Analysis of zz-www.sudokuoftheday.co.uk-20060725-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006
level: medium
position: ..9.438......17....3.8.....3....4.1.6......48...19.3.25.....2.....538.7..86.....4 initial
Autosolve
position: ..9.438......17..3.3.8.....3...84.1.6..3...48...19.3.25.34..28....538.7..86...534 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D2: 2,6 => CTR => D2: 9 * DIS # E3: 2,6 => CTR => E3: 5 * PRF # B1: 2,6 => SOL * DIS # D4: 7 => CTR => D4: 2,6 * PRF # G3: 4,6 => SOL * PRF # B2: 2,5 => SOL * DIS # B4: 2,5 => CTR => B4: 9 * PRF # C5: 2,5 => SOL * DIS # C2: 2,5 => CTR => C2: 4,8 * PRF # C2: 4,8 => SOL * DIS # A6: 4,7 => CTR => A6: 8 * PRF # A6: 8 => SOL * PRF # C6: 4,7 => SOL * DIS # C6: 8 => CTR => C6: 4,7 * DIS # E5: 2,5 => CTR => E5: 7 * PRF # C5: 2,5 => SOL * DIS # F3: 2,5 => CTR => F3: 6,9 * DIS # F3: 2,9 => CTR => F3: 5,6 * DIS # I4: 7,9 => CTR => I4: 5,6 * DIS # I4: 7,9 => CTR => I4: 5,6 * DIS # H2: 5,6 => CTR => H2: 2,9 * DIS # B1: 1,7 => CTR => B1: 2,5,6 * PRF # B1: 2,5,6 => SOL * DIS # D9: 9 => CTR => D9: 2,7 * DIS # E5: 5 => CTR => E5: 2,7 * DIS # F7: 6 => CTR => F7: 1,9 * CNT 26 HDP CHAINS / 54 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D2: 2,6 => CTR => D2: 9 * DIS D2: 9 # F3: 5 => CTR => F3: 2,6 * PRF D2: 9 + F3: 2,6 # B1: 2,6 => SOL * STA D2: 9 + F3: 2,6 + B1: 2,6 * CNT 3 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..9.438......17....3.8.....3....4.1.6......48...19.3.25.....2.....538.7..86.....4 | initial |
| ..9.438......17..3.3.8.....3...84.1.6..3...48...19.3.25.34..28....538.7..86...534 | autosolve |
| 769243851458917623231856497392684715615372948847195362573461289924538176186729534 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) D1: 2,6 G2: 4,6 C4: 2,5 B6: 4,7 F5: 2,5 F6: 5,6 G5: 7,9 H6: 5,6 B7: 1,7 E7: 6,7 E9: 2,7 I7: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B5,C5: 1.. / B5 = 1 => 0 pairs (*) / C5 = 1 => 0 pairs (X) F7,F9: 1.. / F7 = 1 => 19 pairs (_) / F9 = 1 => 14 pairs (_) A9,F9: 1.. / A9 = 1 => 19 pairs (_) / F9 = 1 => 14 pairs (_) G3,G8: 1.. / G3 = 1 => 14 pairs (_) / G8 = 1 => 17 pairs (_) G2,G3: 4.. / G2 = 4 => 12 pairs (_) / G3 = 4 => 0 pairs (*) E3,F3: 5.. / E3 = 5 => 15 pairs (_) / F3 = 5 => 0 pairs (X) I4,H6: 5.. / I4 = 5 => 17 pairs (_) / H6 = 5 => 0 pairs (X) F6,H6: 5.. / F6 = 5 => 17 pairs (_) / H6 = 5 => 0 pairs (X) E3,E5: 5.. / E3 = 5 => 15 pairs (_) / E5 = 5 => 0 pairs (X) I1,I4: 5.. / I1 = 5 => 0 pairs (X) / I4 = 5 => 17 pairs (_) B1,B2: 6.. / B1 = 6 => 0 pairs (*) / B2 = 6 => 0 pairs (X) D4,F6: 6.. / D4 = 6 => 17 pairs (_) / F6 = 6 => 0 pairs (X) E7,F7: 6.. / E7 = 6 => 15 pairs (_) / F7 = 6 => 0 pairs (X) G8,I8: 6.. / G8 = 6 => 16 pairs (_) / I8 = 6 => 14 pairs (_) F6,H6: 6.. / F6 = 6 => 0 pairs (X) / H6 = 6 => 17 pairs (_) E3,E7: 6.. / E3 = 6 => 0 pairs (X) / E7 = 6 => 15 pairs (_) D4,E5: 7.. / D4 = 7 => 0 pairs (X) / E5 = 7 => 17 pairs (_) B7,A9: 7.. / B7 = 7 => 15 pairs (_) / A9 = 7 => 0 pairs (X) E5,G5: 7.. / E5 = 7 => 17 pairs (_) / G5 = 7 => 0 pairs (X) B7,E7: 7.. / B7 = 7 => 15 pairs (_) / E7 = 7 => 0 pairs (X) C3,C6: 7.. / C3 = 7 => 0 pairs (X) / C6 = 7 => 0 pairs (_) D4,D9: 7.. / D4 = 7 => 0 pairs (X) / D9 = 7 => 17 pairs (_) A2,C2: 8.. / A2 = 8 => 0 pairs (X) / C2 = 8 => 0 pairs (_) A6,C6: 8.. / A6 = 8 => 0 pairs (*) / C6 = 8 => 0 pairs (X) A2,A6: 8.. / A2 = 8 => 0 pairs (X) / A6 = 8 => 0 pairs (_) C2,C6: 8.. / C2 = 8 => 0 pairs (*) / C6 = 8 => 0 pairs (X) D2,F3: 9.. / D2 = 9 => 17 pairs (_) / F3 = 9 => 0 pairs (X) H2,H3: 9.. / H2 = 9 => 0 pairs (X) / H3 = 9 => 17 pairs (_) B4,B5: 9.. / B4 = 9 => 17 pairs (_) / B5 = 9 => 0 pairs (X) A8,A9: 9.. / A8 = 9 => 17 pairs (_) / A9 = 9 => 16 pairs (_) D2,H2: 9.. / D2 = 9 => 17 pairs (_) / H2 = 9 => 0 pairs (X) F3,H3: 9.. / F3 = 9 => 0 pairs (X) / H3 = 9 => 17 pairs (_) B5,G5: 9.. / B5 = 9 => 0 pairs (X) / G5 = 9 => 17 pairs (_) F7,I7: 9.. / F7 = 9 => 16 pairs (_) / I7 = 9 => 17 pairs (_) D2,D9: 9.. / D2 = 9 => 17 pairs (_) / D9 = 9 => 0 pairs (X) * DURATION: 0:00:45.265179 START: 01:16:35.198589 END: 01:17:20.463768 2019-05-01 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,B7,C4,D1,E7,E9,F5,F6,G2,G5,H6,I7) * ..9.438......17..3.3.8.....3...84.1.6..3...48...19.3.25.34..28....538.7..86...534 * PAIR D1: 2,6 BLK 2 D2: 2,6,9 # reduction candidate for 2,6 D2: 2,6 => CTR * 719.438.5.6..17.93.3.859..73..784916691325748..71963525734612899..538671186972534 D2: 9 # 17 pairs E3: 2,6,5 # reduction candidate for 2,6 E3: 2,6 => CTR * ..9.438.5...917..3.3.825.973..784.1.691352748..719635257346.28....538.7..8627.534 E3: 5 # 15 pairs F3: 2,6,5,9 # reduction candidate for 2,6 F3: 2,6 # 18 pairs * PAIR D1: 2,6 ROW 1 B1: 2,6,1,5,7 # reduction candidate for 2,6 B1: 2,6 => SOLVED * 769243851458917623231856497392684715615372948847195362573461289924538176186729534 B1: 1,5,7 # 13 pairs H1: 2,6,5 # reduction candidate for 2,6 H1: 2,6 # 15 pairs * PAIR D1: 2,6 COL D D4: 2,6,7 # reduction candidate for 2,6 D4: 7 => CTR * 719.438.5.6..17..3.3.8....73..784.1.6913..748..719635257346.28....538.7..86.7.534 D4: 2,6 # 17 pairs * PAIR G2: 4,6 BLK 3 G3: 4,6,1,7 # reduction candidate for 4,6 G3: 4,6 => SOLVED * 769243851458917623231856497392684715615372948847195362573461289924538176186729534 G3: 1,7 # 13 pairs * PAIR G2: 4,6 ROW 2 B2: 4,6,2,5 # reduction candidate for 4,6 B2: 2,5 => SOLVED * 769243851458917623231856497392684715615372948847195362573461289924538176186729534 B2: 4,6 # 15 pairs * PAIR C4: 2,5 BLK 4 B4: 2,5,9 # reduction candidate for 2,5 B4: 2,5 => CTR * 719.438.5.6..17..3.3.8....73..784.1.6913..748..719635257346.28....538.7..86.7.534 B4: 9 # 17 pairs B5: 2,5,1,9 # reduction candidate for 2,5 B5: 2,5 # 19 pairs C5: 2,5,1 # reduction candidate for 2,5 C5: 2,5 => SOLVED * 769243851458917623231856497392684715615372948847195362573461289924538176186729534 C5: 1 # 13 pairs * PAIR C4: 2,5 COL C C2: 2,5,4,8 # reduction candidate for 2,5 C2: 2,5 => CTR * .692438578.5917623237856491392684715651372948..819536257346.28...4538.7..8672.534 C2: 4,8 => SOLVED * 769243851458917623231856497392684715615372948847195362573461289924538176186729534 * PAIR B6: 4,7 BLK 4 A6: 4,7,8 # reduction candidate for 4,7 A6: 4,7 => CTR * .692438578..9176232378564913926847156..372948748195362573461289...538.7..8672.534 A6: 8 => SOLVED * 769243851458917623231856497392684715615372948847195362573461289924538176186729534 C6: 4,7,8 # reduction candidate for 4,7 C6: 4,7 => SOLVED * 769243851458917623231856497392684715615372948847195362573461289924538176186729534 C6: 8 => CTR * .692438578..9176232378564913926847156..372948748195362573461289...538.7..8672.534 * PAIR F5: 2,5 BLK 5 E5: 2,5,7 # reduction candidate for 2,5 E5: 2,5 => CTR * 719.438.5.6..17..3.3.8....73..784.1.6913..748..719635257346.28....538.7..86.7.534 E5: 7 # 17 pairs * PAIR F5: 2,5 ROW 5 B5: 2,5,1,9 # reduction candidate for 2,5 B5: 2,5 # 19 pairs C5: 2,5,1 # reduction candidate for 2,5 C5: 2,5 => SOLVED * 769243851458917623231856497392684715615372948847195362573461289924538176186729534 C5: 1 # 13 pairs * PAIR F5: 2,5 COL F F3: 2,5,6,9 # reduction candidate for 2,5 F3: 2,5 => CTR * ..9643825.6.917..3.3.8...9.3...84.1.6..3...48...19635257346.28....538.7..86...534 F3: 6,9 # 19 pairs * PAIR F6: 5,6 COL F F3: 5,6,2,9 # reduction candidate for 5,6 F3: 2,9 => CTR * 719.438.5.65.174.3.3.85....35..84.1.6..3.5.48.4.19635257346.28....538.7..86...534 F3: 5,6 # 20 pairs * PAIR G5: 7,9 BLK 6 G4: 7,9,6 # reduction candidate for 7,9 G4: 7,9 # 15 pairs I4: 7,9,5,6 # reduction candidate for 7,9 I4: 7,9 => CTR * 719643825.65.17493.3.8.9.6.35..8461.6..3...48...19635257346.28....538.76.86...534 I4: 5,6 # 15 pairs * PAIR H6: 5,6 BLK 6 I4: 5,6,7,9 # reduction candidate for 5,6 I4: 7,9 => CTR * 719643825.65.17493.3.8.9.6.35..8461.6..3...48...19635257346.28....538.76.86...534 I4: 5,6 # 15 pairs * PAIR H6: 5,6 COL H H1: 5,6,2 # reduction candidate for 5,6 H1: 5,6 # 15 pairs H2: 5,6,2,9 # reduction candidate for 5,6 H2: 5,6 => CTR * ..964382..6.917453.3.8...9.3...84.156.53.2.48...19.3.25.34..28....538.7..86...534 H2: 2,9 # 13 pairs * PAIR B7: 1,7 BLK 7 A9: 1,7,9 # reduction candidate for 1,7 A9: 1,7 # 17 pairs A9: 9 # 16 pairs * PAIR B7: 1,7 COL B B1: 1,7,2,5,6 # reduction candidate for 1,7 B1: 1,7 => CTR * 219643857865.174.34378.....3.2784.1.6.13...4874819.3.257346.28..24538.7..86...534 B1: 2,5,6 => SOLVED * 769243851458917623231856497392684715615372948847195362573461289924538176186729534 * PAIR E9: 2,7 BLK 8 D9: 2,7,9 # reduction candidate for 2,7 D9: 9 => CTR * 719.438.5.6..17.93.3.8.9..73..784.1.691325748..71963525734612899..538.71186972534 D9: 2,7 # 17 pairs * PAIR E9: 2,7 COL E E5: 2,7,5 # reduction candidate for 2,7 E5: 5 => CTR * ..9.438.5....17..3.3.825.973..784.1.691352748..719635257346.28....538.7..8627.534 E5: 2,7 # 15 pairs * PAIR I7: 1,9 BLK 9 G8: 1,9,6 # reduction candidate for 1,9 G8: 1,9 # 14 pairs I8: 1,9,6 # reduction candidate for 1,9 I8: 1,9 # 16 pairs * PAIR I7: 1,9 ROW 7 F7: 1,9,6 # reduction candidate for 1,9 F7: 6 => CTR * ..9.438......17..3.3.86....3...84.1.6..3...48...19.3.25.34.62899..538.7..86..1534 F7: 1,9 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060725-absurd-base-pr-000.dot * REASONING * DIS # D2: 2,6 => CTR => D2: 9 * DIS # E3: 2,6 => CTR => E3: 5 * PRF # B1: 2,6 => SOL * DIS # D4: 7 => CTR => D4: 2,6 * PRF # G3: 4,6 => SOL * PRF # B2: 2,5 => SOL * DIS # B4: 2,5 => CTR => B4: 9 * PRF # C5: 2,5 => SOL * DIS # C2: 2,5 => CTR => C2: 4,8 * PRF # C2: 4,8 => SOL * DIS # A6: 4,7 => CTR => A6: 8 * PRF # A6: 8 => SOL * PRF # C6: 4,7 => SOL * DIS # C6: 8 => CTR => C6: 4,7 * DIS # E5: 2,5 => CTR => E5: 7 * PRF # C5: 2,5 => SOL * DIS # F3: 2,5 => CTR => F3: 6,9 * DIS # F3: 2,9 => CTR => F3: 5,6 * DIS # I4: 7,9 => CTR => I4: 5,6 * DIS # I4: 7,9 => CTR => I4: 5,6 * DIS # H2: 5,6 => CTR => H2: 2,9 * DIS # B1: 1,7 => CTR => B1: 2,5,6 * PRF # B1: 2,5,6 => SOL * DIS # D9: 9 => CTR => D9: 2,7 * DIS # E5: 5 => CTR => E5: 2,7 * DIS # F7: 6 => CTR => F7: 1,9 * CNT 26 HDP CHAINS / 54 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,B7,C4,D1,E7,E9,F5,F6,G2,G5,H6,I7) * ..9.438......17..3.3.8.....3...84.1.6..3...48...19.3.25.34..28....538.7..86...534 * PAIR D1: 2,6 BLK 2 D2: 2,6,9 # reduction candidate for 2,6 D2: 2,6 => CTR * 719.438.5.6..17.93.3.859..73..784916691325748..71963525734612899..538671186972534 F3: 2,6,5 # reduction candidate for 2,6 F3: 2,6 # 18 pairs * RESTART * PAIR D1: 2,6 BLK 2 F3: 2,6,5 # reduction candidate for 2,6 F3: 5 => CTR * ..96438...6.9174.3.3.825.9.3...84.1.6..352748.4.19.3.257346.28....538.7..86...534 * PAIR D1: 2,6 ROW 1 B1: 2,6,1,5 # reduction candidate for 2,6 B1: 2,6 => SOLVED * 769243851458917623231856497392684715615372948847195362573461289924538176186729534 * DURATION: 0:00:04.752042 START: 01:17:59.686298 END: 01:18:04.438340 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060725-absurd-base-pr-001.dot * REASONING * DIS # D2: 2,6 => CTR => D2: 9 * DIS D2: 9 # F3: 5 => CTR => F3: 2,6 * PRF D2: 9 + F3: 2,6 # B1: 2,6 => SOL * STA D2: 9 + F3: 2,6 + B1: 2,6 * CNT 3 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060725, absurd
Solution
position: 769243851458917623231856497392684715615372948847195362573461289924538176186729534 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 # D2: 2,6 => CTR => D2: 9 * INC # D2: 9 => UNS * DIS # E3: 2,6 => CTR => E3: 5 * INC # E3: 5 => UNS * INC # F3: 2,6 => UNS * PRF # B1: 2,6 => SOL * INC # B1: 1,5,7 => UNS * INC # H1: 2,6 => UNS * INC # D4: 2,6 => UNS * DIS # D4: 7 => CTR => D4: 2,6 * PRF # G3: 4,6 => SOL * INC # G3: 1,7 => UNS * INC # B2: 4,6 => UNS * PRF # B2: 2,5 => SOL * DIS # B4: 2,5 => CTR => B4: 9 * INC # B4: 9 => UNS * INC # B5: 2,5 => UNS * PRF # C5: 2,5 => SOL * INC # C5: 1 => UNS * DIS # C2: 2,5 => CTR => C2: 4,8 * PRF # C2: 4,8 => SOL * DIS # A6: 4,7 => CTR => A6: 8 * PRF # A6: 8 => SOL * PRF # C6: 4,7 => SOL * DIS # C6: 8 => CTR => C6: 4,7 * DIS # E5: 2,5 => CTR => E5: 7 * INC # E5: 7 => UNS * INC # B5: 2,5 => UNS * PRF # C5: 2,5 => SOL * INC # C5: 1 => UNS * DIS # F3: 2,5 => CTR => F3: 6,9 * INC # F3: 6,9 => UNS * INC # F3: 5,6 => UNS * DIS # F3: 2,9 => CTR => F3: 5,6 * INC # G4: 7,9 => UNS * DIS # I4: 7,9 => CTR => I4: 5,6 * INC # I4: 5,6 => UNS * INC # I4: 5,6 => UNS * DIS # I4: 7,9 => CTR => I4: 5,6 * INC # H1: 5,6 => UNS * DIS # H2: 5,6 => CTR => H2: 2,9 * INC # H2: 2,9 => UNS * INC # A9: 1,7 => UNS * INC # A9: 9 => UNS * DIS # B1: 1,7 => CTR => B1: 2,5,6 * PRF # B1: 2,5,6 => SOL * INC # D9: 2,7 => UNS * DIS # D9: 9 => CTR => D9: 2,7 * INC # E5: 2,7 => UNS * DIS # E5: 5 => CTR => E5: 2,7 * INC # G8: 1,9 => UNS * INC # I8: 1,9 => UNS * INC # F7: 1,9 => UNS * DIS # F7: 6 => CTR => F7: 1,9 * CNT 54 HDP CHAINS / 54 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D2: 2,6 => CTR => D2: 9 * INC D2: 9 # F3: 2,6 => UNS * INC D2: 9 # F3: 2,6 => UNS * DIS D2: 9 # F3: 5 => CTR => F3: 2,6 * PRF D2: 9 + F3: 2,6 # B1: 2,6 => SOL * STA D2: 9 + F3: 2,6 + B1: 2,6 * CNT 5 HDP CHAINS / 5 HYP OPENED