Analysis of zz-www.sudokuwiki.org-0025-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=25
level: medium
position: 7........2...3.1.5...28.6..5...4...36.48.32.18...1...6..5.94...4.7.2...9........8 initial
Autosolve
position: 7........2...3.1.5...28.6..5...4...36.48.32.18...1...6.85.94...4.7.28..9........8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D1: 5,6 => CTR => D1: 1,4,9 * DIS # F1: 5,6 => CTR => F1: 1,9 * DIS # B1: 1,3,4,9 => CTR => B1: 5,6 * DIS # E9: 7 => CTR => E9: 5,6 * DIS # B4: 7,9 => CTR => B4: 1,2 * DIS # H5: 7,9 => CTR => H5: 5 * DIS # F6: 5,7 => CTR => F6: 2,9 * DIS # H5: 9 => CTR => H5: 5,7 * DIS # E9: 6 => CTR => E9: 5,7 * DIS # A9: 1,3 => CTR => A9: 9 * PRF # D7: 1,3 => SOL * DIS # H7: 1,3 => CTR => H7: 2,6,7 * DIS # A3: 9 => CTR => A3: 1,3 * DIS # H7: 3,7 => CTR => H7: 1,2,6 * DIS # G9: 3,7 => CTR => G9: 4,5 * PRF # H9: 3,7 => SOL * PRF # D7: 3,7 => SOL * DIS # H7: 2,7 => CTR => H7: 1,3,6 * PRF # H7: 1,3,6 => SOL * DIS # H8: 3,5 => CTR => H8: 1,6 * DIS # G9: 3,5 => CTR => G9: 4,7 * PRF # H9: 3,5 => SOL * CNT 22 HDP CHAINS / 49 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D1: 5,6 => CTR => D1: 1,4,9 * DIS D1: 1,4,9 # F1: 5,6 => CTR => F1: 1,9 * DIS D1: 1,4,9 + F1: 1,9 # B1: 1,3,4,9 => CTR => B1: 5,6 * DIS D1: 1,4,9 + F1: 1,9 + B1: 5,6 # E9: 7 => CTR => E9: 5,6 * DIS D1: 1,4,9 + F1: 1,9 + B1: 5,6 + E9: 5,6 # A9: 1,3 => CTR => A9: 9 * DIS D1: 1,4,9 + F1: 1,9 + B1: 5,6 + E9: 5,6 + A9: 9 # B9: 1,3 => CTR => B9: 2,6 * DIS D1: 1,4,9 + F1: 1,9 + B1: 5,6 + E9: 5,6 + A9: 9 + B9: 2,6 # C9: 1,3 => CTR => C9: 2,6 * PRF D1: 1,4,9 + F1: 1,9 + B1: 5,6 + E9: 5,6 + A9: 9 + B9: 2,6 + C9: 2,6 # D7: 1,3 => SOL * STA D1: 1,4,9 + F1: 1,9 + B1: 5,6 + E9: 5,6 + A9: 9 + B9: 2,6 + C9: 2,6 + D7: 1,3 * CNT 8 HDP CHAINS / 11 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 7........2...3.1.5...28.6..5...4...36.48.32.18...1...6..5.94...4.7.2...9........8 | initial |
| 7........2...3.1.5...28.6..5...4...36.48.32.18...1...6.85.94...4.7.28..9........8 | autosolve |
| 758169324269437185341285697512946873694873251873512946185394762437628519926751438 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) E1: 5,6 I1: 2,4 I3: 4,7 B5: 7,9 E5: 5,7 A7: 1,3 G7: 3,7 I7: 2,7 G8: 3,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B4,C4: 1.. / B4 = 1 => 11 pairs (_) / C4 = 1 => 10 pairs (_) H1,I1: 2.. / H1 = 2 => 0 pairs (*) / I1 = 2 => 0 pairs (X) F4,F6: 2.. / F4 = 2 => 0 pairs (X) / F6 = 2 => 12 pairs (_) B9,C9: 2.. / B9 = 2 => 9 pairs (_) / C9 = 2 => 14 pairs (_) H7,I7: 2.. / H7 = 2 => 0 pairs (X) / I7 = 2 => 0 pairs (_) H1,H7: 2.. / H1 = 2 => 0 pairs (*) / H7 = 2 => 0 pairs (X) I1,I7: 2.. / I1 = 2 => 0 pairs (X) / I7 = 2 => 0 pairs (_) B6,C6: 3.. / B6 = 3 => 11 pairs (_) / C6 = 3 => 10 pairs (_) D1,D2: 4.. / D1 = 4 => 0 pairs (X) / D2 = 4 => 12 pairs (_) I1,I3: 4.. / I1 = 4 => 0 pairs (*) / I3 = 4 => 0 pairs (X) G6,H6: 4.. / G6 = 4 => 0 pairs (X) / H6 = 4 => 9 pairs (_) G9,H9: 4.. / G9 = 4 => 9 pairs (_) / H9 = 4 => 0 pairs (X) B2,D2: 4.. / B2 = 4 => 0 pairs (X) / D2 = 4 => 12 pairs (_) B3,I3: 4.. / B3 = 4 => 0 pairs (*) / I3 = 4 => 0 pairs (X) G6,G9: 4.. / G6 = 4 => 0 pairs (X) / G9 = 4 => 9 pairs (_) H6,H9: 4.. / H6 = 4 => 9 pairs (_) / H9 = 4 => 0 pairs (X) B1,B3: 5.. / B1 = 5 => 12 pairs (_) / B3 = 5 => 0 pairs (X) B3,F3: 5.. / B3 = 5 => 0 pairs (X) / F3 = 5 => 12 pairs (_) E5,H5: 5.. / E5 = 5 => 0 pairs (X) / H5 = 5 => 13 pairs (_) D4,F4: 6.. / D4 = 6 => 0 pairs (X) / F4 = 6 => 14 pairs (_) D7,H7: 6.. / D7 = 6 => 15 pairs (_) / H7 = 6 => 0 pairs (*) E1,E9: 6.. / E1 = 6 => 10 pairs (_) / E9 = 6 => 0 pairs (X) E5,E9: 7.. / E5 = 7 => 13 pairs (_) / E9 = 7 => 0 pairs (X) I3,I7: 7.. / I3 = 7 => 0 pairs (*) / I7 = 7 => 0 pairs (X) C1,C2: 8.. / C1 = 8 => 12 pairs (_) / C2 = 8 => 10 pairs (_) G4,H4: 8.. / G4 = 8 => 11 pairs (_) / H4 = 8 => 14 pairs (_) C2,H2: 8.. / C2 = 8 => 10 pairs (_) / H2 = 8 => 12 pairs (_) G1,G4: 8.. / G1 = 8 => 14 pairs (_) / G4 = 8 => 11 pairs (_) B5,H5: 9.. / B5 = 9 => 12 pairs (_) / H5 = 9 => 0 pairs (X) A3,A9: 9.. / A3 = 9 => 0 pairs (X) / A9 = 9 => 10 pairs (_) * DURATION: 0:00:42.639851 START: 03:53:40.868454 END: 03:54:23.508305 2017-05-01 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B5,E1,E5,G7,G8,I1,I3,I7) * 7........2...3.1.5...28.6..5...4...36.48.32.18...1...6.85.94...4.7.28..9........8 * PAIR E1: 5,6 BLK 2 D1: 5,6,1,4,9 # reduction candidate for 5,6 D1: 5,6 => CTR * 74.56...22..43.1.5.5.28.6.45...46..36.48532.18...12..6.856943274.7.285.9.....54.8 D1: 1,4,9 # 9 pairs F1: 5,6,1,9 # reduction candidate for 5,6 F1: 5,6 => CTR * 7...658.226843.1.5.5.2816.45..9467836948732518735129461856943274.7.285.9..6.5.418 F1: 1,9 # 10 pairs * PAIR E1: 5,6 ROW 1 B1: 5,6,1,3,4,9 # reduction candidate for 5,6 B1: 1,3,4,9 => CTR * 7...658.226843.1.5.5.2816.45..9467836948732518735129461856943274.7.285.9..6.5.418 B1: 5,6 # 11 pairs * PAIR E1: 5,6 COL E E9: 5,6,7 # reduction candidate for 5,6 E9: 7 => CTR * 753.6.8242.8437195.4.2856375...4.983694853271832719..6.85.947.24.7.28..9.26.71..8 E9: 5,6 # 13 pairs * PAIR B5: 7,9 BLK 4 B4: 7,9,1,2 # reduction candidate for 7,9 B4: 7,9 => CTR * 75..6..24296437185143285697571642..36.48.32.18...1...6.85.94.62467.28..9........8 B4: 1,2 # 10 pairs B6: 7,9,2,3 # reduction candidate for 7,9 B6: 7,9 # 14 pairs * PAIR B5: 7,9 ROW 5 H5: 7,9,5 # reduction candidate for 7,9 H5: 7,9 => CTR * 753.6.8242.8437195.4.2856375...4.983694853271832719..6.85.947.24.7.28..9.26.71..8 H5: 5 # 13 pairs * PAIR E5: 5,7 BLK 5 D6: 5,7,9 # reduction candidate for 5,7 D6: 5,7 # 12 pairs F6: 5,7,2,9 # reduction candidate for 5,7 F6: 5,7 => CTR * 7......242..43.1.5.4.2856.75..642..36.48532.18..917..6.85.94.62467.28..9....76..8 F6: 2,9 # 10 pairs * PAIR E5: 5,7 ROW 5 H5: 5,7,9 # reduction candidate for 5,7 H5: 9 => CTR * 7...6.9242..437185.4.28.6..5...4.8736748532918...1...6.85.947.24.7.28..9....7...8 H5: 5,7 # 12 pairs * PAIR E5: 5,7 COL E E9: 5,7,6 # reduction candidate for 5,7 E9: 6 => CTR * 7...5....2...3.1.5.5.28.6.45...4...36948732518...1...6.85.94.6.4.7.28..9....6...8 E9: 5,7 # 10 pairs * PAIR A7: 1,3 BLK 7 B8: 1,3,6 # reduction candidate for 1,3 B8: 1,3 # 19 pairs A9: 1,3,9 # reduction candidate for 1,3 A9: 1,3 => CTR * 7..46...2246.3.1859..28.6745...468936948732.18...1...6.85.943274673285193.....468 A9: 9 # 10 pairs B9: 1,3,2,6,9 # reduction candidate for 1,3 B9: 1,3 # 16 pairs C9: 1,3,2,6,9 # reduction candidate for 1,3 C9: 1,3 # 14 pairs * PAIR A7: 1,3 ROW 7 D7: 1,3,6,7 # reduction candidate for 1,3 D7: 1,3 => SOLVED * 758169324269437185341285697512946873694873251873512946185394762437628519926751438 D7: 6,7 # 10 pairs H7: 1,3,2,6,7 # reduction candidate for 1,3 H7: 1,3 => CTR * 758169324269437185341285697512.468736948.32.18.3.12..6.856947.24.7.28..9.....1..8 H7: 2,6,7 # 9 pairs * PAIR A7: 1,3 COL A A3: 1,3,9 # reduction candidate for 1,3 A3: 9 => CTR * 7..46...2246.3.1859..28.6745...468936948732.18...1...6.85.943274673285193.....468 A3: 1,3 # 10 pairs * PAIR G7: 3,7 BLK 9 H7: 3,7,1,2,6 # reduction candidate for 3,7 H7: 3,7 => CTR * 75.169.242.6437185.41285697512.468736948.32.18...12..6185694..24.7.28.19.2...1.68 H7: 1,2,6 # 9 pairs G9: 3,7,4,5 # reduction candidate for 3,7 G9: 3,7 => CTR * 753.6.8242.8437195.4.2856375...4.9836948.32.1832.194.6.85.94..24.73285.9.26..1.48 G9: 4,5 # 10 pairs H9: 3,7,1,4,5,6 # reduction candidate for 3,7 H9: 3,7 => SOLVED * 758169324269437185341285697512946873694873251873512946185394762437628519926751438 H9: 1,4,5,6 # 9 pairs * PAIR G7: 3,7 ROW 7 D7: 3,7,1,6 # reduction candidate for 3,7 D7: 3,7 => SOLVED * 758169324269437185341285697512946873694873251873512946185394762437628519926751438 D7: 1,6 # 10 pairs * PAIR I7: 2,7 BLK 9 H7: 2,7,1,3,6 # reduction candidate for 2,7 H7: 2,7 => CTR * 7...6.8..26843.1.5...28.6..5.29467836948732518735129461856943..4371285.9..6.5.418 H7: 1,3,6 => SOLVED * 758169324269437185341285697512946873694873251873512946185394762437628519926751438 * PAIR G8: 3,5 BLK 9 H8: 3,5,1,6 # reduction candidate for 3,5 H8: 3,5 => CTR * 75..6..2426.4371.5.4.2856.75...4...36948.32.18...1..46.85.947.2417628..9..6..14.8 H8: 1,6 # 10 pairs G9: 3,5,4,7 # reduction candidate for 3,5 G9: 3,5 => CTR * 753.6.8242.8437195.4.2856375...4.9836948.32.1832.194.6.85.947.24.7.28..9.26..1.48 G9: 4,7 # 10 pairs H9: 3,5,1,4,6,7 # reduction candidate for 3,5 H9: 3,5 => SOLVED * 758169324269437185341285697512946873694873251873512946185394762437628519926751438 H9: 1,4,6,7 # 9 pairs * PAIR G8: 3,5 ROW 8 D8: 3,5,1,6 # reduction candidate for 3,5 D8: 3,5 # 12 pairs D8: 1,6 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0025-base-pr-000.dot * REASONING * DIS # D1: 5,6 => CTR => D1: 1,4,9 * DIS # F1: 5,6 => CTR => F1: 1,9 * DIS # B1: 1,3,4,9 => CTR => B1: 5,6 * DIS # E9: 7 => CTR => E9: 5,6 * DIS # B4: 7,9 => CTR => B4: 1,2 * DIS # H5: 7,9 => CTR => H5: 5 * DIS # F6: 5,7 => CTR => F6: 2,9 * DIS # H5: 9 => CTR => H5: 5,7 * DIS # E9: 6 => CTR => E9: 5,7 * DIS # A9: 1,3 => CTR => A9: 9 * PRF # D7: 1,3 => SOL * DIS # H7: 1,3 => CTR => H7: 2,6,7 * DIS # A3: 9 => CTR => A3: 1,3 * DIS # H7: 3,7 => CTR => H7: 1,2,6 * DIS # G9: 3,7 => CTR => G9: 4,5 * PRF # H9: 3,7 => SOL * PRF # D7: 3,7 => SOL * DIS # H7: 2,7 => CTR => H7: 1,3,6 * PRF # H7: 1,3,6 => SOL * DIS # H8: 3,5 => CTR => H8: 1,6 * DIS # G9: 3,5 => CTR => G9: 4,7 * PRF # H9: 3,5 => SOL * CNT 22 HDP CHAINS / 49 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B5,E1,E5,G7,G8,I1,I3,I7) * 7........2...3.1.5...28.6..5...4...36.48.32.18...1...6.85.94...4.7.28..9........8 * PAIR E1: 5,6 BLK 2 D1: 5,6,1,4,9 # reduction candidate for 5,6 D1: 5,6 => CTR * 74.56...22..43.1.5.5.28.6.45...46..36.48532.18...12..6.856943274.7.285.9.....54.8 F1: 5,6,1,9 # reduction candidate for 5,6 F1: 5,6 => CTR * 7...658.226843.1.5.5.2816.45..9467836948732518735129461856943274.7.285.9..6.5.418 * RESTART * PAIR E1: 5,6 ROW 1 B1: 5,6,1,3,4,9 # reduction candidate for 5,6 B1: 1,3,4,9 => CTR * 7...5....2...3.1.5.5.28.6.45...4...36.48732518...1...6.85.94..74.7.28..9....6...8 * PAIR E1: 5,6 COL E E9: 5,6,7 # reduction candidate for 5,6 E9: 7 => CTR * 753.6.8242.8437195.4.2856375...4.983694853271832719..6.85.947.24.7.28..9.26.71..8 * PAIR RESTART * PAIR A7: 1,3 BLK 7 B8: 1,3,6 # reduction candidate for 1,3 B8: 1,3 # 25 pairs A9: 1,3,9 # reduction candidate for 1,3 A9: 1,3 => CTR * 758461..2246.3.1859..285674571.42893694873251832519746.85.9432746732851932915...8 B9: 1,3,2,6 # reduction candidate for 1,3 B9: 1,3 => CTR * 758461..2246.3.185..9285674571.42893694873251823519746.85.9432746732851993215...8 C9: 1,3,2,6 # reduction candidate for 1,3 C9: 1,3 => CTR * 758461..2246.3.185..9285674571.42893694873251832519746185.9432746732851992315...8 * RESTART * PAIR A7: 1,3 ROW 7 D7: 1,3,6,7 # reduction candidate for 1,3 D7: 1,3 => SOLVED * 758169324269437185341285697512946873694873251873512946185394762437628519926751438 * DURATION: 0:00:13.177796 START: 03:55:02.213868 END: 03:55:15.391664 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0025-base-pr-001.dot * REASONING * DIS # D1: 5,6 => CTR => D1: 1,4,9 * DIS D1: 1,4,9 # F1: 5,6 => CTR => F1: 1,9 * DIS D1: 1,4,9 + F1: 1,9 # B1: 1,3,4,9 => CTR => B1: 5,6 * DIS D1: 1,4,9 + F1: 1,9 + B1: 5,6 # E9: 7 => CTR => E9: 5,6 * DIS D1: 1,4,9 + F1: 1,9 + B1: 5,6 + E9: 5,6 # A9: 1,3 => CTR => A9: 9 * DIS D1: 1,4,9 + F1: 1,9 + B1: 5,6 + E9: 5,6 + A9: 9 # B9: 1,3 => CTR => B9: 2,6 * DIS D1: 1,4,9 + F1: 1,9 + B1: 5,6 + E9: 5,6 + A9: 9 + B9: 2,6 # C9: 1,3 => CTR => C9: 2,6 * PRF D1: 1,4,9 + F1: 1,9 + B1: 5,6 + E9: 5,6 + A9: 9 + B9: 2,6 + C9: 2,6 # D7: 1,3 => SOL * STA D1: 1,4,9 + F1: 1,9 + B1: 5,6 + E9: 5,6 + A9: 9 + B9: 2,6 + C9: 2,6 + D7: 1,3 * CNT 8 HDP CHAINS / 11 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=25
Solution
position: 758169324269437185341285697512946873694873251873512946185394762437628519926751438 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 # D1: 5,6 => CTR => D1: 1,4,9 * INC # D1: 1,4,9 => UNS * DIS # F1: 5,6 => CTR => F1: 1,9 * INC # F1: 1,9 => UNS * INC # B1: 5,6 => UNS * DIS # B1: 1,3,4,9 => CTR => B1: 5,6 * INC # E9: 5,6 => UNS * DIS # E9: 7 => CTR => E9: 5,6 * DIS # B4: 7,9 => CTR => B4: 1,2 * INC # B4: 1,2 => UNS * INC # B6: 7,9 => UNS * DIS # H5: 7,9 => CTR => H5: 5 * INC # H5: 5 => UNS * INC # D6: 5,7 => UNS * DIS # F6: 5,7 => CTR => F6: 2,9 * INC # F6: 2,9 => UNS * INC # H5: 5,7 => UNS * DIS # H5: 9 => CTR => H5: 5,7 * INC # E9: 5,7 => UNS * DIS # E9: 6 => CTR => E9: 5,7 * INC # B8: 1,3 => UNS * DIS # A9: 1,3 => CTR => A9: 9 * INC # A9: 9 => UNS * INC # B9: 1,3 => UNS * INC # C9: 1,3 => UNS * PRF # D7: 1,3 => SOL * INC # D7: 6,7 => UNS * DIS # H7: 1,3 => CTR => H7: 2,6,7 * INC # H7: 2,6,7 => UNS * INC # A3: 1,3 => UNS * DIS # A3: 9 => CTR => A3: 1,3 * DIS # H7: 3,7 => CTR => H7: 1,2,6 * INC # H7: 1,2,6 => UNS * DIS # G9: 3,7 => CTR => G9: 4,5 * INC # G9: 4,5 => UNS * PRF # H9: 3,7 => SOL * INC # H9: 1,4,5,6 => UNS * PRF # D7: 3,7 => SOL * INC # D7: 1,6 => UNS * DIS # H7: 2,7 => CTR => H7: 1,3,6 * PRF # H7: 1,3,6 => SOL * DIS # H8: 3,5 => CTR => H8: 1,6 * INC # H8: 1,6 => UNS * DIS # G9: 3,5 => CTR => G9: 4,7 * INC # G9: 4,7 => UNS * PRF # H9: 3,5 => SOL * INC # H9: 1,4,6,7 => UNS * INC # D8: 3,5 => UNS * INC # D8: 1,6 => UNS * CNT 49 HDP CHAINS / 49 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D1: 5,6 => CTR => D1: 1,4,9 * DIS D1: 1,4,9 # F1: 5,6 => CTR => F1: 1,9 * INC D1: 1,4,9 + F1: 1,9 # B1: 5,6 => UNS * DIS D1: 1,4,9 + F1: 1,9 # B1: 1,3,4,9 => CTR => B1: 5,6 * INC D1: 1,4,9 + F1: 1,9 + B1: 5,6 # E9: 5,6 => UNS * DIS D1: 1,4,9 + F1: 1,9 + B1: 5,6 # E9: 7 => CTR => E9: 5,6 * INC D1: 1,4,9 + F1: 1,9 + B1: 5,6 + E9: 5,6 # B8: 1,3 => UNS * DIS D1: 1,4,9 + F1: 1,9 + B1: 5,6 + E9: 5,6 # A9: 1,3 => CTR => A9: 9 * DIS D1: 1,4,9 + F1: 1,9 + B1: 5,6 + E9: 5,6 + A9: 9 # B9: 1,3 => CTR => B9: 2,6 * DIS D1: 1,4,9 + F1: 1,9 + B1: 5,6 + E9: 5,6 + A9: 9 + B9: 2,6 # C9: 1,3 => CTR => C9: 2,6 * PRF D1: 1,4,9 + F1: 1,9 + B1: 5,6 + E9: 5,6 + A9: 9 + B9: 2,6 + C9: 2,6 # D7: 1,3 => SOL * STA D1: 1,4,9 + F1: 1,9 + B1: 5,6 + E9: 5,6 + A9: 9 + B9: 2,6 + C9: 2,6 + D7: 1,3 * CNT 11 HDP CHAINS / 11 HYP OPENED