Analysis of zz-www.sudokuwiki.org-0108-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=108
level: medium
position: .....6..42.7...1.....29..5.......31..1.5.4.6...2.......5..42.....1...8.79..6..... initial
Autosolve
position: .....6..42.74..1.....29..5.......31..1.5.4.6...2.......5..42.....1...8.79..6..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 3,8 => CTR => C1: 5,9 * DIS # I7: 3,9 => CTR => I7: 1,6 * DIS # H1: 3,9 => CTR => H1: 2,7,8 * PRF # H9: 3 => SOL * DIS # B8: 6 => CTR => B8: 2,4 * CNT 5 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 3,8 => CTR => C1: 5,9 * DIS C1: 5,9 # I7: 3,9 => CTR => I7: 1,6 * DIS C1: 5,9 + I7: 1,6 # H1: 3,9 => CTR => H1: 2,7,8 * PRF C1: 5,9 + I7: 1,6 + H1: 2,7,8 # H9: 3 => SOL * STA C1: 5,9 + I7: 1,6 + H1: 2,7,8 + H9: 3 * CNT 4 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....6..42.7...1.....29..5.......31..1.5.4.6...2.......5..42.....1...8.79..6..... | initial |
| .....6..42.74..1.....29..5.......31..1.5.4.6...2.......5..42.....1...8.79..6..... | autosolve |
| 135786924297435186864291753476928315319574268582163479753842691621359847948617532 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) G3: 6,7 G6: 4,5 C7: 3,8 A8: 4,6 D8: 3,9 E8: 3,5 G7: 6,9 H7: 3,9 H8: 2,4 G9: 4,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A3: 1.. / A1 = 1 => 11 pairs (_) / A3 = 1 => 10 pairs (_) I7,I9: 1.. / I7 = 1 => 14 pairs (_) / I9 = 1 => 14 pairs (_) A3,F3: 1.. / A3 = 1 => 10 pairs (_) / F3 = 1 => 11 pairs (_) D7,I7: 1.. / D7 = 1 => 14 pairs (_) / I7 = 1 => 14 pairs (_) G1,H1: 2.. / G1 = 2 => 11 pairs (_) / H1 = 2 => 0 pairs (*) E4,E5: 2.. / E4 = 2 => 10 pairs (_) / E5 = 2 => 12 pairs (_) B8,B9: 2.. / B8 = 2 => 7 pairs (_) / B9 = 2 => 16 pairs (_) E4,I4: 2.. / E4 = 2 => 10 pairs (_) / I4 = 2 => 12 pairs (_) B8,H8: 2.. / B8 = 2 => 7 pairs (_) / H8 = 2 => 16 pairs (_) G1,G5: 2.. / G1 = 2 => 11 pairs (_) / G5 = 2 => 0 pairs (*) G6,H6: 4.. / G6 = 4 => 8 pairs (_) / H6 = 4 => 0 pairs (X) G6,G9: 4.. / G6 = 4 => 8 pairs (_) / G9 = 4 => 0 pairs (X) A1,C1: 5.. / A1 = 5 => 22 pairs (_) / C1 = 5 => 10 pairs (_) E2,F2: 5.. / E2 = 5 => 10 pairs (_) / F2 = 5 => 11 pairs (_) E8,F8: 5.. / E8 = 5 => 11 pairs (_) / F8 = 5 => 10 pairs (_) G9,I9: 5.. / G9 = 5 => 8 pairs (_) / I9 = 5 => 0 pairs (X) C1,C4: 5.. / C1 = 5 => 10 pairs (_) / C4 = 5 => 22 pairs (_) E2,E8: 5.. / E2 = 5 => 10 pairs (_) / E8 = 5 => 11 pairs (_) F2,F8: 5.. / F2 = 5 => 11 pairs (_) / F8 = 5 => 10 pairs (_) G6,G9: 5.. / G6 = 5 => 0 pairs (X) / G9 = 5 => 8 pairs (_) E4,E6: 6.. / E4 = 6 => 0 pairs (X) / E6 = 6 => 10 pairs (_) A8,B8: 6.. / A8 = 6 => 10 pairs (_) / B8 = 6 => 0 pairs (X) G7,I7: 6.. / G7 = 6 => 9 pairs (_) / I7 = 6 => 20 pairs (_) B2,I2: 6.. / B2 = 6 => 20 pairs (_) / I2 = 6 => 12 pairs (_) C3,C4: 6.. / C3 = 6 => 13 pairs (_) / C4 = 6 => 12 pairs (_) G3,G7: 6.. / G3 = 6 => 20 pairs (_) / G7 = 6 => 9 pairs (_) G5,H6: 7.. / G5 = 7 => 20 pairs (_) / H6 = 7 => 10 pairs (_) A7,B9: 7.. / A7 = 7 => 12 pairs (_) / B9 = 7 => 15 pairs (_) F3,G3: 7.. / F3 = 7 => 20 pairs (_) / G3 = 7 => 9 pairs (_) A7,D7: 7.. / A7 = 7 => 12 pairs (_) / D7 = 7 => 15 pairs (_) H1,H6: 7.. / H1 = 7 => 20 pairs (_) / H6 = 7 => 10 pairs (_) D8,F8: 9.. / D8 = 9 => 11 pairs (_) / F8 = 9 => 10 pairs (_) * DURATION: 0:00:46.115258 START: 05:24:45.088098 END: 05:25:31.203356 2017-05-01 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,C7,D8,E8,G3,G6,G7,G9,H7,H8) * .....6..42.74..1.....29..5.......31..1.5.4.6...2.......5..42.....1...8.79..6..... * PAIR C7: 3,8 BLK 7 A7: 3,8,7 # reduction candidate for 3,8 A7: 3,8 # 15 pairs B9: 3,8,2,4,7 # reduction candidate for 3,8 B9: 3,8 # 10 pairs C9: 3,8,4 # reduction candidate for 3,8 C9: 3,8 # 18 pairs * PAIR C7: 3,8 COL C C1: 3,8,5,9 # reduction candidate for 3,8 C1: 3,8 => CTR * 5...169242974..186146298753465827319719534268..2169475.5.74269162195.8479.4681532 C1: 5,9 # 11 pairs C3: 3,8,4,6 # reduction candidate for 3,8 C3: 3,8 # 10 pairs C5: 3,8,9 # reduction candidate for 3,8 C5: 3,8 # 16 pairs * PAIR A8: 4,6 BLK 7 B8: 4,6,2 # reduction candidate for 4,6 B8: 4,6 # 16 pairs B8: 2 # 7 pairs * PAIR A8: 4,6 COL A A3: 4,6,1,3,8 # reduction candidate for 4,6 A3: 4,6 # 12 pairs A4: 4,6,5,7,8 # reduction candidate for 4,6 A4: 4,6 # 11 pairs * PAIR D8: 3,9 BLK 8 F8: 3,9,5 # reduction candidate for 3,9 F8: 3,9 # 11 pairs F8: 5 # 10 pairs * PAIR D8: 3,9 COL D D6: 3,9,1,7,8 # reduction candidate for 3,9 D6: 3,9 # 12 pairs D6: 1,7,8 # 10 pairs * PAIR E8: 3,5 BLK 8 F8: 3,5,9 # reduction candidate for 3,5 F8: 3,5 # 11 pairs F8: 9 # 10 pairs * PAIR E8: 3,5 COL E E2: 3,5,8 # reduction candidate for 3,5 E2: 8 # 16 pairs E2: 3,5 # 11 pairs * PAIR G7: 6,9 BLK 9 I7: 6,9,1,3 # reduction candidate for 6,9 I7: 6,9 # 15 pairs I7: 1,3 # 12 pairs * PAIR H7: 3,9 BLK 9 I7: 3,9,1,6 # reduction candidate for 3,9 I7: 3,9 => CTR * ...7162.42.74..1..1..29.75..7..2.31.8135749625923614787581426....19..8.79346875.1 I7: 1,6 # 11 pairs * PAIR H7: 3,9 COL H H1: 3,9,2,7,8 # reduction candidate for 3,9 H1: 3,9 => CTR * 3.5..62942974..186146298753479...31..1.5.496...2...47..5..42639..1...8.79346..521 H1: 2,7,8 # 10 pairs H2: 3,9,8 # reduction candidate for 3,9 H2: 3,9 # 14 pairs * PAIR H8: 2,4 BLK 9 H9: 2,4,3 # reduction candidate for 2,4 H9: 3 => SOLVED * 135786924297435186864291753476928315319574268582163479753842691621359847948617532 H9: 2,4 # 11 pairs * PAIR H8: 2,4 ROW 8 B8: 2,4,6 # reduction candidate for 2,4 B8: 6 => CTR * .....62.42.74..1.6...29.753.74...31..1.574962.92...47.75.142639461...8279236...41 B8: 2,4 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0108-base-pr-000.dot * REASONING * DIS # C1: 3,8 => CTR => C1: 5,9 * DIS # I7: 3,9 => CTR => I7: 1,6 * DIS # H1: 3,9 => CTR => H1: 2,7,8 * PRF # H9: 3 => SOL * DIS # B8: 6 => CTR => B8: 2,4 * CNT 5 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,C7,D8,E8,G3,G6,G7,G9,H7,H8) * .....6..42.74..1.....29..5.......31..1.5.4.6...2.......5..42.....1...8.79..6..... * PAIR C7: 3,8 BLK 7 A7: 3,8,7 # reduction candidate for 3,8 A7: 3,8 # 15 pairs B9: 3,8,2,4,7 # reduction candidate for 3,8 B9: 3,8 # 10 pairs C9: 3,8,4 # reduction candidate for 3,8 C9: 3,8 # 18 pairs * PAIR C7: 3,8 COL C C1: 3,8,5,9 # reduction candidate for 3,8 C1: 3,8 => CTR * 5...169242974..186146298753465827319719534268..2169475.5.74269162195.8479.4681532 C3: 3,8,4,6 # reduction candidate for 3,8 C3: 3,8 # 10 pairs C5: 3,8,9 # reduction candidate for 3,8 C5: 3,8 # 16 pairs * PAIR RESTART * PAIR C7: 3,8 BLK 7 A7: 3,8,7 # reduction candidate for 3,8 A7: 3,8 # 16 pairs B9: 3,8,2,4,7 # reduction candidate for 3,8 B9: 3,8 # 11 pairs C9: 3,8,4 # reduction candidate for 3,8 C9: 3,8 # 18 pairs * PAIR C7: 3,8 COL C C3: 3,8,4,6 # reduction candidate for 3,8 C3: 3,8 # 10 pairs C5: 3,8,9 # reduction candidate for 3,8 C5: 3,8 # 16 pairs * PAIR A8: 4,6 BLK 7 B8: 4,6,2 # reduction candidate for 4,6 B8: 4,6 # 16 pairs B8: 2 # 8 pairs * PAIR A8: 4,6 COL A A3: 4,6,1,3,8 # reduction candidate for 4,6 A3: 4,6 # 12 pairs A4: 4,6,5,7,8 # reduction candidate for 4,6 A4: 4,6 # 12 pairs * PAIR D8: 3,9 BLK 8 F8: 3,9,5 # reduction candidate for 3,9 F8: 3,9 # 12 pairs F8: 5 # 11 pairs * PAIR D8: 3,9 COL D D6: 3,9,1,7,8 # reduction candidate for 3,9 D6: 3,9 # 13 pairs D6: 1,7,8 # 11 pairs * PAIR E8: 3,5 BLK 8 F8: 3,5,9 # reduction candidate for 3,5 F8: 3,5 # 12 pairs F8: 9 # 11 pairs * PAIR E8: 3,5 COL E E2: 3,5,8 # reduction candidate for 3,5 E2: 8 # 17 pairs E2: 3,5 # 12 pairs * PAIR G7: 6,9 BLK 9 I7: 6,9,1,3 # reduction candidate for 6,9 I7: 6,9 # 16 pairs I7: 1,3 # 13 pairs * PAIR H7: 3,9 BLK 9 I7: 3,9,1,6 # reduction candidate for 3,9 I7: 3,9 => CTR * ...7162.42.74..1..1..29.75..7..2.31.8135749625923614787581426....19..8.79346875.1 * PAIR H7: 3,9 COL H H1: 3,9,2,7,8 # reduction candidate for 3,9 H1: 3,9 => CTR * .....62342.74..189...29.756..6...31..1.5.496...2.6.47..5..426916.1...8.79..6..5.3 H2: 3,9,8 # reduction candidate for 3,9 H2: 3,9 # 16 pairs * RESTART * PAIR H7: 3,9 COL H H2: 3,9,8 # reduction candidate for 3,9 H2: 8 # 17 pairs H2: 3,9 # 16 pairs * PAIR RESTART * PAIR H7: 3,9 COL H H2: 3,9,8 # reduction candidate for 3,9 H2: 8 # 17 pairs H2: 3,9 # 16 pairs * PAIR H8: 2,4 BLK 9 H9: 2,4,3 # reduction candidate for 2,4 H9: 3 => SOLVED * 135786924297435186864291753476928315319574268582163479753842691621359847948617532 * DURATION: 0:00:29.264777 START: 05:25:54.903798 END: 05:26:24.168575 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0108-base-pr-001.dot * REASONING * DIS # C1: 3,8 => CTR => C1: 5,9 * DIS C1: 5,9 # I7: 3,9 => CTR => I7: 1,6 * DIS C1: 5,9 + I7: 1,6 # H1: 3,9 => CTR => H1: 2,7,8 * PRF C1: 5,9 + I7: 1,6 + H1: 2,7,8 # H9: 3 => SOL * STA C1: 5,9 + I7: 1,6 + H1: 2,7,8 + H9: 3 * CNT 4 HDP CHAINS / 34 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=108
Solution
position: 135786924297435186864291753476928315319574268582163479753842691621359847948617532 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 # A7: 3,8 => UNS * INC # B9: 3,8 => UNS * INC # C9: 3,8 => UNS * DIS # C1: 3,8 => CTR => C1: 5,9 * INC # C1: 5,9 => UNS * INC # C3: 3,8 => UNS * INC # C5: 3,8 => UNS * INC # B8: 4,6 => UNS * INC # B8: 2 => UNS * INC # A3: 4,6 => UNS * INC # A4: 4,6 => UNS * INC # F8: 3,9 => UNS * INC # F8: 5 => UNS * INC # D6: 3,9 => UNS * INC # D6: 1,7,8 => UNS * INC # F8: 3,5 => UNS * INC # F8: 9 => UNS * INC # E2: 3,5 => UNS * INC # E2: 8 => UNS * INC # I7: 6,9 => UNS * INC # I7: 1,3 => UNS * DIS # I7: 3,9 => CTR => I7: 1,6 * INC # I7: 1,6 => UNS * DIS # H1: 3,9 => CTR => H1: 2,7,8 * INC # H1: 2,7,8 => UNS * INC # H2: 3,9 => UNS * INC # H9: 2,4 => UNS * PRF # H9: 3 => SOL * INC # B8: 2,4 => UNS * DIS # B8: 6 => CTR => B8: 2,4 * CNT 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A7: 3,8 => UNS * INC # B9: 3,8 => UNS * INC # C9: 3,8 => UNS * DIS # C1: 3,8 => CTR => C1: 5,9 * INC C1: 5,9 # C3: 3,8 => UNS * INC C1: 5,9 # C5: 3,8 => UNS * INC C1: 5,9 # A7: 3,8 => UNS * INC C1: 5,9 # B9: 3,8 => UNS * INC C1: 5,9 # C9: 3,8 => UNS * INC C1: 5,9 # C3: 3,8 => UNS * INC C1: 5,9 # C5: 3,8 => UNS * INC C1: 5,9 # B8: 4,6 => UNS * INC C1: 5,9 # B8: 2 => UNS * INC C1: 5,9 # A3: 4,6 => UNS * INC C1: 5,9 # A4: 4,6 => UNS * INC C1: 5,9 # F8: 3,9 => UNS * INC C1: 5,9 # F8: 5 => UNS * INC C1: 5,9 # D6: 3,9 => UNS * INC C1: 5,9 # D6: 1,7,8 => UNS * INC C1: 5,9 # F8: 3,5 => UNS * INC C1: 5,9 # F8: 9 => UNS * INC C1: 5,9 # E2: 3,5 => UNS * INC C1: 5,9 # E2: 8 => UNS * INC C1: 5,9 # I7: 6,9 => UNS * INC C1: 5,9 # I7: 1,3 => UNS * DIS C1: 5,9 # I7: 3,9 => CTR => I7: 1,6 * DIS C1: 5,9 + I7: 1,6 # H1: 3,9 => CTR => H1: 2,7,8 * INC C1: 5,9 + I7: 1,6 + H1: 2,7,8 # H2: 3,9 => UNS * INC C1: 5,9 + I7: 1,6 + H1: 2,7,8 # H2: 3,9 => UNS * INC C1: 5,9 + I7: 1,6 + H1: 2,7,8 # H2: 8 => UNS * INC C1: 5,9 + I7: 1,6 + H1: 2,7,8 # H2: 3,9 => UNS * INC C1: 5,9 + I7: 1,6 + H1: 2,7,8 # H2: 8 => UNS * INC C1: 5,9 + I7: 1,6 + H1: 2,7,8 # H9: 2,4 => UNS * PRF C1: 5,9 + I7: 1,6 + H1: 2,7,8 # H9: 3 => SOL * STA C1: 5,9 + I7: 1,6 + H1: 2,7,8 + H9: 3 * CNT 34 HDP CHAINS / 34 HYP OPENED