Analysis of zz-www.sudokuoftheday.co.uk-20190122-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019
level: medium
position: ...3.4....5.8....3..........3.......9....8..68.4..91...8.....1....92.45.7....19.. initial
Autosolve
position: ...3.45...5.8....3.....5...53.......9....83.6864.391.5289..3617.1.927458745681932 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A3: 1,6 => SOL * DIS # E1: 1,6 => CTR => E1: 7,9 * PRF # A3: 1,4 => SOL * DIS # A3: 3,6 => CTR => A3: 1,4 * PRF # E1: 1,9 => SOL * PRF # C2: 7 => SOL * DIS # I3: 1,9 => CTR => I3: 4 * PRF # I3: 4 => SOL * PRF # E1: 1,9 => SOL * PRF # H1: 2,7 => SOL * DIS # H3: 2,7 => CTR => H3: 6,8 * PRF # C2: 2,7 => SOL * DIS # C2: 6 => CTR => C2: 2,7 * PRF # G4: 2,7 => SOL * PRF # I3: 4,9 => SOL * DIS # I3: 1 => CTR => I3: 4,9 * PRF # H4: 2,7,8 => SOL * PRF # C5: 2,7 => SOL * DIS # D5: 2,7 => CTR => D5: 1,4,5 * DIS # B3: 2,7 => CTR => B3: 9 * DIS # D4: 2,7 => CTR => D4: 1,4 * DIS # D5: 2,7 => CTR => D5: 1,4,5 * DIS # D3: 1 => CTR => D3: 2,7 * PRF # H4: 2,7,8 => SOL * PRF # I3: 4,9 => SOL * DIS # I3: 1 => CTR => I3: 4,9 * PRF # G4: 2,7 => SOL * DIS # H4: 2,7 => CTR => H4: 4,8,9 * PRF # H1: 2,7 => SOL * DIS # H3: 2,7 => CTR => H3: 6,8 * DIS # A3: 3,6 => CTR => A3: 1,4 * PRF # A3: 1,4 => SOL * PRF # C3: 3,6 => SOL * DIS # C3: 2,7,8 => CTR => C3: 3,6 * PRF # D5: 1,2,7 => SOL * DIS # E5: 1,7 => CTR => E5: 4,5 * CNT 36 HDP CHAINS / 64 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A3: 1,6 => SOL * STA A3: 1,6 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...3.4....5.8....3..........3.......9....8..68.4..91...8.....1....92.45.7....19.. | initial |
| ...3.45...5.8....3.....5...53.......9....83.6864.391.5289..3617.1.927458745681932 | autosolve |
| 628394571457816293193275864531462789972158346864739125289543617316927458745681932 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) A1: 1,6 A2: 1,4 E2: 1,9 F2: 2,6 I1: 1,9 G2: 2,7 H2: 4,9 B5: 2,7 F4: 2,6 D6: 2,7 I4: 4,9 H6: 2,7 A8: 3,6 C8: 3,6 D7: 4,5 E7: 4,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I1,I3: 1.. / I1 = 1 => 0 pairs (*) / I3 = 1 => 0 pairs (X) C4,C5: 1.. / C4 = 1 => 0 pairs (*) / C5 = 1 => 0 pairs (X) A2,E2: 1.. / A2 = 1 => 0 pairs (X) / E2 = 1 => 0 pairs (_) F2,D3: 2.. / F2 = 2 => 0 pairs (X) / D3 = 2 => 0 pairs (_) D6,H6: 2.. / D6 = 2 => 0 pairs (X) / H6 = 2 => 19 pairs (_) F2,F4: 2.. / F2 = 2 => 0 pairs (X) / F4 = 2 => 0 pairs (_) A3,C3: 3.. / A3 = 3 => 0 pairs (X) / C3 = 3 => 0 pairs (_) A8,C8: 3.. / A8 = 3 => 0 pairs (*) / C8 = 3 => 0 pairs (X) A3,A8: 3.. / A3 = 3 => 0 pairs (X) / A8 = 3 => 0 pairs (_) C3,C8: 3.. / C3 = 3 => 0 pairs (*) / C8 = 3 => 0 pairs (X) A2,A3: 4.. / A2 = 4 => 0 pairs (*) / A3 = 4 => 0 pairs (X) H2,I3: 4.. / H2 = 4 => 0 pairs (X) / I3 = 4 => 0 pairs (_) D7,E7: 4.. / D7 = 4 => 14 pairs (_) / E7 = 4 => 14 pairs (_) A2,H2: 4.. / A2 = 4 => 0 pairs (*) / H2 = 4 => 0 pairs (X) A3,I3: 4.. / A3 = 4 => 0 pairs (X) / I3 = 4 => 0 pairs (_) I3,I4: 4.. / I3 = 4 => 0 pairs (*) / I4 = 4 => 0 pairs (X) D5,E5: 5.. / D5 = 5 => 14 pairs (_) / E5 = 5 => 14 pairs (_) D7,E7: 5.. / D7 = 5 => 14 pairs (_) / E7 = 5 => 14 pairs (_) D5,D7: 5.. / D5 = 5 => 14 pairs (_) / D7 = 5 => 14 pairs (_) E5,E7: 5.. / E5 = 5 => 14 pairs (_) / E7 = 5 => 14 pairs (_) H1,H3: 6.. / H1 = 6 => 0 pairs (X) / H3 = 6 => 16 pairs (_) E4,F4: 6.. / E4 = 6 => 0 pairs (*) / F4 = 6 => 0 pairs (X) A8,C8: 6.. / A8 = 6 => 0 pairs (X) / C8 = 6 => 0 pairs (_) C2,F2: 6.. / C2 = 6 => 0 pairs (X) / F2 = 6 => 0 pairs (_) F2,F4: 6.. / F2 = 6 => 0 pairs (*) / F4 = 6 => 0 pairs (X) C2,G2: 7.. / C2 = 7 => 0 pairs (*) / G2 = 7 => 0 pairs (X) D6,H6: 7.. / D6 = 7 => 19 pairs (_) / H6 = 7 => 0 pairs (X) C1,C3: 8.. / C1 = 8 => 16 pairs (_) / C3 = 8 => 0 pairs (X) G4,H4: 8.. / G4 = 8 => 21 pairs (_) / H4 = 8 => 0 pairs (*) C1,H1: 8.. / C1 = 8 => 16 pairs (_) / H1 = 8 => 0 pairs (X) G3,G4: 8.. / G3 = 8 => 0 pairs (*) / G4 = 8 => 0 pairs (X) B1,B3: 9.. / B1 = 9 => 0 pairs (X) / B3 = 9 => 18 pairs (_) H4,I4: 9.. / H4 = 9 => 0 pairs (X) / I4 = 9 => 0 pairs (_) E2,H2: 9.. / E2 = 9 => 0 pairs (X) / H2 = 9 => 0 pairs (_) H2,H4: 9.. / H2 = 9 => 0 pairs (*) / H4 = 9 => 0 pairs (X) * DURATION: 0:00:42.011158 START: 03:07:30.786005 END: 03:08:12.797163 2019-05-01 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A8,B5,C8,D6,D7,E2,E7,F2,F4,G2,H2,H6,I1,I4) * ...3.45...5.8....3.....5...53.......9....83.6864.391.5289..3617.1.927458745681932 * PAIR A1: 1,6 BLK 1 A3: 1,6,3,4 # reduction candidate for 1,6 A3: 1,6 => SOLVED * 628394571457816293193275864531462789972158346864739125289543617316927458745681932 A3: 3,4 # 17 pairs * PAIR A1: 1,6 ROW 1 E1: 1,6,7,9 # reduction candidate for 1,6 E1: 1,6 => CTR * 6.83145.915.896.4349327586153..627949....8326864.391.5289..3617316927458745681932 E1: 7,9 # 17 pairs * PAIR A2: 1,4 BLK 1 A3: 1,4,3,6 # reduction candidate for 1,4 A3: 1,4 => SOLVED * 628394571457816293193275864531462789972158346864739125289543617316927458745681932 A3: 3,6 => CTR * ...3.45..45.81..93.....5...53.......9....83.6864.391.5289..3617.1.927458745681932 * PAIR E2: 1,9 BLK 2 E1: 1,9,6,7 # reduction candidate for 1,9 E1: 1,9 => SOLVED * 628394571457816293193275864531462789972158346864739125289543617316927458745681932 E1: 6,7 # 17 pairs E3: 1,9,6,7 # reduction candidate for 1,9 E3: 1,9 # 20 pairs * PAIR F2: 2,6 ROW 2 C2: 2,6,7 # reduction candidate for 2,6 C2: 7 => SOLVED * 628394571457816293193275864531462789972158346864739125289543617316927458745681932 C2: 2,6 # 18 pairs * PAIR I1: 1,9 BLK 3 I3: 1,9,4 # reduction candidate for 1,9 I3: 1,9 => CTR * 6.83.45..15.896.434.32.5...53.....949....83.6864.391.5289..3617316927458745681932 I3: 4 => SOLVED * 628394571457816293193275864531462789972158346864739125289543617316927458745681932 * PAIR I1: 1,9 ROW 1 E1: 1,9,6,7 # reduction candidate for 1,9 E1: 1,9 => SOLVED * 628394571457816293193275864531462789972158346864739125289543617316927458745681932 E1: 6,7 # 17 pairs * PAIR G2: 2,7 BLK 3 H1: 2,7,6,8 # reduction candidate for 2,7 H1: 2,7 => SOLVED * 628394571457816293193275864531462789972158346864739125289543617316927458745681932 H1: 6,8 # 19 pairs G3: 2,7,8 # reduction candidate for 2,7 G3: 2,7 # 21 pairs H3: 2,7,6,8 # reduction candidate for 2,7 H3: 2,7 => CTR * ...3.456..5.8....3.....58..53.....899....8346864.391.5289..3617.1.927458745681932 H3: 6,8 # 17 pairs * PAIR G2: 2,7 ROW 2 C2: 2,7,6 # reduction candidate for 2,7 C2: 2,7 => SOLVED * 628394571457816293193275864531462789972158346864739125289543617316927458745681932 C2: 6 => CTR * 1..3.45.94568.27.3.....5...53...6...9....83.6864.391.5289..3617613927458745681932 * PAIR G2: 2,7 COL G G4: 2,7,8 # reduction candidate for 2,7 G4: 2,7 => SOLVED * 628394571457816293193275864531462789972158346864739125289543617316927458745681932 G4: 8 # 21 pairs * PAIR H2: 4,9 BLK 3 I3: 4,9,1 # reduction candidate for 4,9 I3: 4,9 => SOLVED * 628394571457816293193275864531462789972158346864739125289543617316927458745681932 I3: 1 => CTR * 6.83145.9.5.8...434.3..5..153.....949....83.6864.391.5289..3617316927458745681932 * PAIR H2: 4,9 COL H H4: 4,9,2,7,8 # reduction candidate for 4,9 H4: 2,7,8 => SOLVED * 628394571457816293193275864531462789972158346864739125289543617316927458745681932 H4: 4,9 # 26 pairs * PAIR B5: 2,7 BLK 4 C4: 2,7,1 # reduction candidate for 2,7 C4: 2,7 # 17 pairs C5: 2,7,1 # reduction candidate for 2,7 C5: 2,7 => SOLVED * 628394571457816293193275864531462789972158346864739125289543617316927458745681932 C5: 1 # 17 pairs * PAIR B5: 2,7 ROW 5 D5: 2,7,1,4,5 # reduction candidate for 2,7 D5: 2,7 => CTR * ...3.45..45.81..93.....5..453.......9...58346864.391.5289543617.1.927458745681932 D5: 1,4,5 # 16 pairs H5: 2,7,4 # reduction candidate for 2,7 H5: 2,7 # 26 pairs * PAIR B5: 2,7 COL B B1: 2,7,9 # reduction candidate for 2,7 B1: 2,7 # 18 pairs B3: 2,7,9 # reduction candidate for 2,7 B3: 2,7 => CTR * 692374581.578.6..3...2.5.6.53..62...92...83.6864739125289..3617316927458745681932 B3: 9 # 18 pairs * PAIR D6: 2,7 BLK 5 D4: 2,7,1,4 # reduction candidate for 2,7 D4: 2,7 => CTR * ...3.45..15.8927434.31.5..953...6.949....83.6864.391.5289..3617316927458745681932 D4: 1,4 # 17 pairs D5: 2,7,1,4,5 # reduction candidate for 2,7 D5: 2,7 => CTR * ...3.45..45.81..93.....5..453.......9...58346864.391.5289543617.1.927458745681932 D5: 1,4,5 # 16 pairs * PAIR D6: 2,7 COL D D3: 2,7,1 # reduction candidate for 2,7 D3: 1 => CTR * ...3.45.11568.27.3...1.5...53...6...9....83.6864.391.5289..3617.1.927458745681932 D3: 2,7 # 18 pairs * PAIR I4: 4,9 BLK 6 H4: 4,9,2,7,8 # reduction candidate for 4,9 H4: 2,7,8 => SOLVED * 628394571457816293193275864531462789972158346864739125289543617316927458745681932 H4: 4,9 # 26 pairs * PAIR I4: 4,9 COL I I3: 4,9,1 # reduction candidate for 4,9 I3: 4,9 => SOLVED * 628394571457816293193275864531462789972158346864739125289543617316927458745681932 I3: 1 => CTR * 6.83145.9.5.8...434.3..5..153.....949....83.6864.391.5289..3617316927458745681932 * PAIR H6: 2,7 BLK 6 G4: 2,7,8 # reduction candidate for 2,7 G4: 2,7 => SOLVED * 628394571457816293193275864531462789972158346864739125289543617316927458745681932 G4: 8 # 21 pairs H4: 2,7,4,8,9 # reduction candidate for 2,7 H4: 2,7 => CTR * 6.83.45.145.816.931.32.578453..628799....8346864739125289..3617316927458745681932 H4: 4,8,9 # 16 pairs H5: 2,7,4 # reduction candidate for 2,7 H5: 2,7 # 26 pairs * PAIR H6: 2,7 COL H H1: 2,7,6,8 # reduction candidate for 2,7 H1: 2,7 => SOLVED * 628394571457816293193275864531462789972158346864739125289543617316927458745681932 H1: 6,8 # 19 pairs H3: 2,7,6,8 # reduction candidate for 2,7 H3: 2,7 => CTR * ...3.456..5.8....3.....58..53.....899....8346864.391.5289..3617.1.927458745681932 H3: 6,8 # 17 pairs * PAIR A8: 3,6 COL A A3: 3,6,1,4 # reduction candidate for 3,6 A3: 3,6 => CTR * ...3.45..45.81..93.....5...53.......9....83.6864.391.5289..3617.1.927458745681932 A3: 1,4 => SOLVED * 628394571457816293193275864531462789972158346864739125289543617316927458745681932 * PAIR C8: 3,6 COL C C3: 3,6,2,7,8 # reduction candidate for 3,6 C3: 3,6 => SOLVED * 628394571457816293193275864531462789972158346864739125289543617316927458745681932 C3: 2,7,8 => CTR * ...3.45...5.8....33....5..453......99....83.6864.391.5289..3617613927458745681932 * PAIR D7: 4,5 COL D D5: 4,5,1,2,7 # reduction candidate for 4,5 D5: 1,2,7 => SOLVED * 628394571457816293193275864531462789972158346864739125289543617316927458745681932 D5: 4,5 # 17 pairs * PAIR E7: 4,5 COL E E5: 4,5,1,7 # reduction candidate for 4,5 E5: 1,7 => CTR * ...3.45.145681..93.....5..453.146..99.1578346864239175289453617.1.927458745681932 E5: 4,5 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190122-absurd-base-pr-000.dot * REASONING * PRF # A3: 1,6 => SOL * DIS # E1: 1,6 => CTR => E1: 7,9 * PRF # A3: 1,4 => SOL * DIS # A3: 3,6 => CTR => A3: 1,4 * PRF # E1: 1,9 => SOL * PRF # C2: 7 => SOL * DIS # I3: 1,9 => CTR => I3: 4 * PRF # I3: 4 => SOL * PRF # E1: 1,9 => SOL * PRF # H1: 2,7 => SOL * DIS # H3: 2,7 => CTR => H3: 6,8 * PRF # C2: 2,7 => SOL * DIS # C2: 6 => CTR => C2: 2,7 * PRF # G4: 2,7 => SOL * PRF # I3: 4,9 => SOL * DIS # I3: 1 => CTR => I3: 4,9 * PRF # H4: 2,7,8 => SOL * PRF # C5: 2,7 => SOL * DIS # D5: 2,7 => CTR => D5: 1,4,5 * DIS # B3: 2,7 => CTR => B3: 9 * DIS # D4: 2,7 => CTR => D4: 1,4 * DIS # D5: 2,7 => CTR => D5: 1,4,5 * DIS # D3: 1 => CTR => D3: 2,7 * PRF # H4: 2,7,8 => SOL * PRF # I3: 4,9 => SOL * DIS # I3: 1 => CTR => I3: 4,9 * PRF # G4: 2,7 => SOL * DIS # H4: 2,7 => CTR => H4: 4,8,9 * PRF # H1: 2,7 => SOL * DIS # H3: 2,7 => CTR => H3: 6,8 * DIS # A3: 3,6 => CTR => A3: 1,4 * PRF # A3: 1,4 => SOL * PRF # C3: 3,6 => SOL * DIS # C3: 2,7,8 => CTR => C3: 3,6 * PRF # D5: 1,2,7 => SOL * DIS # E5: 1,7 => CTR => E5: 4,5 * CNT 36 HDP CHAINS / 64 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A8,B5,C8,D6,D7,E2,E7,F2,F4,G2,H2,H6,I1,I4) * ...3.45...5.8....3.....5...53.......9....83.6864.391.5289..3617.1.927458745681932 * PAIR A1: 1,6 BLK 1 A3: 1,6,3,4 # reduction candidate for 1,6 A3: 1,6 => SOLVED * 628394571457816293193275864531462789972158346864739125289543617316927458745681932 * DURATION: 0:00:01.573272 START: 03:08:59.248514 END: 03:09:00.821786 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190122-absurd-base-pr-001.dot * REASONING * PRF # A3: 1,6 => SOL * STA A3: 1,6 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190122, absurd
Solution
position: 628394571457816293193275864531462789972158346864739125289543617316927458745681932 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:
* PRF # A3: 1,6 => SOL * INC # A3: 3,4 => UNS * DIS # E1: 1,6 => CTR => E1: 7,9 * INC # E1: 7,9 => UNS * PRF # A3: 1,4 => SOL * DIS # A3: 3,6 => CTR => A3: 1,4 * PRF # E1: 1,9 => SOL * INC # E1: 6,7 => UNS * INC # E3: 1,9 => UNS * INC # C2: 2,6 => UNS * PRF # C2: 7 => SOL * DIS # I3: 1,9 => CTR => I3: 4 * PRF # I3: 4 => SOL * PRF # E1: 1,9 => SOL * INC # E1: 6,7 => UNS * PRF # H1: 2,7 => SOL * INC # H1: 6,8 => UNS * INC # G3: 2,7 => UNS * DIS # H3: 2,7 => CTR => H3: 6,8 * INC # H3: 6,8 => UNS * PRF # C2: 2,7 => SOL * DIS # C2: 6 => CTR => C2: 2,7 * PRF # G4: 2,7 => SOL * INC # G4: 8 => UNS * PRF # I3: 4,9 => SOL * DIS # I3: 1 => CTR => I3: 4,9 * INC # H4: 4,9 => UNS * PRF # H4: 2,7,8 => SOL * INC # C4: 2,7 => UNS * PRF # C5: 2,7 => SOL * INC # C5: 1 => UNS * DIS # D5: 2,7 => CTR => D5: 1,4,5 * INC # D5: 1,4,5 => UNS * INC # H5: 2,7 => UNS * INC # B1: 2,7 => UNS * DIS # B3: 2,7 => CTR => B3: 9 * INC # B3: 9 => UNS * DIS # D4: 2,7 => CTR => D4: 1,4 * INC # D4: 1,4 => UNS * DIS # D5: 2,7 => CTR => D5: 1,4,5 * INC # D5: 1,4,5 => UNS * INC # D3: 2,7 => UNS * DIS # D3: 1 => CTR => D3: 2,7 * INC # H4: 4,9 => UNS * PRF # H4: 2,7,8 => SOL * PRF # I3: 4,9 => SOL * DIS # I3: 1 => CTR => I3: 4,9 * PRF # G4: 2,7 => SOL * INC # G4: 8 => UNS * DIS # H4: 2,7 => CTR => H4: 4,8,9 * INC # H4: 4,8,9 => UNS * INC # H5: 2,7 => UNS * PRF # H1: 2,7 => SOL * INC # H1: 6,8 => UNS * DIS # H3: 2,7 => CTR => H3: 6,8 * INC # H3: 6,8 => UNS * DIS # A3: 3,6 => CTR => A3: 1,4 * PRF # A3: 1,4 => SOL * PRF # C3: 3,6 => SOL * DIS # C3: 2,7,8 => CTR => C3: 3,6 * INC # D5: 4,5 => UNS * PRF # D5: 1,2,7 => SOL * INC # E5: 4,5 => UNS * DIS # E5: 1,7 => CTR => E5: 4,5 * CNT 64 HDP CHAINS / 64 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A3: 1,6 => SOL * STA A3: 1,6 * CNT 1 HDP CHAINS / 1 HYP OPENED