Analysis of zz-www.sudokuoftheday.co.uk-20190321-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019
level: medium
position: .....9..51.9...........3...7.64.21.9.4.8.6..7...3...6.9..1.8524......9....5.6..8. initial
Autosolve
position: .....9..51.9...........3.9.786452139341896257592371468967138524......9.6..596..8. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 4,8 => CTR => A1: 2,6 * PRF # C1: 4,8 => SOL * DIS # C1: 3 => CTR => C1: 4,8 * DIS # A3: 4,8 => CTR => A3: 2,6 * DIS # E3: 4,8 => CTR => E3: 1,2 * DIS # C8: 4,8 => CTR => C8: 3 * PRF # C8: 3 => SOL * DIS # H1: 4,7 => CTR => H1: 1 * PRF # H1: 1 => SOL * DIS # E3: 4,8 => CTR => E3: 1,2 * DIS # C8: 4,8 => CTR => C8: 3 * PRF # C8: 3 => SOL * DIS # A1: 4,8 => CTR => A1: 2,6 * DIS # A3: 4,8 => CTR => A3: 2,6 * PRF # E1: 2,4 => SOL * DIS # E2: 2,4 => CTR => E2: 8 * DIS # E3: 2,4 => CTR => E3: 1,8 * DIS # H1: 4 => CTR => H1: 1,7 * CNT 18 HDP CHAINS / 40 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 4,8 => CTR => A1: 2,6 * PRF A1: 2,6 # C1: 4,8 => SOL * STA A1: 2,6 + C1: 4,8 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....9..51.9...........3...7.64.21.9.4.8.6..7...3...6.9..1.8524......9....5.6..8. | initial |
| .....9..51.9...........3.9.786452139341896257592371468967138524......9.6..596..8. | autosolve |
| 238649715179285643654713892786452139341896257592371468967138524813524976425967381 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) C3: 4,8 H2: 4,7 I2: 2,3 I3: 1,2 A8: 4,8 B8: 1,3 A9: 2,4 B9: 1,2 E8: 2,4 F9: 4,7 H8: 1,7 G9: 3,7 I9: 1,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,E3: 1.. / E1 = 1 => 0 pairs (X) / E3 = 1 => 0 pairs (_) H1,I3: 1.. / H1 = 1 => 0 pairs (*) / I3 = 1 => 0 pairs (X) B8,B9: 1.. / B8 = 1 => 0 pairs (*) / B9 = 1 => 0 pairs (X) H8,I9: 1.. / H8 = 1 => 0 pairs (X) / I9 = 1 => 0 pairs (_) E1,H1: 1.. / E1 = 1 => 0 pairs (X) / H1 = 1 => 0 pairs (_) E3,I3: 1.. / E3 = 1 => 0 pairs (*) / I3 = 1 => 0 pairs (X) B8,H8: 1.. / B8 = 1 => 0 pairs (*) / H8 = 1 => 0 pairs (X) B9,I9: 1.. / B9 = 1 => 0 pairs (X) / I9 = 1 => 0 pairs (_) H1,H8: 1.. / H1 = 1 => 0 pairs (*) / H8 = 1 => 0 pairs (X) I3,I9: 1.. / I3 = 1 => 0 pairs (X) / I9 = 1 => 0 pairs (_) I2,I3: 2.. / I2 = 2 => 0 pairs (X) / I3 = 2 => 0 pairs (_) A9,B9: 2.. / A9 = 2 => 0 pairs (X) / B9 = 2 => 0 pairs (_) D8,E8: 2.. / D8 = 2 => 0 pairs (X) / E8 = 2 => 15 pairs (_) B8,C8: 3.. / B8 = 3 => 0 pairs (X) / C8 = 3 => 0 pairs (_) G9,I9: 3.. / G9 = 3 => 0 pairs (*) / I9 = 3 => 0 pairs (X) C1,C8: 3.. / C1 = 3 => 0 pairs (X) / C8 = 3 => 0 pairs (_) I2,I9: 3.. / I2 = 3 => 0 pairs (*) / I9 = 3 => 0 pairs (X) H1,H2: 4.. / H1 = 4 => 0 pairs (X) / H2 = 4 => 16 pairs (_) A9,F9: 4.. / A9 = 4 => 0 pairs (*) / F9 = 4 => 0 pairs (X) B2,B3: 5.. / B2 = 5 => 18 pairs (_) / B3 = 5 => 13 pairs (_) D8,F8: 5.. / D8 = 5 => 14 pairs (_) / F8 = 5 => 16 pairs (_) B3,D3: 5.. / B3 = 5 => 13 pairs (_) / D3 = 5 => 18 pairs (_) F2,F8: 5.. / F2 = 5 => 14 pairs (_) / F8 = 5 => 16 pairs (_) A1,A3: 6.. / A1 = 6 => 16 pairs (_) / A3 = 6 => 14 pairs (_) D2,G2: 6.. / D2 = 6 => 14 pairs (_) / G2 = 6 => 14 pairs (_) H8,G9: 7.. / H8 = 7 => 0 pairs (*) / G9 = 7 => 0 pairs (X) F9,G9: 7.. / F9 = 7 => 0 pairs (*) / G9 = 7 => 0 pairs (X) A8,C8: 8.. / A8 = 8 => 13 pairs (_) / C8 = 8 => 0 pairs (X) E2,G2: 8.. / E2 = 8 => 13 pairs (_) / G2 = 8 => 0 pairs (X) * DURATION: 0:00:33.642473 START: 04:41:17.753143 END: 04:41:51.395616 2019-05-01 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,B8,B9,C3,E8,F9,G9,H2,H8,I2,I3,I9) * .....9..51.9...........3.9.786452139341896257592371468967138524......9.6..596..8. * PAIR C3: 4,8 BLK 1 A1: 4,8,2,6 # reduction candidate for 4,8 A1: 4,8 => CTR * .....9..51.9.....26....3891786452139341896257592371468967138524.3..2.916215964783 A1: 2,6 # 14 pairs C1: 4,8,3 # reduction candidate for 4,8 C1: 4,8 => SOLVED * 238649715179285643654713892786452139341896257592371468967138524813524976425967381 C1: 3 => CTR * 4.3.19..51.968.342....43.91786452139341896257592371468967138524.34.2.916215964783 A3: 4,8,2,6 # reduction candidate for 4,8 A3: 4,8 => CTR * 6.3.198451.9.....2.....3.91786452139341896257592371468967138524.3..2.916215964783 A3: 2,6 # 14 pairs * PAIR C3: 4,8 ROW 3 E3: 4,8,1,2 # reduction candidate for 4,8 E3: 4,8 => CTR * 4.3.19..51.968.342....43.91786452139341896257592371468967138524.34.2.916215964783 E3: 1,2 # 18 pairs * PAIR C3: 4,8 COL C C8: 4,8,3 # reduction candidate for 4,8 C8: 4,8 => CTR * 4.3.19..51.968.342....43.91786452139341896257592371468967138524.34.2.916215964783 C8: 3 => SOLVED * 238649715179285643654713892786452139341896257592371468967138524813524976425967381 * PAIR H2: 4,7 BLK 3 H1: 4,7,1 # reduction candidate for 4,7 H1: 4,7 => CTR * 4.3.19..51.968.342....43.91786452139341896257592371468967138524.34.2.916215964783 H1: 1 => SOLVED * 238649715179285643654713892786452139341896257592371468967138524813524976425967381 * PAIR H2: 4,7 ROW 2 F2: 4,7,5 # reduction candidate for 4,7 F2: 4,7 # 16 pairs F2: 5 # 14 pairs * PAIR I2: 2,3 ROW 2 B2: 2,3,5,7 # reduction candidate for 2,3 B2: 2,3 # 17 pairs B2: 5,7 # 16 pairs * PAIR I3: 1,2 ROW 3 E3: 1,2,4,8 # reduction candidate for 1,2 E3: 4,8 => CTR * 4.3.19..51.968.342....43.91786452139341896257592371468967138524.34.2.916215964783 E3: 1,2 # 18 pairs * PAIR A8: 4,8 BLK 7 C8: 4,8,3 # reduction candidate for 4,8 C8: 4,8 => CTR * 4.3.19..51.968.342....43.91786452139341896257592371468967138524.34.2.916215964783 C8: 3 => SOLVED * 238649715179285643654713892786452139341896257592371468967138524813524976425967381 * PAIR A8: 4,8 COL A A1: 4,8,2,6 # reduction candidate for 4,8 A1: 4,8 => CTR * .....9..51.9.....26....3891786452139341896257592371468967138524.3..2.916215964783 A1: 2,6 # 14 pairs A3: 4,8,2,6 # reduction candidate for 4,8 A3: 4,8 => CTR * 6.3.198451.9.....2.....3.91786452139341896257592371468967138524.3..2.916215964783 A3: 2,6 # 14 pairs * PAIR A9: 2,4 COL A A1: 2,4,6,8 # reduction candidate for 2,4 A1: 2,4 # 15 pairs A3: 2,4,6,8 # reduction candidate for 2,4 A3: 2,4 # 17 pairs * PAIR E8: 2,4 COL E E1: 2,4,1,8 # reduction candidate for 2,4 E1: 2,4 => SOLVED * 238649715179285643654713892786452139341896257592371468967138524813524976425967381 E1: 1,8 # 14 pairs E2: 2,4,8 # reduction candidate for 2,4 E2: 2,4 => CTR * 6...193451396..87......3691786452139341896257592371468967138524......916.1596.783 E2: 8 # 13 pairs E3: 2,4,1,8 # reduction candidate for 2,4 E3: 2,4 => CTR * 4.3.198751.968.3426...43.91786452139341896257592371468967138524.34.2.916215964783 E3: 1,8 # 17 pairs * PAIR F9: 4,7 BLK 8 F8: 4,7,5 # reduction candidate for 4,7 F8: 5 # 16 pairs F8: 4,7 # 14 pairs * PAIR F9: 4,7 COL F F2: 4,7,5 # reduction candidate for 4,7 F2: 4,7 # 16 pairs F2: 5 # 14 pairs * PAIR H8: 1,7 COL H H1: 1,7,4 # reduction candidate for 1,7 H1: 4 => CTR * ....19.451.9....72.....3.91786452139341896257592371468967138524.3...7916215964783 H1: 1,7 # 16 pairs * PAIR G9: 3,7 COL G G1: 3,7,6,8 # reduction candidate for 3,7 G1: 3,7 # 18 pairs G2: 3,7,6,8 # reduction candidate for 3,7 G2: 3,7 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190321-absurd-base-pr-000.dot * REASONING * DIS # A1: 4,8 => CTR => A1: 2,6 * PRF # C1: 4,8 => SOL * DIS # C1: 3 => CTR => C1: 4,8 * DIS # A3: 4,8 => CTR => A3: 2,6 * DIS # E3: 4,8 => CTR => E3: 1,2 * DIS # C8: 4,8 => CTR => C8: 3 * PRF # C8: 3 => SOL * DIS # H1: 4,7 => CTR => H1: 1 * PRF # H1: 1 => SOL * DIS # E3: 4,8 => CTR => E3: 1,2 * DIS # C8: 4,8 => CTR => C8: 3 * PRF # C8: 3 => SOL * DIS # A1: 4,8 => CTR => A1: 2,6 * DIS # A3: 4,8 => CTR => A3: 2,6 * PRF # E1: 2,4 => SOL * DIS # E2: 2,4 => CTR => E2: 8 * DIS # E3: 2,4 => CTR => E3: 1,8 * DIS # H1: 4 => CTR => H1: 1,7 * CNT 18 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,B8,B9,C3,E8,F9,G9,H2,H8,I2,I3,I9) * .....9..51.9...........3.9.786452139341896257592371468967138524......9.6..596..8. * PAIR C3: 4,8 BLK 1 A1: 4,8,2,6 # reduction candidate for 4,8 A1: 4,8 => CTR * .....9..51.9.....26....3891786452139341896257592371468967138524.3..2.916215964783 C1: 4,8,3 # reduction candidate for 4,8 C1: 4,8 => SOLVED * 238649715179285643654713892786452139341896257592371468967138524813524976425967381 * DURATION: 0:00:02.240167 START: 04:42:17.795733 END: 04:42:20.035900 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190321-absurd-base-pr-001.dot * REASONING * DIS # A1: 4,8 => CTR => A1: 2,6 * PRF A1: 2,6 # C1: 4,8 => SOL * STA A1: 2,6 + C1: 4,8 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190321, absurd
Solution
position: 238649715179285643654713892786452139341896257592371468967138524813524976425967381 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 # A1: 4,8 => CTR => A1: 2,6 * INC # A1: 2,6 => UNS * PRF # C1: 4,8 => SOL * DIS # C1: 3 => CTR => C1: 4,8 * DIS # A3: 4,8 => CTR => A3: 2,6 * INC # A3: 2,6 => UNS * DIS # E3: 4,8 => CTR => E3: 1,2 * INC # E3: 1,2 => UNS * DIS # C8: 4,8 => CTR => C8: 3 * PRF # C8: 3 => SOL * DIS # H1: 4,7 => CTR => H1: 1 * PRF # H1: 1 => SOL * INC # F2: 4,7 => UNS * INC # F2: 5 => UNS * INC # B2: 2,3 => UNS * INC # B2: 5,7 => UNS * INC # E3: 1,2 => UNS * DIS # E3: 4,8 => CTR => E3: 1,2 * DIS # C8: 4,8 => CTR => C8: 3 * PRF # C8: 3 => SOL * DIS # A1: 4,8 => CTR => A1: 2,6 * INC # A1: 2,6 => UNS * DIS # A3: 4,8 => CTR => A3: 2,6 * INC # A3: 2,6 => UNS * INC # A1: 2,4 => UNS * INC # A3: 2,4 => UNS * PRF # E1: 2,4 => SOL * INC # E1: 1,8 => UNS * DIS # E2: 2,4 => CTR => E2: 8 * INC # E2: 8 => UNS * DIS # E3: 2,4 => CTR => E3: 1,8 * INC # E3: 1,8 => UNS * INC # F8: 4,7 => UNS * INC # F8: 5 => UNS * INC # F2: 4,7 => UNS * INC # F2: 5 => UNS * INC # H1: 1,7 => UNS * DIS # H1: 4 => CTR => H1: 1,7 * INC # G1: 3,7 => UNS * INC # G2: 3,7 => UNS * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 4,8 => CTR => A1: 2,6 * PRF A1: 2,6 # C1: 4,8 => SOL * STA A1: 2,6 + C1: 4,8 * CNT 2 HDP CHAINS / 2 HYP OPENED