Analysis of zz-www.sudokuwiki.org-0281-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=281
level: medium
position: .2.34....4...5......6..17..5..2......3.....4...1..68....9....7....1..9.......9.68 initial
Autosolve
position: .2.34....4..65......6..17.45..2......3.....4...1..68....9....7....1..9.......9.68 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F2: 2 => CTR => F2: 7,8 * DIS # C1: 5 => CTR => C1: 7,8 * DIS # E3: 8,9 => CTR => E3: 2 * DIS # B4: 4,8 => CTR => B4: 6,7,9 * PRF # C8: 4,8 => SOL * DIS # A5: 2,8 => CTR => A5: 6,7,9 * DIS # C8: 2,8 => CTR => C8: 3,4,5 * PRF # D5: 5,8 => SOL * DIS # F7: 5,8 => CTR => F7: 2,3,4 * DIS # F8: 5,8 => CTR => F8: 2,3,4 * CNT 10 HDP CHAINS / 40 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F2: 2 => CTR => F2: 7,8 * DIS F2: 7,8 # C1: 5 => CTR => C1: 7,8 * DIS F2: 7,8 + C1: 7,8 # B4: 4,8 => CTR => B4: 6,7,9 * DIS F2: 7,8 + C1: 7,8 + B4: 6,7,9 # A5: 2,8 => CTR => A5: 6,7,9 * DIS F2: 7,8 + C1: 7,8 + B4: 6,7,9 + A5: 6,7,9 # I1: 1,9 => CTR => I1: 5,6 * DIS F2: 7,8 + C1: 7,8 + B4: 6,7,9 + A5: 6,7,9 + I1: 5,6 # H1: 5 => CTR => H1: 1,9 * DIS F2: 7,8 + C1: 7,8 + B4: 6,7,9 + A5: 6,7,9 + I1: 5,6 + H1: 1,9 # I2: 9 => CTR => I2: 1,2 * DIS F2: 7,8 + C1: 7,8 + B4: 6,7,9 + A5: 6,7,9 + I1: 5,6 + H1: 1,9 + I2: 1,2 # G7: 1,2 => CTR => G7: 3,4,5 * PRF F2: 7,8 + C1: 7,8 + B4: 6,7,9 + A5: 6,7,9 + I1: 5,6 + H1: 1,9 + I2: 1,2 + G7: 3,4,5 # G9: 1,2 => SOL * STA F2: 7,8 + C1: 7,8 + B4: 6,7,9 + A5: 6,7,9 + I1: 5,6 + H1: 1,9 + I2: 1,2 + G7: 3,4,5 + G9: 1,2 * CNT 9 HDP CHAINS / 32 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2.34....4...5......6..17..5..2......3.....4...1..68....9....7....1..9.......9.68 | initial |
| .2.34....4..65......6..17.45..2......3.....4...1..68....9....7....1..9.......9.68 | autosolve |
| 127348596493657182856921734568294317732815649941736825289563471674182953315479268 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) A1: 1,9 B2: 1,9 A3: 3,8 B3: 5,8 F1: 7,8 D3: 8,9 C4: 4,8 C5: 2,8 F5: 5,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,B2: 1.. / A1 = 1 => 9 pairs (_) / B2 = 1 => 9 pairs (_) E4,E5: 1.. / E4 = 1 => 13 pairs (_) / E5 = 1 => 9 pairs (_) F2,E3: 2.. / F2 = 2 => 0 pairs (X) / E3 = 2 => 12 pairs (_) E3,H3: 2.. / E3 = 2 => 12 pairs (_) / H3 = 2 => 0 pairs (X) C2,A3: 3.. / C2 = 3 => 11 pairs (_) / A3 = 3 => 9 pairs (_) A3,H3: 3.. / A3 = 3 => 9 pairs (_) / H3 = 3 => 11 pairs (_) F4,D6: 4.. / F4 = 4 => 0 pairs (*) / D6 = 4 => 0 pairs (X) G7,G9: 4.. / G7 = 4 => 10 pairs (_) / G9 = 4 => 10 pairs (_) B6,D6: 4.. / B6 = 4 => 0 pairs (*) / D6 = 4 => 0 pairs (X) C1,B3: 5.. / C1 = 5 => 0 pairs (X) / B3 = 5 => 9 pairs (_) B3,H3: 5.. / B3 = 5 => 9 pairs (_) / H3 = 5 => 0 pairs (X) G1,I1: 6.. / G1 = 6 => 10 pairs (_) / I1 = 6 => 10 pairs (_) B4,A5: 6.. / B4 = 6 => 10 pairs (_) / A5 = 6 => 9 pairs (_) E7,E8: 6.. / E7 = 6 => 9 pairs (_) / E8 = 6 => 9 pairs (_) C1,C2: 7.. / C1 = 7 => 11 pairs (_) / C2 = 7 => 9 pairs (_) F1,F2: 7.. / F1 = 7 => 9 pairs (_) / F2 = 7 => 11 pairs (_) C1,F1: 7.. / C1 = 7 => 11 pairs (_) / F1 = 7 => 9 pairs (_) C2,F2: 7.. / C2 = 7 => 9 pairs (_) / F2 = 7 => 11 pairs (_) A1,B2: 9.. / A1 = 9 => 9 pairs (_) / B2 = 9 => 9 pairs (_) D3,E3: 9.. / D3 = 9 => 9 pairs (_) / E3 = 9 => 0 pairs (X) * DURATION: 0:00:16.818960 START: 14:46:26.769017 END: 14:46:43.587977 2019-04-28 * CP COUNT: (20) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B2,B3,C4,C5,D3,F1,F5) * .2.34....4..65......6..17.45..2......3.....4...1..68....9....7....1..9.......9.68 * PAIR A1: 1,9 ROW 1 H1: 1,9,5,8 # reduction candidate for 1,9 H1: 1,9 # 12 pairs I1: 1,9,5,6 # reduction candidate for 1,9 I1: 1,9 # 13 pairs * PAIR B2: 1,9 ROW 2 H2: 1,9,2,3,8 # reduction candidate for 1,9 H2: 1,9 # 16 pairs I2: 1,9,2,3 # reduction candidate for 1,9 I2: 1,9 # 11 pairs * PAIR A3: 3,8 BLK 1 C2: 3,8,7 # reduction candidate for 3,8 C2: 3,8 # 11 pairs C2: 7 # 9 pairs * PAIR A3: 3,8 ROW 3 H3: 3,8,2,5 # reduction candidate for 3,8 H3: 3,8 # 13 pairs H3: 2,5 # 10 pairs * PAIR A3: 3,8 COL A A7: 3,8,1,2,6 # reduction candidate for 3,8 A7: 3,8 # 10 pairs A8: 3,8,2,6,7 # reduction candidate for 3,8 A8: 3,8 # 12 pairs * PAIR B3: 5,8 BLK 1 C1: 5,8,7 # reduction candidate for 5,8 C1: 7 # 11 pairs C1: 5,8 # 9 pairs * PAIR B3: 5,8 ROW 3 H3: 5,8,2,3 # reduction candidate for 5,8 H3: 5,8 # 13 pairs H3: 2,3 # 12 pairs * PAIR B3: 5,8 COL B B7: 5,8,1,4,6 # reduction candidate for 5,8 B7: 5,8 # 10 pairs B8: 5,8,4,6,7 # reduction candidate for 5,8 B8: 5,8 # 12 pairs * PAIR F1: 7,8 BLK 2 F2: 7,8,2 # reduction candidate for 7,8 F2: 2 => CTR * .28347...4.7652.8.356..17245.42......32....4...14.6852..9....7....1..935.....9.68 F2: 7,8 # 12 pairs * PAIR F1: 7,8 ROW 1 C1: 7,8,5 # reduction candidate for 7,8 C1: 5 => CTR * .25347.8.4.7658...3869217545.4283...83271564...1..68.5..9..2.71.581.49....3.79.68 C1: 7,8 # 9 pairs * PAIR D3: 8,9 BLK 2 E3: 8,9,2 # reduction candidate for 8,9 E3: 8,9 => CTR * .28347...4.7652.8.356..17245.42......32....4...14.6852..9....7....1..935.....9.68 E3: 2 # 12 pairs * PAIR D3: 8,9 COL D D5: 8,9,5,7 # reduction candidate for 8,9 D5: 8,9 # 11 pairs D5: 5,7 # 10 pairs * PAIR C4: 4,8 BLK 4 B4: 4,8,6,7,9 # reduction candidate for 4,8 B4: 4,8 => CTR * .2.34....4..65......6..17.45..2.....63.....4...1.368....9....7....1..9.......9.68 B4: 6,7,9 # 9 pairs * PAIR C4: 4,8 ROW 4 F4: 4,8,3 # reduction candidate for 4,8 F4: 3 # 29 pairs F4: 4,8 # 11 pairs * PAIR C4: 4,8 COL C C8: 4,8,2,3,5 # reduction candidate for 4,8 C8: 4,8 => SOLVED * 127348596493657182856921734568294317732815649941736825289563471674182953315479268 C8: 2,3,5 # 10 pairs * PAIR C5: 2,8 BLK 4 A5: 2,8,6,7,9 # reduction candidate for 2,8 A5: 2,8 => CTR * .2.347...4.7652.8.3.6..17245642.8....3...5.4...1436852..9....7....1..935..3..9.68 A5: 6,7,9 # 9 pairs * PAIR C5: 2,8 COL C C8: 2,8,3,4,5 # reduction candidate for 2,8 C8: 2,8 => CTR * 92.34....41.65......69217.45.42.3....3...5.4.2.14.68....9....7...21..9.......9.68 C8: 3,4,5 # 9 pairs * PAIR F5: 5,8 BLK 5 D5: 5,8,7,9 # reduction candidate for 5,8 D5: 5,8 => SOLVED * 127348596493657182856921734568294317732815649941736825289563471674182953315479268 D5: 7,9 # 10 pairs * PAIR F5: 5,8 COL F F7: 5,8,2,3,4 # reduction candidate for 5,8 F7: 5,8 => CTR * .28347...4.7652.8.356..17245.42.3....32....4...14.68.2..9....7....1.49.......9.68 F7: 2,3,4 # 9 pairs F8: 5,8,2,3,4 # reduction candidate for 5,8 F8: 5,8 => CTR * .28347...4.7652.8.356..17245.42.3....32....4...14.68.2..9..4.7..4.1..9.......9468 F8: 2,3,4 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0281-base-pr-000.dot * REASONING * DIS # F2: 2 => CTR => F2: 7,8 * DIS # C1: 5 => CTR => C1: 7,8 * DIS # E3: 8,9 => CTR => E3: 2 * DIS # B4: 4,8 => CTR => B4: 6,7,9 * PRF # C8: 4,8 => SOL * DIS # A5: 2,8 => CTR => A5: 6,7,9 * DIS # C8: 2,8 => CTR => C8: 3,4,5 * PRF # D5: 5,8 => SOL * DIS # F7: 5,8 => CTR => F7: 2,3,4 * DIS # F8: 5,8 => CTR => F8: 2,3,4 * CNT 10 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B2,B3,C4,C5,D3,F1,F5) * .2.34....4..65......6..17.45..2......3.....4...1..68....9....7....1..9.......9.68 * PAIR A1: 1,9 ROW 1 H1: 1,9,5,8 # reduction candidate for 1,9 H1: 1,9 # 12 pairs I1: 1,9,5,6 # reduction candidate for 1,9 I1: 1,9 # 13 pairs * PAIR B2: 1,9 ROW 2 H2: 1,9,2,3,8 # reduction candidate for 1,9 H2: 1,9 # 16 pairs I2: 1,9,2,3 # reduction candidate for 1,9 I2: 1,9 # 11 pairs * PAIR A3: 3,8 BLK 1 C2: 3,8,7 # reduction candidate for 3,8 C2: 3,8 # 11 pairs C2: 7 # 9 pairs * PAIR A3: 3,8 ROW 3 H3: 3,8,2,5 # reduction candidate for 3,8 H3: 3,8 # 13 pairs H3: 2,5 # 10 pairs * PAIR A3: 3,8 COL A A7: 3,8,1,2,6 # reduction candidate for 3,8 A7: 3,8 # 10 pairs A8: 3,8,2,6,7 # reduction candidate for 3,8 A8: 3,8 # 12 pairs * PAIR B3: 5,8 BLK 1 C1: 5,8,7 # reduction candidate for 5,8 C1: 7 # 11 pairs C1: 5,8 # 9 pairs * PAIR B3: 5,8 ROW 3 H3: 5,8,2,3 # reduction candidate for 5,8 H3: 5,8 # 13 pairs H3: 2,3 # 12 pairs * PAIR B3: 5,8 COL B B7: 5,8,1,4,6 # reduction candidate for 5,8 B7: 5,8 # 10 pairs B8: 5,8,4,6,7 # reduction candidate for 5,8 B8: 5,8 # 12 pairs * PAIR F1: 7,8 BLK 2 F2: 7,8,2 # reduction candidate for 7,8 F2: 2 => CTR * .28347...4.7652.8.356..17245.42......32....4...14.6852..9....7....1..935.....9.68 * PAIR F1: 7,8 ROW 1 C1: 7,8,5 # reduction candidate for 7,8 C1: 5 => CTR * .25347.8.4.7658...3869217545.4283...83271564...1..68.5..9..2.71.581.49....3.79.68 * PAIR RESTART * PAIR C4: 4,8 BLK 4 B4: 4,8,6,7,9 # reduction candidate for 4,8 B4: 4,8 => CTR * .2.34....4..65.....569217.45..2.....63...5.4...14368....9....7....1..9.......9.68 * PAIR C5: 2,8 BLK 4 A5: 2,8,6,7,9 # reduction candidate for 2,8 A5: 2,8 => CTR * .2.34....4..65.....569217.456.2......3...5.4...14368....9....7....1..9.......9.68 * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A1,A8,B2,C4,C5,D5,D6,E9,F4,G2,H4,H8) * .27348...4.3657.8.8569217345..2......3...5.4...1..68....9....7....1..9.......9.68 * PAIR A1: 1,9 ROW 1 H1: 1,9,5 # reduction candidate for 1,9 H1: 1,9 # 16 pairs I1: 1,9,5,6 # reduction candidate for 1,9 I1: 1,9 => CTR * .2734865.4.3657.8.8569217345..2...1..3..1524.2.1..6895..9....7...51.4923..2..9.68 * RESTART * PAIR A1: 1,9 ROW 1 H1: 1,9,5 # reduction candidate for 1,9 H1: 5 => CTR * 9273481564136572898569217345..2...1..3...5.4...1..68....9....7....1..9.......9.68 * PAIR RESTART * PAIR B2: 1,9 ROW 2 I2: 1,9,2 # reduction candidate for 1,9 I2: 2 # 18 pairs I2: 1,9 # 18 pairs * PAIR G2: 1,2 BLK 3 I2: 1,2,9 # reduction candidate for 1,2 I2: 9 => CTR * 927348.1.4136572898569217345.4283.9..3...5.4..914.68....9....7....1..9.......9.68 * PAIR G2: 1,2 COL G G7: 1,2,3,4,5 # reduction candidate for 1,2 G7: 1,2 => CTR * 127348596493657.8.85692173456.294317.38.1564...1.368....9....7....1..9..312579468 G9: 1,2,3,4,5 # reduction candidate for 1,2 G9: 1,2 => SOLVED * 127348596493657182856921734568294317732815649941736825289563471674182953315479268 * DURATION: 0:00:20.348645 START: 14:47:03.666438 END: 14:47:24.015083 2019-04-28 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0281-base-pr-001.dot * REASONING * DIS # F2: 2 => CTR => F2: 7,8 * DIS F2: 7,8 # C1: 5 => CTR => C1: 7,8 * DIS F2: 7,8 + C1: 7,8 # B4: 4,8 => CTR => B4: 6,7,9 * DIS F2: 7,8 + C1: 7,8 + B4: 6,7,9 # A5: 2,8 => CTR => A5: 6,7,9 * DIS F2: 7,8 + C1: 7,8 + B4: 6,7,9 + A5: 6,7,9 # I1: 1,9 => CTR => I1: 5,6 * DIS F2: 7,8 + C1: 7,8 + B4: 6,7,9 + A5: 6,7,9 + I1: 5,6 # H1: 5 => CTR => H1: 1,9 * DIS F2: 7,8 + C1: 7,8 + B4: 6,7,9 + A5: 6,7,9 + I1: 5,6 + H1: 1,9 # I2: 9 => CTR => I2: 1,2 * DIS F2: 7,8 + C1: 7,8 + B4: 6,7,9 + A5: 6,7,9 + I1: 5,6 + H1: 1,9 + I2: 1,2 # G7: 1,2 => CTR => G7: 3,4,5 * PRF F2: 7,8 + C1: 7,8 + B4: 6,7,9 + A5: 6,7,9 + I1: 5,6 + H1: 1,9 + I2: 1,2 + G7: 3,4,5 # G9: 1,2 => SOL * STA F2: 7,8 + C1: 7,8 + B4: 6,7,9 + A5: 6,7,9 + I1: 5,6 + H1: 1,9 + I2: 1,2 + G7: 3,4,5 + G9: 1,2 * CNT 9 HDP CHAINS / 32 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=281
Solution
position: 127348596493657182856921734568294317732815649941736825289563471674182953315479268 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 # H1: 1,9 => UNS * INC # I1: 1,9 => UNS * INC # H2: 1,9 => UNS * INC # I2: 1,9 => UNS * INC # C2: 3,8 => UNS * INC # C2: 7 => UNS * INC # H3: 3,8 => UNS * INC # H3: 2,5 => UNS * INC # A7: 3,8 => UNS * INC # A8: 3,8 => UNS * INC # C1: 5,8 => UNS * INC # C1: 7 => UNS * INC # H3: 5,8 => UNS * INC # H3: 2,3 => UNS * INC # B7: 5,8 => UNS * INC # B8: 5,8 => UNS * INC # F2: 7,8 => UNS * DIS # F2: 2 => CTR => F2: 7,8 * INC # C1: 7,8 => UNS * DIS # C1: 5 => CTR => C1: 7,8 * DIS # E3: 8,9 => CTR => E3: 2 * INC # E3: 2 => UNS * INC # D5: 8,9 => UNS * INC # D5: 5,7 => UNS * DIS # B4: 4,8 => CTR => B4: 6,7,9 * INC # B4: 6,7,9 => UNS * INC # F4: 4,8 => UNS * INC # F4: 3 => UNS * PRF # C8: 4,8 => SOL * INC # C8: 2,3,5 => UNS * DIS # A5: 2,8 => CTR => A5: 6,7,9 * INC # A5: 6,7,9 => UNS * DIS # C8: 2,8 => CTR => C8: 3,4,5 * INC # C8: 3,4,5 => UNS * PRF # D5: 5,8 => SOL * INC # D5: 7,9 => UNS * DIS # F7: 5,8 => CTR => F7: 2,3,4 * INC # F7: 2,3,4 => UNS * DIS # F8: 5,8 => CTR => F8: 2,3,4 * INC # F8: 2,3,4 => UNS * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # H1: 1,9 => UNS * INC # I1: 1,9 => UNS * INC # H2: 1,9 => UNS * INC # I2: 1,9 => UNS * INC # C2: 3,8 => UNS * INC # C2: 7 => UNS * INC # H3: 3,8 => UNS * INC # H3: 2,5 => UNS * INC # A7: 3,8 => UNS * INC # A8: 3,8 => UNS * INC # C1: 5,8 => UNS * INC # C1: 7 => UNS * INC # H3: 5,8 => UNS * INC # H3: 2,3 => UNS * INC # B7: 5,8 => UNS * INC # B8: 5,8 => UNS * INC # F2: 7,8 => UNS * DIS # F2: 2 => CTR => F2: 7,8 * INC F2: 7,8 # C1: 7,8 => UNS * DIS F2: 7,8 # C1: 5 => CTR => C1: 7,8 * DIS F2: 7,8 + C1: 7,8 # B4: 4,8 => CTR => B4: 6,7,9 * DIS F2: 7,8 + C1: 7,8 + B4: 6,7,9 # A5: 2,8 => CTR => A5: 6,7,9 * INC F2: 7,8 + C1: 7,8 + B4: 6,7,9 + A5: 6,7,9 # H1: 1,9 => UNS * DIS F2: 7,8 + C1: 7,8 + B4: 6,7,9 + A5: 6,7,9 # I1: 1,9 => CTR => I1: 5,6 * INC F2: 7,8 + C1: 7,8 + B4: 6,7,9 + A5: 6,7,9 + I1: 5,6 # H1: 1,9 => UNS * DIS F2: 7,8 + C1: 7,8 + B4: 6,7,9 + A5: 6,7,9 + I1: 5,6 # H1: 5 => CTR => H1: 1,9 * INC F2: 7,8 + C1: 7,8 + B4: 6,7,9 + A5: 6,7,9 + I1: 5,6 + H1: 1,9 # I2: 1,9 => UNS * INC F2: 7,8 + C1: 7,8 + B4: 6,7,9 + A5: 6,7,9 + I1: 5,6 + H1: 1,9 # I2: 2 => UNS * INC F2: 7,8 + C1: 7,8 + B4: 6,7,9 + A5: 6,7,9 + I1: 5,6 + H1: 1,9 # I2: 1,2 => UNS * DIS F2: 7,8 + C1: 7,8 + B4: 6,7,9 + A5: 6,7,9 + I1: 5,6 + H1: 1,9 # I2: 9 => CTR => I2: 1,2 * DIS F2: 7,8 + C1: 7,8 + B4: 6,7,9 + A5: 6,7,9 + I1: 5,6 + H1: 1,9 + I2: 1,2 # G7: 1,2 => CTR => G7: 3,4,5 * PRF F2: 7,8 + C1: 7,8 + B4: 6,7,9 + A5: 6,7,9 + I1: 5,6 + H1: 1,9 + I2: 1,2 + G7: 3,4,5 # G9: 1,2 => SOL * STA F2: 7,8 + C1: 7,8 + B4: 6,7,9 + A5: 6,7,9 + I1: 5,6 + H1: 1,9 + I2: 1,2 + G7: 3,4,5 + G9: 1,2 * CNT 32 HDP CHAINS / 32 HYP OPENED