Analysis of zz-www.sudokuoftheday.co.uk-20060520-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006
level: medium
position: ...9...7....5.89.6..8..41.2...13....3.5..9.1......764.2.97.....7..2.....5...41... initial
Autosolve
position: .5.9...7.4..5.8936..8..41528..13....3.54.9.1....8576432.978..6.7..29..8.58..41... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F1: 2 => CTR => F1: 3,6 * DIS # B6: 2 => CTR => B6: 1,9 * DIS # B6: 1,2 => CTR => B6: 9 * PRF # C1: 1,2 => SOL * DIS # C1: 3 => CTR => C1: 1,2 * DIS # C2: 1,2 => CTR => C2: 7 * DIS # F1: 2,6 => CTR => F1: 3 * PRF # F1: 3 => SOL * DIS # E1: 1 => CTR => E1: 2,6 * DIS # G5: 7,8 => CTR => G5: 2 * PRF # C8: 3,6 => SOL * DIS # F8: 3,5 => CTR => F8: 6 * PRF # F8: 6 => SOL * DIS # F8: 5 => CTR => F8: 3,6 * DIS # G4: 2,7 => CTR => G4: 5 * DIS # I4: 5 => CTR => I4: 7,9 * CNT 16 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F1: 2 => CTR => F1: 3,6 * DIS F1: 3,6 # B6: 2 => CTR => B6: 1,9 * PRF F1: 3,6 + B6: 1,9 # C8: 3,6 => SOL * STA F1: 3,6 + B6: 1,9 + C8: 3,6 * CNT 3 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...9...7....5.89.6..8..41.2...13....3.5..9.1......764.2.97.....7..2.....5...41... | initial |
| .5.9...7.4..5.8936..8..41528..13....3.54.9.1....8576432.978..6.7..29..8.58..41... | autosolve |
| 651923874427518936938674152864132597375469218192857643249785361713296485586341729 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) A1: 1,6 A3: 6,9 D3: 3,6 E3: 6,7 G1: 4,8 I1: 4,8 B5: 6,7 A6: 1,9 C6: 1,2 F4: 2,6 E5: 2,6 H4: 2,9 I5: 7,8 C9: 3,6 F7: 3,5 D9: 3,6 G9: 2,7 H9: 2,9 I9: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,E2: 1.. / E1 = 1 => 0 pairs (X) / E2 = 1 => 23 pairs (_) I7,I8: 1.. / I7 = 1 => 21 pairs (_) / I8 = 1 => 23 pairs (_) B7,I7: 1.. / B7 = 1 => 23 pairs (_) / I7 = 1 => 21 pairs (_) A1,A6: 1.. / A1 = 1 => 0 pairs (X) / A6 = 1 => 21 pairs (_) B6,C6: 2.. / B6 = 2 => 0 pairs (X) / C6 = 2 => 22 pairs (_) F4,E5: 2.. / F4 = 2 => 19 pairs (_) / E5 = 2 => 0 pairs (X) G9,H9: 2.. / G9 = 2 => 0 pairs (X) / H9 = 2 => 18 pairs (_) E5,G5: 2.. / E5 = 2 => 0 pairs (X) / G5 = 2 => 19 pairs (_) B2,B6: 2.. / B2 = 2 => 22 pairs (_) / B6 = 2 => 0 pairs (X) F1,F4: 2.. / F1 = 2 => 0 pairs (X) / F4 = 2 => 19 pairs (_) H4,H9: 2.. / H4 = 2 => 0 pairs (X) / H9 = 2 => 18 pairs (_) C1,B3: 3.. / C1 = 3 => 0 pairs (X) / B3 = 3 => 0 pairs (_) F1,D3: 3.. / F1 = 3 => 0 pairs (*) / D3 = 3 => 0 pairs (X) G7,G8: 3.. / G7 = 3 => 22 pairs (_) / G8 = 3 => 21 pairs (_) C1,F1: 3.. / C1 = 3 => 0 pairs (X) / F1 = 3 => 0 pairs (_) B3,D3: 3.. / B3 = 3 => 0 pairs (*) / D3 = 3 => 0 pairs (X) C9,D9: 3.. / C9 = 3 => 0 pairs (X) / D9 = 3 => 0 pairs (_) D3,D9: 3.. / D3 = 3 => 0 pairs (X) / D9 = 3 => 0 pairs (_) G1,I1: 4.. / G1 = 4 => 0 pairs (X) / I1 = 4 => 22 pairs (_) B4,C4: 4.. / B4 = 4 => 25 pairs (_) / C4 = 4 => 22 pairs (_) C4,C8: 4.. / C4 = 4 => 22 pairs (_) / C8 = 4 => 25 pairs (_) G4,I4: 5.. / G4 = 5 => 22 pairs (_) / I4 = 5 => 0 pairs (X) F7,F8: 5.. / F7 = 5 => 21 pairs (_) / F8 = 5 => 0 pairs (X) A1,A3: 6.. / A1 = 6 => 21 pairs (_) / A3 = 6 => 0 pairs (X) F4,E5: 6.. / F4 = 6 => 0 pairs (X) / E5 = 6 => 19 pairs (_) F8,D9: 6.. / F8 = 6 => 0 pairs (*) / D9 = 6 => 0 pairs (X) B5,E5: 6.. / B5 = 6 => 0 pairs (X) / E5 = 6 => 19 pairs (_) C9,D9: 6.. / C9 = 6 => 0 pairs (*) / D9 = 6 => 0 pairs (X) D3,D9: 6.. / D3 = 6 => 0 pairs (*) / D9 = 6 => 0 pairs (X) E2,E3: 7.. / E2 = 7 => 0 pairs (X) / E3 = 7 => 20 pairs (_) G9,I9: 7.. / G9 = 7 => 18 pairs (_) / I9 = 7 => 0 pairs (X) B3,E3: 7.. / B3 = 7 => 0 pairs (X) / E3 = 7 => 20 pairs (_) C2,C4: 7.. / C2 = 7 => 22 pairs (_) / C4 = 7 => 0 pairs (X) G1,I1: 8.. / G1 = 8 => 22 pairs (_) / I1 = 8 => 0 pairs (X) G5,I5: 8.. / G5 = 8 => 0 pairs (X) / I5 = 8 => 22 pairs (_) G1,G5: 8.. / G1 = 8 => 22 pairs (_) / G5 = 8 => 0 pairs (X) I1,I5: 8.. / I1 = 8 => 0 pairs (X) / I5 = 8 => 22 pairs (_) A3,B3: 9.. / A3 = 9 => 21 pairs (_) / B3 = 9 => 0 pairs (X) A6,B6: 9.. / A6 = 9 => 0 pairs (X) / B6 = 9 => 21 pairs (_) H4,I4: 9.. / H4 = 9 => 18 pairs (_) / I4 = 9 => 0 pairs (X) H9,I9: 9.. / H9 = 9 => 0 pairs (X) / I9 = 9 => 18 pairs (_) A3,A6: 9.. / A3 = 9 => 21 pairs (_) / A6 = 9 => 0 pairs (X) B3,B6: 9.. / B3 = 9 => 0 pairs (X) / B6 = 9 => 21 pairs (_) H4,H9: 9.. / H4 = 9 => 18 pairs (_) / H9 = 9 => 0 pairs (X) I4,I9: 9.. / I4 = 9 => 0 pairs (X) / I9 = 9 => 18 pairs (_) * DURATION: 0:00:51.789769 START: 23:16:57.912886 END: 23:17:49.702655 2019-04-30 * CP COUNT: (45) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A6,B5,C6,C9,D3,D9,E3,E5,F4,F7,G1,G9,H4,H9,I1,I5,I9) * .5.9...7.4..5.8936..8..41528..13....3.54.9.1....8576432.978..6.7..29..8.58..41... * PAIR A1: 1,6 ROW 1 E1: 1,6,2 # reduction candidate for 1,6 E1: 1,6 # 22 pairs E1: 2 # 17 pairs * PAIR D3: 3,6 BLK 2 F1: 3,6,2 # reduction candidate for 3,6 F1: 2 => CTR * .539.2.7.4..5.8936..83.41528..136...365429.1....8576432.978..6.7.629..8.58..41... F1: 3,6 # 19 pairs * PAIR B5: 6,7 BLK 4 B4: 6,7,4 # reduction candidate for 6,7 B4: 6,7 # 22 pairs C4: 6,7,4 # reduction candidate for 6,7 C4: 6,7 # 25 pairs * PAIR A6: 1,9 BLK 4 B6: 1,9,2 # reduction candidate for 1,9 B6: 2 => CTR * .5.9...7.4..5.8936.983741528..13....3.54.9.1.9218576432.978..6.7..29..8.583641... B6: 1,9 # 22 pairs * PAIR C6: 1,2 BLK 4 B6: 1,2,9 # reduction candidate for 1,2 B6: 1,2 => CTR * .5.9...7.4..5.8936.983741528..13....3.54.9.1.9..8576432.978..6.7..29..8.583641... B6: 9 # 21 pairs * PAIR C6: 1,2 COL C C1: 1,2,3 # reduction candidate for 1,2 C1: 1,2 => SOLVED * 651923874427518936938674152864132597375469218192857643249785361713296485586341729 C1: 3 => CTR * .539...7.4..5.8936..83.41528..13....3.54.9.1....8576432.978..6.7..29..8.586.41... C2: 1,2,7 # reduction candidate for 1,2 C2: 1,2 => CTR * .5.9...7.4..5.8936..8..41528.713....365429.1....8576432.978..6.7.4296.8.58..41... C2: 7 # 22 pairs * PAIR F4: 2,6 COL F F1: 2,6,3 # reduction candidate for 2,6 F1: 2,6 => CTR * .539...7.4..5.8936..83.41528..13....3.54.9.1....8576432.978..6.7..29..8.586.41... F1: 3 => SOLVED * 651923874427518936938674152864132597375469218192857643249785361713296485586341729 * PAIR E5: 2,6 COL E E1: 2,6,1 # reduction candidate for 2,6 E1: 1 => CTR * 653912.7.4215789369783641528.7136...365429.1.1928576432.978..6.7..29..8.58..41... E1: 2,6 # 23 pairs * PAIR I5: 7,8 BLK 6 G5: 7,8,2 # reduction candidate for 7,8 G5: 7,8 => CTR * .5.9.2.7.4..5.8936..83.41528..136...365429.1....8576432.978..6.7.629..8.583641... G5: 2 # 19 pairs * PAIR C9: 3,6 BLK 7 B8: 3,6,1,4 # reduction candidate for 3,6 B8: 3,6 # 22 pairs C8: 3,6,1,4 # reduction candidate for 3,6 C8: 3,6 => SOLVED * 651923874427518936938674152864132597375469218192857643249785361713296485586341729 C8: 1,4 # 20 pairs * PAIR F7: 3,5 BLK 8 F8: 3,5,6 # reduction candidate for 3,5 F8: 3,5 => CTR * .5.9...7.4..5.8936..83.41528..13....3.54.9.1....8576432.978..6.7..29..8.583641... F8: 6 => SOLVED * 651923874427518936938674152864132597375469218192857643249785361713296485586341729 * PAIR F7: 3,5 ROW 7 G7: 3,5,4 # reduction candidate for 3,5 G7: 4 # 22 pairs G7: 3,5 # 22 pairs * PAIR D9: 3,6 BLK 8 F8: 3,6,5 # reduction candidate for 3,6 F8: 5 => CTR * .5.9...7.4..5.8936..83.41528..13....3.54.9.1....8576432.9783.6.73.295.8.58.641... F8: 3,6 # 21 pairs * PAIR G9: 2,7 COL G G4: 2,7,5 # reduction candidate for 2,7 G4: 2,7 => CTR * .5.9.24784..5.8936..83.41528..136295365429817...8576432.978..6.7.629..8.583641729 G4: 5 # 22 pairs G5: 2,7,8 # reduction candidate for 2,7 G5: 2,7 # 22 pairs * PAIR I9: 7,9 COL I I4: 7,9,5 # reduction candidate for 7,9 I4: 5 => CTR * .5.9.24784..5.8936..83.41528..136295365429817...8576432.978..6.7.629..8.583641729 I4: 7,9 # 22 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060520-absurd-base-pr-000.dot * REASONING * DIS # F1: 2 => CTR => F1: 3,6 * DIS # B6: 2 => CTR => B6: 1,9 * DIS # B6: 1,2 => CTR => B6: 9 * PRF # C1: 1,2 => SOL * DIS # C1: 3 => CTR => C1: 1,2 * DIS # C2: 1,2 => CTR => C2: 7 * DIS # F1: 2,6 => CTR => F1: 3 * PRF # F1: 3 => SOL * DIS # E1: 1 => CTR => E1: 2,6 * DIS # G5: 7,8 => CTR => G5: 2 * PRF # C8: 3,6 => SOL * DIS # F8: 3,5 => CTR => F8: 6 * PRF # F8: 6 => SOL * DIS # F8: 5 => CTR => F8: 3,6 * DIS # G4: 2,7 => CTR => G4: 5 * DIS # I4: 5 => CTR => I4: 7,9 * CNT 16 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A6,B5,C6,C9,D3,D9,E3,E5,F4,F7,G1,G9,H4,H9,I1,I5,I9) * .5.9...7.4..5.8936..8..41528..13....3.54.9.1....8576432.978..6.7..29..8.58..41... * PAIR A1: 1,6 ROW 1 E1: 1,6,2 # reduction candidate for 1,6 E1: 1,6 # 22 pairs E1: 2 # 17 pairs * PAIR D3: 3,6 BLK 2 F1: 3,6,2 # reduction candidate for 3,6 F1: 2 => CTR * .539.2.7.4..5.8936..83.41528..136...365429.1....8576432.978..6.7.629..8.58..41... * PAIR A6: 1,9 BLK 4 B6: 1,9,2 # reduction candidate for 1,9 B6: 2 => CTR * .5.9..8744.75.8936.983741528..1325973754692189218576432.978..6.7..29..8.58..41729 * PAIR C9: 3,6 BLK 7 B8: 3,6,1,4 # reduction candidate for 3,6 B8: 3,6 # 20 pairs C8: 3,6,1,4 # reduction candidate for 3,6 C8: 3,6 => SOLVED * 651923874427518936938674152864132597375469218192857643249785361713296485586341729 * DURATION: 0:00:06.995489 START: 23:18:12.326379 END: 23:18:19.321868 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060520-absurd-base-pr-001.dot * REASONING * DIS # F1: 2 => CTR => F1: 3,6 * DIS F1: 3,6 # B6: 2 => CTR => B6: 1,9 * PRF F1: 3,6 + B6: 1,9 # C8: 3,6 => SOL * STA F1: 3,6 + B6: 1,9 + C8: 3,6 * CNT 3 HDP CHAINS / 8 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060520, absurd
Solution
position: 651923874427518936938674152864132597375469218192857643249785361713296485586341729 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:
* INC # E1: 1,6 => UNS * INC # E1: 2 => UNS * INC # F1: 3,6 => UNS * DIS # F1: 2 => CTR => F1: 3,6 * INC # B4: 6,7 => UNS * INC # C4: 6,7 => UNS * INC # B6: 1,9 => UNS * DIS # B6: 2 => CTR => B6: 1,9 * DIS # B6: 1,2 => CTR => B6: 9 * INC # B6: 9 => UNS * PRF # C1: 1,2 => SOL * DIS # C1: 3 => CTR => C1: 1,2 * DIS # C2: 1,2 => CTR => C2: 7 * INC # C2: 7 => UNS * DIS # F1: 2,6 => CTR => F1: 3 * PRF # F1: 3 => SOL * INC # E1: 2,6 => UNS * DIS # E1: 1 => CTR => E1: 2,6 * DIS # G5: 7,8 => CTR => G5: 2 * INC # G5: 2 => UNS * INC # B8: 3,6 => UNS * PRF # C8: 3,6 => SOL * INC # C8: 1,4 => UNS * DIS # F8: 3,5 => CTR => F8: 6 * PRF # F8: 6 => SOL * INC # G7: 3,5 => UNS * INC # G7: 4 => UNS * INC # F8: 3,6 => UNS * DIS # F8: 5 => CTR => F8: 3,6 * DIS # G4: 2,7 => CTR => G4: 5 * INC # G4: 5 => UNS * INC # G5: 2,7 => UNS * INC # I4: 7,9 => UNS * DIS # I4: 5 => CTR => I4: 7,9 * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E1: 1,6 => UNS * INC # E1: 2 => UNS * INC # F1: 3,6 => UNS * DIS # F1: 2 => CTR => F1: 3,6 * INC F1: 3,6 # B6: 1,9 => UNS * DIS F1: 3,6 # B6: 2 => CTR => B6: 1,9 * INC F1: 3,6 + B6: 1,9 # B8: 3,6 => UNS * PRF F1: 3,6 + B6: 1,9 # C8: 3,6 => SOL * STA F1: 3,6 + B6: 1,9 + C8: 3,6 * CNT 8 HDP CHAINS / 8 HYP OPENED