5: 9 => SOLVED * 123456789456789132789231564217648953534912876968375421371824695642597318895163247 D5: 4,7 # 12 pairs * PAIR H5: 4,7 COL H H9: 4,7,3,5 # reduction candidate for 4,7 H9: 3,5 # 11 pairs H9: 4,7 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-mith-te3-00069919-base-pr-000.dot * REASONING * DIS # F1: 4,9 => CTR => F1: 6 * DIS # D2: 4,9 => CTR => D2: 1,2,7,8 * DIS # D5: 7 => CTR => D5: 4,9 * PRF # F4: 4,8 => SOL * PRF # D5: 9 => SOL * DIS # I6: 4,7 => CTR => I6: 1,6,9 * DIS # I5: 4,7 => CTR => I5: 6,9 * DIS # I6: 4,7 => CTR => I6: 1,6,9 * PRF # D5: 9 => SOL * CNT 9 HDP CHAINS / 31 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,D1,E4,E6,H5) * 12....78..........7.9....6.2176.........128.....3.5.2..71.2.69.6.2.9..1889..6.2.. * PAIR D1: 4,9 BLK 2 F1: 4,9,6 # reduction candidate for 4,9 F1: 4,9 => CTR * 126...78.....76...7.9....6.2176........71284....345.27.71.2.69.6.2.97.1889..6.27. D2: 4,9,1,2,7,8 # reduction candidate for 4,9 D2: 4,9 => CTR * 12...678.....7...27.92...6.2176........71284....345.27.7182.69.6.2597.1889.16.27. F2: 4,9,1,7,8 # reduction candidate for 4,9 F2: 4,9 # 11 pairs * RESTART * PAIR D1: 4,9 BLK 2 F2: 4,9,1,7,8 # reduction candidate for 4,9 F2: 1,7,8 # 12 pairs F2: 4,9 # 11 pairs * PAIR D1: 4,9 ROW 1 I1: 4,9,3,5 # reduction candidate for 4,9 I1: 3,5 # 13 pairs I1: 4,9 # 8 pairs * PAIR D1: 4,9 COL D D5: 4,9,7 # reduction candidate for 4,9 D5: 7 => CTR * 12.9.678..........7.9....6.2176.9......71284....345.2..71.2.69.6.2.9..1889..6.2.. * PAIR RESTART * PAIR D1: 4,9 ROW 1 I1: 4,9,3,5 # reduction candidate for 4,9 I1: 4,9 # 14 pairs I1: 3,5 # 13 pairs * PAIR A6: 4,9 BLK 4 A5: 4,9,3,5 # reduction candidate for 4,9 A5: 4,9 # 18 pairs A5: 3,5 # 12 pairs * PAIR A6: 4,9 ROW 6 G6: 4,9,1 # reduction candidate for 4,9 G6: 4,9 # 15 pairs I6: 4,9,1,6 # reduction candidate for 4,9 I6: 4,9 # 15 pairs * PAIR E4: 4,8 COL E E2: 4,8,3,5 # reduction candidate for 4,8 E2: 4,8 # 14 pairs E3: 4,8,3,5 # reduction candidate for 4,8 E3: 4,8 # 16 pairs * PAIR H5: 4,7 BLK 6 I5: 4,7,6,9 # reduction candidate for 4,7 I5: 4,7 => CTR * 12...678.......9..7.9....6.2176.9...9..41287....375126.71.2.69.6.2.9..1889..6.2.. * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A6,D1,D5,D7,D8,D9,E4,F3,F4,G2,I5) * 12...678..........7.9....6.2176.........1287....375.2..71.2.69.6.2.9..1889..6.2.7 * PAIR D1: 4,9 ROW 1 I1: 4,9,3,5 # reduction candidate for 4,9 I1: 4,9 # 14 pairs I1: 3,5 # 13 pairs * PAIR F3: 1,8 BLK 2 D3: 1,8,2 # reduction candidate for 1,8 D3: 2 # 12 pairs D3: 1,8 # 12 pairs * PAIR G2: 1,9 BLK 3 I2: 1,9,2 # reduction candidate for 1,9 I2: 2 # 12 pairs I2: 1,9 # 12 pairs * PAIR G2: 1,9 ROW 2 F2: 1,9,7 # reduction candidate for 1,9 F2: 1,9 # 13 pairs F2: 7 # 12 pairs * PAIR G2: 1,9 COL G G6: 1,9,4 # reduction candidate for 1,9 G6: 4 => SOLVED * 123456789456789132789231564217648953534912876968375421371824695642597318895163247 * DURATION: 0:00:05.556150 START: 19:08:33.833025 END: 19:08:39.389175 2025-04-04 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00069919-base-pr-001.dot * REASONING * DIS # F1: 4,9 => CTR => F1: 6 * DIS F1: 6 # D2: 4,9 => CTR => D2: 1,2,7,8 * DIS F1: 6 + D2: 1,2,7,8 # D5: 7 => CTR => D5: 4,9 * DIS F1: 6 + D2: 1,2,7,8 + D5: 4,9 # I5: 4,7 => CTR => I5: 6,9 * PRF F1: 6 + D2: 1,2,7,8 + D5: 4,9 + I5: 6,9 # G6: 4 => SOL * STA F1: 6 + D2: 1,2,7,8 + D5: 4,9 + I5: 6,9 + G6: 4 * CNT 5 HDP CHAINS / 28 HYP OPENED
Header Info
rating: 15500; r2: 419874; index: 69919
Solution
position: 123456789456789132789231564217648953534912876968375421371824695642597318895163247 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:
* DIS # F1: 4,9 => CTR => F1: 6 * INC # F1: 6 => UNS * DIS # D2: 4,9 => CTR => D2: 1,2,7,8 * INC # D2: 1,2,7,8 => UNS * INC # F2: 4,9 => UNS * INC # I1: 4,9 => UNS * INC # I1: 3,5 => UNS * INC # D5: 4,9 => UNS * DIS # D5: 7 => CTR => D5: 4,9 * INC # A5: 4,9 => UNS * INC # A5: 3,5 => UNS * INC # G6: 4,9 => UNS * INC # I6: 4,9 => UNS * PRF # F4: 4,8 => SOL * INC # F4: 9 => UNS * INC # E2: 4,8 => UNS * INC # E3: 4,8 => UNS * INC # D5: 4,7 => UNS * PRF # D5: 9 => SOL * DIS # I6: 4,7 => CTR => I6: 1,6,9 * INC # I6: 1,6,9 => UNS * INC # E2: 4,7 => UNS * INC # E2: 3,5,8 => UNS * DIS # I5: 4,7 => CTR => I5: 6,9 * INC # I5: 6,9 => UNS * DIS # I6: 4,7 => CTR => I6: 1,6,9 * INC # I6: 1,6,9 => UNS * INC # D5: 4,7 => UNS * PRF # D5: 9 => SOL * INC # H9: 4,7 => UNS * INC # H9: 3,5 => UNS * CNT 31 HDP CHAINS / 31 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # F1: 4,9 => CTR => F1: 6 * DIS F1: 6 # D2: 4,9 => CTR => D2: 1,2,7,8 * INC F1: 6 + D2: 1,2,7,8 # F2: 4,9 => UNS * INC F1: 6 + D2: 1,2,7,8 # F2: 4,9 => UNS * INC F1: 6 + D2: 1,2,7,8 # F2: 1,7,8 => UNS * INC F1: 6 + D2: 1,2,7,8 # I1: 4,9 => UNS * INC F1: 6 + D2: 1,2,7,8 # I1: 3,5 => UNS * INC F1: 6 + D2: 1,2,7,8 # D5: 4,9 => UNS * DIS F1: 6 + D2: 1,2,7,8 # D5: 7 => CTR => D5: 4,9 * INC F1: 6 + D2: 1,2,7,8 + D5: 4,9 # I1: 4,9 => UNS * INC F1: 6 + D2: 1,2,7,8 + D5: 4,9 # I1: 3,5 => UNS * INC F1: 6 + D2: 1,2,7,8 + D5: 4,9 # A5: 4,9 => UNS * INC F1: 6 + D2: 1,2,7,8 + D5: 4,9 # A5: 3,5 => UNS * INC F1: 6 + D2: 1,2,7,8 + D5: 4,9 # G6: 4,9 => UNS * INC F1: 6 + D2: 1,2,7,8 + D5: 4,9 # I6: 4,9 => UNS * INC F1: 6 + D2: 1,2,7,8 + D5: 4,9 # E2: 4,8 => UNS * INC F1: 6 + D2: 1,2,7,8 + D5: 4,9 # E3: 4,8 => UNS * DIS F1: 6 + D2: 1,2,7,8 + D5: 4,9 # I5: 4,7 => CTR => I5: 6,9 * INC F1: 6 + D2: 1,2,7,8 + D5: 4,9 + I5: 6,9 # I1: 4,9 => UNS * INC F1: 6 + D2: 1,2,7,8 + D5: 4,9 + I5: 6,9 # I1: 3,5 => UNS * INC F1: 6 + D2: 1,2,7,8 + D5: 4,9 + I5: 6,9 # D3: 1,8 => UNS * INC F1: 6 + D2: 1,2,7,8 + D5: 4,9 + I5: 6,9 # D3: 2 => UNS * INC F1: 6 + D2: 1,2,7,8 + D5: 4,9 + I5: 6,9 # I2: 1,9 => UNS * INC F1: 6 + D2: 1,2,7,8 + D5: 4,9 + I5: 6,9 # I2: 2 => UNS * INC F1: 6 + D2: 1,2,7,8 + D5: 4,9 + I5: 6,9 # F2: 1,9 => UNS * INC F1: 6 + D2: 1,2,7,8 + D5: 4,9 + I5: 6,9 # F2: 7 => UNS * INC F1: 6 + D2: 1,2,7,8 + D5: 4,9 + I5: 6,9 # G6: 1,9 => UNS * PRF F1: 6 + D2: 1,2,7,8 + D5: 4,9 + I5: 6,9 # G6: 4 => SOL * STA F1: 6 + D2: 1,2,7,8 + D5: 4,9 + I5: 6,9 + G6: 4 * CNT 28 HDP CHAINS / 28 HYP OPENED