Analysis of zz-www.sudokuwiki.org-0083-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=83
level: medium
position: 6....13......97.1....6....29.....45..4..7..9..82.....38....5....1.76......32....1 initial
Autosolve
position: 6...213......97.1....6....29....245..4..7.29..82...1.38....5....1.76......32....1 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 5,7 => CTR => A3: 1,3,4 * DIS # D6: 4,5 => CTR => D6: 9 * PRF # F5: 3 => SOL * DIS # I4: 8 => CTR => I4: 6,7 * CNT 4 HDP CHAINS / 21 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 5,7 => CTR => A3: 1,3,4 * DIS A3: 1,3,4 # A9: 4 => CTR => A9: 5,7 * DIS A3: 1,3,4 + A9: 5,7 # D6: 4,5 => CTR => D6: 9 * PRF A3: 1,3,4 + A9: 5,7 + D6: 9 # F5: 3 => SOL * STA A3: 1,3,4 + A9: 5,7 + D6: 9 + F5: 3 * CNT 4 HDP CHAINS / 11 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6....13......97.1....6....29.....45..4..7..9..82.....38....5....1.76......32....1 | initial |
| 6...213......97.1....6....29....245..4..7.29..82...1.38....5....1.76......32....1 | autosolve |
| 659421387428397615371658942937812456146573298582946173864135729215769834793284561 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) A6: 5,7 E6: 4,5 I5: 6,8 H6: 6,7 E9: 4,8 H7: 2,3 H8: 2,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A3,C3: 1.. / A3 = 1 => 8 pairs (_) / C3 = 1 => 14 pairs (_) D7,E7: 1.. / D7 = 1 => 12 pairs (_) / E7 = 1 => 8 pairs (_) A3,A5: 1.. / A3 = 1 => 8 pairs (_) / A5 = 1 => 14 pairs (_) E4,E7: 1.. / E4 = 1 => 12 pairs (_) / E7 = 1 => 8 pairs (_) A2,B2: 2.. / A2 = 2 => 16 pairs (_) / B2 = 2 => 9 pairs (_) B7,A8: 2.. / B7 = 2 => 16 pairs (_) / A8 = 2 => 9 pairs (_) H7,H8: 2.. / H7 = 2 => 9 pairs (_) / H8 = 2 => 16 pairs (_) B7,H7: 2.. / B7 = 2 => 16 pairs (_) / H7 = 2 => 9 pairs (_) A8,H8: 2.. / A8 = 2 => 9 pairs (_) / H8 = 2 => 16 pairs (_) A2,A8: 2.. / A2 = 2 => 16 pairs (_) / A8 = 2 => 9 pairs (_) B2,B7: 2.. / B2 = 2 => 9 pairs (_) / B7 = 2 => 16 pairs (_) B4,A5: 3.. / B4 = 3 => 14 pairs (_) / A5 = 3 => 12 pairs (_) H7,H8: 3.. / H7 = 3 => 16 pairs (_) / H8 = 3 => 9 pairs (_) F8,H8: 3.. / F8 = 3 => 16 pairs (_) / H8 = 3 => 9 pairs (_) E3,E6: 5.. / E3 = 5 => 13 pairs (_) / E6 = 5 => 10 pairs (_) G2,I2: 6.. / G2 = 6 => 9 pairs (_) / I2 = 6 => 12 pairs (_) F5,F6: 6.. / F5 = 6 => 10 pairs (_) / F6 = 6 => 24 pairs (_) F6,H6: 6.. / F6 = 6 => 24 pairs (_) / H6 = 6 => 10 pairs (_) H6,H9: 6.. / H6 = 6 => 10 pairs (_) / H9 = 6 => 24 pairs (_) I4,H6: 7.. / I4 = 7 => 10 pairs (_) / H6 = 7 => 24 pairs (_) A6,H6: 7.. / A6 = 7 => 10 pairs (_) / H6 = 7 => 24 pairs (_) I4,I5: 8.. / I4 = 8 => 0 pairs (X) / I5 = 8 => 8 pairs (_) F8,G8: 8.. / F8 = 8 => 0 pairs (X) / G8 = 8 => 8 pairs (_) I1,G3: 9.. / I1 = 9 => 9 pairs (_) / G3 = 9 => 9 pairs (_) D6,F6: 9.. / D6 = 9 => 8 pairs (_) / F6 = 9 => 0 pairs (X) D6,D7: 9.. / D6 = 9 => 8 pairs (_) / D7 = 9 => 0 pairs (X) * DURATION: 0:00:34.047780 START: 04:55:24.661635 END: 04:55:58.709415 2017-05-01 * CP COUNT: (26) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,E6,E9,H6,H7,H8,I5) * 6...213......97.1....6....29....245..4..7.29..82...1.38....5....1.76......32....1 * PAIR A6: 5,7 COL A A3: 5,7,1,3,4 # reduction candidate for 5,7 A3: 5,7 => CTR * 6...213..32..97.1...16.3.8293.81245.14.37629..829..1.38..135.2421.76483.4.3289..1 A3: 1,3,4 # 7 pairs A9: 5,7,4 # reduction candidate for 5,7 A9: 5,7 # 10 pairs * PAIR E6: 4,5 BLK 5 D6: 4,5,9 # reduction candidate for 4,5 D6: 4,5 => CTR * 67.5213.92...97516...6..7.29....2457.45.76298782..91638279156344197638255632..971 D6: 9 # 8 pairs * PAIR E6: 4,5 COL E E3: 4,5,3,8 # reduction candidate for 4,5 E3: 3,8 # 12 pairs E3: 4,5 # 11 pairs * PAIR I5: 6,8 BLK 6 I4: 6,8,7 # reduction candidate for 6,8 I4: 6,8 # 24 pairs I4: 7 # 10 pairs * PAIR I5: 6,8 ROW 5 F5: 6,8,3 # reduction candidate for 6,8 F5: 3 => SOLVED * 659421387428397615371658942937812456146573298582946173864135729215769834793284561 F5: 6,8 # 10 pairs * PAIR H6: 6,7 BLK 6 I4: 6,7,8 # reduction candidate for 6,7 I4: 8 => CTR * 6...213..4...9761.1..653..29....24583415782965829461738....5....15769834793284561 I4: 6,7 # 8 pairs * PAIR H6: 6,7 COL H H9: 6,7,4,8 # reduction candidate for 6,7 H9: 6,7 # 16 pairs H9: 4,8 # 15 pairs * PAIR E9: 4,8 BLK 8 F8: 4,8,3,9 # reduction candidate for 4,8 F8: 4,8 # 10 pairs F9: 4,8,9 # reduction candidate for 4,8 F9: 4,8 # 22 pairs * PAIR E9: 4,8 ROW 9 H9: 4,8,6,7 # reduction candidate for 4,8 H9: 6,7 # 16 pairs H9: 4,8 # 15 pairs * PAIR E9: 4,8 COL E E3: 4,8,3,5 # reduction candidate for 4,8 E3: 4,8 # 15 pairs E3: 3,5 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0083-base-pr-000.dot * REASONING * DIS # A3: 5,7 => CTR => A3: 1,3,4 * DIS # D6: 4,5 => CTR => D6: 9 * PRF # F5: 3 => SOL * DIS # I4: 8 => CTR => I4: 6,7 * CNT 4 HDP CHAINS / 21 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,E6,E9,H6,H7,H8,I5) * 6...213......97.1....6....29....245..4..7.29..82...1.38....5....1.76......32....1 * PAIR A6: 5,7 COL A A3: 5,7,1,3,4 # reduction candidate for 5,7 A3: 5,7 => CTR * 6...213..32..97.1...16.3.8293.81245.14.37629..829..1.38..135.2421.76483.4.3289..1 A9: 5,7,4 # reduction candidate for 5,7 A9: 5,7 # 10 pairs * RESTART * PAIR A6: 5,7 COL A A9: 5,7,4 # reduction candidate for 5,7 A9: 4 => CTR * 6...213.92...97615...6.87429..8.2457.4..76298782954163827.45936519763824463289571 * PAIR RESTART * PAIR E6: 4,5 BLK 5 D6: 4,5,9 # reduction candidate for 4,5 D6: 4,5 => CTR * 67.5213.925..97.16.9.6..7.29....2457.45.76298782..91638279156344197638255632..971 * PAIR E6: 4,5 COL E E3: 4,5,3,8 # reduction candidate for 4,5 E3: 3,8 # 21 pairs E3: 4,5 # 15 pairs * PAIR I5: 6,8 BLK 6 I4: 6,8,7 # reduction candidate for 6,8 I4: 6,8 # 22 pairs I4: 7 # 12 pairs * PAIR I5: 6,8 ROW 5 F5: 6,8,3 # reduction candidate for 6,8 F5: 3 => SOLVED * 659421387428397615371658942937812456146573298582946173864135729215769834793284561 * DURATION: 0:00:11.594416 START: 04:56:14.927606 END: 04:56:26.522022 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0083-base-pr-001.dot * REASONING * DIS # A3: 5,7 => CTR => A3: 1,3,4 * DIS A3: 1,3,4 # A9: 4 => CTR => A9: 5,7 * DIS A3: 1,3,4 + A9: 5,7 # D6: 4,5 => CTR => D6: 9 * PRF A3: 1,3,4 + A9: 5,7 + D6: 9 # F5: 3 => SOL * STA A3: 1,3,4 + A9: 5,7 + D6: 9 + F5: 3 * CNT 4 HDP CHAINS / 11 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=83
Solution
position: 659421387428397615371658942937812456146573298582946173864135729215769834793284561 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 # A3: 5,7 => CTR => A3: 1,3,4 * INC # A3: 1,3,4 => UNS * INC # A9: 5,7 => UNS * DIS # D6: 4,5 => CTR => D6: 9 * INC # D6: 9 => UNS * INC # E3: 4,5 => UNS * INC # E3: 3,8 => UNS * INC # I4: 6,8 => UNS * INC # I4: 7 => UNS * INC # F5: 6,8 => UNS * PRF # F5: 3 => SOL * INC # I4: 6,7 => UNS * DIS # I4: 8 => CTR => I4: 6,7 * INC # H9: 6,7 => UNS * INC # H9: 4,8 => UNS * INC # F8: 4,8 => UNS * INC # F9: 4,8 => UNS * INC # H9: 4,8 => UNS * INC # H9: 6,7 => UNS * INC # E3: 4,8 => UNS * INC # E3: 3,5 => UNS * CNT 21 HDP CHAINS / 21 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A3: 5,7 => CTR => A3: 1,3,4 * INC A3: 1,3,4 # A9: 5,7 => UNS * INC A3: 1,3,4 # A9: 5,7 => UNS * DIS A3: 1,3,4 # A9: 4 => CTR => A9: 5,7 * DIS A3: 1,3,4 + A9: 5,7 # D6: 4,5 => CTR => D6: 9 * INC A3: 1,3,4 + A9: 5,7 + D6: 9 # E3: 4,5 => UNS * INC A3: 1,3,4 + A9: 5,7 + D6: 9 # E3: 3,8 => UNS * INC A3: 1,3,4 + A9: 5,7 + D6: 9 # I4: 6,8 => UNS * INC A3: 1,3,4 + A9: 5,7 + D6: 9 # I4: 7 => UNS * INC A3: 1,3,4 + A9: 5,7 + D6: 9 # F5: 6,8 => UNS * PRF A3: 1,3,4 + A9: 5,7 + D6: 9 # F5: 3 => SOL * STA A3: 1,3,4 + A9: 5,7 + D6: 9 + F5: 3 * CNT 11 HDP CHAINS / 11 HYP OPENED