Analysis of zz-www.sudokuwiki.org-0002-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=2
level: medium
position: ..1...76.6...9.4.8.....2...2..8.......7.6.5.......9..3...1.......6.4...5.15.7.9.. initial
Autosolve
position: ..1...76.6...9.4.8...6.2...2..8.......7.6.5.......9..3...1.......694...5.15.7.9.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 2,3 => CTR => B1: 5,8,9 * DIS # H2: 2,3 => CTR => H2: 1,5 * DIS # H3: 1,3 => CTR => H3: 5,9 * DIS # I4: 1,9 => CTR => I4: 4,6,7 * DIS # A6: 4,8 => CTR => A6: 1,5 * DIS # B6: 4,8 => CTR => B6: 5,6 * PRF # H6: 4,8 => SOL * DIS # C7: 4,8 => CTR => C7: 2,3,9 * DIS # G6: 1,6 => CTR => G6: 2,8 * DIS # B8: 3,8 => CTR => B8: 2,7 * CNT 10 HDP CHAINS / 53 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 2,3 => CTR => B1: 5,8,9 * DIS B1: 5,8,9 # B2: 5 => CTR => B2: 2,3 * DIS B1: 5,8,9 + B2: 2,3 # H3: 1,3 => CTR => H3: 5,9 * DIS B1: 5,8,9 + B2: 2,3 + H3: 5,9 # I4: 1,9 => CTR => I4: 4,6,7 * DIS B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 # A6: 4,8 => CTR => A6: 1,5 * DIS B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 + A6: 1,5 # B6: 4,8 => CTR => B6: 5,6 * PRF B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 + A6: 1,5 + B6: 5,6 # H6: 4,8 => SOL * STA B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 + A6: 1,5 + B6: 5,6 + H6: 4,8 * CNT 7 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..1...76.6...9.4.8.....2...2..8.......7.6.5.......9..3...1.......6.4...5.15.7.9.. | initial |
| ..1...76.6...9.4.8...6.2...2..8.......7.6.5.......9..3...1.......694...5.15.7.9.. | autosolve |
| 591483762632597418478612359259831647387264591164759283943125876726948135815376924 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) C2: 2,3 I1: 2,9 G3: 1,3 I3: 1,9 C6: 4,8 G4: 1,6 F8: 3,8 D9: 2,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F2,E3: 1.. / F2 = 1 => 9 pairs (_) / E3 = 1 => 0 pairs (*) A5,A6: 1.. / A5 = 1 => 11 pairs (_) / A6 = 1 => 17 pairs (_) G8,H8: 1.. / G8 = 1 => 8 pairs (_) / H8 = 1 => 10 pairs (_) F2,H2: 1.. / F2 = 1 => 9 pairs (_) / H2 = 1 => 0 pairs (*) I1,H2: 2.. / I1 = 2 => 8 pairs (_) / H2 = 2 => 0 pairs (X) E7,D9: 2.. / E7 = 2 => 0 pairs (*) / D9 = 2 => 0 pairs (X) B1,I1: 2.. / B1 = 2 => 0 pairs (X) / I1 = 2 => 8 pairs (_) C2,C7: 2.. / C2 = 2 => 8 pairs (_) / C7 = 2 => 0 pairs (X) E6,E7: 2.. / E6 = 2 => 9 pairs (_) / E7 = 2 => 0 pairs (*) D1,F1: 4.. / D1 = 4 => 13 pairs (_) / F1 = 4 => 10 pairs (_) H2,H3: 5.. / H2 = 5 => 15 pairs (_) / H3 = 5 => 8 pairs (_) E7,F7: 5.. / E7 = 5 => 15 pairs (_) / F7 = 5 => 11 pairs (_) B4,B6: 6.. / B4 = 6 => 0 pairs (X) / B6 = 6 => 8 pairs (_) F7,F9: 6.. / F7 = 6 => 17 pairs (_) / F9 = 6 => 11 pairs (_) B6,G6: 6.. / B6 = 6 => 8 pairs (_) / G6 = 6 => 0 pairs (X) F9,I9: 6.. / F9 = 6 => 11 pairs (_) / I9 = 6 => 17 pairs (_) A3,B3: 7.. / A3 = 7 => 11 pairs (_) / B3 = 7 => 8 pairs (_) D2,F2: 7.. / D2 = 7 => 8 pairs (_) / F2 = 7 => 0 pairs (*) F4,D6: 7.. / F4 = 7 => 8 pairs (_) / D6 = 7 => 0 pairs (*) D6,H6: 7.. / D6 = 7 => 0 pairs (*) / H6 = 7 => 0 pairs (X) D2,D6: 7.. / D2 = 7 => 8 pairs (_) / D6 = 7 => 0 pairs (*) F2,F4: 7.. / F2 = 7 => 0 pairs (*) / F4 = 7 => 0 pairs (X) I4,I7: 7.. / I4 = 7 => 0 pairs (*) / I7 = 7 => 0 pairs (X) * DURATION: 0:00:30.829756 START: 03:21:44.829963 END: 03:22:15.659719 2017-05-01 * CP COUNT: (23) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C2,C6,D9,F8,G3,G4,I1,I3) * ..1...76.6...9.4.8...6.2...2..8.......7.6.5.......9..3...1.......694...5.15.7.9.. * PAIR C2: 2,3 BLK 1 B1: 2,3,5,8,9 # reduction candidate for 2,3 B1: 2,3 => CTR * .21534769653791428...68235123.857..61.7.635..56..19.73..21.5.....6948..5.15.769.. B1: 5,8,9 # 8 pairs B2: 2,3,5 # reduction candidate for 2,3 B2: 2,3 # 13 pairs * PAIR C2: 2,3 ROW 2 H2: 2,3,1,5 # reduction candidate for 2,3 H2: 2,3 => CTR * ..15.4762652791438.7.6.215.2..857.....7.6.5..5...19.73...1256.7.2694...5.153769.. H2: 1,5 # 11 pairs * PAIR C2: 2,3 COL C C7: 2,3,4,8,9 # reduction candidate for 2,3 C7: 2,3 # 10 pairs C7: 4,8,9 # 8 pairs * PAIR I1: 2,9 ROW 1 B1: 2,9,3,5,8 # reduction candidate for 2,9 B1: 2,9 # 9 pairs B1: 3,5,8 # 8 pairs * PAIR I1: 2,9 COL I I5: 2,9,1,4 # reduction candidate for 2,9 I5: 2,9 # 13 pairs I5: 1,4 # 9 pairs * PAIR G3: 1,3 BLK 3 H2: 1,3,2,5 # reduction candidate for 1,3 H2: 1,3 # 9 pairs H3: 1,3,5,9 # reduction candidate for 1,3 H3: 1,3 => CTR * ..1..57626..791458...682..92..8.76....7.645.1164..9.73...1.6..7..694...5.15.7.9.6 H3: 5,9 # 9 pairs * PAIR G3: 1,3 ROW 3 E3: 1,3,5,8 # reduction candidate for 1,3 E3: 1,3 # 12 pairs E3: 5,8 # 10 pairs * PAIR G3: 1,3 COL G G8: 1,3,2,8 # reduction candidate for 1,3 G8: 2,8 # 11 pairs G8: 1,3 # 10 pairs * PAIR I3: 1,9 BLK 3 H3: 1,9,3,5 # reduction candidate for 1,9 H3: 1,9 # 15 pairs H3: 3,5 # 9 pairs * PAIR I3: 1,9 COL I I4: 1,9,4,6,7 # reduction candidate for 1,9 I4: 1,9 => CTR * ..1...7626...9.4.8...6.2...2..8.......73615.4.....9..3...156..7..694...5.1527.9.6 I4: 4,6,7 # 8 pairs I5: 1,9,2,4 # reduction candidate for 1,9 I5: 1,9 # 9 pairs * PAIR C6: 4,8 BLK 4 A5: 4,8,1,3,9 # reduction candidate for 4,8 A5: 4,8 # 20 pairs B5: 4,8,3,9 # reduction candidate for 4,8 B5: 4,8 # 12 pairs A6: 4,8,1,5 # reduction candidate for 4,8 A6: 4,8 => CTR * ..1...7626...9.4.8...6.2...2..8.....1.7264589.....9..3...125....2694...5.15376924 A6: 1,5 # 9 pairs B6: 4,8,5,6 # reduction candidate for 4,8 B6: 4,8 => CTR * ..1...76.6...9.4.8...6.2...26.8..1....7.6.5..5...196.3...125..6.2694..15.153769.. B6: 5,6 # 9 pairs * PAIR C6: 4,8 ROW 6 H6: 4,8,1,2,7 # reduction candidate for 4,8 H6: 4,8 => SOLVED * 591483762632597418478612359259831647387264591164759283943125876726948135815376924 H6: 1,2,7 # 8 pairs * PAIR C6: 4,8 COL C C3: 4,8,3,9 # reduction candidate for 4,8 C3: 4,8 # 10 pairs C7: 4,8,2,3,9 # reduction candidate for 4,8 C7: 4,8 => CTR * ..1...762652.91438..36.21592.98.7641..7.6.59..6...9..3...1.......694..15.15.7.9.. C7: 2,3,9 # 8 pairs * PAIR G4: 1,6 BLK 6 I4: 1,6,4,7,9 # reduction candidate for 1,6 I4: 1,6 # 11 pairs G6: 1,6,2,8 # reduction candidate for 1,6 G6: 1,6 => CTR * ..1...76.6..7914.8...6.23.12538176..197.6.582.6.529173...1.6..7..694..15.1527.9.6 G6: 2,8 # 9 pairs * PAIR F8: 3,8 BLK 8 E7: 3,8,2,5 # reduction candidate for 3,8 E7: 3,8 # 13 pairs F7: 3,8,5,6 # reduction candidate for 3,8 F7: 3,8 # 19 pairs F9: 3,8,6 # reduction candidate for 3,8 F9: 3,8 # 17 pairs * PAIR F8: 3,8 ROW 8 A8: 3,8,7 # reduction candidate for 3,8 A8: 3,8 # 11 pairs B8: 3,8,2,7 # reduction candidate for 3,8 B8: 3,8 => CTR * ..1..576.6.2791458574682...2538176....7.6452.468529.73...1.6..77.694.215.1527.9.6 B8: 2,7 # 9 pairs G8: 3,8,1,2 # reduction candidate for 3,8 G8: 3,8 # 14 pairs H8: 3,8,1,2,7 # reduction candidate for 3,8 H8: 3,8 # 13 pairs * PAIR F8: 3,8 COL F F1: 3,8,4,5 # reduction candidate for 3,8 F1: 3,8 # 17 pairs F1: 4,5 # 9 pairs * PAIR D9: 2,3 BLK 8 E7: 2,3,5,8 # reduction candidate for 2,3 E7: 2,3 # 13 pairs E7: 5,8 # 11 pairs * PAIR D9: 2,3 ROW 9 H9: 2,3,4,8 # reduction candidate for 2,3 H9: 2,3 # 12 pairs H9: 4,8 # 9 pairs * PAIR D9: 2,3 COL D D5: 2,3,4 # reduction candidate for 2,3 D5: 4 # 13 pairs D5: 2,3 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0002-base-pr-000.dot * REASONING * DIS # B1: 2,3 => CTR => B1: 5,8,9 * DIS # H2: 2,3 => CTR => H2: 1,5 * DIS # H3: 1,3 => CTR => H3: 5,9 * DIS # I4: 1,9 => CTR => I4: 4,6,7 * DIS # A6: 4,8 => CTR => A6: 1,5 * DIS # B6: 4,8 => CTR => B6: 5,6 * PRF # H6: 4,8 => SOL * DIS # C7: 4,8 => CTR => C7: 2,3,9 * DIS # G6: 1,6 => CTR => G6: 2,8 * DIS # B8: 3,8 => CTR => B8: 2,7 * CNT 10 HDP CHAINS / 53 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C2,C6,D9,F8,G3,G4,I1,I3) * ..1...76.6...9.4.8...6.2...2..8.......7.6.5.......9..3...1.......694...5.15.7.9.. * PAIR C2: 2,3 BLK 1 B1: 2,3,5,8,9 # reduction candidate for 2,3 B1: 2,3 => CTR * .21534769653791428...68235123.857..61.7.635..56..19.73..21.5.....6948..5.15.769.. B2: 2,3,5 # reduction candidate for 2,3 B2: 2,3 # 13 pairs * RESTART * PAIR C2: 2,3 BLK 1 B2: 2,3,5 # reduction candidate for 2,3 B2: 5 => CTR * ..15.4762652.9.4.8...6.2.592..8.....1.7.635.45..4.9.73...1....7..6948..5.15.769.. * PAIR C2: 2,3 COL C C7: 2,3,9 # reduction candidate for 2,3 C7: 2,3 # 13 pairs C7: 9 # 11 pairs * PAIR G3: 1,3 BLK 3 H3: 1,3,5,9 # reduction candidate for 1,3 H3: 1,3 => CTR * ..1..57626..791458...682..92..8.76....7.645.116...9.73...1.6..7..694...5.15.7.9.6 * PAIR I3: 1,9 COL I I4: 1,9,4,6,7 # reduction candidate for 1,9 I4: 1,9 => CTR * ..1...7626...9.4.8...6.23..2..8.......73615.4.....9..3...156..7..694...5.1527.9.6 * RESTART * PAIR RESTART * PAIR C6: 4,8 BLK 4 A5: 4,8,1,3,9 # reduction candidate for 4,8 A5: 4,8 # 21 pairs B5: 4,8,3,9 # reduction candidate for 4,8 B5: 4,8 # 17 pairs A6: 4,8,1,5 # reduction candidate for 4,8 A6: 4,8 => CTR * ..1...7626.3791458...6.23912.9837...137.64589.6..19273..21....7..694..25.1527.9.. B6: 4,8,5,6 # reduction candidate for 4,8 B6: 4,8 => CTR * ..1...7626...9.4.8...6.23..26.8..1....7.6.5.95...196.3...1258.6.2694...5.15.7.9.. * PAIR C6: 4,8 ROW 6 H6: 4,8,1,2,7 # reduction candidate for 4,8 H6: 4,8 => SOLVED * 591483762632597418478612359259831647387264591164759283943125876726948135815376924 * DURATION: 0:00:13.639782 START: 03:22:48.996415 END: 03:23:02.636197 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0002-base-pr-001.dot * REASONING * DIS # B1: 2,3 => CTR => B1: 5,8,9 * DIS B1: 5,8,9 # B2: 5 => CTR => B2: 2,3 * DIS B1: 5,8,9 + B2: 2,3 # H3: 1,3 => CTR => H3: 5,9 * DIS B1: 5,8,9 + B2: 2,3 + H3: 5,9 # I4: 1,9 => CTR => I4: 4,6,7 * DIS B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 # A6: 4,8 => CTR => A6: 1,5 * DIS B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 + A6: 1,5 # B6: 4,8 => CTR => B6: 5,6 * PRF B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 + A6: 1,5 + B6: 5,6 # H6: 4,8 => SOL * STA B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 + A6: 1,5 + B6: 5,6 + H6: 4,8 * CNT 7 HDP CHAINS / 13 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=2
Solution
position: 591483762632597418478612359259831647387264591164759283943125876726948135815376924 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 # B1: 2,3 => CTR => B1: 5,8,9 * INC # B1: 5,8,9 => UNS * INC # B2: 2,3 => UNS * DIS # H2: 2,3 => CTR => H2: 1,5 * INC # H2: 1,5 => UNS * INC # C7: 2,3 => UNS * INC # C7: 4,8,9 => UNS * INC # B1: 2,9 => UNS * INC # B1: 3,5,8 => UNS * INC # I5: 2,9 => UNS * INC # I5: 1,4 => UNS * INC # H2: 1,3 => UNS * DIS # H3: 1,3 => CTR => H3: 5,9 * INC # H3: 5,9 => UNS * INC # E3: 1,3 => UNS * INC # E3: 5,8 => UNS * INC # G8: 1,3 => UNS * INC # G8: 2,8 => UNS * INC # H3: 1,9 => UNS * INC # H3: 3,5 => UNS * DIS # I4: 1,9 => CTR => I4: 4,6,7 * INC # I4: 4,6,7 => UNS * INC # I5: 1,9 => UNS * INC # A5: 4,8 => UNS * INC # B5: 4,8 => UNS * DIS # A6: 4,8 => CTR => A6: 1,5 * INC # A6: 1,5 => UNS * DIS # B6: 4,8 => CTR => B6: 5,6 * INC # B6: 5,6 => UNS * PRF # H6: 4,8 => SOL * INC # H6: 1,2,7 => UNS * INC # C3: 4,8 => UNS * DIS # C7: 4,8 => CTR => C7: 2,3,9 * INC # C7: 2,3,9 => UNS * INC # I4: 1,6 => UNS * DIS # G6: 1,6 => CTR => G6: 2,8 * INC # G6: 2,8 => UNS * INC # E7: 3,8 => UNS * INC # F7: 3,8 => UNS * INC # F9: 3,8 => UNS * INC # A8: 3,8 => UNS * DIS # B8: 3,8 => CTR => B8: 2,7 * INC # B8: 2,7 => UNS * INC # G8: 3,8 => UNS * INC # H8: 3,8 => UNS * INC # F1: 3,8 => UNS * INC # F1: 4,5 => UNS * INC # E7: 2,3 => UNS * INC # E7: 5,8 => UNS * INC # H9: 2,3 => UNS * INC # H9: 4,8 => UNS * INC # D5: 2,3 => UNS * INC # D5: 4 => UNS * CNT 53 HDP CHAINS / 53 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B1: 2,3 => CTR => B1: 5,8,9 * INC B1: 5,8,9 # B2: 2,3 => UNS * INC B1: 5,8,9 # B2: 2,3 => UNS * DIS B1: 5,8,9 # B2: 5 => CTR => B2: 2,3 * INC B1: 5,8,9 + B2: 2,3 # C7: 2,3 => UNS * INC B1: 5,8,9 + B2: 2,3 # C7: 9 => UNS * DIS B1: 5,8,9 + B2: 2,3 # H3: 1,3 => CTR => H3: 5,9 * DIS B1: 5,8,9 + B2: 2,3 + H3: 5,9 # I4: 1,9 => CTR => I4: 4,6,7 * INC B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 # A5: 4,8 => UNS * INC B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 # B5: 4,8 => UNS * DIS B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 # A6: 4,8 => CTR => A6: 1,5 * DIS B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 + A6: 1,5 # B6: 4,8 => CTR => B6: 5,6 * PRF B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 + A6: 1,5 + B6: 5,6 # H6: 4,8 => SOL * STA B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 + A6: 1,5 + B6: 5,6 + H6: 4,8 * CNT 13 HDP CHAINS / 13 HYP OPENED