Analysis of zz-www.sudokuwiki.org-interesting-squeezed-naughts-base.sdk
Contents
Original Sudoku
level: medium
position: 9....165..5..6...7....9...2.....812...........137.....6...8....5...2..6..746....3 initial
Autosolve
position: 9..37165..5..6...7....9...2....3812...........137.....6...8....5...2..6..746....3 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 2,8 => CTR => B1: 4 * DIS # A2: 1,8 => CTR => A2: 3,4 * DIS # A3: 1,8 => CTR => A3: 3,4,7 * DIS # H2: 1,8 => CTR => H2: 3,4,9 * DIS # C4: 5 => CTR => C4: 6,7 * DIS # G2: 4,8 => CTR => G2: 3,9 * PRF # H2: 4,8 => SOL * DIS # H3: 4,8 => CTR => H3: 1,3 * DIS # B1: 2 => CTR => B1: 4,8 * PRF # I5: 4,8 => SOL * DIS # I6: 4,8 => CTR => I6: 5,6,9 * DIS # I8: 4,8 => CTR => I8: 1,9 * PRF # A3: 4,7 => SOL * PRF # C4: 7 => SOL * DIS # D5: 5,9 => CTR => D5: 1,2 * DIS # F5: 5,9 => CTR => F5: 2,6 * PRF # F6: 5,9 => SOL * PRF # I4: 5,9 => SOL * DIS # D7: 5,9 => CTR => D7: 1,4 * DIS # E5: 4,5 => CTR => E5: 1 * PRF # E5: 1 => SOL * DIS # I6: 4,5 => CTR => I6: 6,8,9 * DIS # E5: 4 => CTR => E5: 1,5 * DIS # D7: 5,9 => CTR => D7: 1,4 * DIS # G9: 5,9 => CTR => G9: 2,8 * DIS # F5: 5,9 => CTR => F5: 2,6 * PRF # F6: 5,9 => SOL * DIS # G9: 8,9 => CTR => G9: 2,5 * DIS # H2: 8,9 => CTR => H2: 1,3,4 * CNT 29 HDP CHAINS / 67 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 2,8 => CTR => B1: 4 * DIS B1: 4 # A2: 1,8 => CTR => A2: 3 * DIS B1: 4 + A2: 3 # A3: 1,8 => CTR => A3: 7 * PRF B1: 4 + A2: 3 + A3: 7 => SOL * STA B1: 4 + A2: 3 + A3: 7 * CNT 4 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 9....165..5..6...7....9...2.....812...........137.....6...8....5...2..6..746....3 | initial |
| 9..37165..5..6...7....9...2....3812...........137.....6...8....5...2..6..746....3 | autosolve |
| 942371658351862947786594312467938125895216734213745896629483571538127469174659283 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (21) C1: 2,8 C2: 1,8 C3: 6,7 D2: 2,8 F2: 2,4 D3: 5,8 F3: 4,5 I1: 4,8 A4: 4,7 C5: 5,6 D4: 5,9 E6: 4,5 G5: 3,7 H5: 3,7 B7: 2,3 B8: 3,8 F7: 3,7 F8: 3,7 E9: 1,5 F9: 5,9 H9: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H2,H3: 1.. / H2 = 1 => 0 pairs (X) / H3 = 1 => 21 pairs (_) D5,E5: 1.. / D5 = 1 => 0 pairs (X) / E5 = 1 => 0 pairs (_) I7,I8: 1.. / I7 = 1 => 24 pairs (_) / I8 = 1 => 23 pairs (_) A3,H3: 1.. / A3 = 1 => 0 pairs (X) / H3 = 1 => 21 pairs (_) A9,E9: 1.. / A9 = 1 => 0 pairs (*) / E9 = 1 => 0 pairs (X) E5,E9: 1.. / E5 = 1 => 0 pairs (*) / E9 = 1 => 0 pairs (X) B1,C1: 2.. / B1 = 2 => 0 pairs (X) / C1 = 2 => 22 pairs (_) D2,F2: 2.. / D2 = 2 => 23 pairs (_) / F2 = 2 => 0 pairs (*) G7,G9: 2.. / G7 = 2 => 0 pairs (X) / G9 = 2 => 22 pairs (_) A6,F6: 2.. / A6 = 2 => 23 pairs (_) / F6 = 2 => 0 pairs (X) A9,G9: 2.. / A9 = 2 => 0 pairs (X) / G9 = 2 => 22 pairs (_) C1,C7: 2.. / C1 = 2 => 22 pairs (_) / C7 = 2 => 0 pairs (X) D2,D5: 2.. / D2 = 2 => 23 pairs (_) / D5 = 2 => 0 pairs (*) A2,A3: 3.. / A2 = 3 => 21 pairs (_) / A3 = 3 => 24 pairs (_) G5,H5: 3.. / G5 = 3 => 24 pairs (_) / H5 = 3 => 17 pairs (_) B7,B8: 3.. / B7 = 3 => 23 pairs (_) / B8 = 3 => 19 pairs (_) F7,F8: 3.. / F7 = 3 => 19 pairs (_) / F8 = 3 => 23 pairs (_) B7,F7: 3.. / B7 = 3 => 23 pairs (_) / F7 = 3 => 19 pairs (_) B8,F8: 3.. / B8 = 3 => 19 pairs (_) / F8 = 3 => 23 pairs (_) F2,F3: 4.. / F2 = 4 => 23 pairs (_) / F3 = 4 => 0 pairs (*) E5,E6: 4.. / E5 = 4 => 0 pairs (X) / E6 = 4 => 26 pairs (_) D7,D8: 4.. / D7 = 4 => 23 pairs (_) / D8 = 4 => 21 pairs (_) B1,I1: 4.. / B1 = 4 => 24 pairs (_) / I1 = 4 => 0 pairs (X) D3,F3: 5.. / D3 = 5 => 0 pairs (*) / F3 = 5 => 0 pairs (X) C4,C5: 5.. / C4 = 5 => 0 pairs (X) / C5 = 5 => 22 pairs (_) B3,C3: 6.. / B3 = 6 => 21 pairs (_) / C3 = 6 => 0 pairs (*) F5,F6: 6.. / F5 = 6 => 22 pairs (_) / F6 = 6 => 23 pairs (_) F6,I6: 6.. / F6 = 6 => 23 pairs (_) / I6 = 6 => 22 pairs (_) A3,C3: 7.. / A3 = 7 => 0 pairs (*) / C3 = 7 => 0 pairs (X) A4,C4: 7.. / A4 = 7 => 21 pairs (_) / C4 = 7 => 0 pairs (*) G5,H5: 7.. / G5 = 7 => 17 pairs (_) / H5 = 7 => 24 pairs (_) F7,F8: 7.. / F7 = 7 => 23 pairs (_) / F8 = 7 => 19 pairs (_) F8,G8: 7.. / F8 = 7 => 19 pairs (_) / G8 = 7 => 23 pairs (_) A3,A4: 7.. / A3 = 7 => 0 pairs (*) / A4 = 7 => 0 pairs (X) C3,C4: 7.. / C3 = 7 => 21 pairs (_) / C4 = 7 => 0 pairs (*) H5,H7: 7.. / H5 = 7 => 24 pairs (_) / H7 = 7 => 17 pairs (_) D2,D3: 8.. / D2 = 8 => 0 pairs (*) / D3 = 8 => 0 pairs (X) G2,H2: 9.. / G2 = 9 => 21 pairs (_) / H2 = 9 => 0 pairs (X) B4,B5: 9.. / B4 = 9 => 0 pairs (X) / B5 = 9 => 0 pairs (_) C7,C8: 9.. / C7 = 9 => 23 pairs (_) / C8 = 9 => 25 pairs (_) * DURATION: 0:00:53.295462 START: 23:25:57.258944 END: 23:26:50.554406 2019-04-28 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B7,B8,C1,C2,C3,C5,D2,D3,D4,E6,E9,F2,F3,F7,F8,F9,G5,H5,H9,I1) * 9..37165..5..6...7....9...2....3812...........137.....6...8....5...2..6..746....3 * PAIR C1: 2,8 BLK 1 B1: 2,8,4 # reduction candidate for 2,8 B1: 2,8 => CTR * 9..371654.51.6...7....9..12....3812.....4.....1375....6...8....5...2..6.1746....3 B1: 4 # 24 pairs * PAIR C2: 1,8 BLK 1 A2: 1,8,3,4 # reduction candidate for 1,8 A2: 1,8 => CTR * 942371658.5.264..7367895412796538124485912.7621374689562.183.4.5..42..6..74659.83 A2: 3,4 # 22 pairs A3: 1,8,3,4,7 # reduction candidate for 1,8 A3: 1,8 => CTR * 94237165835..6...7.67895..2796538124485912..621374689562..8357.538.27469174659.83 A3: 3,4,7 # 21 pairs * PAIR C2: 1,8 ROW 2 H2: 1,8,3,4,9 # reduction candidate for 1,8 H2: 1,8 => CTR * 9.2371658358264917167895..27...3812.82.1.6..94137..8..6...8....5...2..6.274619583 H2: 3,4,9 # 21 pairs * PAIR C2: 1,8 COL C C8: 1,8,9 # reduction candidate for 1,8 C8: 9 # 25 pairs C8: 1,8 # 23 pairs * PAIR C3: 6,7 COL C C4: 6,7,5 # reduction candidate for 6,7 C4: 5 => CTR * 9..371654.51.6...7.67.9..12745938126896......2137.6...6...8....5...2..6.174659283 C4: 6,7 # 22 pairs * PAIR I1: 4,8 BLK 3 G2: 4,8,3,9 # reduction candidate for 4,8 G2: 4,8 => CTR * 9..37165.351.6..97....9.312....3812.......73..137...4.6...83.7.538.27.6.17465..83 G2: 3,9 # 22 pairs H2: 4,8,1,3,9 # reduction candidate for 4,8 H2: 4,8 => SOLVED * 942371658351862947786594312467938125895216734213745896629483571538127469174659283 H2: 1,3,9 # 21 pairs G3: 4,8,3 # reduction candidate for 4,8 G3: 4,8 # 25 pairs H3: 4,8,1,3 # reduction candidate for 4,8 H3: 4,8 => CTR * 9..37165.3582649171678953427...3812....1..73..137.....6..583.7.53.42786.874619..3 H3: 1,3 # 22 pairs * PAIR I1: 4,8 ROW 1 B1: 4,8,2 # reduction candidate for 4,8 B1: 2 => CTR * 928371654.51.6...7....9..12....3812.....1.37..1374..9.6321874..589.23761174659283 B1: 4,8 # 22 pairs * PAIR I1: 4,8 COL I I5: 4,8,5,6,9 # reduction candidate for 4,8 I5: 4,8 => SOLVED * 942371658351862947786594312467938125895216734213745896629483571538127469174659283 I5: 5,6,9 # 22 pairs I6: 4,8,5,6,9 # reduction candidate for 4,8 I6: 4,8 => CTR * 9..37165..51.6...7....9..12....3812.....1....2137465986...8...55...2..6.174659283 I6: 5,6,9 # 21 pairs I8: 4,8,1,9 # reduction candidate for 4,8 I8: 4,8 => CTR * 9..37165..5..6...7....9...2....3812.....4....21375....6...8...15...2..6..7461.2.3 I8: 1,9 # 22 pairs * PAIR A4: 4,7 COL A A3: 4,7,1,3,8 # reduction candidate for 4,7 A3: 4,7 => SOLVED * 942371658351862947786594312467938125895216734213745896629483571538127469174659283 A3: 1,3,8 # 21 pairs * PAIR C5: 5,6 BLK 4 C4: 5,6,7 # reduction candidate for 5,6 C4: 7 => SOLVED * 942371658351862947786594312467938125895216734213745896629483571538127469174659283 C4: 5,6 # 21 pairs * PAIR C5: 5,6 ROW 5 F5: 5,6,2,9 # reduction candidate for 5,6 F5: 5,6 # 23 pairs I5: 5,6,4,8,9 # reduction candidate for 5,6 I5: 5,6 # 26 pairs * PAIR D4: 5,9 BLK 5 D5: 5,9,1,2 # reduction candidate for 5,9 D5: 5,9 => CTR * 94.37165..512649373.78954127...3812.4...1.37.2137468956..18.5495.942.761174659283 D5: 1,2 # 22 pairs F5: 5,9,2,6 # reduction candidate for 5,9 F5: 5,9 => CTR * 94.37165..518629.7...594.12..593812.896215..4213746.9.6...8....5...2..6.174659283 F5: 2,6 # 22 pairs F6: 5,9,2,6 # reduction candidate for 5,9 F6: 5,9 => SOLVED * 942371658351862947786594312467938125895216734213745896629483571538127469174659283 F6: 2,6 # 22 pairs * PAIR D4: 5,9 ROW 4 I4: 5,9,4,6 # reduction candidate for 5,9 I4: 5,9 => SOLVED * 942371658351862947786594312467938125895216734213745896629483571538127469174659283 I4: 4,6 # 22 pairs * PAIR D4: 5,9 COL D D7: 5,9,1,4 # reduction candidate for 5,9 D7: 5,9 => CTR * 9..37165..5.264..7...895..2...93812..9.1......137.....6..58.2..5..42..6.274619583 D7: 1,4 # 22 pairs * PAIR E6: 4,5 BLK 5 E5: 4,5,1 # reduction candidate for 4,5 E5: 4,5 => CTR * 9..37165..5.264..7...895..2...93812..9.1......137.....6..58.2..5..42..6.274619583 E5: 1 => SOLVED * 942371658351862947786594312467938125895216734213745896629483571538127469174659283 * PAIR E6: 4,5 ROW 6 G6: 4,5,8,9 # reduction candidate for 4,5 G6: 4,5 # 25 pairs I6: 4,5,6,8,9 # reduction candidate for 4,5 I6: 4,5 => CTR * 942371658351862947...594312..593812..96.1573.213746895629483571538127469174659283 I6: 6,8,9 # 21 pairs * PAIR E9: 1,5 BLK 8 D7: 1,5,4,9 # reduction candidate for 1,5 D7: 1,5 # 25 pairs D7: 4,9 # 22 pairs * PAIR E9: 1,5 COL E E5: 1,5,4 # reduction candidate for 1,5 E5: 4 => CTR * 9..37165..5.264..7...895..2...93812..9.14.....1375....6..58.2..5..42..6.274619583 E5: 1,5 # 26 pairs * PAIR F9: 5,9 BLK 8 D7: 5,9,1,4 # reduction candidate for 5,9 D7: 5,9 => CTR * 9..37165..5.264..7...895..2...93812..9.1......137.....6..58.2..5..42..6.274619583 D7: 1,4 # 22 pairs * PAIR F9: 5,9 ROW 9 G9: 5,9,2,8 # reduction candidate for 5,9 G9: 5,9 => CTR * 942371658.58264..7.67895..279653812..2.1......137.2..663..872..58..2376.27461..83 G9: 2,8 # 22 pairs * PAIR F9: 5,9 COL F F5: 5,9,2,6 # reduction candidate for 5,9 F5: 5,9 => CTR * 94.37165..518629.7...594.12..593812.896215..4213746.9.6...8....5...2..6.174659283 F5: 2,6 # 22 pairs F6: 5,9,2,6 # reduction candidate for 5,9 F6: 5,9 => SOLVED * 942371658351862947786594312467938125895216734213745896629483571538127469174659283 F6: 2,6 # 22 pairs * PAIR H9: 8,9 BLK 9 G8: 8,9,4,7 # reduction candidate for 8,9 G8: 8,9 # 27 pairs I8: 8,9,1,4 # reduction candidate for 8,9 I8: 8,9 # 27 pairs G9: 8,9,2,5 # reduction candidate for 8,9 G9: 8,9 => CTR * 9.237165..5..6...7...594..2..593812...........137.....6...8.2.55...2..61274615..3 G9: 2,5 # 22 pairs * PAIR H9: 8,9 COL H H2: 8,9,1,3,4 # reduction candidate for 8,9 H2: 8,9 => CTR * 9.237165.1582643973.7895.12....3812.....4.73..1375..4.62..83.7.53..27.6..7461.2.3 H2: 1,3,4 # 21 pairs H6: 8,9,4 # reduction candidate for 8,9 H6: 8,9 # 23 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-interesting-squeezed-naughts-base-pr-000.dot * REASONING * DIS # B1: 2,8 => CTR => B1: 4 * DIS # A2: 1,8 => CTR => A2: 3,4 * DIS # A3: 1,8 => CTR => A3: 3,4,7 * DIS # H2: 1,8 => CTR => H2: 3,4,9 * DIS # C4: 5 => CTR => C4: 6,7 * DIS # G2: 4,8 => CTR => G2: 3,9 * PRF # H2: 4,8 => SOL * DIS # H3: 4,8 => CTR => H3: 1,3 * DIS # B1: 2 => CTR => B1: 4,8 * PRF # I5: 4,8 => SOL * DIS # I6: 4,8 => CTR => I6: 5,6,9 * DIS # I8: 4,8 => CTR => I8: 1,9 * PRF # A3: 4,7 => SOL * PRF # C4: 7 => SOL * DIS # D5: 5,9 => CTR => D5: 1,2 * DIS # F5: 5,9 => CTR => F5: 2,6 * PRF # F6: 5,9 => SOL * PRF # I4: 5,9 => SOL * DIS # D7: 5,9 => CTR => D7: 1,4 * DIS # E5: 4,5 => CTR => E5: 1 * PRF # E5: 1 => SOL * DIS # I6: 4,5 => CTR => I6: 6,8,9 * DIS # E5: 4 => CTR => E5: 1,5 * DIS # D7: 5,9 => CTR => D7: 1,4 * DIS # G9: 5,9 => CTR => G9: 2,8 * DIS # F5: 5,9 => CTR => F5: 2,6 * PRF # F6: 5,9 => SOL * DIS # G9: 8,9 => CTR => G9: 2,5 * DIS # H2: 8,9 => CTR => H2: 1,3,4 * CNT 29 HDP CHAINS / 67 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B7,B8,C1,C2,C3,C5,D2,D3,D4,E6,E9,F2,F3,F7,F8,F9,G5,H5,H9,I1) * 9..37165..5..6...7....9...2....3812...........137.....6...8....5...2..6..746....3 * PAIR C1: 2,8 BLK 1 B1: 2,8,4 # reduction candidate for 2,8 B1: 2,8 => CTR * 9..371654.51.6...7....9..12....3812.....4.....1375....6...8....5...2..6.1746....3 * PAIR C2: 1,8 BLK 1 A2: 1,8,3 # reduction candidate for 1,8 A2: 1,8 => CTR * 942371658.5.264.3736789541279653812448591237621374689562.183.4.5..42..6..74659.83 A3: 1,8,7 # reduction candidate for 1,8 A3: 1,8 => CTR * 94237165835..6...7.67895..2796538124..5.......1374....6...8....5...2..6..74659.83 A3: 7 => SOLVED * 942371658351862947786594312467938125895216734213745896629483571538127469174659283 * DURATION: 0:00:03.765794 START: 23:27:38.908198 END: 23:27:42.673992 2019-04-28 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-interesting-squeezed-naughts-base-pr-001.dot * REASONING * DIS # B1: 2,8 => CTR => B1: 4 * DIS B1: 4 # A2: 1,8 => CTR => A2: 3 * DIS B1: 4 + A2: 3 # A3: 1,8 => CTR => A3: 7 * PRF B1: 4 + A2: 3 + A3: 7 => SOL * STA B1: 4 + A2: 3 + A3: 7 * CNT 4 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuwiki.org/Interesting_Sudokus 24 Clues, minimal "2 squeezed naughts mirrored by diagonal" Discovered by Klaus Brenner
Solution
position: 942371658351862947786594312467938125895216734213745896629483571538127469174659283 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: 2,8 => CTR => B1: 4 * INC # B1: 4 => UNS * DIS # A2: 1,8 => CTR => A2: 3,4 * INC # A2: 3,4 => UNS * DIS # A3: 1,8 => CTR => A3: 3,4,7 * INC # A3: 3,4,7 => UNS * DIS # H2: 1,8 => CTR => H2: 3,4,9 * INC # H2: 3,4,9 => UNS * INC # C8: 1,8 => UNS * INC # C8: 9 => UNS * INC # C4: 6,7 => UNS * DIS # C4: 5 => CTR => C4: 6,7 * DIS # G2: 4,8 => CTR => G2: 3,9 * INC # G2: 3,9 => UNS * PRF # H2: 4,8 => SOL * INC # H2: 1,3,9 => UNS * INC # G3: 4,8 => UNS * DIS # H3: 4,8 => CTR => H3: 1,3 * INC # H3: 1,3 => UNS * INC # B1: 4,8 => UNS * DIS # B1: 2 => CTR => B1: 4,8 * PRF # I5: 4,8 => SOL * INC # I5: 5,6,9 => UNS * DIS # I6: 4,8 => CTR => I6: 5,6,9 * INC # I6: 5,6,9 => UNS * DIS # I8: 4,8 => CTR => I8: 1,9 * INC # I8: 1,9 => UNS * PRF # A3: 4,7 => SOL * INC # A3: 1,3,8 => UNS * INC # C4: 5,6 => UNS * PRF # C4: 7 => SOL * INC # F5: 5,6 => UNS * INC # I5: 5,6 => UNS * DIS # D5: 5,9 => CTR => D5: 1,2 * INC # D5: 1,2 => UNS * DIS # F5: 5,9 => CTR => F5: 2,6 * INC # F5: 2,6 => UNS * PRF # F6: 5,9 => SOL * INC # F6: 2,6 => UNS * PRF # I4: 5,9 => SOL * INC # I4: 4,6 => UNS * DIS # D7: 5,9 => CTR => D7: 1,4 * INC # D7: 1,4 => UNS * DIS # E5: 4,5 => CTR => E5: 1 * PRF # E5: 1 => SOL * INC # G6: 4,5 => UNS * DIS # I6: 4,5 => CTR => I6: 6,8,9 * INC # I6: 6,8,9 => UNS * INC # D7: 1,5 => UNS * INC # D7: 4,9 => UNS * INC # E5: 1,5 => UNS * DIS # E5: 4 => CTR => E5: 1,5 * DIS # D7: 5,9 => CTR => D7: 1,4 * INC # D7: 1,4 => UNS * DIS # G9: 5,9 => CTR => G9: 2,8 * INC # G9: 2,8 => UNS * DIS # F5: 5,9 => CTR => F5: 2,6 * INC # F5: 2,6 => UNS * PRF # F6: 5,9 => SOL * INC # F6: 2,6 => UNS * INC # G8: 8,9 => UNS * INC # I8: 8,9 => UNS * DIS # G9: 8,9 => CTR => G9: 2,5 * INC # G9: 2,5 => UNS * DIS # H2: 8,9 => CTR => H2: 1,3,4 * INC # H2: 1,3,4 => UNS * INC # H6: 8,9 => UNS * CNT 67 HDP CHAINS / 67 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B1: 2,8 => CTR => B1: 4 * DIS B1: 4 # A2: 1,8 => CTR => A2: 3 * DIS B1: 4 + A2: 3 # A3: 1,8 => CTR => A3: 7 * PRF B1: 4 + A2: 3 + A3: 7 => SOL * STA B1: 4 + A2: 3 + A3: 7 * CNT 4 HDP CHAINS / 3 HYP OPENED