Analysis of zz-www.sudokuwiki.org-0053-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=53
level: medium
position: 32.8.9...14.........7.6....6....3.2.2...8...1.8.5....3....3.4.........17...9.4.68 initial
Autosolve
position: 32.8.9...14.........7.6....6....382.2...8...1.8.5....3....3.4.........17...9.4.68 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 5,9 => CTR => A3: 8 * DIS # I3: 5,9 => CTR => I3: 2,4 * DIS # B4: 5,9 => CTR => B4: 1,7 * DIS # F6: 6,7 => CTR => F6: 1,2 * DIS # F7: 2,5 => CTR => F7: 1,6,7,8 * PRF # E9: 2,5 => SOL * CNT 6 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 5,9 => CTR => A3: 8 * DIS A3: 8 # I3: 5,9 => CTR => I3: 2,4 * DIS A3: 8 + I3: 2,4 # B4: 5,9 => CTR => B4: 1,7 * DIS A3: 8 + I3: 2,4 + B4: 1,7 # B5: 3,7 => CTR => B5: 5,9 * DIS A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 # D5: 6,7 => CTR => D5: 4 * DIS A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 # F6: 6,7 => CTR => F6: 1,2 * DIS A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 + F6: 1,2 # D7: 2,6 => CTR => D7: 1,7 * PRF A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 + F6: 1,2 + D7: 1,7 # C7: 2,8 => SOL * STA A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 + F6: 1,2 + D7: 1,7 + C7: 2,8 * CNT 8 HDP CHAINS / 25 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 32.8.9...14.........7.6....6....3.2.2...8...1.8.5....3....3.4.........17...9.4.68 | initial |
| 32.8.9...14.........7.6....6....382.2...8...1.8.5....3....3.4.........17...9.4.68 | autosolve |
| 325849176146375289897261534614793825253486791789512643968137452432658917571924368 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) C1: 5,6 B3: 5,9 H2: 3,8 H3: 3,8 F5: 6,7 A9: 5,7 D8: 2,6 E8: 2,5 H7: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G1,G3: 1.. / G1 = 1 => 9 pairs (_) / G3 = 1 => 0 pairs (X) E1,G1: 1.. / E1 = 1 => 0 pairs (X) / G1 = 1 => 9 pairs (_) E6,F6: 2.. / E6 = 2 => 0 pairs (X) / F6 = 2 => 11 pairs (_) D2,D3: 3.. / D2 = 3 => 7 pairs (_) / D3 = 3 => 0 pairs (X) H2,H3: 3.. / H2 = 3 => 0 pairs (X) / H3 = 3 => 7 pairs (_) B5,C5: 3.. / B5 = 3 => 9 pairs (_) / C5 = 3 => 9 pairs (_) G8,G9: 3.. / G8 = 3 => 10 pairs (_) / G9 = 3 => 9 pairs (_) D2,H2: 3.. / D2 = 3 => 7 pairs (_) / H2 = 3 => 0 pairs (X) D3,H3: 3.. / D3 = 3 => 0 pairs (X) / H3 = 3 => 7 pairs (_) E1,D3: 4.. / E1 = 4 => 17 pairs (_) / D3 = 4 => 22 pairs (_) A8,C8: 4.. / A8 = 4 => 10 pairs (_) / C8 = 4 => 11 pairs (_) D3,I3: 4.. / D3 = 4 => 22 pairs (_) / I3 = 4 => 17 pairs (_) A6,A8: 4.. / A6 = 4 => 11 pairs (_) / A8 = 4 => 10 pairs (_) C1,C2: 6.. / C1 = 6 => 9 pairs (_) / C2 = 6 => 8 pairs (_) I1,I2: 6.. / I1 = 6 => 8 pairs (_) / I2 = 6 => 9 pairs (_) G5,G6: 6.. / G5 = 6 => 0 pairs (X) / G6 = 6 => 9 pairs (_) B7,B8: 6.. / B7 = 6 => 9 pairs (_) / B8 = 6 => 12 pairs (_) C1,I1: 6.. / C1 = 6 => 9 pairs (_) / I1 = 6 => 8 pairs (_) C2,I2: 6.. / C2 = 6 => 8 pairs (_) / I2 = 6 => 9 pairs (_) F6,G6: 6.. / F6 = 6 => 0 pairs (X) / G6 = 6 => 9 pairs (_) C2,A3: 8.. / C2 = 8 => 0 pairs (X) / A3 = 8 => 7 pairs (_) H2,H3: 8.. / H2 = 8 => 7 pairs (_) / H3 = 8 => 0 pairs (X) F7,F8: 8.. / F7 = 8 => 15 pairs (_) / F8 = 8 => 9 pairs (_) C2,H2: 8.. / C2 = 8 => 0 pairs (X) / H2 = 8 => 7 pairs (_) A3,H3: 8.. / A3 = 8 => 7 pairs (_) / H3 = 8 => 0 pairs (X) E4,E6: 9.. / E4 = 9 => 10 pairs (_) / E6 = 9 => 13 pairs (_) * DURATION: 0:00:34.411319 START: 04:25:04.809951 END: 04:25:39.221270 2017-05-01 * CP COUNT: (26) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B3,C1,D8,E8,F5,H2,H3,H7) * 32.8.9...14.........7.6....6....382.2...8...1.8.5....3....3.4.........17...9.4.68 * PAIR C1: 5,6 BLK 1 C2: 5,6,8,9 # reduction candidate for 5,6 C2: 8,9 # 11 pairs C2: 5,6 # 8 pairs * PAIR C1: 5,6 ROW 1 I1: 5,6,4 # reduction candidate for 5,6 I1: 4 # 27 pairs I1: 5,6 # 12 pairs * PAIR B3: 5,9 BLK 1 C2: 5,9,6,8 # reduction candidate for 5,9 C2: 5,9 # 8 pairs A3: 5,9,8 # reduction candidate for 5,9 A3: 5,9 => CTR * 326849175148...9369573612846.54138292.4.8.7.1.8.592643....3.4924....8.17...9.4.68 A3: 8 # 7 pairs * PAIR B3: 5,9 ROW 3 G3: 5,9,1,2 # reduction candidate for 5,9 G3: 5,9 # 10 pairs I3: 5,9,2,4 # reduction candidate for 5,9 I3: 5,9 => CTR * 32.87915414.3257868.746123.67.1.382.2.3.8.941.815.2673518.3.492.6.258317732914568 I3: 2,4 # 10 pairs * PAIR B3: 5,9 COL B B4: 5,9,1,7 # reduction candidate for 5,9 B4: 5,9 => CTR * 32.84917.14..2.5.9..7.652.46.4..382.23.4867.1781592643...63.4.246.258.175.29.4368 B4: 1,7 # 10 pairs B5: 5,9,3,7 # reduction candidate for 5,9 B5: 5,9 # 12 pairs B7: 5,9,1,6,7 # reduction candidate for 5,9 B7: 5,9 # 21 pairs B8: 5,9,3,6 # reduction candidate for 5,9 B8: 5,9 # 14 pairs * PAIR F5: 6,7 BLK 5 D5: 6,7,4 # reduction candidate for 6,7 D5: 6,7 # 22 pairs F6: 6,7,1,2 # reduction candidate for 6,7 F6: 6,7 => CTR * 32.84917.14..7......7.61..46..1938252..48..9198152..43.1.73645.46.258.17...914.68 F6: 1,2 # 10 pairs * PAIR F5: 6,7 ROW 5 G5: 6,7,5,9 # reduction candidate for 6,7 G5: 5,9 # 22 pairs G5: 6,7 # 17 pairs * PAIR F5: 6,7 COL F F7: 6,7,1,2,5,8 # reduction candidate for 6,7 F7: 6,7 # 13 pairs F7: 1,2,5,8 # 9 pairs * PAIR A9: 5,7 BLK 7 A7: 5,7,8,9 # reduction candidate for 5,7 A7: 5,7 # 13 pairs B7: 5,7,1,6,9 # reduction candidate for 5,7 B7: 5,7 # 15 pairs B9: 5,7,1,3 # reduction candidate for 5,7 B9: 5,7 # 13 pairs * PAIR A9: 5,7 ROW 9 E9: 5,7,1,2 # reduction candidate for 5,7 E9: 5,7 # 15 pairs E9: 1,2 # 10 pairs * PAIR D8: 2,6 BLK 8 D7: 2,6,1,7 # reduction candidate for 2,6 D7: 2,6 # 15 pairs F7: 2,6,1,5,7,8 # reduction candidate for 2,6 F7: 2,6 # 13 pairs F8: 2,6,5,8 # reduction candidate for 2,6 F8: 2,6 # 16 pairs * PAIR E8: 2,5 BLK 8 F7: 2,5,1,6,7,8 # reduction candidate for 2,5 F7: 2,5 => CTR * 325849176146.759828972615346.4.9382525348..9198152..4376..3.4594..658.17...9.4.68 F7: 1,6,7,8 # 9 pairs F8: 2,5,6,8 # reduction candidate for 2,5 F8: 2,5 # 16 pairs E9: 2,5,1,7 # reduction candidate for 2,5 E9: 2,5 => SOLVED * 325849176146375289897261534614793825253486791789512643968137452432658917571924368 E9: 1,7 # 10 pairs * PAIR E8: 2,5 ROW 8 C8: 2,5,3,4,8,9 # reduction candidate for 2,5 C8: 2,5 # 13 pairs G8: 2,5,3,9 # reduction candidate for 2,5 G8: 2,5 # 12 pairs * PAIR E8: 2,5 COL E E2: 2,5,7 # reduction candidate for 2,5 E2: 2,5 # 13 pairs E2: 7 # 11 pairs * PAIR H7: 5,9 BLK 9 I7: 5,9,2 # reduction candidate for 5,9 I7: 5,9 # 13 pairs G8: 5,9,2,3 # reduction candidate for 5,9 G8: 5,9 # 10 pairs * PAIR H7: 5,9 ROW 7 A7: 5,9,7,8 # reduction candidate for 5,9 A7: 5,9 # 12 pairs B7: 5,9,1,6,7 # reduction candidate for 5,9 B7: 5,9 # 21 pairs C7: 5,9,1,2,8 # reduction candidate for 5,9 C7: 5,9 # 12 pairs * PAIR H7: 5,9 COL H H5: 5,9,4,7 # reduction candidate for 5,9 H5: 4,7 # 27 pairs H5: 5,9 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0053-base-pr-000.dot * REASONING * DIS # A3: 5,9 => CTR => A3: 8 * DIS # I3: 5,9 => CTR => I3: 2,4 * DIS # B4: 5,9 => CTR => B4: 1,7 * DIS # F6: 6,7 => CTR => F6: 1,2 * DIS # F7: 2,5 => CTR => F7: 1,6,7,8 * PRF # E9: 2,5 => SOL * CNT 6 HDP CHAINS / 46 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B3,C1,D8,E8,F5,H2,H3,H7) * 32.8.9...14.........7.6....6....382.2...8...1.8.5....3....3.4.........17...9.4.68 * PAIR C1: 5,6 BLK 1 C2: 5,6,8,9 # reduction candidate for 5,6 C2: 8,9 # 11 pairs C2: 5,6 # 8 pairs * PAIR C1: 5,6 ROW 1 I1: 5,6,4 # reduction candidate for 5,6 I1: 4 # 27 pairs I1: 5,6 # 12 pairs * PAIR B3: 5,9 BLK 1 C2: 5,9,6,8 # reduction candidate for 5,9 C2: 5,9 # 8 pairs A3: 5,9,8 # reduction candidate for 5,9 A3: 5,9 => CTR * 326849175148...9369573612846.54138292.4.8.7.1.8.592643....3.4924....8.17...9.4.68 * RESTART * PAIR B3: 5,9 BLK 1 C2: 5,9,6 # reduction candidate for 5,9 C2: 6 # 8 pairs C2: 5,9 # 8 pairs * PAIR B3: 5,9 ROW 3 G3: 5,9,1,2 # reduction candidate for 5,9 G3: 5,9 # 10 pairs I3: 5,9,2,4 # reduction candidate for 5,9 I3: 5,9 => CTR * 32.87915414.3257868.746123.67.1.382.2.3.8.941.815.2673518.3.492.6.258317732914568 * RESTART * PAIR B3: 5,9 ROW 3 G3: 5,9,1,2 # reduction candidate for 5,9 G3: 1,2 # 17 pairs G3: 5,9 # 10 pairs * PAIR B3: 5,9 COL B B4: 5,9,1,7 # reduction candidate for 5,9 B4: 5,9 => CTR * 32.84917.14.3...89897.6..34654..382.2..4867.17815926439...3.4524.....9175..9.4368 B5: 5,9,3,7 # reduction candidate for 5,9 B5: 5,9 # 12 pairs * RESTART * PAIR B3: 5,9 COL B B5: 5,9,3,7 # reduction candidate for 5,9 B5: 3,7 => CTR * 3268.91741493.75868574619326.4.9382.2...8..9198.5....376..3.45949.....175..974.68 * PAIR RESTART * PAIR B3: 5,9 BLK 1 C2: 5,9,6 # reduction candidate for 5,9 C2: 5,9 # 20 pairs C2: 6 # 17 pairs * PAIR B3: 5,9 ROW 3 G3: 5,9,1,2 # reduction candidate for 5,9 G3: 1,2 # 25 pairs G3: 5,9 # 14 pairs * PAIR F5: 6,7 BLK 5 D5: 6,7,4 # reduction candidate for 6,7 D5: 6,7 => CTR * 32681975414.3...868.746..3267.1.3829293.8.541481592673....3.4959.4..8.175.2974368 F6: 6,7,1,2 # reduction candidate for 6,7 F6: 6,7 => CTR * 32584917614637..8.897.615346.419382525348..91.8152..43.1..3.45.4...5..175..914.68 * PAIR D8: 2,6 BLK 8 D7: 2,6,1,7 # reduction candidate for 2,6 D7: 2,6 => CTR * 3258491761463...8989716..346147938252534867917895..6439..63.4524.....9175..9.4368 * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A6,A7,B4,B9,C6,C9,D4,D7,E2,E6,E8,F2,F7,F8,G2,G8,I2,I7) * 3258491761463...8.8972615346.4.93825253486791.8.5.2643.6..3.45.43.6...175..9.4368 * PAIR C6: 1,9 COL C C7: 1,9,2,8 # reduction candidate for 1,9 C7: 2,8 => SOLVED * 325849176146375289897261534614793825253486791789512643968137452432658917571924368 * DURATION: 0:00:27.337114 START: 04:26:15.174801 END: 04:26:42.511915 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0053-base-pr-001.dot * REASONING * DIS # A3: 5,9 => CTR => A3: 8 * DIS A3: 8 # I3: 5,9 => CTR => I3: 2,4 * DIS A3: 8 + I3: 2,4 # B4: 5,9 => CTR => B4: 1,7 * DIS A3: 8 + I3: 2,4 + B4: 1,7 # B5: 3,7 => CTR => B5: 5,9 * DIS A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 # D5: 6,7 => CTR => D5: 4 * DIS A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 # F6: 6,7 => CTR => F6: 1,2 * DIS A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 + F6: 1,2 # D7: 2,6 => CTR => D7: 1,7 * PRF A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 + F6: 1,2 + D7: 1,7 # C7: 2,8 => SOL * STA A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 + F6: 1,2 + D7: 1,7 + C7: 2,8 * CNT 8 HDP CHAINS / 25 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=53
Solution
position: 325849176146375289897261534614793825253486791789512643968137452432658917571924368 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 # C2: 5,6 => UNS * INC # C2: 8,9 => UNS * INC # I1: 5,6 => UNS * INC # I1: 4 => UNS * INC # C2: 5,9 => UNS * DIS # A3: 5,9 => CTR => A3: 8 * INC # A3: 8 => UNS * INC # G3: 5,9 => UNS * DIS # I3: 5,9 => CTR => I3: 2,4 * INC # I3: 2,4 => UNS * DIS # B4: 5,9 => CTR => B4: 1,7 * INC # B4: 1,7 => UNS * INC # B5: 5,9 => UNS * INC # B7: 5,9 => UNS * INC # B8: 5,9 => UNS * INC # D5: 6,7 => UNS * DIS # F6: 6,7 => CTR => F6: 1,2 * INC # F6: 1,2 => UNS * INC # G5: 6,7 => UNS * INC # G5: 5,9 => UNS * INC # F7: 6,7 => UNS * INC # F7: 1,2,5,8 => UNS * INC # A7: 5,7 => UNS * INC # B7: 5,7 => UNS * INC # B9: 5,7 => UNS * INC # E9: 5,7 => UNS * INC # E9: 1,2 => UNS * INC # D7: 2,6 => UNS * INC # F7: 2,6 => UNS * INC # F8: 2,6 => UNS * DIS # F7: 2,5 => CTR => F7: 1,6,7,8 * INC # F7: 1,6,7,8 => UNS * INC # F8: 2,5 => UNS * PRF # E9: 2,5 => SOL * INC # E9: 1,7 => UNS * INC # C8: 2,5 => UNS * INC # G8: 2,5 => UNS * INC # E2: 2,5 => UNS * INC # E2: 7 => UNS * INC # I7: 5,9 => UNS * INC # G8: 5,9 => UNS * INC # A7: 5,9 => UNS * INC # B7: 5,9 => UNS * INC # C7: 5,9 => UNS * INC # H5: 5,9 => UNS * INC # H5: 4,7 => UNS * CNT 46 HDP CHAINS / 46 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 5,6 => UNS * INC # C2: 8,9 => UNS * INC # I1: 5,6 => UNS * INC # I1: 4 => UNS * INC # C2: 5,9 => UNS * DIS # A3: 5,9 => CTR => A3: 8 * INC A3: 8 # C2: 5,9 => UNS * INC A3: 8 # C2: 6 => UNS * INC A3: 8 # G3: 5,9 => UNS * DIS A3: 8 # I3: 5,9 => CTR => I3: 2,4 * INC A3: 8 + I3: 2,4 # G3: 5,9 => UNS * INC A3: 8 + I3: 2,4 # G3: 1,2 => UNS * DIS A3: 8 + I3: 2,4 # B4: 5,9 => CTR => B4: 1,7 * INC A3: 8 + I3: 2,4 + B4: 1,7 # B5: 5,9 => UNS * INC A3: 8 + I3: 2,4 + B4: 1,7 # B5: 5,9 => UNS * DIS A3: 8 + I3: 2,4 + B4: 1,7 # B5: 3,7 => CTR => B5: 5,9 * INC A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 # C2: 5,9 => UNS * INC A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 # C2: 6 => UNS * INC A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 # G3: 5,9 => UNS * INC A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 # G3: 1,2 => UNS * DIS A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 # D5: 6,7 => CTR => D5: 4 * DIS A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 # F6: 6,7 => CTR => F6: 1,2 * DIS A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 + F6: 1,2 # D7: 2,6 => CTR => D7: 1,7 * INC A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 + F6: 1,2 + D7: 1,7 # C7: 1,9 => UNS * PRF A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 + F6: 1,2 + D7: 1,7 # C7: 2,8 => SOL * STA A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 + F6: 1,2 + D7: 1,7 + C7: 2,8 * CNT 25 HDP CHAINS / 25 HYP OPENED