Analysis of zz-www.sudokuoftheday.co.uk-20190413-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019
level: medium
position: ..5.....2......65.2..97........6...96.....1.5...24.....89.....6.2.4.8.7..7....23. initial
Autosolve
position: ..5....92......65.26.975.1...256.4896.....125.5.24..6..89...546.264.8971.7....238 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G1: 3,8 => CTR => G1: 7 * DIS # C3: 4 => CTR => C3: 3,8 * DIS # I2: 7 => CTR => I2: 3,4 * DIS # C3: 8 => CTR => C3: 3,4 * PRF # F4: 3 => SOL * PRF # A1: 1,7 => SOL * DIS # A2: 1,7 => CTR => A2: 4,8,9 * PRF # F4: 1,3 => SOL * DIS # F4: 7 => CTR => F4: 1,3 * DIS # B2: 1,3 => CTR => B2: 4,9 * DIS # A6: 1,8 => CTR => A6: 9 * DIS # C2: 1,8 => CTR => C2: 3,4,7 * DIS # A6: 8 => CTR => A6: 1,9 * DIS # G1: 8 => CTR => G1: 3,7 * DIS # I2: 4 => CTR => I2: 3,7 * DIS # D7: 1,3 => CTR => D7: 7 * DIS # A9: 5 => CTR => A9: 1,4 * DIS # C2: 1,4 => CTR => C2: 3,7,8 * PRF # D1: 3,8 => SOL * CNT 19 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G1: 3,8 => CTR => G1: 7 * PRF G1: 7 # F4: 3 => SOL * STA G1: 7 + F4: 3 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..5.....2......65.2..97........6...96.....1.5...24.....89.....6.2.4.8.7..7....23. | initial |
| ..5....92......65.26.975.1...256.4896.....125.5.24..6..89...546.264.8971.7....238 | autosolve |
| 145386792897124653263975814712563489634897125958241367389712546526438971471659238 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) G3: 3,8 I3: 3,4 A4: 1,7 B4: 1,3 C6: 1,8 F6: 1,9 G6: 3,7 I6: 3,7 A7: 1,3 A8: 3,5 C9: 1,4 E8: 3,5 D9: 1,6 F9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F4,F6: 1.. / F4 = 1 => 0 pairs (X) / F6 = 1 => 15 pairs (_) E2,F2: 2.. / E2 = 2 => 19 pairs (_) / F2 = 2 => 0 pairs (X) E7,F7: 2.. / E7 = 2 => 0 pairs (X) / F7 = 2 => 19 pairs (_) E2,E7: 2.. / E2 = 2 => 19 pairs (_) / E7 = 2 => 0 pairs (X) F2,F7: 2.. / F2 = 2 => 0 pairs (X) / F7 = 2 => 19 pairs (_) G6,I6: 3.. / G6 = 3 => 13 pairs (_) / I6 = 3 => 0 pairs (X) A7,A8: 3.. / A7 = 3 => 16 pairs (_) / A8 = 3 => 0 pairs (X) B4,F4: 3.. / B4 = 3 => 17 pairs (_) / F4 = 3 => 0 pairs (*) A8,E8: 3.. / A8 = 3 => 0 pairs (X) / E8 = 3 => 16 pairs (_) F1,F2: 4.. / F1 = 4 => 0 pairs (X) / F2 = 4 => 20 pairs (_) I2,I3: 4.. / I2 = 4 => 0 pairs (X) / I3 = 4 => 15 pairs (_) B5,C5: 4.. / B5 = 4 => 16 pairs (_) / C5 = 4 => 0 pairs (*) A9,C9: 4.. / A9 = 4 => 0 pairs (*) / C9 = 4 => 0 pairs (X) C3,I3: 4.. / C3 = 4 => 0 pairs (X) / I3 = 4 => 15 pairs (_) A8,A9: 5.. / A8 = 5 => 16 pairs (_) / A9 = 5 => 0 pairs (X) E8,E9: 5.. / E8 = 5 => 0 pairs (X) / E9 = 5 => 16 pairs (_) A8,E8: 5.. / A8 = 5 => 16 pairs (_) / E8 = 5 => 0 pairs (X) A9,E9: 5.. / A9 = 5 => 0 pairs (X) / E9 = 5 => 16 pairs (_) D1,F1: 6.. / D1 = 6 => 0 pairs (X) / F1 = 6 => 20 pairs (_) D9,F9: 6.. / D9 = 6 => 20 pairs (_) / F9 = 6 => 0 pairs (X) D1,D9: 6.. / D1 = 6 => 0 pairs (X) / D9 = 6 => 20 pairs (_) F1,F9: 6.. / F1 = 6 => 20 pairs (_) / F9 = 6 => 0 pairs (X) G1,I2: 7.. / G1 = 7 => 13 pairs (_) / I2 = 7 => 0 pairs (X) A4,C5: 7.. / A4 = 7 => 0 pairs (*) / C5 = 7 => 0 pairs (X) G6,I6: 7.. / G6 = 7 => 0 pairs (X) / I6 = 7 => 13 pairs (_) D7,F7: 7.. / D7 = 7 => 16 pairs (_) / F7 = 7 => 0 pairs (X) A1,G1: 7.. / A1 = 7 => 0 pairs (X) / G1 = 7 => 13 pairs (_) A4,F4: 7.. / A4 = 7 => 0 pairs (*) / F4 = 7 => 0 pairs (X) C2,C5: 7.. / C2 = 7 => 0 pairs (*) / C5 = 7 => 0 pairs (X) D5,D7: 7.. / D5 = 7 => 0 pairs (X) / D7 = 7 => 16 pairs (_) G1,G6: 7.. / G1 = 7 => 13 pairs (_) / G6 = 7 => 0 pairs (X) I2,I6: 7.. / I2 = 7 => 0 pairs (X) / I6 = 7 => 13 pairs (_) G1,G3: 8.. / G1 = 8 => 0 pairs (X) / G3 = 8 => 15 pairs (_) A6,C6: 8.. / A6 = 8 => 0 pairs (X) / C6 = 8 => 15 pairs (_) D5,E5: 8.. / D5 = 8 => 20 pairs (_) / E5 = 8 => 0 pairs (X) C3,G3: 8.. / C3 = 8 => 0 pairs (X) / G3 = 8 => 15 pairs (_) A2,B2: 9.. / A2 = 9 => 0 pairs (X) / B2 = 9 => 15 pairs (_) B5,A6: 9.. / B5 = 9 => 0 pairs (X) / A6 = 9 => 15 pairs (_) E9,F9: 9.. / E9 = 9 => 0 pairs (X) / F9 = 9 => 20 pairs (_) A6,F6: 9.. / A6 = 9 => 15 pairs (_) / F6 = 9 => 0 pairs (X) A2,A6: 9.. / A2 = 9 => 0 pairs (X) / A6 = 9 => 15 pairs (_) B2,B5: 9.. / B2 = 9 => 15 pairs (_) / B5 = 9 => 0 pairs (X) E5,E9: 9.. / E5 = 9 => 20 pairs (_) / E9 = 9 => 0 pairs (X) * DURATION: 0:00:54.035138 START: 05:16:03.087889 END: 05:16:57.123027 2019-05-01 * CP COUNT: (43) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,A8,B4,C6,C9,D9,E8,F6,F9,G3,G6,I3,I6) * ..5....92......65.26.975.1...256.4896.....125.5.24..6..89...546.264.8971.7....238 * PAIR G3: 3,8 BLK 3 G1: 3,8,7 # reduction candidate for 3,8 G1: 3,8 => CTR * 7.5.86392894...65726.975.141325674896.7...125.58241763389712546526438971471659238 G1: 7 # 13 pairs * PAIR G3: 3,8 ROW 3 C3: 3,8,4 # reduction candidate for 3,8 C3: 4 => CTR * ..5....92......65.264975813..256.48964....125958241367.89...546.264.8971471659238 C3: 3,8 # 15 pairs * PAIR I3: 3,4 BLK 3 I2: 3,4,7 # reduction candidate for 3,4 I2: 7 => CTR * 7.5....92......65726.975.14132567489647...125958241763389712546526438971471659238 I2: 3,4 # 13 pairs * PAIR I3: 3,4 ROW 3 C3: 3,4,8 # reduction candidate for 3,4 C3: 8 => CTR * ..5....92......65.268975314..256.4896.....125851249763.89...546.264.8971.74.96238 C3: 3,4 # 15 pairs * PAIR A4: 1,7 ROW 4 F4: 1,7,3 # reduction candidate for 1,7 F4: 3 => SOLVED * 145386792897124653263975814712563489634897125958241367389712546526438971471659238 F4: 1,7 # 17 pairs * PAIR A4: 1,7 COL A A1: 1,7,4,8 # reduction candidate for 1,7 A1: 1,7 => SOLVED * 145386792897124653263975814712563489634897125958241367389712546526438971471659238 A1: 4,8 # 14 pairs A2: 1,7,4,8,9 # reduction candidate for 1,7 A2: 1,7 => CTR * 8.5..6792.9...4653263975814..256.4896.4.9.125958241367389..2546526438971471659238 A2: 4,8,9 # 14 pairs * PAIR B4: 1,3 ROW 4 F4: 1,3,7 # reduction candidate for 1,3 F4: 1,3 => SOLVED * 145386792897124653263975814712563489634897125958241367389712546526438971471659238 F4: 7 => CTR * ..5....92......65.26.975.1.132567489647...125958241.6.389712546526438971471659238 * PAIR B4: 1,3 COL B B1: 1,3,4 # reduction candidate for 1,3 B1: 1,3 # 17 pairs B2: 1,3,4,9 # reduction candidate for 1,3 B2: 1,3 => CTR * ..5....929.....65.26.975.1...256.489694...125.5.249.6..89...546.264.8971471...238 B2: 4,9 # 15 pairs * PAIR C6: 1,8 BLK 4 A6: 1,8,9 # reduction candidate for 1,8 A6: 1,8 => CTR * ..5....929.....65.26.975.1...256.489694...125.5.249.6..89...546.264.8971471...238 A6: 9 # 15 pairs * PAIR C6: 1,8 COL C C2: 1,8,3,4,7 # reduction candidate for 1,8 C2: 1,8 => CTR * ..5....92......65.263975814132567489647...12595824..6..897..546.264.8971.7....238 C2: 3,4,7 # 14 pairs * PAIR F6: 1,9 ROW 6 A6: 1,9,8 # reduction candidate for 1,9 A6: 8 => CTR * ..5....929.....65.26.975.1...256.489694...12585124..6..89...546.264.8971.7....238 A6: 1,9 # 15 pairs * PAIR G6: 3,7 COL G G1: 3,7,8 # reduction candidate for 3,7 G1: 8 => CTR * 7.5...892......6572689753141.256.4896.....125.5.24..6..89...546.264.8971.7....238 G1: 3,7 # 15 pairs * PAIR I6: 3,7 COL I I2: 3,7,4 # reduction candidate for 3,7 I2: 4 => CTR * ..5...792......654264975813..256.48964....125958241367.89...546.264.8971471659238 I2: 3,7 # 15 pairs * PAIR A7: 1,3 ROW 7 D7: 1,3,7 # reduction candidate for 1,3 D7: 1,3 => CTR * ..56.4792497812653263975.1.7.256.4896..78.125.5.24..67.89327546326458971574196238 D7: 7 # 16 pairs E7: 1,3,2 # reduction candidate for 1,3 E7: 1,3 # 19 pairs * PAIR C9: 1,4 BLK 7 A9: 1,4,5 # reduction candidate for 1,4 A9: 5 => CTR * ..5....92.91...65.263975.14..256.48964....125958241.6.189...546326458971574...238 A9: 1,4 # 16 pairs * PAIR C9: 1,4 COL C C2: 1,4,3,7,8 # reduction candidate for 1,4 C2: 1,4 => CTR * ..5....92......65.263975814132567489647...125958241.6.389712546526438971471659238 C2: 3,7,8 # 14 pairs * PAIR D9: 1,6 COL D D1: 1,6,3,8 # reduction candidate for 1,6 D1: 3,8 => SOLVED * 145386792897124653263975814712563489634897125958241367389712546526438971471659238 D1: 1,6 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190413-absurd-base-pr-000.dot * REASONING * DIS # G1: 3,8 => CTR => G1: 7 * DIS # C3: 4 => CTR => C3: 3,8 * DIS # I2: 7 => CTR => I2: 3,4 * DIS # C3: 8 => CTR => C3: 3,4 * PRF # F4: 3 => SOL * PRF # A1: 1,7 => SOL * DIS # A2: 1,7 => CTR => A2: 4,8,9 * PRF # F4: 1,3 => SOL * DIS # F4: 7 => CTR => F4: 1,3 * DIS # B2: 1,3 => CTR => B2: 4,9 * DIS # A6: 1,8 => CTR => A6: 9 * DIS # C2: 1,8 => CTR => C2: 3,4,7 * DIS # A6: 8 => CTR => A6: 1,9 * DIS # G1: 8 => CTR => G1: 3,7 * DIS # I2: 4 => CTR => I2: 3,7 * DIS # D7: 1,3 => CTR => D7: 7 * DIS # A9: 5 => CTR => A9: 1,4 * DIS # C2: 1,4 => CTR => C2: 3,7,8 * PRF # D1: 3,8 => SOL * CNT 19 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,A8,B4,C6,C9,D9,E8,F6,F9,G3,G6,I3,I6) * ..5....92......65.26.975.1...256.4896.....125.5.24..6..89...546.264.8971.7....238 * PAIR G3: 3,8 BLK 3 G1: 3,8,7 # reduction candidate for 3,8 G1: 3,8 => CTR * 7.5.86392894...65726.975.141325674896.7...125.58241763389712546526438971471659238 * PAIR A4: 1,7 ROW 4 F4: 1,7,3 # reduction candidate for 1,7 F4: 3 => SOLVED * 145386792897124653263975814712563489634897125958241367389712546526438971471659238 * DURATION: 0:00:03.806540 START: 05:17:23.205191 END: 05:17:27.011731 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190413-absurd-base-pr-001.dot * REASONING * DIS # G1: 3,8 => CTR => G1: 7 * PRF G1: 7 # F4: 3 => SOL * STA G1: 7 + F4: 3 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190413, absurd
Solution
position: 145386792897124653263975814712563489634897125958241367389712546526438971471659238 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 # G1: 3,8 => CTR => G1: 7 * INC # G1: 7 => UNS * INC # C3: 3,8 => UNS * DIS # C3: 4 => CTR => C3: 3,8 * INC # I2: 3,4 => UNS * DIS # I2: 7 => CTR => I2: 3,4 * INC # C3: 3,4 => UNS * DIS # C3: 8 => CTR => C3: 3,4 * INC # F4: 1,7 => UNS * PRF # F4: 3 => SOL * PRF # A1: 1,7 => SOL * INC # A1: 4,8 => UNS * DIS # A2: 1,7 => CTR => A2: 4,8,9 * INC # A2: 4,8,9 => UNS * PRF # F4: 1,3 => SOL * DIS # F4: 7 => CTR => F4: 1,3 * INC # B1: 1,3 => UNS * DIS # B2: 1,3 => CTR => B2: 4,9 * INC # B2: 4,9 => UNS * DIS # A6: 1,8 => CTR => A6: 9 * INC # A6: 9 => UNS * DIS # C2: 1,8 => CTR => C2: 3,4,7 * INC # C2: 3,4,7 => UNS * INC # A6: 1,9 => UNS * DIS # A6: 8 => CTR => A6: 1,9 * INC # G1: 3,7 => UNS * DIS # G1: 8 => CTR => G1: 3,7 * INC # I2: 3,7 => UNS * DIS # I2: 4 => CTR => I2: 3,7 * DIS # D7: 1,3 => CTR => D7: 7 * INC # D7: 7 => UNS * INC # E7: 1,3 => UNS * INC # A9: 1,4 => UNS * DIS # A9: 5 => CTR => A9: 1,4 * DIS # C2: 1,4 => CTR => C2: 3,7,8 * INC # C2: 3,7,8 => UNS * INC # D1: 1,6 => UNS * PRF # D1: 3,8 => SOL * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # G1: 3,8 => CTR => G1: 7 * INC G1: 7 # F4: 1,7 => UNS * PRF G1: 7 # F4: 3 => SOL * STA G1: 7 + F4: 3 * CNT 3 HDP CHAINS / 3 HYP OPENED