Analysis of zz-www.sudokuwiki.org-0032-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=32
level: medium
position: 2.......3..87.4....3....4..5..1...9..1..9..3..8...6..5.93....1....6.1...8.......2 initial
Autosolve
position: 2...1...3..8734....3..6.4..5..1.3.9..1..9..3.389..61.5.93....1....6.13.98.13.9..2 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F3: 5,8 => CTR => F3: 2 * DIS # G1: 5,8 => CTR => G1: 6,7,9 * DIS # H1: 5,8 => CTR => H1: 6,7 * DIS # F5: 2,7 => CTR => F5: 5,8 * PRF # A7: 4,7 => SOL * PRF # A5: 6 => SOL * CNT 6 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 # F3: 5,8 => CTR => F3: 2 * DIS F3: 2 # G1: 5,8 => CTR => G1: 6,7,9 * DIS F3: 2 + G1: 6,7,9 # H1: 5,8 => CTR => H1: 6,7 * DIS F3: 2 + G1: 6,7,9 + H1: 6,7 # F5: 7 => CTR => F5: 5,8 * DIS F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 # D1: 9 => CTR => D1: 5,8 * DIS F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 # E6: 2,4 => CTR => E6: 7 * DIS F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 # B8: 4,7 => CTR => B8: 2,5 * DIS F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 + B8: 2,5 # C8: 4,7 => CTR => C8: 2,5 * PRF F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 + B8: 2,5 + C8: 2,5 # B9: 6 => SOL * STA F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 + B8: 2,5 + C8: 2,5 + B9: 6 * CNT 9 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2.......3..87.4....3....4..5..1...9..1..9..3..8...6..5.93....1....6.1...8.......2 | initial |
| 2...1...3..8734....3..6.4..5..1.3.9..1..9..3.389..61.5.93....1....6.13.98.13.9..2 | autosolve |
| 246518973958734261137962458572183694614295837389476125493827516725641389861359742 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) A2: 1,9 B2: 5,6 A3: 1,9 C3: 5,7 F1: 5,8 I2: 1,6 D6: 2,4 A8: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,A3: 1.. / A2 = 1 => 15 pairs (_) / A3 = 1 => 9 pairs (_) I2,I3: 1.. / I2 = 1 => 9 pairs (_) / I3 = 1 => 15 pairs (_) A2,I2: 1.. / A2 = 1 => 15 pairs (_) / I2 = 1 => 9 pairs (_) A3,I3: 1.. / A3 = 1 => 9 pairs (_) / I3 = 1 => 15 pairs (_) D3,F3: 2.. / D3 = 2 => 0 pairs (X) / F3 = 2 => 9 pairs (_) G2,H2: 2.. / G2 = 2 => 15 pairs (_) / H2 = 2 => 9 pairs (_) B8,C8: 2.. / B8 = 2 => 8 pairs (_) / C8 = 2 => 13 pairs (_) B4,B8: 2.. / B4 = 2 => 13 pairs (_) / B8 = 2 => 8 pairs (_) H2,H6: 2.. / H2 = 2 => 9 pairs (_) / H6 = 2 => 15 pairs (_) B1,C1: 4.. / B1 = 4 => 8 pairs (_) / C1 = 4 => 9 pairs (_) D5,F5: 5.. / D5 = 5 => 9 pairs (_) / F5 = 5 => 11 pairs (_) E7,G7: 5.. / E7 = 5 => 0 pairs (X) / G7 = 5 => 9 pairs (_) A7,B9: 6.. / A7 = 6 => 9 pairs (_) / B9 = 6 => 0 pairs (*) A5,A7: 6.. / A5 = 6 => 0 pairs (*) / A7 = 6 => 0 pairs (X) E6,H6: 7.. / E6 = 7 => 11 pairs (_) / H6 = 7 => 12 pairs (_) F5,F7: 7.. / F5 = 7 => 0 pairs (X) / F7 = 7 => 10 pairs (_) E8,H8: 8.. / E8 = 8 => 14 pairs (_) / H8 = 8 => 22 pairs (_) A2,A3: 9.. / A2 = 9 => 9 pairs (_) / A3 = 9 => 15 pairs (_) D1,D3: 9.. / D1 = 9 => 15 pairs (_) / D3 = 9 => 9 pairs (_) G1,G2: 9.. / G1 = 9 => 9 pairs (_) / G2 = 9 => 15 pairs (_) D1,G1: 9.. / D1 = 9 => 15 pairs (_) / G1 = 9 => 9 pairs (_) A2,G2: 9.. / A2 = 9 => 9 pairs (_) / G2 = 9 => 15 pairs (_) A3,D3: 9.. / A3 = 9 => 15 pairs (_) / D3 = 9 => 9 pairs (_) * DURATION: 0:00:34.473140 START: 04:01:14.937755 END: 04:01:49.410895 2017-05-01 * CP COUNT: (23) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A8,B2,C3,D6,F1,I2) * 2...1...3..8734....3..6.4..5..1.3.9..1..9..3.389..61.5.93....1....6.13.98.13.9..2 * PAIR B2: 5,6 BLK 1 B1: 5,6,4,7 # reduction candidate for 5,6 B1: 5,6 # 15 pairs C1: 5,6,4,7 # reduction candidate for 5,6 C1: 5,6 # 10 pairs * PAIR B2: 5,6 ROW 2 G2: 5,6,2,9 # reduction candidate for 5,6 G2: 5,6 # 11 pairs H2: 5,6,2 # reduction candidate for 5,6 H2: 5,6 # 15 pairs * PAIR B2: 5,6 COL B B9: 5,6,4,7 # reduction candidate for 5,6 B9: 4,7 # 12 pairs B9: 5,6 # 10 pairs * PAIR C3: 5,7 BLK 1 B1: 5,7,4,6 # reduction candidate for 5,7 B1: 5,7 # 13 pairs C1: 5,7,4,6 # reduction candidate for 5,7 C1: 5,7 # 13 pairs * PAIR C3: 5,7 ROW 3 H3: 5,7,8 # reduction candidate for 5,7 H3: 8 # 15 pairs H3: 5,7 # 11 pairs * PAIR C3: 5,7 COL C C8: 5,7,2,4 # reduction candidate for 5,7 C8: 2,4 # 13 pairs C8: 5,7 # 10 pairs * PAIR F1: 5,8 BLK 2 D1: 5,8,9 # reduction candidate for 5,8 D1: 5,8 # 9 pairs D3: 5,8,2,9 # reduction candidate for 5,8 D3: 5,8 # 17 pairs F3: 5,8,2 # reduction candidate for 5,8 F3: 5,8 => CTR * 2..91...3..873492.93.26.4.15..183.9..1.59..38389426175.938.2.17...6.13898.13.9.42 F3: 2 # 9 pairs * PAIR F1: 5,8 ROW 1 G1: 5,8,6,7,9 # reduction candidate for 5,8 G1: 5,8 => CTR * 2..91..73158734926937.6.4515..1.3.9..1.59..3.389.761456934.7.18..56.13.98.13.9.62 G1: 6,7,9 # 8 pairs H1: 5,8,6,7 # reduction candidate for 5,8 H1: 5,8 => CTR * 2..91.7.3158734926937.6.4.15..1.3.98.1..9..3.38942617569325.81..256813.98.13.9562 H1: 6,7 # 9 pairs * PAIR F1: 5,8 COL F F5: 5,8,2,7 # reduction candidate for 5,8 F5: 2,7 => CTR * 2...1...3..8734..113.9624.85..183.9..1.59783.389..6175.93..8.177..6.13898.1379.42 F5: 5,8 # 11 pairs * PAIR D6: 2,4 BLK 5 E4: 2,4,7,8 # reduction candidate for 2,4 E4: 2,4 # 15 pairs D5: 2,4,5,8 # reduction candidate for 2,4 D5: 2,4 # 15 pairs E6: 2,4,7 # reduction candidate for 2,4 E6: 2,4 # 12 pairs * PAIR D6: 2,4 ROW 6 H6: 2,4,7 # reduction candidate for 2,4 H6: 7 # 12 pairs H6: 2,4 # 11 pairs * PAIR D6: 2,4 COL D D7: 2,4,8 # reduction candidate for 2,4 D7: 8 # 23 pairs D7: 2,4 # 11 pairs * PAIR A8: 4,7 BLK 7 A7: 4,7,6 # reduction candidate for 4,7 A7: 4,7 => SOLVED * 246518973958734261137962458572183694614295837389476125493827516725641389861359742 A7: 6 # 9 pairs B8: 4,7,2,5 # reduction candidate for 4,7 B8: 4,7 # 18 pairs C8: 4,7,2,5 # reduction candidate for 4,7 C8: 4,7 # 20 pairs B9: 4,7,5,6 # reduction candidate for 4,7 B9: 4,7 # 12 pairs * PAIR A8: 4,7 ROW 8 E8: 4,7,5,8 # reduction candidate for 4,7 E8: 4,7 # 23 pairs H8: 4,7,5,8 # reduction candidate for 4,7 H8: 4,7 # 17 pairs * PAIR A8: 4,7 COL A A5: 4,7,6 # reduction candidate for 4,7 A5: 6 => SOLVED * 246518973958734261137962458572183694614295837389476125493827516725641389861359742 A5: 4,7 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0032-base-pr-000.dot * REASONING * DIS # F3: 5,8 => CTR => F3: 2 * DIS # G1: 5,8 => CTR => G1: 6,7,9 * DIS # H1: 5,8 => CTR => H1: 6,7 * DIS # F5: 2,7 => CTR => F5: 5,8 * PRF # A7: 4,7 => SOL * PRF # A5: 6 => SOL * CNT 6 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A8,B2,C3,D6,F1,I2) * 2...1...3..8734....3..6.4..5..1.3.9..1..9..3.389..61.5.93....1....6.13.98.13.9..2 * PAIR B2: 5,6 BLK 1 B1: 5,6,4,7 # reduction candidate for 5,6 B1: 5,6 # 15 pairs C1: 5,6,4,7 # reduction candidate for 5,6 C1: 5,6 # 10 pairs * PAIR B2: 5,6 ROW 2 G2: 5,6,2,9 # reduction candidate for 5,6 G2: 5,6 # 11 pairs H2: 5,6,2 # reduction candidate for 5,6 H2: 5,6 # 15 pairs * PAIR B2: 5,6 COL B B9: 5,6,4,7 # reduction candidate for 5,6 B9: 4,7 # 12 pairs B9: 5,6 # 10 pairs * PAIR C3: 5,7 BLK 1 B1: 5,7,4,6 # reduction candidate for 5,7 B1: 5,7 # 13 pairs C1: 5,7,4,6 # reduction candidate for 5,7 C1: 5,7 # 13 pairs * PAIR C3: 5,7 ROW 3 H3: 5,7,8 # reduction candidate for 5,7 H3: 8 # 15 pairs H3: 5,7 # 11 pairs * PAIR C3: 5,7 COL C C8: 5,7,2,4 # reduction candidate for 5,7 C8: 2,4 # 13 pairs C8: 5,7 # 10 pairs * PAIR F1: 5,8 BLK 2 D1: 5,8,9 # reduction candidate for 5,8 D1: 5,8 # 9 pairs D3: 5,8,2,9 # reduction candidate for 5,8 D3: 5,8 # 17 pairs F3: 5,8,2 # reduction candidate for 5,8 F3: 5,8 => CTR * 2..91...3..873492.93.26.4.15..183.9..1.59..38389426175.938.2.17...6.13898.13.9.42 * PAIR F1: 5,8 ROW 1 G1: 5,8,6,7,9 # reduction candidate for 5,8 G1: 5,8 => CTR * 2..91..73158734926937.624515..1.3.9..1.59..3.389.76145693427518..56.13.98.13.9.62 H1: 5,8,6,7 # reduction candidate for 5,8 H1: 5,8 => CTR * 2..91.7.3158734926937.624.15..1.3.98.1..9..3.389..61.5693257814425681379871349562 * RESTART * PAIR F1: 5,8 COL F F5: 5,8,7 # reduction candidate for 5,8 F5: 7 => CTR * 2..815963..8734....3.9624..5..1.3.9..1.597.3.389..6175.93..8.1....6.13898.13.9.42 * PAIR RESTART * PAIR F1: 5,8 BLK 2 D1: 5,8,9 # reduction candidate for 5,8 D1: 9 => CTR * 2..918..3..873492.93.5624.15..1.3.9..1..95.3.389..61.5.93..7.1....6.13.98.13.9..2 * PAIR D6: 2,4 BLK 5 E4: 2,4,7,8 # reduction candidate for 2,4 E4: 2,4 # 15 pairs D5: 2,4,5,8 # reduction candidate for 2,4 D5: 2,4 # 15 pairs E6: 2,4,7 # reduction candidate for 2,4 E6: 2,4 => CTR * 2...1.963968734.211359624875..173.9..1..9..3.389..6175693..7.1....6813.98.13.97.2 * PAIR D6: 2,4 COL D D7: 2,4,8 # reduction candidate for 2,4 D7: 8 # 15 pairs D7: 2,4 # 15 pairs * PAIR RESTART * PAIR D6: 2,4 BLK 5 E4: 2,4,8 # reduction candidate for 2,4 E4: 2,4 # 15 pairs D5: 2,4,5,8 # reduction candidate for 2,4 D5: 2,4 # 15 pairs * PAIR D6: 2,4 COL D D7: 2,4,8 # reduction candidate for 2,4 D7: 8 # 15 pairs D7: 2,4 # 15 pairs * PAIR A8: 4,7 BLK 7 B8: 4,7,2,5 # reduction candidate for 4,7 B8: 4,7 => CTR * 2...1.9.396873425113.9624..52.1.3.9..1..9..3.389.761.5.93.2751...2651389851349..2 C8: 4,7,2,5 # reduction candidate for 4,7 C8: 4,7 => CTR * 2...1.963968734.211359624875..1.3.9..1.495.3.389276145693827514.2.6.13.9851349672 B9: 4,7,6 # reduction candidate for 4,7 B9: 4,7 # 18 pairs * RESTART * PAIR A8: 4,7 BLK 7 B9: 4,7,6 # reduction candidate for 4,7 B9: 6 => SOLVED * 246518973958734261137962458572183694614295837389476125493827516725641389861359742 * DURATION: 0:00:32.702588 START: 04:02:20.737642 END: 04:02:53.440230 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0032-base-pr-001.dot * REASONING * DIS # F3: 5,8 => CTR => F3: 2 * DIS F3: 2 # G1: 5,8 => CTR => G1: 6,7,9 * DIS F3: 2 + G1: 6,7,9 # H1: 5,8 => CTR => H1: 6,7 * DIS F3: 2 + G1: 6,7,9 + H1: 6,7 # F5: 7 => CTR => F5: 5,8 * DIS F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 # D1: 9 => CTR => D1: 5,8 * DIS F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 # E6: 2,4 => CTR => E6: 7 * DIS F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 # B8: 4,7 => CTR => B8: 2,5 * DIS F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 + B8: 2,5 # C8: 4,7 => CTR => C8: 2,5 * PRF F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 + B8: 2,5 + C8: 2,5 # B9: 6 => SOL * STA F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 + B8: 2,5 + C8: 2,5 + B9: 6 * CNT 9 HDP CHAINS / 35 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=32
Solution
position: 246518973958734261137962458572183694614295837389476125493827516725641389861359742 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 # B1: 5,6 => UNS * INC # C1: 5,6 => UNS * INC # G2: 5,6 => UNS * INC # H2: 5,6 => UNS * INC # B9: 5,6 => UNS * INC # B9: 4,7 => UNS * INC # B1: 5,7 => UNS * INC # C1: 5,7 => UNS * INC # H3: 5,7 => UNS * INC # H3: 8 => UNS * INC # C8: 5,7 => UNS * INC # C8: 2,4 => UNS * INC # D1: 5,8 => UNS * INC # D3: 5,8 => UNS * DIS # F3: 5,8 => CTR => F3: 2 * INC # F3: 2 => UNS * DIS # G1: 5,8 => CTR => G1: 6,7,9 * INC # G1: 6,7,9 => UNS * DIS # H1: 5,8 => CTR => H1: 6,7 * INC # H1: 6,7 => UNS * INC # F5: 5,8 => UNS * DIS # F5: 2,7 => CTR => F5: 5,8 * INC # E4: 2,4 => UNS * INC # D5: 2,4 => UNS * INC # E6: 2,4 => UNS * INC # H6: 2,4 => UNS * INC # H6: 7 => UNS * INC # D7: 2,4 => UNS * INC # D7: 8 => UNS * PRF # A7: 4,7 => SOL * INC # A7: 6 => UNS * INC # B8: 4,7 => UNS * INC # C8: 4,7 => UNS * INC # B9: 4,7 => UNS * INC # E8: 4,7 => UNS * INC # H8: 4,7 => UNS * INC # A5: 4,7 => UNS * PRF # A5: 6 => SOL * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 5,6 => UNS * INC # C1: 5,6 => UNS * INC # G2: 5,6 => UNS * INC # H2: 5,6 => UNS * INC # B9: 5,6 => UNS * INC # B9: 4,7 => UNS * INC # B1: 5,7 => UNS * INC # C1: 5,7 => UNS * INC # H3: 5,7 => UNS * INC # H3: 8 => UNS * INC # C8: 5,7 => UNS * INC # C8: 2,4 => UNS * INC # D1: 5,8 => UNS * INC # D3: 5,8 => UNS * DIS # F3: 5,8 => CTR => F3: 2 * DIS F3: 2 # G1: 5,8 => CTR => G1: 6,7,9 * DIS F3: 2 + G1: 6,7,9 # H1: 5,8 => CTR => H1: 6,7 * INC F3: 2 + G1: 6,7,9 + H1: 6,7 # F5: 5,8 => UNS * DIS F3: 2 + G1: 6,7,9 + H1: 6,7 # F5: 7 => CTR => F5: 5,8 * INC F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 # D1: 5,8 => UNS * DIS F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 # D1: 9 => CTR => D1: 5,8 * INC F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 # E4: 2,4 => UNS * INC F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 # D5: 2,4 => UNS * DIS F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 # E6: 2,4 => CTR => E6: 7 * INC F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 # D7: 2,4 => UNS * INC F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 # D7: 8 => UNS * INC F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 # E4: 2,4 => UNS * INC F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 # D5: 2,4 => UNS * INC F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 # D7: 2,4 => UNS * INC F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 # D7: 8 => UNS * DIS F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 # B8: 4,7 => CTR => B8: 2,5 * DIS F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 + B8: 2,5 # C8: 4,7 => CTR => C8: 2,5 * INC F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 + B8: 2,5 + C8: 2,5 # B9: 4,7 => UNS * INC F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 + B8: 2,5 + C8: 2,5 # B9: 4,7 => UNS * PRF F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 + B8: 2,5 + C8: 2,5 # B9: 6 => SOL * STA F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 + B8: 2,5 + C8: 2,5 + B9: 6 * CNT 35 HDP CHAINS / 35 HYP OPENED