Analysis of zz-www.sudokuwiki.org-0078-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=78
level: medium
position: .9...8.....2....98...3...547..5....6..3.4.9..2....1..316...9...92....4.....4...1. initial
Autosolve
position: 49...8.....2..4.98...39..547.95....6..3.4.9..2..9.1..3164..9...92....4.7...4...19 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 6,8 => CTR => C3: 1,7 * DIS # C3: 7,8 => CTR => C3: 1,6 * DIS # G1: 1,2 => CTR => G1: 3,6,7 * DIS # E1: 1,2 => CTR => E1: 5,6,7 * DIS # I5: 1 => CTR => I5: 2,5 * CNT 5 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 6,8 => CTR => C3: 1,7 * DIS C3: 1,7 # A5: 5 => CTR => A5: 6,8 * DIS C3: 1,7 + A5: 6,8 # G1: 1,2 => CTR => G1: 3,6,7 * DIS C3: 1,7 + A5: 6,8 + G1: 3,6,7 # G3: 6,7 => CTR => G3: 1,2 * DIS C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 # B9: 5,8 => CTR => B9: 3,7 * DIS C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 + B9: 3,7 # G7: 3,8 => CTR => G7: 2,5 * DIS C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 + B9: 3,7 + G7: 2,5 # B2: 7 => CTR => B2: 3,5 * DIS C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 + B9: 3,7 + G7: 2,5 + B2: 3,5 # C1: 6 => CTR => C1: 1,7 * DIS C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 + B9: 3,7 + G7: 2,5 + B2: 3,5 + C1: 1,7 # D1: 6,7 => CTR => D1: 2 * PRF C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 + B9: 3,7 + G7: 2,5 + B2: 3,5 + C1: 1,7 + D1: 2 => SOL * STA C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 + B9: 3,7 + G7: 2,5 + B2: 3,5 + C1: 1,7 + D1: 2 * CNT 10 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .9...8.....2....98...3...547..5....6..3.4.9..2....1..316...9...92....4.....4...1. | initial |
| 49...8.....2..4.98...39..547.95....6..3.4.9..2..9.1..3164..9...92....4.7...4...19 | autosolve |
| 497258361532164798681397254749583126813642975256971843164739582925816437378425619 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) A3: 6,8 B3: 7,8 I1: 1,2 F4: 2,3 C8: 5,8 I7: 2,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,C3: 1.. / C1 = 1 => 0 pairs (X) / C3 = 1 => 6 pairs (_) B4,B5: 1.. / B4 = 1 => 0 pairs (X) / B5 = 1 => 8 pairs (_) G4,I5: 1.. / G4 = 1 => 8 pairs (_) / I5 = 1 => 0 pairs (X) D8,E8: 1.. / D8 = 1 => 9 pairs (_) / E8 = 1 => 7 pairs (_) C3,G3: 1.. / C3 = 1 => 6 pairs (_) / G3 = 1 => 0 pairs (X) B4,G4: 1.. / B4 = 1 => 0 pairs (X) / G4 = 1 => 8 pairs (_) B5,I5: 1.. / B5 = 1 => 8 pairs (_) / I5 = 1 => 0 pairs (X) I1,I5: 1.. / I1 = 1 => 8 pairs (_) / I5 = 1 => 0 pairs (X) F3,G3: 2.. / F3 = 2 => 22 pairs (_) / G3 = 2 => 11 pairs (_) A2,B2: 3.. / A2 = 3 => 8 pairs (_) / B2 = 3 => 7 pairs (_) G1,H1: 3.. / G1 = 3 => 6 pairs (_) / H1 = 3 => 12 pairs (_) E4,F4: 3.. / E4 = 3 => 0 pairs (X) / F4 = 3 => 7 pairs (_) A9,B9: 3.. / A9 = 3 => 7 pairs (_) / B9 = 3 => 8 pairs (_) A2,A9: 3.. / A2 = 3 => 8 pairs (_) / A9 = 3 => 7 pairs (_) B2,B9: 3.. / B2 = 3 => 7 pairs (_) / B9 = 3 => 8 pairs (_) F4,F8: 3.. / F4 = 3 => 7 pairs (_) / F8 = 3 => 0 pairs (X) G1,G7: 3.. / G1 = 3 => 6 pairs (_) / G7 = 3 => 12 pairs (_) B4,B6: 4.. / B4 = 4 => 9 pairs (_) / B6 = 4 => 8 pairs (_) H4,H6: 4.. / H4 = 4 => 8 pairs (_) / H6 = 4 => 9 pairs (_) B4,H4: 4.. / B4 = 4 => 9 pairs (_) / H4 = 4 => 8 pairs (_) B6,H6: 4.. / B6 = 4 => 8 pairs (_) / H6 = 4 => 9 pairs (_) E1,E2: 5.. / E1 = 5 => 8 pairs (_) / E2 = 5 => 14 pairs (_) I5,G6: 5.. / I5 = 5 => 15 pairs (_) / G6 = 5 => 8 pairs (_) F8,F9: 5.. / F8 = 5 => 11 pairs (_) / F9 = 5 => 13 pairs (_) G7,I7: 5.. / G7 = 5 => 15 pairs (_) / I7 = 5 => 8 pairs (_) C1,E1: 5.. / C1 = 5 => 14 pairs (_) / E1 = 5 => 8 pairs (_) C8,F8: 5.. / C8 = 5 => 13 pairs (_) / F8 = 5 => 11 pairs (_) G6,G7: 5.. / G6 = 5 => 8 pairs (_) / G7 = 5 => 15 pairs (_) I5,I7: 5.. / I5 = 5 => 15 pairs (_) / I7 = 5 => 8 pairs (_) A5,C6: 6.. / A5 = 6 => 17 pairs (_) / C6 = 6 => 8 pairs (_) H8,G9: 6.. / H8 = 6 => 9 pairs (_) / G9 = 6 => 12 pairs (_) C6,E6: 6.. / C6 = 6 => 8 pairs (_) / E6 = 6 => 17 pairs (_) H1,H8: 6.. / H1 = 6 => 12 pairs (_) / H8 = 6 => 9 pairs (_) B9,C9: 7.. / B9 = 7 => 15 pairs (_) / C9 = 7 => 6 pairs (_) D7,E7: 7.. / D7 = 7 => 7 pairs (_) / E7 = 7 => 10 pairs (_) F3,F5: 7.. / F3 = 7 => 21 pairs (_) / F5 = 7 => 9 pairs (_) * DURATION: 0:00:52.628146 START: 04:48:48.451775 END: 04:49:41.079921 2017-05-01 * CP COUNT: (36) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B3,C8,F4,I1,I7) * 49...8.....2..4.98...39..547.95....6..3.4.9..2..9.1..3164..9...92....4.7...4...19 * PAIR A3: 6,8 BLK 1 C3: 6,8,1,7 # reduction candidate for 6,8 C3: 6,8 => CTR * 491.58.62..2..4798.7.3921547195.3.46..3.479.124.9.1573164.79..5925.36487..7425619 C3: 1,7 # 7 pairs * PAIR A3: 6,8 COL A A5: 6,8,5 # reduction candidate for 6,8 A5: 5 # 20 pairs A5: 6,8 # 11 pairs * PAIR B3: 7,8 BLK 1 C3: 7,8,1,6 # reduction candidate for 7,8 C3: 7,8 => CTR * 491.58..2..2..4.986..392154719523846..364792124698157316427938592.8..4.7...4...19 C3: 1,6 # 7 pairs * PAIR B3: 7,8 COL B B9: 7,8,3,5 # reduction candidate for 7,8 B9: 7,8 # 13 pairs B9: 3,5 # 7 pairs * PAIR I1: 1,2 BLK 3 G1: 1,2,3,6,7 # reduction candidate for 1,2 G1: 1,2 => CTR * 49..58.3...2.14.98..1392.547.95.3.46..3.479..2469.1573164..93.5928135467...4.6.19 G1: 3,6,7 # 6 pairs G3: 1,2,6,7 # reduction candidate for 1,2 G3: 1,2 # 8 pairs * PAIR I1: 1,2 ROW 1 D1: 1,2,6,7 # reduction candidate for 1,2 D1: 1,2 # 7 pairs E1: 1,2,5,6,7 # reduction candidate for 1,2 E1: 1,2 => CTR * 495.18..2..2.54198..139..54719523846..3.4.921246981573164879235928135467..74.2.19 E1: 5,6,7 # 6 pairs * PAIR I1: 1,2 COL I I5: 1,2,5 # reduction candidate for 1,2 I5: 5 # 15 pairs I5: 1,2 # 8 pairs * PAIR F4: 2,3 BLK 5 E4: 2,3,8 # reduction candidate for 2,3 E4: 8 # 18 pairs E4: 2,3 # 10 pairs * PAIR C8: 5,8 BLK 7 A9: 5,8,3 # reduction candidate for 5,8 A9: 5,8 # 8 pairs B9: 5,8,3,7 # reduction candidate for 5,8 B9: 5,8 # 10 pairs C9: 5,8,7 # reduction candidate for 5,8 C9: 5,8 # 15 pairs * PAIR C8: 5,8 COL C C6: 5,8,6 # reduction candidate for 5,8 C6: 5,8 # 17 pairs C6: 6 # 8 pairs * PAIR I7: 2,5 BLK 9 G7: 2,5,3,8 # reduction candidate for 2,5 G7: 2,5 # 10 pairs G7: 3,8 # 9 pairs * PAIR I7: 2,5 COL I I5: 2,5,1 # reduction candidate for 2,5 I5: 1 => CTR * 4917583625326147988763921547195832466532479812489615731648.9..5925..64.7..7425619 I5: 2,5 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0078-base-pr-000.dot * REASONING * DIS # C3: 6,8 => CTR => C3: 1,7 * DIS # C3: 7,8 => CTR => C3: 1,6 * DIS # G1: 1,2 => CTR => G1: 3,6,7 * DIS # E1: 1,2 => CTR => E1: 5,6,7 * DIS # I5: 1 => CTR => I5: 2,5 * CNT 5 HDP CHAINS / 27 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B3,C8,F4,I1,I7) * 49...8.....2..4.98...39..547.95....6..3.4.9..2..9.1..3164..9...92....4.7...4...19 * PAIR A3: 6,8 BLK 1 C3: 6,8,1,7 # reduction candidate for 6,8 C3: 6,8 => CTR * 491.58.62..2..4798.7.3921547195.3.46..3.479.124.9.1573164.79..5925.36487..7425619 * PAIR A3: 6,8 COL A A5: 6,8,5 # reduction candidate for 6,8 A5: 5 => CTR * 495218...632.54.9887139..547.95...465.3647982246981573164879..59281.54673574..819 * PAIR RESTART * PAIR B3: 7,8 COL B B9: 7,8,3,5 # reduction candidate for 7,8 B9: 3,5 # 16 pairs B9: 7,8 # 14 pairs * PAIR I1: 1,2 BLK 3 G1: 1,2,3,6,7 # reduction candidate for 1,2 G1: 1,2 => CTR * 49..58132532.14.98.813927547195.3.468536479.124.9.1573164..93.5928135467...4.6.19 G3: 1,2,6,7 # reduction candidate for 1,2 G3: 1,2 # 14 pairs * RESTART * PAIR I1: 1,2 BLK 3 G3: 1,2,6,7 # reduction candidate for 1,2 G3: 6,7 => CTR * 496.58.....26147988713926547.95.31.6613.479.52.5961873164.795..92..35467..74.6.19 * PAIR F4: 2,3 BLK 5 E4: 2,3,8 # reduction candidate for 2,3 E4: 8 # 25 pairs E4: 2,3 # 20 pairs * PAIR C8: 5,8 BLK 7 B9: 5,8,3,7 # reduction candidate for 5,8 B9: 5,8 => CTR * 49...83.1532..4.988713962547.95..1.6613.479.52..961..3164..95.292.61.4.73.74..619 C9: 5,8,7 # reduction candidate for 5,8 C9: 5,8 # 17 pairs * RESTART * PAIR C8: 5,8 BLK 7 C9: 5,8,7 # reduction candidate for 5,8 C9: 7 # 18 pairs C9: 5,8 # 17 pairs * PAIR I7: 2,5 BLK 9 G7: 2,5,3,8 # reduction candidate for 2,5 G7: 3,8 => CTR * 491.58..2532..4.9868739215471952384685364792124698157316427938592.8..4.7...4...19 * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A2,A3,A5,A9,B3,B5,B9,C3,C6,C8,D7,F4,G2,G3,G4,G7,G9,H1,H7,I1,I5,I7) * 49...83....2..4.98...39..547.95....6..3.4.9..2..9.1..3164..9...92....4.7...4...19 * PAIR A2: 3,5 BLK 1 B2: 3,5,7 # reduction candidate for 3,5 B2: 7 => CTR * 49...83..372.54698.813972547.95..1.6813.4.9.52569.1743164.7953292..134675374..819 * PAIR C3: 1,7 BLK 1 C1: 1,7,6 # reduction candidate for 1,7 C1: 6 => CTR * 496.58371..2..46988713962547.95..1.6613.479.52.59617.3164..95.29286154375374.2819 * PAIR H1: 6,7 ROW 1 D1: 6,7,2 # reduction candidate for 6,7 D1: 6,7 => CTR * 49..583.2532..4.9868.3921547195.384685324.9..2.69.1..3164..9...92....4.737.4...19 D1: 2 => SOLVED * 497258361532164798681397254749583126813642975256971843164739582925816437378425619 * DURATION: 0:00:26.212413 START: 04:50:02.822021 END: 04:50:29.034434 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0078-base-pr-001.dot * REASONING * DIS # C3: 6,8 => CTR => C3: 1,7 * DIS C3: 1,7 # A5: 5 => CTR => A5: 6,8 * DIS C3: 1,7 + A5: 6,8 # G1: 1,2 => CTR => G1: 3,6,7 * DIS C3: 1,7 + A5: 6,8 + G1: 3,6,7 # G3: 6,7 => CTR => G3: 1,2 * DIS C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 # B9: 5,8 => CTR => B9: 3,7 * DIS C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 + B9: 3,7 # G7: 3,8 => CTR => G7: 2,5 * DIS C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 + B9: 3,7 + G7: 2,5 # B2: 7 => CTR => B2: 3,5 * DIS C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 + B9: 3,7 + G7: 2,5 + B2: 3,5 # C1: 6 => CTR => C1: 1,7 * DIS C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 + B9: 3,7 + G7: 2,5 + B2: 3,5 + C1: 1,7 # D1: 6,7 => CTR => D1: 2 * PRF C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 + B9: 3,7 + G7: 2,5 + B2: 3,5 + C1: 1,7 + D1: 2 => SOL * STA C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 + B9: 3,7 + G7: 2,5 + B2: 3,5 + C1: 1,7 + D1: 2 * CNT 10 HDP CHAINS / 22 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=78
Solution
position: 497258361532164798681397254749583126813642975256971843164739582925816437378425619 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 # C3: 6,8 => CTR => C3: 1,7 * INC # C3: 1,7 => UNS * INC # A5: 6,8 => UNS * INC # A5: 5 => UNS * DIS # C3: 7,8 => CTR => C3: 1,6 * INC # C3: 1,6 => UNS * INC # B9: 7,8 => UNS * INC # B9: 3,5 => UNS * DIS # G1: 1,2 => CTR => G1: 3,6,7 * INC # G1: 3,6,7 => UNS * INC # G3: 1,2 => UNS * INC # D1: 1,2 => UNS * DIS # E1: 1,2 => CTR => E1: 5,6,7 * INC # E1: 5,6,7 => UNS * INC # I5: 1,2 => UNS * INC # I5: 5 => UNS * INC # E4: 2,3 => UNS * INC # E4: 8 => UNS * INC # A9: 5,8 => UNS * INC # B9: 5,8 => UNS * INC # C9: 5,8 => UNS * INC # C6: 5,8 => UNS * INC # C6: 6 => UNS * INC # G7: 2,5 => UNS * INC # G7: 3,8 => UNS * INC # I5: 2,5 => UNS * DIS # I5: 1 => CTR => I5: 2,5 * CNT 27 HDP CHAINS / 27 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C3: 6,8 => CTR => C3: 1,7 * INC C3: 1,7 # A5: 6,8 => UNS * DIS C3: 1,7 # A5: 5 => CTR => A5: 6,8 * INC C3: 1,7 + A5: 6,8 # B9: 7,8 => UNS * INC C3: 1,7 + A5: 6,8 # B9: 3,5 => UNS * DIS C3: 1,7 + A5: 6,8 # G1: 1,2 => CTR => G1: 3,6,7 * INC C3: 1,7 + A5: 6,8 + G1: 3,6,7 # G3: 1,2 => UNS * INC C3: 1,7 + A5: 6,8 + G1: 3,6,7 # G3: 1,2 => UNS * DIS C3: 1,7 + A5: 6,8 + G1: 3,6,7 # G3: 6,7 => CTR => G3: 1,2 * INC C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 # E4: 2,3 => UNS * INC C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 # E4: 8 => UNS * DIS C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 # B9: 5,8 => CTR => B9: 3,7 * INC C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 + B9: 3,7 # C9: 5,8 => UNS * INC C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 + B9: 3,7 # C9: 5,8 => UNS * INC C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 + B9: 3,7 # C9: 7 => UNS * INC C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 + B9: 3,7 # G7: 2,5 => UNS * DIS C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 + B9: 3,7 # G7: 3,8 => CTR => G7: 2,5 * INC C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 + B9: 3,7 + G7: 2,5 # B2: 3,5 => UNS * DIS C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 + B9: 3,7 + G7: 2,5 # B2: 7 => CTR => B2: 3,5 * INC C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 + B9: 3,7 + G7: 2,5 + B2: 3,5 # C1: 1,7 => UNS * DIS C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 + B9: 3,7 + G7: 2,5 + B2: 3,5 # C1: 6 => CTR => C1: 1,7 * DIS C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 + B9: 3,7 + G7: 2,5 + B2: 3,5 + C1: 1,7 # D1: 6,7 => CTR => D1: 2 * PRF C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 + B9: 3,7 + G7: 2,5 + B2: 3,5 + C1: 1,7 + D1: 2 => SOL * STA C3: 1,7 + A5: 6,8 + G1: 3,6,7 + G3: 1,2 + B9: 3,7 + G7: 2,5 + B2: 3,5 + C1: 1,7 + D1: 2 * CNT 23 HDP CHAINS / 22 HYP OPENED