Analysis of zz-www.sudokuwiki.org-0148-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=148
level: medium
position: .....3..1...1..2...57........4.3....9...6..74....5.3...8....96...9..2...3..4....5 initial
Autosolve
position: .....3..1..31..2..157.2......4.3....93..6..74....543..48....96...9..2...3..4....5 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F2: 6,8 => CTR => F2: 5,7,9 * DIS # E8: 1,7 => CTR => E8: 8 * DIS # E9: 1,7 => CTR => E9: 8,9 * DIS # D7: 5,7 => CTR => D7: 3 * DIS # F2: 6,8,9 => CTR => F2: 5,7 * CNT 5 HDP CHAINS / 28 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F2: 6,8 => CTR => F2: 5,7,9 * DIS F2: 5,7,9 # E8: 1,7 => CTR => E8: 8 * DIS F2: 5,7,9 + E8: 8 # E9: 1,7 => CTR => E9: 9 * DIS F2: 5,7,9 + E8: 8 + E9: 9 # D7: 5,7 => CTR => D7: 3 * DIS F2: 5,7,9 + E8: 8 + E9: 9 + D7: 3 # D8: 6 => CTR => D8: 5,7 * DIS F2: 5,7,9 + E8: 8 + E9: 9 + D7: 3 + D8: 5,7 # A1: 6,8 => CTR => A1: 2 * DIS F2: 5,7,9 + E8: 8 + E9: 9 + D7: 3 + D8: 5,7 + A1: 2 # I2: 7,9 => CTR => I2: 6,8 * DIS F2: 5,7,9 + E8: 8 + E9: 9 + D7: 3 + D8: 5,7 + A1: 2 + I2: 6,8 # A4: 6,8 => CTR => A4: 5,7 * DIS F2: 5,7,9 + E8: 8 + E9: 9 + D7: 3 + D8: 5,7 + A1: 2 + I2: 6,8 + A4: 5,7 # A6: 6,8 => CTR => A6: 7 * PRF F2: 5,7,9 + E8: 8 + E9: 9 + D7: 3 + D8: 5,7 + A1: 2 + I2: 6,8 + A4: 5,7 + A6: 7 => SOL * STA F2: 5,7,9 + E8: 8 + E9: 9 + D7: 3 + D8: 5,7 + A1: 2 + I2: 6,8 + A4: 5,7 + A6: 7 * CNT 10 HDP CHAINS / 37 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....3..1...1..2...57........4.3....9...6..74....5.3...8....96...9..2...3..4....5 | initial |
| .....3..1..31..2..157.2......4.3....93..6..74....543..48....96...9..2...3..4....5 | autosolve |
| 296843751843175296157629843524738619938261574761954328485317962619582437372496185 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) B1: 4,9 A2: 6,8 B2: 4,9 H3: 3,4 D5: 2,8 F5: 1,8 E7: 1,7 F7: 5,7 H8: 3,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F4,F5: 1.. / F4 = 1 => 14 pairs (_) / F5 = 1 => 9 pairs (_) C7,E7: 1.. / C7 = 1 => 0 pairs (X) / E7 = 1 => 10 pairs (_) A1,C1: 2.. / A1 = 2 => 10 pairs (_) / C1 = 2 => 20 pairs (_) I7,H9: 2.. / I7 = 2 => 12 pairs (_) / H9 = 2 => 0 pairs (X) C5,D5: 2.. / C5 = 2 => 0 pairs (X) / D5 = 2 => 8 pairs (_) C7,I7: 2.. / C7 = 2 => 0 pairs (X) / I7 = 2 => 12 pairs (_) H3,I3: 3.. / H3 = 3 => 7 pairs (_) / I3 = 3 => 11 pairs (_) D7,D8: 3.. / D7 = 3 => 10 pairs (_) / D8 = 3 => 0 pairs (X) D7,I7: 3.. / D7 = 3 => 10 pairs (_) / I7 = 3 => 0 pairs (X) H3,H8: 3.. / H3 = 3 => 7 pairs (_) / H8 = 3 => 11 pairs (_) B1,B2: 4.. / B1 = 4 => 8 pairs (_) / B2 = 4 => 8 pairs (_) E1,E2: 4.. / E1 = 4 => 8 pairs (_) / E2 = 4 => 8 pairs (_) G3,H3: 4.. / G3 = 4 => 7 pairs (_) / H3 = 4 => 11 pairs (_) G8,H8: 4.. / G8 = 4 => 11 pairs (_) / H8 = 4 => 7 pairs (_) B1,E1: 4.. / B1 = 4 => 8 pairs (_) / E1 = 4 => 8 pairs (_) B2,E2: 4.. / B2 = 4 => 8 pairs (_) / E2 = 4 => 8 pairs (_) G3,G8: 4.. / G3 = 4 => 7 pairs (_) / G8 = 4 => 11 pairs (_) H3,H8: 4.. / H3 = 4 => 11 pairs (_) / H8 = 4 => 7 pairs (_) D1,F2: 5.. / D1 = 5 => 11 pairs (_) / F2 = 5 => 17 pairs (_) A4,C5: 5.. / A4 = 5 => 15 pairs (_) / C5 = 5 => 10 pairs (_) C7,A8: 5.. / C7 = 5 => 15 pairs (_) / A8 = 5 => 10 pairs (_) F2,H2: 5.. / F2 = 5 => 17 pairs (_) / H2 = 5 => 11 pairs (_) C5,G5: 5.. / C5 = 5 => 10 pairs (_) / G5 = 5 => 15 pairs (_) A8,D8: 5.. / A8 = 5 => 10 pairs (_) / D8 = 5 => 15 pairs (_) A4,A8: 5.. / A4 = 5 => 15 pairs (_) / A8 = 5 => 10 pairs (_) C5,C7: 5.. / C5 = 5 => 10 pairs (_) / C7 = 5 => 15 pairs (_) F2,F7: 5.. / F2 = 5 => 17 pairs (_) / F7 = 5 => 11 pairs (_) D8,F9: 6.. / D8 = 6 => 13 pairs (_) / F9 = 6 => 12 pairs (_) G1,I2: 7.. / G1 = 7 => 10 pairs (_) / I2 = 7 => 12 pairs (_) B1,B2: 9.. / B1 = 9 => 8 pairs (_) / B2 = 9 => 8 pairs (_) E9,F9: 9.. / E9 = 9 => 9 pairs (_) / F9 = 9 => 0 pairs (X) * DURATION: 0:00:44.578695 START: 06:12:17.282304 END: 06:13:01.860999 2017-05-01 * CP COUNT: (31) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B1,B2,D5,E7,F5,F7,H3,H8) * .....3..1..31..2..157.2......4.3....93..6..74....543..48....96...9..2...3..4....5 * PAIR B1: 4,9 ROW 1 E1: 4,9,7,8 # reduction candidate for 4,9 E1: 4,9 # 11 pairs E1: 7,8 # 9 pairs * PAIR A2: 6,8 BLK 1 A1: 6,8,2 # reduction candidate for 6,8 A1: 6,8 # 20 pairs C1: 6,8,2 # reduction candidate for 6,8 C1: 6,8 # 10 pairs * PAIR A2: 6,8 ROW 2 F2: 6,8,5,7,9 # reduction candidate for 6,8 F2: 6,8 => CTR * 2..5.3..1..31..25.157.2......4.3.5..935268174....543..482.1596.519682...37.49.825 F2: 5,7,9 # 9 pairs I2: 6,8,7,9 # reduction candidate for 6,8 I2: 6,8 # 12 pairs * PAIR A2: 6,8 COL A A4: 6,8,2,5,7 # reduction candidate for 6,8 A4: 6,8 # 13 pairs A6: 6,8,2,7 # reduction candidate for 6,8 A6: 6,8 # 13 pairs * PAIR B2: 4,9 ROW 2 E2: 4,9,7,8 # reduction candidate for 4,9 E2: 4,9 # 11 pairs E2: 7,8 # 9 pairs * PAIR D5: 2,8 BLK 5 D4: 2,8,7,9 # reduction candidate for 2,8 D4: 2,8 # 13 pairs D6: 2,8,7,9 # reduction candidate for 2,8 D6: 2,8 # 13 pairs * PAIR D5: 2,8 ROW 5 C5: 2,8,1,5 # reduction candidate for 2,8 C5: 2,8 # 16 pairs C5: 1,5 # 9 pairs * PAIR F5: 1,8 BLK 5 F4: 1,8,7,9 # reduction candidate for 1,8 F4: 1,8 # 14 pairs F4: 7,9 # 11 pairs * PAIR F5: 1,8 ROW 5 C5: 1,8,2,5 # reduction candidate for 1,8 C5: 1,8 # 15 pairs G5: 1,8,5 # reduction candidate for 1,8 G5: 1,8 # 10 pairs * PAIR E7: 1,7 BLK 8 E8: 1,7,8 # reduction candidate for 1,7 E8: 1,7 => CTR * ...5.37.1..31.725.157.2.643..4.3.5..93526..74....543..48.3.596.5.96.24383764..125 E8: 8 # 10 pairs E9: 1,7,8,9 # reduction candidate for 1,7 E9: 1,7 => CTR * ...5.37.1..31.725.157826439..4.3.5..93526..74....543..48.3.596.5.96821433..4.98.5 E9: 8,9 # 10 pairs * PAIR F7: 5,7 BLK 8 D7: 5,7,3 # reduction candidate for 5,7 D7: 5,7 => CTR * 2....37.1..31..2..157.2.43...4.3.65.93..6..74....543..482.1.9635693.214.371496825 D7: 3 # 10 pairs D8: 5,7,3,6,8 # reduction candidate for 5,7 D8: 5,7 # 16 pairs * PAIR F7: 5,7 COL F F2: 5,7,6,8,9 # reduction candidate for 5,7 F2: 6,8,9 => CTR * 2..5.3..1..31..25.157.2......4.3.5..935268174....543..482.1596.519682...37.49.825 F2: 5,7 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0148-base-pr-000.dot * REASONING * DIS # F2: 6,8 => CTR => F2: 5,7,9 * DIS # E8: 1,7 => CTR => E8: 8 * DIS # E9: 1,7 => CTR => E9: 8,9 * DIS # D7: 5,7 => CTR => D7: 3 * DIS # F2: 6,8,9 => CTR => F2: 5,7 * CNT 5 HDP CHAINS / 28 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B1,B2,D5,E7,F5,F7,H3,H8) * .....3..1..31..2..157.2......4.3....93..6..74....543..48....96...9..2...3..4....5 * PAIR B1: 4,9 ROW 1 E1: 4,9,7,8 # reduction candidate for 4,9 E1: 4,9 # 11 pairs E1: 7,8 # 9 pairs * PAIR A2: 6,8 BLK 1 A1: 6,8,2 # reduction candidate for 6,8 A1: 6,8 # 20 pairs C1: 6,8,2 # reduction candidate for 6,8 C1: 6,8 # 10 pairs * PAIR A2: 6,8 ROW 2 F2: 6,8,5,7,9 # reduction candidate for 6,8 F2: 6,8 => CTR * 2..5.3..1..31..25.157.2......4.3.5..935268174....543..482.1596.519682...37.49.825 I2: 6,8,7,9 # reduction candidate for 6,8 I2: 6,8 # 12 pairs * RESTART * PAIR A2: 6,8 ROW 2 I2: 6,8,7,9 # reduction candidate for 6,8 I2: 7,9 # 13 pairs I2: 6,8 # 12 pairs * PAIR A2: 6,8 COL A A4: 6,8,2,5,7 # reduction candidate for 6,8 A4: 6,8 # 13 pairs A6: 6,8,2,7 # reduction candidate for 6,8 A6: 6,8 # 13 pairs * PAIR RESTART * PAIR A2: 6,8 BLK 1 A1: 6,8,2 # reduction candidate for 6,8 A1: 6,8 # 21 pairs C1: 6,8,2 # reduction candidate for 6,8 C1: 6,8 # 10 pairs * PAIR A2: 6,8 ROW 2 I2: 6,8,7,9 # reduction candidate for 6,8 I2: 7,9 # 13 pairs I2: 6,8 # 12 pairs * PAIR A2: 6,8 COL A A4: 6,8,2,5,7 # reduction candidate for 6,8 A4: 6,8 # 13 pairs A6: 6,8,2,7 # reduction candidate for 6,8 A6: 6,8 # 13 pairs * PAIR B2: 4,9 ROW 2 E2: 4,9,7,8 # reduction candidate for 4,9 E2: 4,9 # 13 pairs E2: 7,8 # 9 pairs * PAIR D5: 2,8 BLK 5 D4: 2,8,7,9 # reduction candidate for 2,8 D4: 2,8 # 15 pairs D6: 2,8,7,9 # reduction candidate for 2,8 D6: 2,8 # 15 pairs * PAIR D5: 2,8 ROW 5 C5: 2,8,1,5 # reduction candidate for 2,8 C5: 2,8 # 16 pairs C5: 1,5 # 9 pairs * PAIR F5: 1,8 BLK 5 F4: 1,8,7,9 # reduction candidate for 1,8 F4: 1,8 # 14 pairs F4: 7,9 # 13 pairs * PAIR F5: 1,8 ROW 5 C5: 1,8,2,5 # reduction candidate for 1,8 C5: 1,8 # 15 pairs G5: 1,8,5 # reduction candidate for 1,8 G5: 1,8 # 10 pairs * PAIR E7: 1,7 BLK 8 E8: 1,7,8 # reduction candidate for 1,7 E8: 1,7 => CTR * ...5.37.1..31.725.157.2.643..4.3.5..93526..74....543..48.3.596.5.96.24383764..125 E9: 1,7,9 # reduction candidate for 1,7 E9: 1,7 => CTR * ...5.3..1..31.725.157826439..4.3.5..93526..74....543..48.3.596.5.9682.433..4.9..5 * PAIR F7: 5,7 BLK 8 D7: 5,7,3 # reduction candidate for 5,7 D7: 5,7 => CTR * .....37.1..317.2..157.2.43...4.3.6..93..6.574....543..48..1.963..9382.4737.496.25 D8: 5,7,6 # reduction candidate for 5,7 D8: 5,7 # 17 pairs * RESTART * PAIR F7: 5,7 BLK 8 D8: 5,7,6 # reduction candidate for 5,7 D8: 6 => CTR * .9.5437818431792561578264.9..4.3....93..6..74....543..48.3159675796821433..497825 * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A2,B1,B2,C7,C9,D5,D8,E1,E2,F2,F3,F5,F7,H3,H8,I7,I8) * .....3..1..31..2..157.2......4.3....93..6..74....543..48.31.96...9.82...3..496..5 * PAIR A2: 6,8 BLK 1 A1: 6,8,2 # reduction candidate for 6,8 A1: 6,8 => CTR * ..2.73..1..314529.157.2......4.3....93.26..74..6.543..485317962.69582143321496785 * RESTART * PAIR A2: 6,8 ROW 2 I2: 6,8,7,9 # reduction candidate for 6,8 I2: 7,9 => CTR * 2.8..37516.3175289157.2.436..4.3.6..93..6.574..6.543..48.31.96..69.821433..496825 * PAIR A2: 6,8 COL A A4: 6,8,5,7 # reduction candidate for 6,8 A4: 6,8 => CTR * 29..437.1.4317.2..157.2......4.3.5..93526..747...543..4823159675697821433714968.5 A6: 6,8,7 # reduction candidate for 6,8 A6: 6,8 => CTR * 29..437.1.4317.2..157.2....7.4.3.5..93526..74...7543..48231.96...9.82...37.496..5 A6: 7 => SOLVED * 296843751843175296157629843524738619938261574761954328485317962619582437372496185 * DURATION: 0:00:32.729451 START: 06:13:24.219337 END: 06:13:56.948788 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0148-base-pr-001.dot * REASONING * DIS # F2: 6,8 => CTR => F2: 5,7,9 * DIS F2: 5,7,9 # E8: 1,7 => CTR => E8: 8 * DIS F2: 5,7,9 + E8: 8 # E9: 1,7 => CTR => E9: 9 * DIS F2: 5,7,9 + E8: 8 + E9: 9 # D7: 5,7 => CTR => D7: 3 * DIS F2: 5,7,9 + E8: 8 + E9: 9 + D7: 3 # D8: 6 => CTR => D8: 5,7 * DIS F2: 5,7,9 + E8: 8 + E9: 9 + D7: 3 + D8: 5,7 # A1: 6,8 => CTR => A1: 2 * DIS F2: 5,7,9 + E8: 8 + E9: 9 + D7: 3 + D8: 5,7 + A1: 2 # I2: 7,9 => CTR => I2: 6,8 * DIS F2: 5,7,9 + E8: 8 + E9: 9 + D7: 3 + D8: 5,7 + A1: 2 + I2: 6,8 # A4: 6,8 => CTR => A4: 5,7 * DIS F2: 5,7,9 + E8: 8 + E9: 9 + D7: 3 + D8: 5,7 + A1: 2 + I2: 6,8 + A4: 5,7 # A6: 6,8 => CTR => A6: 7 * PRF F2: 5,7,9 + E8: 8 + E9: 9 + D7: 3 + D8: 5,7 + A1: 2 + I2: 6,8 + A4: 5,7 + A6: 7 => SOL * STA F2: 5,7,9 + E8: 8 + E9: 9 + D7: 3 + D8: 5,7 + A1: 2 + I2: 6,8 + A4: 5,7 + A6: 7 * CNT 10 HDP CHAINS / 37 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=148
Solution
position: 296843751843175296157629843524738619938261574761954328485317962619582437372496185 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 # E1: 4,9 => UNS * INC # E1: 7,8 => UNS * INC # A1: 6,8 => UNS * INC # C1: 6,8 => UNS * DIS # F2: 6,8 => CTR => F2: 5,7,9 * INC # F2: 5,7,9 => UNS * INC # I2: 6,8 => UNS * INC # A4: 6,8 => UNS * INC # A6: 6,8 => UNS * INC # E2: 4,9 => UNS * INC # E2: 7,8 => UNS * INC # D4: 2,8 => UNS * INC # D6: 2,8 => UNS * INC # C5: 2,8 => UNS * INC # C5: 1,5 => UNS * INC # F4: 1,8 => UNS * INC # F4: 7,9 => UNS * INC # C5: 1,8 => UNS * INC # G5: 1,8 => UNS * DIS # E8: 1,7 => CTR => E8: 8 * INC # E8: 8 => UNS * DIS # E9: 1,7 => CTR => E9: 8,9 * INC # E9: 8,9 => UNS * DIS # D7: 5,7 => CTR => D7: 3 * INC # D7: 3 => UNS * INC # D8: 5,7 => UNS * INC # F2: 5,7 => UNS * DIS # F2: 6,8,9 => CTR => F2: 5,7 * CNT 28 HDP CHAINS / 28 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E1: 4,9 => UNS * INC # E1: 7,8 => UNS * INC # A1: 6,8 => UNS * INC # C1: 6,8 => UNS * DIS # F2: 6,8 => CTR => F2: 5,7,9 * INC F2: 5,7,9 # I2: 6,8 => UNS * INC F2: 5,7,9 # I2: 6,8 => UNS * INC F2: 5,7,9 # I2: 7,9 => UNS * INC F2: 5,7,9 # A4: 6,8 => UNS * INC F2: 5,7,9 # A6: 6,8 => UNS * INC F2: 5,7,9 # A1: 6,8 => UNS * INC F2: 5,7,9 # C1: 6,8 => UNS * INC F2: 5,7,9 # I2: 6,8 => UNS * INC F2: 5,7,9 # I2: 7,9 => UNS * INC F2: 5,7,9 # A4: 6,8 => UNS * INC F2: 5,7,9 # A6: 6,8 => UNS * INC F2: 5,7,9 # E2: 4,9 => UNS * INC F2: 5,7,9 # E2: 7,8 => UNS * INC F2: 5,7,9 # D4: 2,8 => UNS * INC F2: 5,7,9 # D6: 2,8 => UNS * INC F2: 5,7,9 # C5: 2,8 => UNS * INC F2: 5,7,9 # C5: 1,5 => UNS * INC F2: 5,7,9 # F4: 1,8 => UNS * INC F2: 5,7,9 # F4: 7,9 => UNS * INC F2: 5,7,9 # C5: 1,8 => UNS * INC F2: 5,7,9 # G5: 1,8 => UNS * DIS F2: 5,7,9 # E8: 1,7 => CTR => E8: 8 * DIS F2: 5,7,9 + E8: 8 # E9: 1,7 => CTR => E9: 9 * DIS F2: 5,7,9 + E8: 8 + E9: 9 # D7: 5,7 => CTR => D7: 3 * INC F2: 5,7,9 + E8: 8 + E9: 9 + D7: 3 # D8: 5,7 => UNS * INC F2: 5,7,9 + E8: 8 + E9: 9 + D7: 3 # D8: 5,7 => UNS * DIS F2: 5,7,9 + E8: 8 + E9: 9 + D7: 3 # D8: 6 => CTR => D8: 5,7 * DIS F2: 5,7,9 + E8: 8 + E9: 9 + D7: 3 + D8: 5,7 # A1: 6,8 => CTR => A1: 2 * INC F2: 5,7,9 + E8: 8 + E9: 9 + D7: 3 + D8: 5,7 + A1: 2 # I2: 6,8 => UNS * DIS F2: 5,7,9 + E8: 8 + E9: 9 + D7: 3 + D8: 5,7 + A1: 2 # I2: 7,9 => CTR => I2: 6,8 * DIS F2: 5,7,9 + E8: 8 + E9: 9 + D7: 3 + D8: 5,7 + A1: 2 + I2: 6,8 # A4: 6,8 => CTR => A4: 5,7 * DIS F2: 5,7,9 + E8: 8 + E9: 9 + D7: 3 + D8: 5,7 + A1: 2 + I2: 6,8 + A4: 5,7 # A6: 6,8 => CTR => A6: 7 * PRF F2: 5,7,9 + E8: 8 + E9: 9 + D7: 3 + D8: 5,7 + A1: 2 + I2: 6,8 + A4: 5,7 + A6: 7 => SOL * STA F2: 5,7,9 + E8: 8 + E9: 9 + D7: 3 + D8: 5,7 + A1: 2 + I2: 6,8 + A4: 5,7 + A6: 7 * CNT 38 HDP CHAINS / 37 HYP OPENED