Analysis of zz-www.sudokuwiki.org-0033-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=33
level: medium
position: ....3.7..6..8....5.7.4.6.1...16...9...3.7.1...9...28...8.3.4.2.9....1..4..4.6.... initial
Autosolve
position: ....3.7..6..8.7..5.7.4.6.1...16.3.9...3.7.1...9...28...8.3.4.2.9....1..4..4.6.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D9: 5,9 => CTR => D9: 2,7 * DIS # A4: 2,7 => CTR => A4: 4,5,8 * DIS # D9: 5,9 => CTR => D9: 2,7 * CNT 3 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D9: 5,9 => CTR => D9: 2,7 * DIS D9: 2,7 # A4: 2,7 => CTR => A4: 4,5,8 * DIS D9: 2,7 + A4: 4,5,8 # F9: 8 => CTR => F9: 5,9 * DIS D9: 2,7 + A4: 4,5,8 + F9: 5,9 # C1: 2,9 => CTR => C1: 5,8 * DIS D9: 2,7 + A4: 4,5,8 + F9: 5,9 + C1: 5,8 # C3: 2,9 => CTR => C3: 5,8 * PRF D9: 2,7 + A4: 4,5,8 + F9: 5,9 + C1: 5,8 + C3: 5,8 => SOL * STA D9: 2,7 + A4: 4,5,8 + F9: 5,9 + C1: 5,8 + C3: 5,8 * CNT 6 HDP CHAINS / 43 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....3.7..6..8....5.7.4.6.1...16...9...3.7.1...9...28...8.3.4.2.9....1..4..4.6.... | initial |
| ....3.7..6..8.7..5.7.4.6.1...16.3.9...3.7.1...9...28...8.3.4.2.9....1..4..4.6.... | autosolve |
| 245139786619827435378456219821643597453978162796512843587394621962781354134265978 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) C2: 2,9 F1: 5,9 H2: 3,4 D5: 5,9 D6: 1,5 I4: 2,7 I5: 2,6 E7: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,E2: 1.. / D1 = 1 => 17 pairs (_) / E2 = 1 => 8 pairs (_) D6,E6: 1.. / D6 = 1 => 8 pairs (_) / E6 = 1 => 17 pairs (_) I7,I9: 1.. / I7 = 1 => 9 pairs (_) / I9 = 1 => 10 pairs (_) B2,E2: 1.. / B2 = 1 => 17 pairs (_) / E2 = 1 => 8 pairs (_) A7,I7: 1.. / A7 = 1 => 10 pairs (_) / I7 = 1 => 9 pairs (_) D1,D6: 1.. / D1 = 1 => 17 pairs (_) / D6 = 1 => 8 pairs (_) E2,E6: 1.. / E2 = 1 => 8 pairs (_) / E6 = 1 => 17 pairs (_) B2,A3: 3.. / B2 = 3 => 17 pairs (_) / A3 = 3 => 9 pairs (_) H6,I6: 3.. / H6 = 3 => 0 pairs (X) / I6 = 3 => 8 pairs (_) A3,A9: 3.. / A3 = 3 => 9 pairs (_) / A9 = 3 => 17 pairs (_) E4,E6: 4.. / E4 = 4 => 20 pairs (_) / E6 = 4 => 9 pairs (_) G2,G4: 4.. / G2 = 4 => 11 pairs (_) / G4 = 4 => 11 pairs (_) H1,I1: 6.. / H1 = 6 => 9 pairs (_) / I1 = 6 => 10 pairs (_) B5,C6: 6.. / B5 = 6 => 12 pairs (_) / C6 = 6 => 13 pairs (_) G7,G8: 6.. / G7 = 6 => 10 pairs (_) / G8 = 6 => 13 pairs (_) C7,G7: 6.. / C7 = 6 => 13 pairs (_) / G7 = 6 => 10 pairs (_) B5,B8: 6.. / B5 = 6 => 12 pairs (_) / B8 = 6 => 13 pairs (_) D8,D9: 7.. / D8 = 7 => 8 pairs (_) / D9 = 7 => 10 pairs (_) A4,I4: 7.. / A4 = 7 => 0 pairs (X) / I4 = 7 => 9 pairs (_) C1,C3: 8.. / C1 = 8 => 9 pairs (_) / C3 = 8 => 10 pairs (_) A4,A5: 8.. / A4 = 8 => 13 pairs (_) / A5 = 8 => 14 pairs (_) E4,F5: 8.. / E4 = 8 => 14 pairs (_) / F5 = 8 => 13 pairs (_) E8,F9: 8.. / E8 = 8 => 13 pairs (_) / F9 = 8 => 14 pairs (_) C3,I3: 8.. / C3 = 8 => 10 pairs (_) / I3 = 8 => 9 pairs (_) A4,E4: 8.. / A4 = 8 => 13 pairs (_) / E4 = 8 => 14 pairs (_) A5,F5: 8.. / A5 = 8 => 14 pairs (_) / F5 = 8 => 13 pairs (_) E8,H8: 8.. / E8 = 8 => 13 pairs (_) / H8 = 8 => 14 pairs (_) E4,E8: 8.. / E4 = 8 => 14 pairs (_) / E8 = 8 => 13 pairs (_) F5,F9: 8.. / F5 = 8 => 13 pairs (_) / F9 = 8 => 14 pairs (_) D5,F5: 9.. / D5 = 9 => 8 pairs (_) / F5 = 9 => 10 pairs (_) * DURATION: 0:00:40.799113 START: 04:03:08.346527 END: 04:03:49.145640 2017-05-01 * CP COUNT: (30) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C2,D5,D6,E7,F1,H2,I4,I5) * ....3.7..6..8.7..5.7.4.6.1...16.3.9...3.7.1...9...28...8.3.4.2.9....1..4..4.6.... * PAIR C2: 2,9 BLK 1 C1: 2,9,5,8 # reduction candidate for 2,9 C1: 2,9 # 13 pairs C3: 2,9,5,8 # reduction candidate for 2,9 C3: 2,9 # 11 pairs * PAIR C2: 2,9 ROW 2 E2: 2,9,1 # reduction candidate for 2,9 E2: 2,9 # 17 pairs G2: 2,9,3,4 # reduction candidate for 2,9 G2: 2,9 # 13 pairs * PAIR F1: 5,9 BLK 2 D1: 5,9,1,2 # reduction candidate for 5,9 D1: 5,9 # 19 pairs E3: 5,9,2 # reduction candidate for 5,9 E3: 5,9 # 14 pairs * PAIR F1: 5,9 ROW 1 C1: 5,9,2,8 # reduction candidate for 5,9 C1: 5,9 # 12 pairs C1: 2,8 # 9 pairs * PAIR F1: 5,9 COL F F5: 5,9,8 # reduction candidate for 5,9 F5: 5,9 # 14 pairs F9: 5,9,8 # reduction candidate for 5,9 F9: 5,9 # 13 pairs * PAIR H2: 3,4 BLK 3 G2: 3,4,2,9 # reduction candidate for 3,4 G2: 2,9 # 13 pairs G2: 3,4 # 12 pairs * PAIR H2: 3,4 ROW 2 B2: 3,4,1,2 # reduction candidate for 3,4 B2: 3,4 # 13 pairs B2: 1,2 # 12 pairs * PAIR H2: 3,4 COL H H6: 3,4,5,6,7 # reduction candidate for 3,4 H6: 3,4 # 14 pairs H6: 5,6,7 # 8 pairs * PAIR D5: 5,9 BLK 5 F5: 5,9,8 # reduction candidate for 5,9 F5: 5,9 # 14 pairs F5: 8 # 13 pairs * PAIR D5: 5,9 COL D D1: 5,9,1,2 # reduction candidate for 5,9 D1: 5,9 # 19 pairs D9: 5,9,2,7 # reduction candidate for 5,9 D9: 5,9 => CTR * ...23.74664.817.3537.456.184.1683.978.3.75162.9.1428...8.3.4.2.9..721.84..4.68... D9: 2,7 # 9 pairs * PAIR D6: 1,5 BLK 5 E6: 1,5,4 # reduction candidate for 1,5 E6: 1,5 # 20 pairs E6: 4 # 9 pairs * PAIR D6: 1,5 COL D D1: 1,5,2,9 # reduction candidate for 1,5 D1: 1,5 # 12 pairs D1: 2,9 # 9 pairs * PAIR I4: 2,7 ROW 4 A4: 2,7,4,5,8 # reduction candidate for 2,7 A4: 2,7 => CTR * 41..3.76.62981743537.4.621..4168359.8.3.7.14..9.142873.8.3.4.2.9....1.84..4.68.5. A4: 4,5,8 # 9 pairs * PAIR I5: 2,6 ROW 5 B5: 2,6,4,5 # reduction candidate for 2,6 B5: 4,5 # 14 pairs B5: 2,6 # 10 pairs * PAIR I5: 2,6 COL I I1: 2,6,8,9 # reduction candidate for 2,6 I1: 8,9 # 10 pairs I1: 2,6 # 10 pairs * PAIR E7: 5,9 BLK 8 D9: 5,9,2,7 # reduction candidate for 5,9 D9: 5,9 => CTR * ...23.74664.817.3537.456.184.1683.978.3.75162.9.1428...8.3.4.2.9..721.84..4.68... D9: 2,7 # 9 pairs F9: 5,9,8 # reduction candidate for 5,9 F9: 5,9 # 13 pairs * PAIR E7: 5,9 ROW 7 G7: 5,9,6 # reduction candidate for 5,9 G7: 5,9 # 13 pairs G7: 6 # 10 pairs * PAIR E7: 5,9 COL E E3: 5,9,2 # reduction candidate for 5,9 E3: 2 # 16 pairs E3: 5,9 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0033-base-pr-000.dot * REASONING * DIS # D9: 5,9 => CTR => D9: 2,7 * DIS # A4: 2,7 => CTR => A4: 4,5,8 * DIS # D9: 5,9 => CTR => D9: 2,7 * CNT 3 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C2,D5,D6,E7,F1,H2,I4,I5) * ....3.7..6..8.7..5.7.4.6.1...16.3.9...3.7.1...9...28...8.3.4.2.9....1..4..4.6.... * PAIR C2: 2,9 BLK 1 C1: 2,9,5,8 # reduction candidate for 2,9 C1: 2,9 # 13 pairs C3: 2,9,5,8 # reduction candidate for 2,9 C3: 2,9 # 11 pairs * PAIR C2: 2,9 ROW 2 E2: 2,9,1 # reduction candidate for 2,9 E2: 2,9 # 17 pairs G2: 2,9,3,4 # reduction candidate for 2,9 G2: 2,9 # 13 pairs * PAIR F1: 5,9 BLK 2 D1: 5,9,1,2 # reduction candidate for 5,9 D1: 5,9 # 19 pairs E3: 5,9,2 # reduction candidate for 5,9 E3: 5,9 # 14 pairs * PAIR F1: 5,9 ROW 1 C1: 5,9,2,8 # reduction candidate for 5,9 C1: 5,9 # 12 pairs C1: 2,8 # 9 pairs * PAIR F1: 5,9 COL F F5: 5,9,8 # reduction candidate for 5,9 F5: 5,9 # 14 pairs F9: 5,9,8 # reduction candidate for 5,9 F9: 5,9 # 13 pairs * PAIR H2: 3,4 BLK 3 G2: 3,4,2,9 # reduction candidate for 3,4 G2: 2,9 # 13 pairs G2: 3,4 # 12 pairs * PAIR H2: 3,4 ROW 2 B2: 3,4,1,2 # reduction candidate for 3,4 B2: 3,4 # 13 pairs B2: 1,2 # 12 pairs * PAIR H2: 3,4 COL H H6: 3,4,5,6,7 # reduction candidate for 3,4 H6: 3,4 # 14 pairs H6: 5,6,7 # 8 pairs * PAIR D5: 5,9 BLK 5 F5: 5,9,8 # reduction candidate for 5,9 F5: 5,9 # 14 pairs F5: 8 # 13 pairs * PAIR D5: 5,9 COL D D1: 5,9,1,2 # reduction candidate for 5,9 D1: 5,9 # 19 pairs D9: 5,9,2,7 # reduction candidate for 5,9 D9: 5,9 => CTR * ...23.74664.817.3537.456.184.1683.978.3.75162.9.1428...8.3.4.2.9..721.84..4.68... * RESTART * PAIR D5: 5,9 COL D D1: 5,9,1,2 # reduction candidate for 5,9 D1: 5,9 # 19 pairs D1: 1,2 # 10 pairs * PAIR RESTART * PAIR D5: 5,9 BLK 5 F5: 5,9,8 # reduction candidate for 5,9 F5: 5,9 # 14 pairs F5: 8 # 13 pairs * PAIR D5: 5,9 COL D D1: 5,9,1,2 # reduction candidate for 5,9 D1: 5,9 # 19 pairs D1: 1,2 # 10 pairs * PAIR D6: 1,5 BLK 5 E6: 1,5,4 # reduction candidate for 1,5 E6: 1,5 # 20 pairs E6: 4 # 10 pairs * PAIR D6: 1,5 COL D D1: 1,5,2,9 # reduction candidate for 1,5 D1: 1,5 # 12 pairs D1: 2,9 # 10 pairs * PAIR I4: 2,7 ROW 4 A4: 2,7,4,5,8 # reduction candidate for 2,7 A4: 2,7 => CTR * 41..3.76.6..81743537.4.6.1..4168359.8.3.7.14..9.142873.8.39462.9....1384..4.68... * PAIR RESTART * PAIR I5: 2,6 ROW 5 B5: 2,6,4,5 # reduction candidate for 2,6 B5: 4,5 # 15 pairs B5: 2,6 # 12 pairs * PAIR I5: 2,6 COL I I1: 2,6,8,9 # reduction candidate for 2,6 I1: 8,9 # 15 pairs I1: 2,6 # 11 pairs * PAIR E7: 5,9 BLK 8 F9: 5,9,8 # reduction candidate for 5,9 F9: 8 => CTR * 21..3.7466498172353754269184216835978.3.7.16..9.1428...8.394.219..751.84..4268.7. * PAIR E7: 5,9 ROW 7 G7: 5,9,6 # reduction candidate for 5,9 G7: 5,9 # 25 pairs G7: 6 # 15 pairs * PAIR E7: 5,9 COL E E3: 5,9,2 # reduction candidate for 5,9 E3: 2 # 19 pairs E3: 5,9 # 16 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (C2,D1,D6,D8,D9,E4,E7,F1,F9,H2,I5,I6,I7) * ....3.7..6..8.7..5.7.4.6.1.8.16.3.97..39781...9...28...8.3.4.2.9...81..4..4.6.... * PAIR C2: 2,9 BLK 1 C1: 2,9,5,8 # reduction candidate for 2,9 C1: 2,9 => CTR * ..2.397..6.98.7..5.784.6.1.8.16.3.97.639781.2.9...28...8.394.219...81..4214765... C3: 2,9,5,8 # reduction candidate for 2,9 C3: 2,9 => CTR * ..8.3.7.26..8.7..5.7.4.6.188.16.3297..39781.6.96..28.3.873.462.965281374..476.58. C3: 5,8 => SOLVED * 245139786619827435378456219821643597453978162796512843587394621962781354134265978 * DURATION: 0:00:33.545500 START: 04:04:15.142220 END: 04:04:48.687720 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0033-base-pr-001.dot * REASONING * DIS # D9: 5,9 => CTR => D9: 2,7 * DIS D9: 2,7 # A4: 2,7 => CTR => A4: 4,5,8 * DIS D9: 2,7 + A4: 4,5,8 # F9: 8 => CTR => F9: 5,9 * DIS D9: 2,7 + A4: 4,5,8 + F9: 5,9 # C1: 2,9 => CTR => C1: 5,8 * DIS D9: 2,7 + A4: 4,5,8 + F9: 5,9 + C1: 5,8 # C3: 2,9 => CTR => C3: 5,8 * PRF D9: 2,7 + A4: 4,5,8 + F9: 5,9 + C1: 5,8 + C3: 5,8 => SOL * STA D9: 2,7 + A4: 4,5,8 + F9: 5,9 + C1: 5,8 + C3: 5,8 * CNT 6 HDP CHAINS / 43 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=33
Solution
position: 245139786619827435378456219821643597453978162796512843587394621962781354134265978 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 # C1: 2,9 => UNS * INC # C3: 2,9 => UNS * INC # E2: 2,9 => UNS * INC # G2: 2,9 => UNS * INC # D1: 5,9 => UNS * INC # E3: 5,9 => UNS * INC # C1: 5,9 => UNS * INC # C1: 2,8 => UNS * INC # F5: 5,9 => UNS * INC # F9: 5,9 => UNS * INC # G2: 3,4 => UNS * INC # G2: 2,9 => UNS * INC # B2: 3,4 => UNS * INC # B2: 1,2 => UNS * INC # H6: 3,4 => UNS * INC # H6: 5,6,7 => UNS * INC # F5: 5,9 => UNS * INC # F5: 8 => UNS * INC # D1: 5,9 => UNS * DIS # D9: 5,9 => CTR => D9: 2,7 * INC # D9: 2,7 => UNS * INC # E6: 1,5 => UNS * INC # E6: 4 => UNS * INC # D1: 1,5 => UNS * INC # D1: 2,9 => UNS * DIS # A4: 2,7 => CTR => A4: 4,5,8 * INC # A4: 4,5,8 => UNS * INC # B5: 2,6 => UNS * INC # B5: 4,5 => UNS * INC # I1: 2,6 => UNS * INC # I1: 8,9 => UNS * DIS # D9: 5,9 => CTR => D9: 2,7 * INC # D9: 2,7 => UNS * INC # F9: 5,9 => UNS * INC # G7: 5,9 => UNS * INC # G7: 6 => UNS * INC # E3: 5,9 => UNS * INC # E3: 2 => UNS * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 2,9 => UNS * INC # C3: 2,9 => UNS * INC # E2: 2,9 => UNS * INC # G2: 2,9 => UNS * INC # D1: 5,9 => UNS * INC # E3: 5,9 => UNS * INC # C1: 5,9 => UNS * INC # C1: 2,8 => UNS * INC # F5: 5,9 => UNS * INC # F9: 5,9 => UNS * INC # G2: 3,4 => UNS * INC # G2: 2,9 => UNS * INC # B2: 3,4 => UNS * INC # B2: 1,2 => UNS * INC # H6: 3,4 => UNS * INC # H6: 5,6,7 => UNS * INC # F5: 5,9 => UNS * INC # F5: 8 => UNS * INC # D1: 5,9 => UNS * DIS # D9: 5,9 => CTR => D9: 2,7 * INC D9: 2,7 # D1: 5,9 => UNS * INC D9: 2,7 # D1: 1,2 => UNS * INC D9: 2,7 # F5: 5,9 => UNS * INC D9: 2,7 # F5: 8 => UNS * INC D9: 2,7 # D1: 5,9 => UNS * INC D9: 2,7 # D1: 1,2 => UNS * INC D9: 2,7 # E6: 1,5 => UNS * INC D9: 2,7 # E6: 4 => UNS * INC D9: 2,7 # D1: 1,5 => UNS * INC D9: 2,7 # D1: 2,9 => UNS * DIS D9: 2,7 # A4: 2,7 => CTR => A4: 4,5,8 * INC D9: 2,7 + A4: 4,5,8 # B5: 2,6 => UNS * INC D9: 2,7 + A4: 4,5,8 # B5: 4,5 => UNS * INC D9: 2,7 + A4: 4,5,8 # I1: 2,6 => UNS * INC D9: 2,7 + A4: 4,5,8 # I1: 8,9 => UNS * INC D9: 2,7 + A4: 4,5,8 # F9: 5,9 => UNS * DIS D9: 2,7 + A4: 4,5,8 # F9: 8 => CTR => F9: 5,9 * INC D9: 2,7 + A4: 4,5,8 + F9: 5,9 # G7: 5,9 => UNS * INC D9: 2,7 + A4: 4,5,8 + F9: 5,9 # G7: 6 => UNS * INC D9: 2,7 + A4: 4,5,8 + F9: 5,9 # E3: 5,9 => UNS * INC D9: 2,7 + A4: 4,5,8 + F9: 5,9 # E3: 2 => UNS * DIS D9: 2,7 + A4: 4,5,8 + F9: 5,9 # C1: 2,9 => CTR => C1: 5,8 * DIS D9: 2,7 + A4: 4,5,8 + F9: 5,9 + C1: 5,8 # C3: 2,9 => CTR => C3: 5,8 * PRF D9: 2,7 + A4: 4,5,8 + F9: 5,9 + C1: 5,8 + C3: 5,8 => SOL * STA D9: 2,7 + A4: 4,5,8 + F9: 5,9 + C1: 5,8 + C3: 5,8 * CNT 44 HDP CHAINS / 43 HYP OPENED