Analysis of zz-menneske-no-06904848-base.sdk
Contents
Original Sudoku
level: medium
position: ..47............17..9..85......6.7.4.8.....2.....4.....7.2..3...15.....29....61.. initial
Autosolve
position: 1.47............177.9..85......6.7.448.....2.....4.....7.2..3..315.....2942..61.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H1: 3,6 => CTR => H1: 8,9 * DIS # I1: 3,6 => CTR => I1: 8,9 * DIS # B3: 3,6 => CTR => B3: 2 * DIS # D3: 3,6 => CTR => D3: 1,4 * DIS # C6: 1,3 => CTR => C6: 6,7 * DIS # G1: 6,9 => CTR => G1: 2,8 * DIS # G2: 6,9 => CTR => G2: 2,4 * DIS # G8: 6,9 => CTR => G8: 4,8 * DIS # F7: 4,9 => CTR => F7: 1,5 * DIS # H8: 4,9 => CTR => H8: 6,7,8 * DIS # D2: 4,9 => CTR => D2: 3,5,6 * DIS # D2: 3,5 => CTR => D2: 4,6,9 * DIS # H7: 5,9 => CTR => H7: 4 * DIS # F7: 5,9 => CTR => F7: 1,4 * DIS # I5: 5,9 => CTR => I5: 1,3,6 * DIS # I6: 5,9 => CTR => I6: 1,3,6,8 * DIS # H9: 5,8 => CTR => H9: 7 * DIS # I6: 5,8 => CTR => I6: 1,3,6,9 * CNT 18 HDP CHAINS / 67 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H1: 3,6 => CTR => H1: 8,9 * DIS H1: 8,9 # I1: 3,6 => CTR => I1: 8,9 * DIS H1: 8,9 + I1: 8,9 # H3: 4 => CTR => H3: 3,6 * PRF H1: 8,9 + I1: 8,9 + H3: 3,6 # C5: 1,3 => SOL * STA H1: 8,9 + I1: 8,9 + H3: 3,6 + C5: 1,3 * CNT 4 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..47............17..9..85......6.7.4.8.....2.....4.....7.2..3...15.....29....61.. | initial |
| 1.47............177.9..85......6.7.448.....2.....4.....7.2..3..315.....2942..61.. | autosolve |
| 164735298538629417729418536291863754483597621657142983876251349315974862942386175 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) I3: 3,6 A4: 2,5 C4: 1,3 G5: 6,9 A7: 6,8 C7: 6,8 D8: 4,9 D9: 3,5 I7: 5,9 I9: 5,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D3,E3: 1.. / D3 = 1 => 0 pairs (X) / E3 = 1 => 19 pairs (_) I5,I6: 1.. / I5 = 1 => 10 pairs (_) / I6 = 1 => 10 pairs (_) E7,F7: 1.. / E7 = 1 => 0 pairs (X) / F7 = 1 => 19 pairs (_) G1,G2: 2.. / G1 = 2 => 10 pairs (_) / G2 = 2 => 0 pairs (X) F4,F6: 2.. / F4 = 2 => 11 pairs (_) / F6 = 2 => 11 pairs (_) B3,E3: 2.. / B3 = 2 => 11 pairs (_) / E3 = 2 => 0 pairs (X) D9,E9: 3.. / D9 = 3 => 9 pairs (_) / E9 = 3 => 11 pairs (_) G2,H3: 4.. / G2 = 4 => 19 pairs (_) / H3 = 4 => 0 pairs (X) D3,H3: 4.. / D3 = 4 => 19 pairs (_) / H3 = 4 => 0 pairs (X) F7,H7: 4.. / F7 = 4 => 0 pairs (X) / H7 = 4 => 19 pairs (_) G2,G8: 4.. / G2 = 4 => 19 pairs (_) / G8 = 4 => 0 pairs (X) D2,D3: 6.. / D2 = 6 => 11 pairs (_) / D3 = 6 => 0 pairs (X) A7,C7: 6.. / A7 = 6 => 11 pairs (_) / C7 = 6 => 9 pairs (_) G8,H8: 6.. / G8 = 6 => 0 pairs (X) / H8 = 6 => 11 pairs (_) C5,C6: 7.. / C5 = 7 => 0 pairs (X) / C6 = 7 => 10 pairs (_) H8,H9: 7.. / H8 = 7 => 0 pairs (X) / H9 = 7 => 10 pairs (_) C6,F6: 7.. / C6 = 7 => 10 pairs (_) / F6 = 7 => 0 pairs (X) E9,H9: 7.. / E9 = 7 => 0 pairs (X) / H9 = 7 => 10 pairs (_) A2,C2: 8.. / A2 = 8 => 11 pairs (_) / C2 = 8 => 9 pairs (_) D4,D6: 8.. / D4 = 8 => 10 pairs (_) / D6 = 8 => 19 pairs (_) A7,C7: 8.. / A7 = 8 => 9 pairs (_) / C7 = 8 => 11 pairs (_) E8,E9: 8.. / E8 = 8 => 10 pairs (_) / E9 = 8 => 19 pairs (_) D4,H4: 8.. / D4 = 8 => 10 pairs (_) / H4 = 8 => 19 pairs (_) A2,A7: 8.. / A2 = 8 => 11 pairs (_) / A7 = 8 => 9 pairs (_) C2,C7: 8.. / C2 = 8 => 9 pairs (_) / C7 = 8 => 11 pairs (_) B4,B6: 9.. / B4 = 9 => 10 pairs (_) / B6 = 9 => 12 pairs (_) * DURATION: 0:00:36.830153 START: 06:41:46.862338 END: 06:42:23.692491 2017-05-01 * CP COUNT: (26) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,C4,C7,D8,D9,G5,I3,I7,I9) * 1.47............177.9..85......6.7.448.....2.....4.....7.2..3..315.....2942..61.. * PAIR I3: 3,6 BLK 3 H1: 3,6,8,9 # reduction candidate for 3,6 H1: 3,6 => CTR * 1647..839.......177.9..854.....6.7.448.....2.....4.....7.2.43..3159.7462942..6178 H1: 8,9 # 11 pairs I1: 3,6,8,9 # reduction candidate for 3,6 I1: 3,6 => CTR * 1.47........4...177.9618543....6.7.448..7..2...7.4.....7.25439.3159.7462942..6178 I1: 8,9 # 13 pairs H3: 3,6,4 # reduction candidate for 3,6 H3: 3,6 # 19 pairs * PAIR I3: 3,6 ROW 3 B3: 3,6,2 # reduction candidate for 3,6 B3: 3,6 => CTR * 1.47............177.912854.....6.7.448.....2.....4.....7.2.43..3159....2942..61.. B3: 2 # 11 pairs D3: 3,6,1,4 # reduction candidate for 3,6 D3: 3,6 => CTR * 1.47............177.9.1854.....6.7.448.....2.....4.....7.2..3..315.....2942..61.. D3: 1,4 # 12 pairs * PAIR I3: 3,6 COL I I5: 3,6,1,5,9 # reduction candidate for 3,6 I5: 3,6 # 14 pairs I6: 3,6,1,5,8,9 # reduction candidate for 3,6 I6: 3,6 # 14 pairs * PAIR A4: 2,5 BLK 4 B4: 2,5,3,9 # reduction candidate for 2,5 B4: 2,5 # 13 pairs A6: 2,5,6 # reduction candidate for 2,5 A6: 2,5 # 13 pairs B6: 2,5,3,6,9 # reduction candidate for 2,5 B6: 2,5 # 11 pairs * PAIR A4: 2,5 ROW 4 F4: 2,5,1,3,9 # reduction candidate for 2,5 F4: 2,5 # 12 pairs F4: 1,3,9 # 11 pairs * PAIR A4: 2,5 COL A A2: 2,5,6,8 # reduction candidate for 2,5 A2: 6,8 # 13 pairs A2: 2,5 # 10 pairs * PAIR C4: 1,3 BLK 4 C5: 1,3,6,7 # reduction candidate for 1,3 C5: 1,3 # 13 pairs C6: 1,3,6,7 # reduction candidate for 1,3 C6: 1,3 => CTR * 1.47..298...6294177294185..59..627.4487....2.....47....7.2513493159.4..29423.61.. C6: 6,7 # 11 pairs * PAIR C4: 1,3 ROW 4 D4: 1,3,5,8,9 # reduction candidate for 1,3 D4: 1,3 # 20 pairs F4: 1,3,2,5,9 # reduction candidate for 1,3 F4: 1,3 # 12 pairs * PAIR G5: 6,9 BLK 6 I5: 6,9,1,3,5 # reduction candidate for 6,9 I5: 6,9 # 17 pairs G6: 6,9,8 # reduction candidate for 6,9 G6: 6,9 # 17 pairs H6: 6,9,3,5,8 # reduction candidate for 6,9 H6: 6,9 # 14 pairs I6: 6,9,1,3,5,8 # reduction candidate for 6,9 I6: 6,9 # 16 pairs * PAIR G5: 6,9 COL G G1: 6,9,2,8 # reduction candidate for 6,9 G1: 6,9 => CTR * 1.47...8....4..2177.9618543...86.7.448..7..2...7.4.8...7.25439.3159.7462942..6178 G1: 2,8 # 11 pairs G2: 6,9,2,4 # reduction candidate for 6,9 G2: 6,9 => CTR * 1.47..28....4...177.9618543...86.7.448..7..2...7.4.8...7.25439.3159.7462942..6178 G2: 2,4 # 12 pairs G8: 6,9,4,8 # reduction candidate for 6,9 G8: 6,9 => CTR * 1.47..2.....6294177294185......6.7.448..9..2.....4.....7.2.134.3159.46.2942..61.. G8: 4,8 # 13 pairs * PAIR A7: 6,8 COL A A2: 6,8,2,5 # reduction candidate for 6,8 A2: 6,8 # 13 pairs A2: 2,5 # 10 pairs * PAIR C7: 6,8 COL C C2: 6,8,3 # reduction candidate for 6,8 C2: 3 # 13 pairs C2: 6,8 # 12 pairs * PAIR D8: 4,9 BLK 8 F7: 4,9,1,5 # reduction candidate for 4,9 F7: 4,9 => CTR * 1.47............177.91.854.....6.7.448.....2.....4.....7.2143..3159....2942..61.. F7: 1,5 # 19 pairs F8: 4,9,7 # reduction candidate for 4,9 F8: 4,9 # 19 pairs * PAIR D8: 4,9 ROW 8 G8: 4,9,6,8 # reduction candidate for 4,9 G8: 4,9 # 13 pairs H8: 4,9,6,7,8 # reduction candidate for 4,9 H8: 4,9 => CTR * 1.47...........4177.94185......6.7.448....92.....4.8...7.2.13453159..6.2942..6178 H8: 6,7,8 # 10 pairs * PAIR D8: 4,9 COL D D2: 4,9,3,5,6 # reduction candidate for 4,9 D2: 4,9 => CTR * 1.47............177.9618543....6.7.448.....2.....4.....7.2..3..315.....2942..61.. D2: 3,5,6 # 10 pairs * PAIR D9: 3,5 BLK 8 E9: 3,5,7,8 # reduction candidate for 3,5 E9: 7,8 # 19 pairs E9: 3,5 # 11 pairs * PAIR D9: 3,5 COL D D2: 3,5,4,6,9 # reduction candidate for 3,5 D2: 3,5 => CTR * 1.47............177.9618543....6.7.448.....2.....4.....7.2..3..315.....2942..61.. D2: 4,6,9 # 10 pairs D4: 3,5,1,8,9 # reduction candidate for 3,5 D4: 3,5 # 21 pairs D5: 3,5,1,9 # reduction candidate for 3,5 D5: 3,5 # 11 pairs D6: 3,5,1,8,9 # reduction candidate for 3,5 D6: 3,5 # 12 pairs * PAIR I7: 5,9 BLK 9 H7: 5,9,4 # reduction candidate for 5,9 H7: 5,9 => CTR * 1.47............177.91.854.....6.7.448..7..2...7.4.....7.2143..315987462942..6178 H7: 4 # 19 pairs * PAIR I7: 5,9 ROW 7 E7: 5,9,1 # reduction candidate for 5,9 E7: 5,9 # 19 pairs F7: 5,9,1,4 # reduction candidate for 5,9 F7: 5,9 => CTR * 1.47............177.9..85......6.7.448.....2.....4.....7.21.34.315.....2942..61.. F7: 1,4 # 11 pairs * PAIR I7: 5,9 COL I I5: 5,9,1,3,6 # reduction candidate for 5,9 I5: 5,9 => CTR * 1.47........4...177.9618543....6.7.448..7..2...7.4...1.7.25439.3159.7462942..6178 I5: 1,3,6 # 10 pairs I6: 5,9,1,3,6,8 # reduction candidate for 5,9 I6: 5,9 => CTR * 1.47........4...177.9618543....6.7.448..7..21..7.4.....7.25439.3159.7462942..6178 I6: 1,3,6,8 # 10 pairs * PAIR I9: 5,8 BLK 9 H9: 5,8,7 # reduction candidate for 5,8 H9: 5,8 => CTR * 1.47..298...6..4177.94185......6.7.448....92.....4.8...7.2.13493159846729423761.. H9: 7 # 10 pairs * PAIR I9: 5,8 ROW 9 E9: 5,8,3,7 # reduction candidate for 5,8 E9: 3,7 # 11 pairs E9: 5,8 # 10 pairs * PAIR I9: 5,8 COL I I6: 5,8,1,3,6,9 # reduction candidate for 5,8 I6: 5,8 => CTR * 1.47........4...177.9618543....6.7.448..7..21..7.4...5.7.25439.3159.7462942..6178 I6: 1,3,6,9 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-menneske-no-06904848-base-pr-000.dot * REASONING * DIS # H1: 3,6 => CTR => H1: 8,9 * DIS # I1: 3,6 => CTR => I1: 8,9 * DIS # B3: 3,6 => CTR => B3: 2 * DIS # D3: 3,6 => CTR => D3: 1,4 * DIS # C6: 1,3 => CTR => C6: 6,7 * DIS # G1: 6,9 => CTR => G1: 2,8 * DIS # G2: 6,9 => CTR => G2: 2,4 * DIS # G8: 6,9 => CTR => G8: 4,8 * DIS # F7: 4,9 => CTR => F7: 1,5 * DIS # H8: 4,9 => CTR => H8: 6,7,8 * DIS # D2: 4,9 => CTR => D2: 3,5,6 * DIS # D2: 3,5 => CTR => D2: 4,6,9 * DIS # H7: 5,9 => CTR => H7: 4 * DIS # F7: 5,9 => CTR => F7: 1,4 * DIS # I5: 5,9 => CTR => I5: 1,3,6 * DIS # I6: 5,9 => CTR => I6: 1,3,6,8 * DIS # H9: 5,8 => CTR => H9: 7 * DIS # I6: 5,8 => CTR => I6: 1,3,6,9 * CNT 18 HDP CHAINS / 67 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,C4,C7,D8,D9,G5,I3,I7,I9) * 1.47............177.9..85......6.7.448.....2.....4.....7.2..3..315.....2942..61.. * PAIR I3: 3,6 BLK 3 H1: 3,6,8,9 # reduction candidate for 3,6 H1: 3,6 => CTR * 1647..839.......177.9..854.....6.7.448.....2.....4.....7.2.43..3159.7462942..6178 I1: 3,6,8,9 # reduction candidate for 3,6 I1: 3,6 => CTR * 1.47........4...177.9618543....6.7.448..7..2...7.4.....7.25439.3159.7462942..6178 H3: 3,6,4 # reduction candidate for 3,6 H3: 3,6 # 19 pairs * RESTART * PAIR I3: 3,6 BLK 3 H3: 3,6,4 # reduction candidate for 3,6 H3: 4 => CTR * 1.47...89...4...177.9618543....6.7.448.....2.....4.....7.2.43953159.7462942..6178 * PAIR C4: 1,3 BLK 4 C5: 1,3,7 # reduction candidate for 1,3 C5: 1,3 => SOLVED * 164735298538629417729418536291863754483597621657142983876251349315974862942386175 * DURATION: 0:00:08.278267 START: 06:43:11.753784 END: 06:43:20.032051 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-menneske-no-06904848-base-pr-001.dot * REASONING * DIS # H1: 3,6 => CTR => H1: 8,9 * DIS H1: 8,9 # I1: 3,6 => CTR => I1: 8,9 * DIS H1: 8,9 + I1: 8,9 # H3: 4 => CTR => H3: 3,6 * PRF H1: 8,9 + I1: 8,9 + H3: 3,6 # C5: 1,3 => SOL * STA H1: 8,9 + I1: 8,9 + H3: 3,6 + C5: 1,3 * CNT 4 HDP CHAINS / 6 HYP OPENED
Header Info
http://www.menneske.no/sudoku/utskrift.html?number=6904848 umulig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1 * 1.47............177.9..85......6.7.448.....2.....4.....7.2..3..315.....2942..61.. I3: 3,6 # * reduce to pair H1: 3,6,8,9 # reduction candidate for 3,6 H1: 3,6 => CTR * 1647..839.......177.9..854.....6.7.448.....2.....4.....7.2.43..3159.7462942..6178 I1: 3,6,8,9 # reduction candidate for 3,6 I1: 3,6 => CTR * 1.47........4...177.9618543....6.7.448..7..2...7.4.....7.25439.3159.7462942..6178 H3: 3,6,4 # reduction candidate for 3,6 H3: 3,6 # 19 pairs * RESTART H3: 3,6,4 # reduction candidate for 3,6 H3: 4 => CTR * 1.47...89...4...177.9618543....6.7.448.....2.....4.....7.2.43953159.7462942..6178 A4: 2,5 # * reduce to pair C4: 1,3 # * reduce to pair C5: 1,3,7 # reduction candidate for 1,3 C5: 1,3 => SOLVED * 164735298538629417729418536291863754483597621657142983876251349315974862942386175 * SOLVED! +-------+-------+-------+ | 1 6 4 | 7 3 5 | 2 9 8 | | 5 3 8 | 6 2 9 | 4 1 7 | | 7 2 9 | 4 1 8 | 5 3 6 | +-------+-------+-------+ | 2 9 1 | 8 6 3 | 7 5 4 | | 4 8 3 | 5 9 7 | 6 2 1 | | 6 5 7 | 1 4 2 | 9 8 3 | +-------+-------+-------+ | 8 7 6 | 2 5 1 | 3 4 9 | | 3 1 5 | 9 7 4 | 8 6 2 | | 9 4 2 | 3 8 6 | 1 7 5 | +-------+-------+-------+
Solution
position: 164735298538629417729418536291863754483597621657142983876251349315974862942386175 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 # H1: 3,6 => CTR => H1: 8,9 * INC # H1: 8,9 => UNS * DIS # I1: 3,6 => CTR => I1: 8,9 * INC # I1: 8,9 => UNS * INC # H3: 3,6 => UNS * DIS # B3: 3,6 => CTR => B3: 2 * INC # B3: 2 => UNS * DIS # D3: 3,6 => CTR => D3: 1,4 * INC # D3: 1,4 => UNS * INC # I5: 3,6 => UNS * INC # I6: 3,6 => UNS * INC # B4: 2,5 => UNS * INC # A6: 2,5 => UNS * INC # B6: 2,5 => UNS * INC # F4: 2,5 => UNS * INC # F4: 1,3,9 => UNS * INC # A2: 2,5 => UNS * INC # A2: 6,8 => UNS * INC # C5: 1,3 => UNS * DIS # C6: 1,3 => CTR => C6: 6,7 * INC # C6: 6,7 => UNS * INC # D4: 1,3 => UNS * INC # F4: 1,3 => UNS * INC # I5: 6,9 => UNS * INC # G6: 6,9 => UNS * INC # H6: 6,9 => UNS * INC # I6: 6,9 => UNS * DIS # G1: 6,9 => CTR => G1: 2,8 * INC # G1: 2,8 => UNS * DIS # G2: 6,9 => CTR => G2: 2,4 * INC # G2: 2,4 => UNS * DIS # G8: 6,9 => CTR => G8: 4,8 * INC # G8: 4,8 => UNS * INC # A2: 6,8 => UNS * INC # A2: 2,5 => UNS * INC # C2: 6,8 => UNS * INC # C2: 3 => UNS * DIS # F7: 4,9 => CTR => F7: 1,5 * INC # F7: 1,5 => UNS * INC # F8: 4,9 => UNS * INC # G8: 4,9 => UNS * DIS # H8: 4,9 => CTR => H8: 6,7,8 * INC # H8: 6,7,8 => UNS * DIS # D2: 4,9 => CTR => D2: 3,5,6 * INC # D2: 3,5,6 => UNS * INC # E9: 3,5 => UNS * INC # E9: 7,8 => UNS * DIS # D2: 3,5 => CTR => D2: 4,6,9 * INC # D2: 4,6,9 => UNS * INC # D4: 3,5 => UNS * INC # D5: 3,5 => UNS * INC # D6: 3,5 => UNS * DIS # H7: 5,9 => CTR => H7: 4 * INC # H7: 4 => UNS * INC # E7: 5,9 => UNS * DIS # F7: 5,9 => CTR => F7: 1,4 * INC # F7: 1,4 => UNS * DIS # I5: 5,9 => CTR => I5: 1,3,6 * INC # I5: 1,3,6 => UNS * DIS # I6: 5,9 => CTR => I6: 1,3,6,8 * INC # I6: 1,3,6,8 => UNS * DIS # H9: 5,8 => CTR => H9: 7 * INC # H9: 7 => UNS * INC # E9: 5,8 => UNS * INC # E9: 3,7 => UNS * DIS # I6: 5,8 => CTR => I6: 1,3,6,9 * INC # I6: 1,3,6,9 => UNS * CNT 67 HDP CHAINS / 67 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # H1: 3,6 => CTR => H1: 8,9 * DIS H1: 8,9 # I1: 3,6 => CTR => I1: 8,9 * INC H1: 8,9 + I1: 8,9 # H3: 3,6 => UNS * INC H1: 8,9 + I1: 8,9 # H3: 3,6 => UNS * DIS H1: 8,9 + I1: 8,9 # H3: 4 => CTR => H3: 3,6 * PRF H1: 8,9 + I1: 8,9 + H3: 3,6 # C5: 1,3 => SOL * STA H1: 8,9 + I1: 8,9 + H3: 3,6 + C5: 1,3 * CNT 6 HDP CHAINS / 6 HYP OPENED