Analysis of zz-www.sudokuoftheday.co.uk-20060427-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006
level: medium
position: 1.........4.6..9..9.8..2.73........44.2...796.95...2....98.6....8..7..69.1.35..2. initial
Autosolve
position: 1.........4.6..9..9.8..2.73..1.....4432...796.95.6.2....98.6....8..7..69.1.359.2. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C1: 3,7 => SOL * DIS # C1: 6 => CTR => C1: 3,7 * PRF # B1: 5,6 => SOL * DIS # G3: 1,4 => CTR => G3: 5,6 * DIS # D3: 5 => CTR => D3: 1,4 * DIS # G3: 1,4 => CTR => G3: 5,6 * PRF # E7: 1,4 => SOL * DIS # E7: 2 => CTR => E7: 1,4 * DIS # A4: 8 => CTR => A4: 6,7 * PRF # B1: 6,7 => SOL * DIS # A4: 7,8 => CTR => A4: 6 * PRF # A4: 6 => SOL * DIS # F6: 3,7 => CTR => F6: 4 * DIS # F5: 8 => CTR => F5: 1,5 * PRF # D3: 4 => SOL * DIS # E2: 1,8 => CTR => E2: 3 * PRF # E2: 3 => SOL * DIS # F6: 3 => CTR => F6: 4,7 * DIS # D1: 4,7 => CTR => D1: 5,9 * DIS # H6: 1,8 => CTR => H6: 3 * DIS # I2: 1,8 => CTR => I2: 2,5 * PRF # G8: 3,4 => SOL * PRF # C9: 6,7 => SOL * DIS # C9: 4 => CTR => C9: 6,7 * DIS # A4: 8 => CTR => A4: 6,7 * PRF # E7: 1,4 => SOL * DIS # E7: 2 => CTR => E7: 1,4 * DIS # D8: 1,4 => CTR => D8: 2 * PRF # D8: 2 => SOL * DIS # G8: 1,4 => CTR => G8: 3,5 * CNT 30 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C1: 3,7 => SOL * STA C1: 3,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.........4.6..9..9.8..2.73........44.2...796.95...2....98.6....8..7..69.1.35..2. | initial |
| 1.........4.6..9..9.8..2.73..1.....4432...796.95.6.2....98.6....8..7..69.1.359.2. | autosolve |
| 163597842247638915958412673671923584432185796895764231329846157584271369716359428 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) C2: 3,7 B3: 5,6 E3: 1,4 B4: 6,7 A6: 7,8 D4: 2,9 E4: 2,9 F4: 3,7 D5: 1,5 E5: 1,8 D6: 4,7 I6: 1,8 C8: 3,4 A9: 6,7 F8: 1,4 G9: 4,8 I9: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H6,I6: 1.. / H6 = 1 => 0 pairs (X) / I6 = 1 => 18 pairs (_) B1,A2: 2.. / B1 = 2 => 21 pairs (_) / A2 = 2 => 0 pairs (*) I1,I2: 2.. / I1 = 2 => 0 pairs (*) / I2 = 2 => 0 pairs (X) D4,E4: 2.. / D4 = 2 => 0 pairs (X) / E4 = 2 => 0 pairs (_) E7,D8: 2.. / E7 = 2 => 0 pairs (X) / D8 = 2 => 0 pairs (_) B1,I1: 2.. / B1 = 2 => 21 pairs (_) / I1 = 2 => 0 pairs (*) A2,I2: 2.. / A2 = 2 => 0 pairs (*) / I2 = 2 => 0 pairs (X) A8,D8: 2.. / A8 = 2 => 0 pairs (X) / D8 = 2 => 0 pairs (_) B1,B7: 2.. / B1 = 2 => 21 pairs (_) / B7 = 2 => 0 pairs (*) D4,D8: 2.. / D4 = 2 => 0 pairs (X) / D8 = 2 => 0 pairs (_) E4,E7: 2.. / E4 = 2 => 0 pairs (*) / E7 = 2 => 0 pairs (X) E1,E2: 3.. / E1 = 3 => 0 pairs (X) / E2 = 3 => 0 pairs (_) F4,F6: 3.. / F4 = 3 => 19 pairs (_) / F6 = 3 => 0 pairs (X) C1,E1: 3.. / C1 = 3 => 0 pairs (*) / E1 = 3 => 0 pairs (X) F6,H6: 3.. / F6 = 3 => 0 pairs (X) / H6 = 3 => 19 pairs (_) D6,F6: 4.. / D6 = 4 => 0 pairs (X) / F6 = 4 => 19 pairs (_) C8,C9: 4.. / C8 = 4 => 0 pairs (*) / C9 = 4 => 0 pairs (X) C9,G9: 4.. / C9 = 4 => 0 pairs (X) / G9 = 4 => 0 pairs (_) H1,H7: 4.. / H1 = 4 => 17 pairs (_) / H7 = 4 => 0 pairs (X) D5,F5: 5.. / D5 = 5 => 22 pairs (_) / F5 = 5 => 18 pairs (_) G4,H4: 5.. / G4 = 5 => 0 pairs (*) / H4 = 5 => 0 pairs (X) A8,G8: 5.. / A8 = 5 => 0 pairs (*) / G8 = 5 => 0 pairs (X) G1,G3: 6.. / G1 = 6 => 0 pairs (X) / G3 = 6 => 21 pairs (_) A4,B4: 6.. / A4 = 6 => 0 pairs (*) / B4 = 6 => 0 pairs (X) A9,C9: 6.. / A9 = 6 => 0 pairs (X) / C9 = 6 => 0 pairs (_) B3,G3: 6.. / B3 = 6 => 0 pairs (X) / G3 = 6 => 21 pairs (_) A4,A9: 6.. / A4 = 6 => 0 pairs (*) / A9 = 6 => 0 pairs (X) C1,C9: 6.. / C1 = 6 => 0 pairs (X) / C9 = 6 => 0 pairs (_) I7,I9: 7.. / I7 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) C2,F2: 7.. / C2 = 7 => 18 pairs (_) / F2 = 7 => 0 pairs (X) B7,I7: 7.. / B7 = 7 => 0 pairs (X) / I7 = 7 => 0 pairs (_) D1,D6: 7.. / D1 = 7 => 0 pairs (X) / D6 = 7 => 19 pairs (_) A4,A6: 8.. / A4 = 8 => 0 pairs (X) / A6 = 8 => 19 pairs (_) E5,F5: 8.. / E5 = 8 => 18 pairs (_) / F5 = 8 => 0 pairs (X) G9,I9: 8.. / G9 = 8 => 0 pairs (X) / I9 = 8 => 0 pairs (_) D1,E1: 9.. / D1 = 9 => 0 pairs (X) / E1 = 9 => 0 pairs (_) D4,E4: 9.. / D4 = 9 => 0 pairs (*) / E4 = 9 => 0 pairs (X) D1,D4: 9.. / D1 = 9 => 0 pairs (X) / D4 = 9 => 0 pairs (_) E1,E4: 9.. / E1 = 9 => 0 pairs (*) / E4 = 9 => 0 pairs (X) * DURATION: 0:00:49.046555 START: 22:41:49.461805 END: 22:42:38.508360 2019-04-30 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A9,B3,B4,C2,C8,D4,D5,D6,E3,E4,E5,F4,F8,G9,I6,I9) * 1.........4.6..9..9.8..2.73..1.....4432...796.95.6.2....98.6....8..7..69.1.359.2. * PAIR C2: 3,7 BLK 1 C1: 3,7,6 # reduction candidate for 3,7 C1: 3,7 => SOLVED * 163597842247638915958412673671923584432185796895764231329846157584271369716359428 C1: 6 => CTR * 126937...3476.59.2958.426737612938.4432...796.95.6.2....9826...28..7.56961.359.2. * PAIR B3: 5,6 BLK 1 B1: 5,6,2,7 # reduction candidate for 5,6 B1: 5,6 => SOLVED * 163597842247638915958412673671923584432185796895764231329846157584271369716359428 B1: 2,7 # 18 pairs * PAIR B3: 5,6 ROW 3 G3: 5,6,1,4 # reduction candidate for 5,6 G3: 1,4 => CTR * 1.....64..4.6..98.968542173671..3854432185796895.6.231..98.6.17.8427..69716359428 G3: 5,6 # 21 pairs * PAIR E3: 1,4 BLK 2 D3: 1,4,5 # reduction candidate for 1,4 D3: 5 => CTR * 1.....64..4.6..98.968542173671..3854432185796895.6.231..98.6.17.8427..69716359428 D3: 1,4 # 21 pairs * PAIR E3: 1,4 ROW 3 G3: 1,4,5,6 # reduction candidate for 1,4 G3: 1,4 => CTR * 1.....64..4.6..98.968542173671..3854432185796895.6.231..98.6.17.8427..69716359428 G3: 5,6 # 21 pairs * PAIR E3: 1,4 COL E E7: 1,4,2 # reduction candidate for 1,4 E7: 1,4 => SOLVED * 163597842247638915958412673671923584432185796895764231329846157584271369716359428 E7: 2 => CTR * 1269374853476.5912958.426738.129..54432...796.95.6.2....9826...283.7.569.14359827 * PAIR B4: 6,7 BLK 4 A4: 6,7,8 # reduction candidate for 6,7 A4: 8 => CTR * 1.67......4.6..9..9.8..2.73861..7..4432...7967954632....98.6....8..7..6961.359.2. A4: 6,7 # 19 pairs * PAIR B4: 6,7 COL B B1: 6,7,2,5 # reduction candidate for 6,7 B1: 6,7 => SOLVED * 163597842247638915958412673671923584432185796895764231329846157584271369716359428 B1: 2,5 # 19 pairs * PAIR A6: 7,8 BLK 4 A4: 7,8,6 # reduction candidate for 7,8 A4: 7,8 => CTR * 126937...3476.59.2958.426737612938.4432...796.95.6.2....9826...28..7.56961.359.2. A4: 6 => SOLVED * 163597842247638915958412673671923584432185796895764231329846157584271369716359428 * PAIR F4: 3,7 BLK 5 F6: 3,7,4 # reduction candidate for 3,7 F6: 3,7 => CTR * 1.379.....4763.9..9.8..2.73..192...4432.8.796.9546.2....98.6....84271.69.16359428 F6: 4 # 19 pairs * PAIR D5: 1,5 BLK 5 F5: 1,5,8 # reduction candidate for 1,5 F5: 8 => CTR * 12........4.6..9.2958142673.6129..54432518796.95.6.2..5798261..28..7.569.1.359.2. F5: 1,5 # 18 pairs * PAIR D5: 1,5 COL D D3: 1,5,4 # reduction candidate for 1,5 D3: 4 => SOLVED * 163597842247638915958412673671923584432185796895764231329846157584271369716359428 D3: 1,5 # 19 pairs * PAIR E5: 1,8 BLK 5 F5: 1,8,5 # reduction candidate for 1,8 F5: 1,8 # 22 pairs F5: 5 # 18 pairs * PAIR E5: 1,8 COL E E2: 1,8,3 # reduction candidate for 1,8 E2: 1,8 => CTR * 12.93.....4.6..9.29.8.42.73..129..54432...796.95764231..98263..28..7.569.1.359.2. E2: 3 => SOLVED * 163597842247638915958412673671923584432185796895764231329846157584271369716359428 * PAIR D6: 4,7 BLK 5 F6: 4,7,3 # reduction candidate for 4,7 F6: 3 => CTR * 1..79.....4763.9..9.8..2.73..1927..4432.8.7967954632...798.6....8.27..69614359.2. F6: 4,7 # 19 pairs * PAIR D6: 4,7 COL D D1: 4,7,5,9 # reduction candidate for 4,7 D1: 4,7 => CTR * 1.3.9..4..4763.9..9.8.12.73671923..4432185796895.64231..9846157584271369716359428 D1: 5,9 # 20 pairs * PAIR I6: 1,8 BLK 6 H6: 1,8,3 # reduction candidate for 1,8 H6: 1,8 => CTR * 1.67......4.6..9..9.8..2.73..1..7..4432...7967954632....98.6....8..7..6961.359.2. H6: 3 # 19 pairs * PAIR I6: 1,8 COL I I2: 1,8,2,5 # reduction candidate for 1,8 I2: 1,8 => CTR * 1.......224.6..9..9.8..2.73..1.....4432...796.95.6.2...298.6....8..7..69.1.359.2. I2: 2,5 # 18 pairs * PAIR C8: 3,4 ROW 8 G8: 3,4,1,5 # reduction candidate for 3,4 G8: 3,4 => SOLVED * 163597842247638915958412673671923584432185796895764231329846157584271369716359428 G8: 1,5 # 19 pairs * PAIR A9: 6,7 BLK 7 C9: 6,7,4 # reduction candidate for 6,7 C9: 6,7 => SOLVED * 163597842247638915958412673671923584432185796895764231329846157584271369716359428 C9: 4 => CTR * 1269374..3476.59.2958.4267376129...4432...796.95.6.2...79826...283.7.569614359827 * PAIR A9: 6,7 COL A A4: 6,7,8 # reduction candidate for 6,7 A4: 8 => CTR * 1.67......4.6..9..9.8..2.73861..7..4432...7967954632....98.6....8..7..6961.359.2. A4: 6,7 # 19 pairs * PAIR F8: 1,4 BLK 8 E7: 1,4,2 # reduction candidate for 1,4 E7: 1,4 => SOLVED * 163597842247638915958412673671923584432185796895764231329846157584271369716359428 E7: 2 => CTR * 1269374853476.5912958.426738.129..54432...796.95.6.2....9826...283.7.569.14359827 D8: 1,4,2 # reduction candidate for 1,4 D8: 1,4 => CTR * 12.9......4.6..9.29.8..2.73..129..54432...796.95764231..98263..28..7.569.1.359.2. D8: 2 => SOLVED * 163597842247638915958412673671923584432185796895764231329846157584271369716359428 * PAIR F8: 1,4 ROW 8 G8: 1,4,3,5 # reduction candidate for 1,4 G8: 1,4 => CTR * 1.6.3....3476..9.2958..2673.61.....4432...796.95.6.2....98.6...58327..69.14359827 G8: 3,5 # 19 pairs * PAIR G9: 4,8 COL G G1: 4,8,5,6 # reduction candidate for 4,8 G1: 4,8 # 23 pairs G1: 5,6 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060427-absurd-base-pr-000.dot * REASONING * PRF # C1: 3,7 => SOL * DIS # C1: 6 => CTR => C1: 3,7 * PRF # B1: 5,6 => SOL * DIS # G3: 1,4 => CTR => G3: 5,6 * DIS # D3: 5 => CTR => D3: 1,4 * DIS # G3: 1,4 => CTR => G3: 5,6 * PRF # E7: 1,4 => SOL * DIS # E7: 2 => CTR => E7: 1,4 * DIS # A4: 8 => CTR => A4: 6,7 * PRF # B1: 6,7 => SOL * DIS # A4: 7,8 => CTR => A4: 6 * PRF # A4: 6 => SOL * DIS # F6: 3,7 => CTR => F6: 4 * DIS # F5: 8 => CTR => F5: 1,5 * PRF # D3: 4 => SOL * DIS # E2: 1,8 => CTR => E2: 3 * PRF # E2: 3 => SOL * DIS # F6: 3 => CTR => F6: 4,7 * DIS # D1: 4,7 => CTR => D1: 5,9 * DIS # H6: 1,8 => CTR => H6: 3 * DIS # I2: 1,8 => CTR => I2: 2,5 * PRF # G8: 3,4 => SOL * PRF # C9: 6,7 => SOL * DIS # C9: 4 => CTR => C9: 6,7 * DIS # A4: 8 => CTR => A4: 6,7 * PRF # E7: 1,4 => SOL * DIS # E7: 2 => CTR => E7: 1,4 * DIS # D8: 1,4 => CTR => D8: 2 * PRF # D8: 2 => SOL * DIS # G8: 1,4 => CTR => G8: 3,5 * CNT 30 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A9,B3,B4,C2,C8,D4,D5,D6,E3,E4,E5,F4,F8,G9,I6,I9) * 1.........4.6..9..9.8..2.73..1.....4432...796.95.6.2....98.6....8..7..69.1.359.2. * PAIR C2: 3,7 BLK 1 C1: 3,7,6 # reduction candidate for 3,7 C1: 3,7 => SOLVED * 163597842247638915958412673671923584432185796895764231329846157584271369716359428 * DURATION: 0:00:01.737724 START: 22:43:13.632206 END: 22:43:15.369930 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060427-absurd-base-pr-001.dot * REASONING * PRF # C1: 3,7 => SOL * STA C1: 3,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060427, absurd
Solution
position: 163597842247638915958412673671923584432185796895764231329846157584271369716359428 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 # C1: 3,7 => SOL * DIS # C1: 6 => CTR => C1: 3,7 * PRF # B1: 5,6 => SOL * INC # B1: 2,7 => UNS * INC # G3: 5,6 => UNS * DIS # G3: 1,4 => CTR => G3: 5,6 * INC # D3: 1,4 => UNS * DIS # D3: 5 => CTR => D3: 1,4 * DIS # G3: 1,4 => CTR => G3: 5,6 * INC # G3: 5,6 => UNS * PRF # E7: 1,4 => SOL * DIS # E7: 2 => CTR => E7: 1,4 * INC # A4: 6,7 => UNS * DIS # A4: 8 => CTR => A4: 6,7 * PRF # B1: 6,7 => SOL * INC # B1: 2,5 => UNS * DIS # A4: 7,8 => CTR => A4: 6 * PRF # A4: 6 => SOL * DIS # F6: 3,7 => CTR => F6: 4 * INC # F6: 4 => UNS * INC # F5: 1,5 => UNS * DIS # F5: 8 => CTR => F5: 1,5 * INC # D3: 1,5 => UNS * PRF # D3: 4 => SOL * INC # F5: 1,8 => UNS * INC # F5: 5 => UNS * DIS # E2: 1,8 => CTR => E2: 3 * PRF # E2: 3 => SOL * INC # F6: 4,7 => UNS * DIS # F6: 3 => CTR => F6: 4,7 * DIS # D1: 4,7 => CTR => D1: 5,9 * INC # D1: 5,9 => UNS * DIS # H6: 1,8 => CTR => H6: 3 * INC # H6: 3 => UNS * DIS # I2: 1,8 => CTR => I2: 2,5 * INC # I2: 2,5 => UNS * PRF # G8: 3,4 => SOL * INC # G8: 1,5 => UNS * PRF # C9: 6,7 => SOL * DIS # C9: 4 => CTR => C9: 6,7 * INC # A4: 6,7 => UNS * DIS # A4: 8 => CTR => A4: 6,7 * PRF # E7: 1,4 => SOL * DIS # E7: 2 => CTR => E7: 1,4 * DIS # D8: 1,4 => CTR => D8: 2 * PRF # D8: 2 => SOL * DIS # G8: 1,4 => CTR => G8: 3,5 * INC # G8: 3,5 => UNS * INC # G1: 4,8 => UNS * INC # G1: 5,6 => UNS * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C1: 3,7 => SOL * STA C1: 3,7 * CNT 1 HDP CHAINS / 1 HYP OPENED