Analysis of zz-www.sudokuoftheday.co.uk-20190405-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019
level: medium
position: 7.6....8....972.4..2......1..9...5...634...1......52.64.21.6...........8..1..9... initial
Autosolve
position: 7.6....82...97264..2....7.12.9...5.4563427819....952.64.21.6.........1.8..1..94.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 5,8 => CTR => B2: 1,3 * PRF # B1: 3,9 => SOL * DIS # B1: 4,5 => CTR => B1: 3,9 * DIS # A8: 6 => CTR => A8: 3,9 * DIS # B1: 4,5 => CTR => B1: 3,9 * PRF # B1: 3,9 => SOL * DIS # D3: 3,5 => CTR => D3: 6,8 * PRF # B1: 3,5 => SOL * PRF # B1: 3,9 => SOL * DIS # B1: 4,5 => CTR => B1: 3,9 * DIS # B2: 3,5 => CTR => B2: 1,8 * DIS # I7: 3,5 => CTR => I7: 7 * DIS # B6: 7,8 => CTR => B6: 1,4 * DIS # B6: 1,8 => CTR => B6: 4,7 * DIS # A2: 3 => CTR => A2: 1,8 * DIS # B8: 5,7 => CTR => B8: 3,9 * CNT 16 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 # B2: 5,8 => CTR => B2: 1,3 * PRF B2: 1,3 # B1: 3,9 => SOL * STA B2: 1,3 + B1: 3,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 7.6....8....972.4..2......1..9...5...634...1......52.64.21.6...........8..1..9... | initial |
| 7.6....82...97264..2....7.12.9...5.4563427819....952.64.21.6.........1.8..1..94.. | autosolve |
| 736541982815972643924863751279618534563427819148395276452186397397254168681739425 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) C2: 5,8 A3: 3,9 C3: 4,5 D1: 3,5 G1: 3,9 I2: 3,5 H3: 5,9 B4: 7,8 A6: 1,8 D6: 3,8 H4: 3,7 H6: 3,7 C8: 5,7 D8: 2,7 F8: 3,4 D9: 2,7 G7: 3,9 H7: 5,9 H8: 2,6 H9: 2,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,B2: 1.. / A2 = 1 => 0 pairs (X) / B2 = 1 => 20 pairs (_) E1,F1: 1.. / E1 = 1 => 22 pairs (_) / F1 = 1 => 22 pairs (_) A6,B6: 1.. / A6 = 1 => 20 pairs (_) / B6 = 1 => 0 pairs (X) E4,F4: 1.. / E4 = 1 => 22 pairs (_) / F4 = 1 => 22 pairs (_) A2,A6: 1.. / A2 = 1 => 0 pairs (X) / A6 = 1 => 20 pairs (_) B2,B6: 1.. / B2 = 1 => 20 pairs (_) / B6 = 1 => 0 pairs (X) E1,E4: 1.. / E1 = 1 => 22 pairs (_) / E4 = 1 => 22 pairs (_) F1,F4: 1.. / F1 = 1 => 22 pairs (_) / F4 = 1 => 22 pairs (_) D8,D9: 2.. / D8 = 2 => 20 pairs (_) / D9 = 2 => 0 pairs (X) H8,H9: 2.. / H8 = 2 => 0 pairs (X) / H9 = 2 => 20 pairs (_) D8,H8: 2.. / D8 = 2 => 20 pairs (_) / H8 = 2 => 0 pairs (X) D9,H9: 2.. / D9 = 2 => 0 pairs (X) / H9 = 2 => 20 pairs (_) G1,I2: 3.. / G1 = 3 => 0 pairs (X) / I2 = 3 => 0 pairs (_) H4,H6: 3.. / H4 = 3 => 20 pairs (_) / H6 = 3 => 0 pairs (X) D6,H6: 3.. / D6 = 3 => 20 pairs (_) / H6 = 3 => 0 pairs (X) G1,G7: 3.. / G1 = 3 => 0 pairs (X) / G7 = 3 => 0 pairs (_) B1,C3: 4.. / B1 = 4 => 0 pairs (X) / C3 = 4 => 24 pairs (_) B6,C6: 4.. / B6 = 4 => 24 pairs (_) / C6 = 4 => 0 pairs (X) E8,F8: 4.. / E8 = 4 => 31 pairs (_) / F8 = 4 => 25 pairs (_) B1,B6: 4.. / B1 = 4 => 0 pairs (X) / B6 = 4 => 24 pairs (_) C3,C6: 4.. / C3 = 4 => 24 pairs (_) / C6 = 4 => 0 pairs (X) D1,D3: 5.. / D1 = 5 => 19 pairs (_) / D3 = 5 => 0 pairs (X) I2,H3: 5.. / I2 = 5 => 0 pairs (X) / H3 = 5 => 0 pairs (_) B1,D1: 5.. / B1 = 5 => 0 pairs (X) / D1 = 5 => 19 pairs (_) H3,H7: 5.. / H3 = 5 => 0 pairs (*) / H7 = 5 => 0 pairs (X) D3,E3: 6.. / D3 = 6 => 22 pairs (_) / E3 = 6 => 21 pairs (_) D4,E4: 6.. / D4 = 6 => 21 pairs (_) / E4 = 6 => 22 pairs (_) A8,A9: 6.. / A8 = 6 => 0 pairs (X) / A9 = 6 => 20 pairs (_) H8,H9: 6.. / H8 = 6 => 20 pairs (_) / H9 = 6 => 0 pairs (X) A8,H8: 6.. / A8 = 6 => 0 pairs (X) / H8 = 6 => 20 pairs (_) A9,H9: 6.. / A9 = 6 => 20 pairs (_) / H9 = 6 => 0 pairs (X) D3,D4: 6.. / D3 = 6 => 22 pairs (_) / D4 = 6 => 21 pairs (_) E3,E4: 6.. / E3 = 6 => 21 pairs (_) / E4 = 6 => 22 pairs (_) H4,H6: 7.. / H4 = 7 => 0 pairs (X) / H6 = 7 => 20 pairs (_) D8,D9: 7.. / D8 = 7 => 0 pairs (X) / D9 = 7 => 20 pairs (_) I7,I9: 7.. / I7 = 7 => 21 pairs (_) / I9 = 7 => 0 pairs (X) B4,H4: 7.. / B4 = 7 => 20 pairs (_) / H4 = 7 => 0 pairs (X) B7,I7: 7.. / B7 = 7 => 0 pairs (X) / I7 = 7 => 21 pairs (_) C6,C8: 7.. / C6 = 7 => 0 pairs (X) / C8 = 7 => 20 pairs (_) D3,F3: 8.. / D3 = 8 => 18 pairs (_) / F3 = 8 => 21 pairs (_) E7,E9: 8.. / E7 = 8 => 21 pairs (_) / E9 = 8 => 22 pairs (_) B7,E7: 8.. / B7 = 8 => 22 pairs (_) / E7 = 8 => 21 pairs (_) C2,C6: 8.. / C2 = 8 => 21 pairs (_) / C6 = 8 => 0 pairs (*) F3,F4: 8.. / F3 = 8 => 21 pairs (_) / F4 = 8 => 18 pairs (_) B1,A3: 9.. / B1 = 9 => 0 pairs (X) / A3 = 9 => 0 pairs (_) G1,H3: 9.. / G1 = 9 => 0 pairs (*) / H3 = 9 => 0 pairs (X) A8,B8: 9.. / A8 = 9 => 0 pairs (X) / B8 = 9 => 0 pairs (_) G7,H7: 9.. / G7 = 9 => 0 pairs (X) / H7 = 9 => 0 pairs (_) B1,G1: 9.. / B1 = 9 => 0 pairs (X) / G1 = 9 => 0 pairs (_) A3,H3: 9.. / A3 = 9 => 0 pairs (*) / H3 = 9 => 0 pairs (X) A3,A8: 9.. / A3 = 9 => 0 pairs (*) / A8 = 9 => 0 pairs (X) B1,B8: 9.. / B1 = 9 => 0 pairs (X) / B8 = 9 => 0 pairs (_) G1,G7: 9.. / G1 = 9 => 0 pairs (*) / G7 = 9 => 0 pairs (X) H3,H7: 9.. / H3 = 9 => 0 pairs (X) / H7 = 9 => 0 pairs (_) * DURATION: 0:01:12.552493 START: 05:04:32.570049 END: 05:05:45.122542 2019-05-01 * CP COUNT: (54) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A6,B4,C2,C3,C8,D1,D6,D8,D9,F8,G1,G7,H3,H4,H6,H7,H8,H9,I2) * 7.6....82...97264..2....7.12.9...5.4563427819....952.64.21.6.........1.8..1..94.. * PAIR C2: 5,8 BLK 1 B2: 5,8,1,3 # reduction candidate for 5,8 B2: 5,8 => CTR * 7.6....821..972643.2....7512.9...5.4563427819814.952.64.21.6.........1.8..1..94.. B2: 1,3 # 21 pairs * PAIR A3: 3,9 BLK 1 B1: 3,9,4,5 # reduction candidate for 3,9 B1: 3,9 => SOLVED * 736541982815972643924863751279618534563427819148395276452186397397254168681739425 B1: 4,5 => CTR * 7.6...982...972643.2....7.12.9...5.4563427819....952.64.21.6.........1.8..1..94.. * PAIR A3: 3,9 COL A A8: 3,9,6 # reduction candidate for 3,9 A8: 6 => CTR * 7365..982.15972643924...7512.9...5.4563427819.4..952.64.21.639.69.7..1283.12.946. A8: 3,9 # 20 pairs * PAIR C3: 4,5 BLK 1 B1: 4,5,3,9 # reduction candidate for 4,5 B1: 4,5 => CTR * 7.6...982...972643.2....7.12.9...5.4563427819....952.64.21.6.........1.8..1..94.. B1: 3,9 => SOLVED * 736541982815972643924863751279618534563427819148395276452186397397254168681739425 * PAIR D1: 3,5 BLK 2 D3: 3,5,6,8 # reduction candidate for 3,5 D3: 3,5 => CTR * 7.6....82318972645924.687.12896..5745634278191478952364.2186.....5...1.88.1.5946. D3: 6,8 # 22 pairs * PAIR D1: 3,5 ROW 1 B1: 3,5,4,9 # reduction candidate for 3,5 B1: 3,5 => SOLVED * 736541982815972643924863751279618534563427819148395276452186397397254168681739425 B1: 4,9 # 20 pairs * PAIR G1: 3,9 ROW 1 B1: 3,9,4,5 # reduction candidate for 3,9 B1: 3,9 => SOLVED * 736541982815972643924863751279618534563427819148395276452186397397254168681739425 B1: 4,5 => CTR * 7.6...982...972643.2....7.12.9...5.4563427819....952.64.21.6.........1.8..1..94.. * PAIR I2: 3,5 ROW 2 B2: 3,5,1,8 # reduction candidate for 3,5 B2: 3,5 => CTR * 7465..9821.8972643.2....7.12.9...5.45634278198143952764.21.6.....72..1686.17.942. B2: 1,8 # 21 pairs * PAIR I2: 3,5 COL I I7: 3,5,7 # reduction candidate for 3,5 I7: 3,5 => CTR * 7563..982..897264..24...7.1289...574563427819147895236472186...6957..128831259467 I7: 7 # 21 pairs I9: 3,5,7 # reduction candidate for 3,5 I9: 3,5 # 21 pairs * PAIR B4: 7,8 BLK 4 B6: 7,8,1,4 # reduction candidate for 7,8 B6: 7,8 => CTR * 7465..982.1.972643.2....7.12.9...5.4563427819....952.64.21.6.........1.8..1..94.. B6: 1,4 # 21 pairs C6: 7,8,4 # reduction candidate for 7,8 C6: 7,8 # 24 pairs * PAIR B4: 7,8 COL B B7: 7,8,3,5 # reduction candidate for 7,8 B7: 7,8 # 23 pairs B9: 7,8,3,5 # reduction candidate for 7,8 B9: 7,8 # 26 pairs * PAIR A6: 1,8 BLK 4 B6: 1,8,4,7 # reduction candidate for 1,8 B6: 1,8 => CTR * 7465..982...972643.2....7.12.9...5.4563427819....952.64.21.6.........1.8..1..94.. B6: 4,7 # 21 pairs * PAIR A6: 1,8 COL A A2: 1,8,3 # reduction candidate for 1,8 A2: 3 => CTR * 7.6....8231897264592....7.12.9...5.4563427819....952.64.21.6.........1.8..1..94.. A2: 1,8 # 20 pairs * PAIR D6: 3,8 BLK 5 D4: 3,8,6 # reduction candidate for 3,8 D4: 3,8 # 22 pairs F4: 3,8,1 # reduction candidate for 3,8 F4: 3,8 # 22 pairs * PAIR D6: 3,8 COL D D3: 3,8,5,6 # reduction candidate for 3,8 D3: 5,6 # 22 pairs D3: 3,8 # 21 pairs * PAIR C8: 5,7 BLK 7 B7: 5,7,3,8 # reduction candidate for 5,7 B7: 5,7 # 25 pairs B8: 5,7,3,9 # reduction candidate for 5,7 B8: 5,7 => CTR * 7965..382...97264532....7.12.9...5.4563427819....952.64.21.6.........1.8..1..94.. B8: 3,9 # 21 pairs B9: 5,7,3,8 # reduction candidate for 5,7 B9: 5,7 # 24 pairs * PAIR F8: 3,4 BLK 8 E8: 3,4,5 # reduction candidate for 3,4 E8: 5 # 28 pairs E8: 3,4 # 28 pairs * PAIR F8: 3,4 COL F F1: 3,4,1 # reduction candidate for 3,4 F1: 3,4 # 22 pairs F3: 3,4,8 # reduction candidate for 3,4 F3: 3,4 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190405-absurd-base-pr-000.dot * REASONING * DIS # B2: 5,8 => CTR => B2: 1,3 * PRF # B1: 3,9 => SOL * DIS # B1: 4,5 => CTR => B1: 3,9 * DIS # A8: 6 => CTR => A8: 3,9 * DIS # B1: 4,5 => CTR => B1: 3,9 * PRF # B1: 3,9 => SOL * DIS # D3: 3,5 => CTR => D3: 6,8 * PRF # B1: 3,5 => SOL * PRF # B1: 3,9 => SOL * DIS # B1: 4,5 => CTR => B1: 3,9 * DIS # B2: 3,5 => CTR => B2: 1,8 * DIS # I7: 3,5 => CTR => I7: 7 * DIS # B6: 7,8 => CTR => B6: 1,4 * DIS # B6: 1,8 => CTR => B6: 4,7 * DIS # A2: 3 => CTR => A2: 1,8 * DIS # B8: 5,7 => CTR => B8: 3,9 * CNT 16 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A6,B4,C2,C3,C8,D1,D6,D8,D9,F8,G1,G7,H3,H4,H6,H7,H8,H9,I2) * 7.6....82...97264..2....7.12.9...5.4563427819....952.64.21.6.........1.8..1..94.. * PAIR C2: 5,8 BLK 1 B2: 5,8,1,3 # reduction candidate for 5,8 B2: 5,8 => CTR * 7.6....821..972643.2....7512.9...5.4563427819814.952.64.21.6.........1.8..1..94.. * PAIR A3: 3,9 BLK 1 B1: 3,9,4,5 # reduction candidate for 3,9 B1: 3,9 => SOLVED * 736541982815972643924863751279618534563427819148395276452186397397254168681739425 * DURATION: 0:00:03.246087 START: 05:06:14.877933 END: 05:06:18.124020 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190405-absurd-base-pr-001.dot * REASONING * DIS # B2: 5,8 => CTR => B2: 1,3 * PRF B2: 1,3 # B1: 3,9 => SOL * STA B2: 1,3 + B1: 3,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190405, absurd
Solution
position: 736541982815972643924863751279618534563427819148395276452186397397254168681739425 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 # B2: 5,8 => CTR => B2: 1,3 * INC # B2: 1,3 => UNS * PRF # B1: 3,9 => SOL * DIS # B1: 4,5 => CTR => B1: 3,9 * INC # A8: 3,9 => UNS * DIS # A8: 6 => CTR => A8: 3,9 * DIS # B1: 4,5 => CTR => B1: 3,9 * PRF # B1: 3,9 => SOL * DIS # D3: 3,5 => CTR => D3: 6,8 * INC # D3: 6,8 => UNS * PRF # B1: 3,5 => SOL * INC # B1: 4,9 => UNS * PRF # B1: 3,9 => SOL * DIS # B1: 4,5 => CTR => B1: 3,9 * DIS # B2: 3,5 => CTR => B2: 1,8 * INC # B2: 1,8 => UNS * DIS # I7: 3,5 => CTR => I7: 7 * INC # I7: 7 => UNS * INC # I9: 3,5 => UNS * DIS # B6: 7,8 => CTR => B6: 1,4 * INC # B6: 1,4 => UNS * INC # C6: 7,8 => UNS * INC # B7: 7,8 => UNS * INC # B9: 7,8 => UNS * DIS # B6: 1,8 => CTR => B6: 4,7 * INC # B6: 4,7 => UNS * INC # A2: 1,8 => UNS * DIS # A2: 3 => CTR => A2: 1,8 * INC # D4: 3,8 => UNS * INC # F4: 3,8 => UNS * INC # D3: 3,8 => UNS * INC # D3: 5,6 => UNS * INC # B7: 5,7 => UNS * DIS # B8: 5,7 => CTR => B8: 3,9 * INC # B8: 3,9 => UNS * INC # B9: 5,7 => UNS * INC # E8: 3,4 => UNS * INC # E8: 5 => UNS * INC # F1: 3,4 => UNS * INC # F3: 3,4 => UNS * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B2: 5,8 => CTR => B2: 1,3 * PRF B2: 1,3 # B1: 3,9 => SOL * STA B2: 1,3 + B1: 3,9 * CNT 2 HDP CHAINS / 2 HYP OPENED