Analysis of zz-www.sudokuwiki.org-0132-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=132
level: medium
position: 2.7..6..4..4.5.8.....4......3...1..9.4..7..6.1......8......3.....1.8.5..5..1..9.6 initial
Autosolve
position: 2.7..6..4..4.5.8.....4..6...3...1..9.4..7..6.1......8....5.3..8..1.8.5..5..1..9.6 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H1: 1,3 => CTR => H1: 5,9 * DIS # H3: 1,3 => CTR => H3: 2,5,7,9 * DIS # I3: 1,3 => CTR => I3: 2,5,7 * DIS # C5: 8,9 => CTR => C5: 2,5 * DIS # D5: 8,9 => CTR => D5: 2,3 * DIS # A3: 3 => CTR => A3: 8,9 * DIS # E7: 2,4 => CTR => E7: 6,9 * CNT 7 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H1: 1,3 => CTR => H1: 5,9 * DIS H1: 5,9 # H3: 1,3 => CTR => H3: 2,5,7,9 * DIS H1: 5,9 + H3: 2,5,7,9 # I3: 1,3 => CTR => I3: 2,5,7 * DIS H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 # E1: 9 => CTR => E1: 1,3 * DIS H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 # C5: 8,9 => CTR => C5: 2,5 * DIS H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 + C5: 2,5 # D5: 8,9 => CTR => D5: 2,3 * DIS H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 + C5: 2,5 + D5: 2,3 # A3: 3 => CTR => A3: 8,9 * DIS H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 + C5: 2,5 + D5: 2,3 + A3: 8,9 # A8: 4,7 => CTR => A8: 3,6 * DIS H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 + C5: 2,5 + D5: 2,3 + A3: 8,9 + A8: 3,6 # B1: 8,9 => CTR => B1: 5 * PRF H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 + C5: 2,5 + D5: 2,3 + A3: 8,9 + A8: 3,6 + B1: 5 => SOL * STA H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 + C5: 2,5 + D5: 2,3 + A3: 8,9 + A8: 3,6 + B1: 5 * CNT 10 HDP CHAINS / 20 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2.7..6..4..4.5.8.....4......3...1..9.4..7..6.1......8......3.....1.8.5..5..1..9.6 | initial |
| 2.7..6..4..4.5.8.....4..6...3...1..9.4..7..6.1......8....5.3..8..1.8.5..5..1..9.6 | autosolve |
| 257816394364759821819432675738641259945278163126395487492563718671984532583127946 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (3) G1: 1,3 A5: 8,9 E9: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,E3: 1.. / E1 = 1 => 6 pairs (_) / E3 = 1 => 4 pairs (_) G5,I5: 1.. / G5 = 1 => 6 pairs (_) / I5 = 1 => 4 pairs (_) G7,H7: 1.. / G7 = 1 => 16 pairs (_) / H7 = 1 => 3 pairs (_) A8,C9: 3.. / A8 = 3 => 9 pairs (_) / C9 = 3 => 12 pairs (_) C9,H9: 3.. / C9 = 3 => 12 pairs (_) / H9 = 3 => 9 pairs (_) C3,C9: 3.. / C3 = 3 => 9 pairs (_) / C9 = 3 => 12 pairs (_) A7,A8: 4.. / A7 = 4 => 3 pairs (_) / A8 = 4 => 0 pairs (X) F5,F6: 5.. / F5 = 5 => 0 pairs (X) / F6 = 5 => 7 pairs (_) B1,H1: 5.. / B1 = 5 => 13 pairs (_) / H1 = 5 => 3 pairs (_) C4,H4: 5.. / C4 = 5 => 3 pairs (_) / H4 = 5 => 13 pairs (_) A2,B2: 6.. / A2 = 6 => 5 pairs (_) / B2 = 6 => 17 pairs (_) E7,D8: 6.. / E7 = 6 => 7 pairs (_) / D8 = 6 => 6 pairs (_) A4,B6: 7.. / A4 = 7 => 4 pairs (_) / B6 = 7 => 0 pairs (X) D2,D8: 7.. / D2 = 7 => 4 pairs (_) / D8 = 7 => 14 pairs (_) D1,F3: 8.. / D1 = 8 => 12 pairs (_) / F3 = 8 => 0 pairs (X) B9,C9: 8.. / B9 = 8 => 12 pairs (_) / C9 = 8 => 0 pairs (X) B1,D1: 8.. / B1 = 8 => 0 pairs (X) / D1 = 8 => 12 pairs (_) F3,F5: 8.. / F3 = 8 => 0 pairs (X) / F5 = 8 => 12 pairs (_) * DURATION: 0:00:22.595980 START: 05:59:03.965475 END: 05:59:26.561455 2017-05-01 * CP COUNT: (18) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,E9,G1) * 2.7..6..4..4.5.8.....4..6...3...1..9.4..7..6.1......8....5.3..8..1.8.5..5..1..9.6 * PAIR G1: 1,3 BLK 3 H1: 1,3,5,9 # reduction candidate for 1,3 H1: 1,3 => CTR * 25789613461435.8973..41762583264175994527836117693548272.563..8.617895.35.3124976 H1: 5,9 # 4 pairs H2: 1,3,2,7,9 # reduction candidate for 1,3 H2: 1,3 # 7 pairs I2: 1,3,2,7 # reduction candidate for 1,3 I2: 1,3 # 6 pairs H3: 1,3,2,5,7,9 # reduction candidate for 1,3 H3: 1,3 => CTR * 2.7..6..461435.8.....4..6...3...1..9.4..7.3611...3..8....5.3..8..178.5.35.31..9.6 H3: 2,5,7,9 # 3 pairs I3: 1,3,2,5,7 # reduction candidate for 1,3 I3: 1,3 => CTR * 2.7.163.461435.897...497621.356.1..9.4..7.1631...3..85...563.18.617895.25..1..9.6 I3: 2,5,7 # 3 pairs * PAIR G1: 1,3 ROW 1 E1: 1,3,9 # reduction candidate for 1,3 E1: 9 # 8 pairs E1: 1,3 # 6 pairs * PAIR G1: 1,3 COL G G5: 1,3,2 # reduction candidate for 1,3 G5: 2 # 8 pairs G5: 1,3 # 4 pairs * PAIR A5: 8,9 BLK 4 C5: 8,9,2,5 # reduction candidate for 8,9 C5: 8,9 => CTR * 287..6.546147528939534186..735861429849.7..6.1......8.4..5.32183.168.5475.81.7936 C5: 2,5 # 4 pairs * PAIR A5: 8,9 ROW 5 D5: 8,9,2,3 # reduction candidate for 8,9 D5: 8,9 => CTR * 287396154614.5.8939534186..7358614298429753611..23478547.5.3.183.1.8.54.5.81..936 D5: 2,3 # 4 pairs F5: 8,9,2,5 # reduction candidate for 8,9 F5: 8,9 # 10 pairs * PAIR A5: 8,9 COL A A3: 8,9,3 # reduction candidate for 8,9 A3: 3 => CTR * 2.78361.4614.5.8.73.841762583..41.5994537826117..95483.295637.8.61.8.53258312.9.6 A3: 8,9 # 6 pairs * PAIR E9: 2,4 BLK 8 E7: 2,4,6,9 # reduction candidate for 2,4 E7: 2,4 => CTR * 287..6.54.14752893953418627735..1..9.4..75.6.1....4.85...523..8371689542528147936 E7: 6,9 # 4 pairs F8: 2,4,7,9 # reduction candidate for 2,4 F8: 2,4 # 9 pairs F9: 2,4,7 # reduction candidate for 2,4 F9: 2,4 # 10 pairs * PAIR E9: 2,4 ROW 9 H9: 2,4,3,7 # reduction candidate for 2,4 H9: 2,4 # 18 pairs H9: 3,7 # 4 pairs * PAIR E9: 2,4 COL E E4: 2,4,6 # reduction candidate for 2,4 E4: 2,4 # 5 pairs E6: 2,4,3,6,9 # reduction candidate for 2,4 E6: 2,4 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0132-base-pr-000.dot * REASONING * DIS # H1: 1,3 => CTR => H1: 5,9 * DIS # H3: 1,3 => CTR => H3: 2,5,7,9 * DIS # I3: 1,3 => CTR => I3: 2,5,7 * DIS # C5: 8,9 => CTR => C5: 2,5 * DIS # D5: 8,9 => CTR => D5: 2,3 * DIS # A3: 3 => CTR => A3: 8,9 * DIS # E7: 2,4 => CTR => E7: 6,9 * CNT 7 HDP CHAINS / 27 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,E9,G1) * 2.7..6..4..4.5.8.....4..6...3...1..9.4..7..6.1......8....5.3..8..1.8.5..5..1..9.6 * PAIR G1: 1,3 BLK 3 H1: 1,3,5,9 # reduction candidate for 1,3 H1: 1,3 => CTR * 25789613461435.8973..41762583264175994527836117693548272.563..8.617895.35.3124976 H2: 1,3,2,7,9 # reduction candidate for 1,3 H2: 1,3 # 7 pairs I2: 1,3,2,7 # reduction candidate for 1,3 I2: 1,3 # 6 pairs H3: 1,3,2,5,7,9 # reduction candidate for 1,3 H3: 1,3 => CTR * 2.7..6..461435.8.....4..6...3...1..9.4..7.3611...3..8....5.3..8..178.5.35.31..9.6 I3: 1,3,2,5,7 # reduction candidate for 1,3 I3: 1,3 => CTR * 2.7.163.461435.897...497621.356.1..9.4..7.1631...3..85...563.18.617895.25..1..9.6 * PAIR G1: 1,3 ROW 1 E1: 1,3,9 # reduction candidate for 1,3 E1: 9 => CTR * 287396154614.5.8939534186..73586142984..753611...3478547.5.3.183.1.8.54.5.81..936 * PAIR G1: 1,3 COL G G5: 1,3,2 # reduction candidate for 1,3 G5: 2 # 8 pairs G5: 1,3 # 7 pairs * PAIR RESTART * PAIR G1: 1,3 BLK 3 H2: 1,3,2,7,9 # reduction candidate for 1,3 H2: 1,3 # 9 pairs I2: 1,3,2,7 # reduction candidate for 1,3 I2: 1,3 # 8 pairs * PAIR G1: 1,3 COL G G5: 1,3,2 # reduction candidate for 1,3 G5: 2 # 8 pairs G5: 1,3 # 7 pairs * PAIR A5: 8,9 BLK 4 C5: 8,9,2,5 # reduction candidate for 8,9 C5: 8,9 => CTR * 2879361546147528939534186727358614298492753611.23.47854765.32183.168.5475.81.7936 * PAIR A5: 8,9 ROW 5 D5: 8,9,2,3 # reduction candidate for 8,9 D5: 8,9 => CTR * 2879.6.54..4.5.8.....4.86..835..1..9942875.6.176....85..95.3.18..1.895..528147936 * RESTART * PAIR A5: 8,9 COL A A3: 8,9,3 # reduction candidate for 8,9 A3: 3 => CTR * 2.78361.4614.5.8.73.841762583..41.5994537826117..95483.295637.8.61.8.53258312.9.6 * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A2,A3,A4,A5,B9,C5,C9,D1,D5,E1,E4,E7,F5,F9,G1,H1) * 2.7..6..4..4.5.8.....4..6...3...1..9.4..7..6.1....5.8....5.3..8..1.8.5..5..12.9.6 * PAIR A2: 3,6 COL A A8: 3,6,4,7 # reduction candidate for 3,6 A8: 4,7 => CTR * 2578163943647598...1.4326...382.1.59945378.6.1..9.5.83...593..8.9168.53258312.9.6 * PAIR RESTART * PAIR A3: 8,9 BLK 1 B1: 8,9,5 # reduction candidate for 8,9 B1: 8,9 => CTR * 2.7..6.54..4.5.8...5.41.6..7358614298423791651..245.8.4..593218..1.8.5..5..12.9.6 B1: 5 => SOLVED * 257816394364759821819432675738641259945278163126395487492563718671984532583127946 * DURATION: 0:00:18.224070 START: 05:59:44.964826 END: 06:00:03.188896 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0132-base-pr-001.dot * REASONING * DIS # H1: 1,3 => CTR => H1: 5,9 * DIS H1: 5,9 # H3: 1,3 => CTR => H3: 2,5,7,9 * DIS H1: 5,9 + H3: 2,5,7,9 # I3: 1,3 => CTR => I3: 2,5,7 * DIS H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 # E1: 9 => CTR => E1: 1,3 * DIS H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 # C5: 8,9 => CTR => C5: 2,5 * DIS H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 + C5: 2,5 # D5: 8,9 => CTR => D5: 2,3 * DIS H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 + C5: 2,5 + D5: 2,3 # A3: 3 => CTR => A3: 8,9 * DIS H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 + C5: 2,5 + D5: 2,3 + A3: 8,9 # A8: 4,7 => CTR => A8: 3,6 * DIS H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 + C5: 2,5 + D5: 2,3 + A3: 8,9 + A8: 3,6 # B1: 8,9 => CTR => B1: 5 * PRF H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 + C5: 2,5 + D5: 2,3 + A3: 8,9 + A8: 3,6 + B1: 5 => SOL * STA H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 + C5: 2,5 + D5: 2,3 + A3: 8,9 + A8: 3,6 + B1: 5 * CNT 10 HDP CHAINS / 20 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=132
Solution
position: 257816394364759821819432675738641259945278163126395487492563718671984532583127946 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: 1,3 => CTR => H1: 5,9 * INC # H1: 5,9 => UNS * INC # H2: 1,3 => UNS * INC # I2: 1,3 => UNS * DIS # H3: 1,3 => CTR => H3: 2,5,7,9 * INC # H3: 2,5,7,9 => UNS * DIS # I3: 1,3 => CTR => I3: 2,5,7 * INC # I3: 2,5,7 => UNS * INC # E1: 1,3 => UNS * INC # E1: 9 => UNS * INC # G5: 1,3 => UNS * INC # G5: 2 => UNS * DIS # C5: 8,9 => CTR => C5: 2,5 * INC # C5: 2,5 => UNS * DIS # D5: 8,9 => CTR => D5: 2,3 * INC # D5: 2,3 => UNS * INC # F5: 8,9 => UNS * INC # A3: 8,9 => UNS * DIS # A3: 3 => CTR => A3: 8,9 * DIS # E7: 2,4 => CTR => E7: 6,9 * INC # E7: 6,9 => UNS * INC # F8: 2,4 => UNS * INC # F9: 2,4 => UNS * INC # H9: 2,4 => UNS * INC # H9: 3,7 => UNS * INC # E4: 2,4 => UNS * INC # E6: 2,4 => UNS * CNT 27 HDP CHAINS / 27 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # H1: 1,3 => CTR => H1: 5,9 * INC H1: 5,9 # H2: 1,3 => UNS * INC H1: 5,9 # I2: 1,3 => UNS * DIS H1: 5,9 # H3: 1,3 => CTR => H3: 2,5,7,9 * DIS H1: 5,9 + H3: 2,5,7,9 # I3: 1,3 => CTR => I3: 2,5,7 * INC H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 # E1: 1,3 => UNS * DIS H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 # E1: 9 => CTR => E1: 1,3 * INC H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 # G5: 1,3 => UNS * INC H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 # G5: 2 => UNS * INC H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 # H2: 1,3 => UNS * INC H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 # I2: 1,3 => UNS * INC H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 # G5: 1,3 => UNS * INC H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 # G5: 2 => UNS * DIS H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 # C5: 8,9 => CTR => C5: 2,5 * DIS H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 + C5: 2,5 # D5: 8,9 => CTR => D5: 2,3 * INC H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 + C5: 2,5 + D5: 2,3 # A3: 8,9 => UNS * DIS H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 + C5: 2,5 + D5: 2,3 # A3: 3 => CTR => A3: 8,9 * INC H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 + C5: 2,5 + D5: 2,3 + A3: 8,9 # A8: 3,6 => UNS * DIS H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 + C5: 2,5 + D5: 2,3 + A3: 8,9 # A8: 4,7 => CTR => A8: 3,6 * DIS H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 + C5: 2,5 + D5: 2,3 + A3: 8,9 + A8: 3,6 # B1: 8,9 => CTR => B1: 5 * PRF H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 + C5: 2,5 + D5: 2,3 + A3: 8,9 + A8: 3,6 + B1: 5 => SOL * STA H1: 5,9 + H3: 2,5,7,9 + I3: 2,5,7 + E1: 1,3 + C5: 2,5 + D5: 2,3 + A3: 8,9 + A8: 3,6 + B1: 5 * CNT 21 HDP CHAINS / 20 HYP OPENED