Analysis of zz-www.sudokuoftheday.co.uk-20060416-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: .8.5.2...57.6.4.2.....91...2.8....4...1.6...2..72.95...2...6..8..63....9.1......4 initial
Autosolve
position: 1845.2...5796.4.2...2.914.52.8....4...1.6...2..72.95...2...6..8.463....9.1......4 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A6: 3,6 => CTR => A6: 4 * PRF # G1: 3,7 => SOL * DIS # G2: 1 => CTR => G2: 3,8 * DIS # D5: 7,8 => CTR => D5: 4 * DIS # D9: 7,8 => CTR => D9: 9 * DIS # G1: 6,7 => CTR => G1: 3,9 * DIS # H1: 6,7 => CTR => H1: 3,9 * DIS # G2: 1,3 => CTR => G2: 8 * PRF # G2: 8 => SOL * PRF # H5: 7,8 => SOL * DIS # A6: 6 => CTR => A6: 3,4 * DIS # A6: 3,6 => CTR => A6: 4 * DIS # E4: 1,7 => CTR => E4: 5 * DIS # G4: 1,7 => CTR => G4: 3,6,9 * PRF # D7: 1,7 => SOL * DIS # G4: 1,3,9 => CTR => G4: 6,7 * DIS # G4: 1,3 => CTR => G4: 6,7,9 * PRF # H6: 1,3 => SOL * DIS # H6: 8 => CTR => H6: 1,3 * PRF # D7: 7,9 => SOL * DIS # A9: 9 => CTR => A9: 7,8 * DIS # E8: 7,8 => CTR => E8: 1,2,5 * DIS # H9: 3,5 => CTR => H9: 6,7 * CNT 23 HDP CHAINS / 48 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A6: 3,6 => CTR => A6: 4 * PRF A6: 4 # G1: 3,7 => SOL * STA A6: 4 + G1: 3,7 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .8.5.2...57.6.4.2.....91...2.8....4...1.6...2..72.95...2...6..8..63....9.1......4 | initial |
| 1845.2...5796.4.2...2.914.52.8....4...1.6...2..72.95...2...6..8.463....9.1......4 | autosolve |
| 184572396579634821632891475298153647351467982467289513925746138746318259813925764 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) A3: 3,6 B3: 3,6 E1: 3,7 E2: 3,8 D3: 7,8 I1: 6,7 I2: 1,3 H3: 7,8 B4: 5,9 A5: 3,4 B5: 5,9 B6: 3,6 D4: 1,7 I4: 6,7 I6: 1,3 A7: 7,9 C7: 3,5 A8: 7,8 C9: 3,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G2,I2: 1.. / G2 = 1 => 0 pairs (X) / I2 = 1 => 16 pairs (_) D4,D7: 1.. / D4 = 1 => 20 pairs (_) / D7 = 1 => 0 pairs (X) I2,I6: 1.. / I2 = 1 => 16 pairs (_) / I6 = 1 => 0 pairs (X) E8,E9: 2.. / E8 = 2 => 0 pairs (X) / E9 = 2 => 19 pairs (_) G8,G9: 2.. / G8 = 2 => 19 pairs (_) / G9 = 2 => 0 pairs (X) E8,G8: 2.. / E8 = 2 => 0 pairs (X) / G8 = 2 => 19 pairs (_) E9,G9: 2.. / E9 = 2 => 19 pairs (_) / G9 = 2 => 0 pairs (X) A3,B3: 3.. / A3 = 3 => 0 pairs (X) / B3 = 3 => 17 pairs (_) E1,E2: 3.. / E1 = 3 => 0 pairs (X) / E2 = 3 => 0 pairs (_) F4,F5: 3.. / F4 = 3 => 19 pairs (_) / F5 = 3 => 0 pairs (X) C7,C9: 3.. / C7 = 3 => 21 pairs (_) / C9 = 3 => 17 pairs (_) F4,G4: 3.. / F4 = 3 => 19 pairs (_) / G4 = 3 => 0 pairs (X) B3,B6: 3.. / B3 = 3 => 17 pairs (_) / B6 = 3 => 0 pairs (X) I2,I6: 3.. / I2 = 3 => 0 pairs (X) / I6 = 3 => 16 pairs (_) A5,A6: 4.. / A5 = 4 => 0 pairs (X) / A6 = 4 => 16 pairs (_) D5,E6: 4.. / D5 = 4 => 16 pairs (_) / E6 = 4 => 0 pairs (X) D7,E7: 4.. / D7 = 4 => 0 pairs (X) / E7 = 4 => 16 pairs (_) A5,D5: 4.. / A5 = 4 => 0 pairs (X) / D5 = 4 => 16 pairs (_) A6,E6: 4.. / A6 = 4 => 16 pairs (_) / E6 = 4 => 0 pairs (X) D5,D7: 4.. / D5 = 4 => 16 pairs (_) / D7 = 4 => 0 pairs (X) E6,E7: 4.. / E6 = 4 => 0 pairs (X) / E7 = 4 => 16 pairs (_) B4,B5: 5.. / B4 = 5 => 0 pairs (X) / B5 = 5 => 17 pairs (_) C7,C9: 5.. / C7 = 5 => 17 pairs (_) / C9 = 5 => 21 pairs (_) B5,F5: 5.. / B5 = 5 => 17 pairs (_) / F5 = 5 => 0 pairs (X) A3,B3: 6.. / A3 = 6 => 17 pairs (_) / B3 = 6 => 0 pairs (X) A6,B6: 6.. / A6 = 6 => 0 pairs (X) / B6 = 6 => 17 pairs (_) G4,I4: 6.. / G4 = 6 => 16 pairs (_) / I4 = 6 => 0 pairs (X) G9,H9: 6.. / G9 = 6 => 0 pairs (X) / H9 = 6 => 19 pairs (_) A3,A6: 6.. / A3 = 6 => 17 pairs (_) / A6 = 6 => 0 pairs (X) B3,B6: 6.. / B3 = 6 => 0 pairs (X) / B6 = 6 => 17 pairs (_) H1,H9: 6.. / H1 = 6 => 0 pairs (X) / H9 = 6 => 19 pairs (_) I1,I4: 6.. / I1 = 6 => 16 pairs (_) / I4 = 6 => 0 pairs (X) E1,D3: 7.. / E1 = 7 => 0 pairs (*) / D3 = 7 => 0 pairs (X) D3,H3: 7.. / D3 = 7 => 0 pairs (X) / H3 = 7 => 0 pairs (_) I1,I4: 7.. / I1 = 7 => 0 pairs (X) / I4 = 7 => 16 pairs (_) E2,D3: 8.. / E2 = 8 => 0 pairs (X) / D3 = 8 => 0 pairs (_) G2,H3: 8.. / G2 = 8 => 0 pairs (*) / H3 = 8 => 0 pairs (X) A8,A9: 8.. / A8 = 8 => 20 pairs (_) / A9 = 8 => 21 pairs (_) E2,G2: 8.. / E2 = 8 => 0 pairs (X) / G2 = 8 => 0 pairs (_) D3,H3: 8.. / D3 = 8 => 0 pairs (*) / H3 = 8 => 0 pairs (X) E6,H6: 8.. / E6 = 8 => 0 pairs (*) / H6 = 8 => 0 pairs (X) G2,G5: 8.. / G2 = 8 => 0 pairs (*) / G5 = 8 => 0 pairs (X) G1,H1: 9.. / G1 = 9 => 17 pairs (_) / H1 = 9 => 19 pairs (_) B4,B5: 9.. / B4 = 9 => 17 pairs (_) / B5 = 9 => 0 pairs (X) A7,A9: 9.. / A7 = 9 => 19 pairs (_) / A9 = 9 => 0 pairs (X) D7,D9: 9.. / D7 = 9 => 0 pairs (X) / D9 = 9 => 19 pairs (_) B4,G4: 9.. / B4 = 9 => 17 pairs (_) / G4 = 9 => 0 pairs (X) A7,D7: 9.. / A7 = 9 => 19 pairs (_) / D7 = 9 => 0 pairs (X) A9,D9: 9.. / A9 = 9 => 0 pairs (X) / D9 = 9 => 19 pairs (_) H1,H5: 9.. / H1 = 9 => 19 pairs (_) / H5 = 9 => 17 pairs (_) * DURATION: 0:00:57.560163 START: 22:25:32.927449 END: 22:26:30.487612 2019-04-30 * CP COUNT: (50) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,A7,A8,B3,B4,B5,B6,C7,C9,D3,D4,E1,E2,H3,I1,I2,I4,I6) * 1845.2...5796.4.2...2.914.52.8....4...1.6...2..72.95...2...6..8.463....9.1......4 * PAIR A3: 3,6 COL A A6: 3,6,4 # reduction candidate for 3,6 A6: 3,6 => CTR * 1845.2...5796.4.2...2.914.52.8....4.4.1.6...2..7249581.2.4.6..8.463....9.1.9....4 A6: 4 # 16 pairs * PAIR E1: 3,7 ROW 1 G1: 3,7,6,9 # reduction candidate for 3,7 G1: 3,7 => SOLVED * 184572396579634821632891475298153647351467982467289513925746138746318259813925764 G1: 6,9 # 20 pairs H1: 3,7,6,9 # reduction candidate for 3,7 H1: 3,7 # 19 pairs * PAIR E2: 3,8 ROW 2 G2: 3,8,1 # reduction candidate for 3,8 G2: 1 => CTR * 1845.2...579684123..27914852.81...4...1.6.8.2..72495...2...6..8.463....9.1......4 G2: 3,8 # 16 pairs * PAIR D3: 7,8 COL D D5: 7,8,4 # reduction candidate for 7,8 D5: 7,8 => CTR * 1845.2...5796.4.2...2.914.52.8....4.4.1.6...2..7249581.2.4.6..8.463....9.1.9....4 D5: 4 # 16 pairs D9: 7,8,9 # reduction candidate for 7,8 D9: 7,8 => CTR * 184572..657963482163289147529815.647351467..24672895..72.946..884631.2.991..28..4 D9: 9 # 19 pairs * PAIR I1: 6,7 BLK 3 G1: 6,7,3,9 # reduction candidate for 6,7 G1: 6,7 => CTR * 184532.9.579684.2...27914852.81...4...1.6.8.2..72495...2...6..8.463....9.1.....64 G1: 3,9 # 20 pairs H1: 6,7,3,9 # reduction candidate for 6,7 H1: 6,7 => CTR * 1845329..579684.2...27914852981...4..51.6.892..72495...2...6..8.463....9.1......4 H1: 3,9 # 20 pairs * PAIR I2: 1,3 BLK 3 G2: 1,3,8 # reduction candidate for 1,3 G2: 1,3 => CTR * 1845.2...579684.2...27914852.81...4...1.6.8.2..72495...2...6..8.463....9.1......4 G2: 8 => SOLVED * 184572396579634821632891475298153647351467982467289513925746138746318259813925764 * PAIR H3: 7,8 COL H H5: 7,8,3,9 # reduction candidate for 7,8 H5: 7,8 => SOLVED * 184572396579634821632891475298153647351467982467289513925746138746318259813925764 H5: 3,9 # 20 pairs * PAIR A5: 3,4 BLK 4 A6: 3,4,6 # reduction candidate for 3,4 A6: 6 => CTR * 1845.2...5796.4.2...2.914.52.8....4.4.1.6...2637249581.2.4.6..8.463....9.1.9....4 A6: 3,4 # 17 pairs * PAIR B6: 3,6 BLK 4 A6: 3,6,4 # reduction candidate for 3,6 A6: 3,6 => CTR * 1845.2...5796.4.2...2.914.52.8....4.4.1.6...2..7249581.2.4.6..8.463....9.1.9....4 A6: 4 # 16 pairs * PAIR D4: 1,7 BLK 5 E4: 1,7,5 # reduction candidate for 1,7 E4: 1,7 => CTR * 1845.2..75796.4.2...27914852.817..46..186...2..72495..92.4.6..8.463....9.1.9....4 E4: 5 # 18 pairs * PAIR D4: 1,7 ROW 4 G4: 1,7,3,6,9 # reduction candidate for 1,7 G4: 1,7 => CTR * 1845.2..75796.4.2...2791485298153746.51.67892..72895...2..46..8.4631.2.9.1.8....4 G4: 3,6,9 # 20 pairs * PAIR D4: 1,7 COL D D7: 1,7,4,9 # reduction candidate for 1,7 D7: 1,7 => SOLVED * 184572396579634821632891475298153647351467982467289513925746138746318259813925764 D7: 4,9 # 21 pairs * PAIR I4: 6,7 BLK 6 G4: 6,7,1,3,9 # reduction candidate for 6,7 G4: 1,3,9 => CTR * 1845.2..75796.4.2...27914852.81...46..1.6.872..72895...2..46..8.4631.259.1.825..4 G4: 6,7 # 19 pairs * PAIR I6: 1,3 BLK 6 G4: 1,3,6,7,9 # reduction candidate for 1,3 G4: 1,3 => CTR * 1845.2..75796.4.2...27914852981..346.51.638.2..72.95...2...6..8.463....9.1......4 G4: 6,7,9 # 20 pairs H6: 1,3,8 # reduction candidate for 1,3 H6: 1,3 => SOLVED * 184572396579634821632891475298153647351467982467289513925746138746318259813925764 H6: 8 => CTR * 1845.2...5796.4821..28914752.8...14...1.6...2..72.958..2...6..8.463....9.1......4 * PAIR A7: 7,9 BLK 7 A9: 7,9,8 # reduction candidate for 7,9 A9: 8 # 21 pairs A9: 7,9 # 20 pairs * PAIR A7: 7,9 ROW 7 D7: 7,9,1,4 # reduction candidate for 7,9 D7: 7,9 => SOLVED * 184572396579634821632891475298153647351467982467289513925746138746318259813925764 D7: 1,4 # 20 pairs * PAIR C7: 3,5 ROW 7 H7: 3,5,1,7 # reduction candidate for 3,5 H7: 3,5 # 21 pairs H7: 1,7 # 20 pairs * PAIR A8: 7,8 BLK 7 A9: 7,8,9 # reduction candidate for 7,8 A9: 9 => CTR * 184572..657963482163289147529815.647351467..24672895..72.946..884631.2.991..28..4 A9: 7,8 # 19 pairs * PAIR A8: 7,8 ROW 8 E8: 7,8,1,2,5 # reduction candidate for 7,8 E8: 7,8 => CTR * 1845.2...5796.4821..2891475298.5.14..51.6...2..72.958.92...6..8.463.5219.1.92...4 E8: 1,2,5 # 19 pairs F8: 7,8,5 # reduction candidate for 7,8 F8: 7,8 # 22 pairs * PAIR C9: 3,5 ROW 9 H9: 3,5,6,7 # reduction candidate for 3,5 H9: 3,5 => CTR * 1845.2.675796.4.2...27914852.81...46..1.6.892..72895...2..46..8.4631.2.9.1.82.6.4 H9: 6,7 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060416-absurd-base-pr-000.dot * REASONING * DIS # A6: 3,6 => CTR => A6: 4 * PRF # G1: 3,7 => SOL * DIS # G2: 1 => CTR => G2: 3,8 * DIS # D5: 7,8 => CTR => D5: 4 * DIS # D9: 7,8 => CTR => D9: 9 * DIS # G1: 6,7 => CTR => G1: 3,9 * DIS # H1: 6,7 => CTR => H1: 3,9 * DIS # G2: 1,3 => CTR => G2: 8 * PRF # G2: 8 => SOL * PRF # H5: 7,8 => SOL * DIS # A6: 6 => CTR => A6: 3,4 * DIS # A6: 3,6 => CTR => A6: 4 * DIS # E4: 1,7 => CTR => E4: 5 * DIS # G4: 1,7 => CTR => G4: 3,6,9 * PRF # D7: 1,7 => SOL * DIS # G4: 1,3,9 => CTR => G4: 6,7 * DIS # G4: 1,3 => CTR => G4: 6,7,9 * PRF # H6: 1,3 => SOL * DIS # H6: 8 => CTR => H6: 1,3 * PRF # D7: 7,9 => SOL * DIS # A9: 9 => CTR => A9: 7,8 * DIS # E8: 7,8 => CTR => E8: 1,2,5 * DIS # H9: 3,5 => CTR => H9: 6,7 * CNT 23 HDP CHAINS / 48 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,A7,A8,B3,B4,B5,B6,C7,C9,D3,D4,E1,E2,H3,I1,I2,I4,I6) * 1845.2...5796.4.2...2.914.52.8....4...1.6...2..72.95...2...6..8.463....9.1......4 * PAIR A3: 3,6 COL A A6: 3,6,4 # reduction candidate for 3,6 A6: 3,6 => CTR * 1845.2...5796.4.2...2.914.52.8....4.4.1.6...2..7249581.2.4.6..8.463....9.1.9....4 * PAIR RESTART * PAIR E1: 3,7 ROW 1 G1: 3,7,6,9 # reduction candidate for 3,7 G1: 3,7 => SOLVED * 184572396579634821632891475298153647351467982467289513925746138746318259813925764 * DURATION: 0:00:03.097208 START: 22:27:02.321587 END: 22:27:05.418795 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060416-absurd-base-pr-001.dot * REASONING * DIS # A6: 3,6 => CTR => A6: 4 * PRF A6: 4 # G1: 3,7 => SOL * STA A6: 4 + G1: 3,7 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060416, absurd
Solution
position: 184572396579634821632891475298153647351467982467289513925746138746318259813925764 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 # A6: 3,6 => CTR => A6: 4 * INC # A6: 4 => UNS * PRF # G1: 3,7 => SOL * INC # G1: 6,9 => UNS * INC # H1: 3,7 => UNS * INC # G2: 3,8 => UNS * DIS # G2: 1 => CTR => G2: 3,8 * DIS # D5: 7,8 => CTR => D5: 4 * INC # D5: 4 => UNS * DIS # D9: 7,8 => CTR => D9: 9 * INC # D9: 9 => UNS * DIS # G1: 6,7 => CTR => G1: 3,9 * INC # G1: 3,9 => UNS * DIS # H1: 6,7 => CTR => H1: 3,9 * INC # H1: 3,9 => UNS * DIS # G2: 1,3 => CTR => G2: 8 * PRF # G2: 8 => SOL * PRF # H5: 7,8 => SOL * INC # H5: 3,9 => UNS * INC # A6: 3,4 => UNS * DIS # A6: 6 => CTR => A6: 3,4 * DIS # A6: 3,6 => CTR => A6: 4 * INC # A6: 4 => UNS * DIS # E4: 1,7 => CTR => E4: 5 * INC # E4: 5 => UNS * DIS # G4: 1,7 => CTR => G4: 3,6,9 * INC # G4: 3,6,9 => UNS * PRF # D7: 1,7 => SOL * INC # D7: 4,9 => UNS * INC # G4: 6,7 => UNS * DIS # G4: 1,3,9 => CTR => G4: 6,7 * DIS # G4: 1,3 => CTR => G4: 6,7,9 * INC # G4: 6,7,9 => UNS * PRF # H6: 1,3 => SOL * DIS # H6: 8 => CTR => H6: 1,3 * INC # A9: 7,9 => UNS * INC # A9: 8 => UNS * PRF # D7: 7,9 => SOL * INC # D7: 1,4 => UNS * INC # H7: 3,5 => UNS * INC # H7: 1,7 => UNS * INC # A9: 7,8 => UNS * DIS # A9: 9 => CTR => A9: 7,8 * DIS # E8: 7,8 => CTR => E8: 1,2,5 * INC # E8: 1,2,5 => UNS * INC # F8: 7,8 => UNS * DIS # H9: 3,5 => CTR => H9: 6,7 * INC # H9: 6,7 => UNS * CNT 48 HDP CHAINS / 48 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A6: 3,6 => CTR => A6: 4 * PRF A6: 4 # G1: 3,7 => SOL * STA A6: 4 + G1: 3,7 * CNT 2 HDP CHAINS / 2 HYP OPENED