Analysis of zz-www.sudokuoftheday.co.uk-20060417-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: ...75.4...9.3...1.7...9...235......66..8....4.42......5.3.8..2...752.8.3........7 initial
Autosolve
position: ...75.4...9.3..71.7...9...235.2....667.8..2.4.42......5.3487.2...752.8.3........7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 4,6 => CTR => C2: 5,8 * DIS # F1: 1,6 => CTR => F1: 2,8 * DIS # F3: 1,6 => CTR => F3: 4,8 * DIS # C3: 1,6 => CTR => C3: 4,5,8 * DIS # H1: 8,9 => CTR => H1: 3,6 * DIS # I6: 8,9 => CTR => I6: 1,5 * DIS # C2: 4,6 => CTR => C2: 5,8 * DIS # I6: 1,9 => CTR => I6: 5,8 * PRF # C4: 1,9 => SOL * DIS # F5: 1,9 => CTR => F5: 3,5 * DIS # F5: 1,3 => CTR => F5: 5,9 * DIS # E6: 1,3 => CTR => E6: 6,7 * DIS # E9: 6 => CTR => E9: 1,3 * DIS # G6: 1,9 => CTR => G6: 3,5 * DIS # I6: 1,9 => CTR => I6: 5,8 * PRF # C4: 1,9 => SOL * DIS # G7: 6 => CTR => G7: 1,9 * DIS # G7: 1,6 => CTR => G7: 9 * PRF # A9: 4,9 => SOL * PRF # F8: 9 => SOL * PRF # A9: 4,9 => SOL * DIS # G7: 6 => CTR => G7: 1,9 * DIS # I6: 1,9 => CTR => I6: 5,8 * CNT 23 HDP CHAINS / 64 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 4,6 => CTR => C2: 5,8 * DIS C2: 5,8 # F2: 2 => CTR => F2: 4,6 * PRF C2: 5,8 + F2: 4,6 # A9: 4,9 => SOL * STA C2: 5,8 + F2: 4,6 + A9: 4,9 * CNT 3 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...75.4...9.3...1.7...9...235......66..8....4.42......5.3.8..2...752.8.3........7 | initial |
| ...75.4...9.3..71.7...9...235.2....667.8..2.4.42......5.3487.2...752.8.3........7 | autosolve |
| 186752439295346718734198652359274186671835294842961375563487921417529863928613547 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) B3: 3,8 E2: 4,6 D3: 1,6 I1: 8,9 I2: 5,8 C5: 1,9 E5: 1,3 G4: 1,9 B7: 1,6 A8: 4,9 B8: 1,6 B9: 2,8 I7: 1,9 H8: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B7,B8: 1.. / B7 = 1 => 0 pairs (X) / B8 = 1 => 16 pairs (_) B8,F8: 1.. / B8 = 1 => 16 pairs (_) / F8 = 1 => 0 pairs (X) A1,A6: 1.. / A1 = 1 => 16 pairs (_) / A6 = 1 => 0 pairs (X) I6,I7: 1.. / I6 = 1 => 0 pairs (X) / I7 = 1 => 16 pairs (_) F1,F2: 2.. / F1 = 2 => 20 pairs (_) / F2 = 2 => 15 pairs (_) A9,B9: 2.. / A9 = 2 => 25 pairs (_) / B9 = 2 => 17 pairs (_) A2,F2: 2.. / A2 = 2 => 20 pairs (_) / F2 = 2 => 15 pairs (_) B1,B9: 2.. / B1 = 2 => 25 pairs (_) / B9 = 2 => 17 pairs (_) B1,B3: 3.. / B1 = 3 => 17 pairs (_) / B3 = 3 => 23 pairs (_) E9,F9: 3.. / E9 = 3 => 22 pairs (_) / F9 = 3 => 15 pairs (_) B1,H1: 3.. / B1 = 3 => 17 pairs (_) / H1 = 3 => 23 pairs (_) G3,G6: 3.. / G3 = 3 => 0 pairs (X) / G6 = 3 => 16 pairs (_) E4,F4: 4.. / E4 = 4 => 23 pairs (_) / F4 = 4 => 0 pairs (*) H8,H9: 4.. / H8 = 4 => 16 pairs (_) / H9 = 4 => 0 pairs (*) C3,F3: 4.. / C3 = 4 => 18 pairs (_) / F3 = 4 => 24 pairs (_) A8,H8: 4.. / A8 = 4 => 0 pairs (*) / H8 = 4 => 0 pairs (X) E2,E4: 4.. / E2 = 4 => 0 pairs (*) / E4 = 4 => 0 pairs (X) C2,C3: 5.. / C2 = 5 => 22 pairs (_) / C3 = 5 => 0 pairs (X) F5,F6: 5.. / F5 = 5 => 15 pairs (_) / F6 = 5 => 0 pairs (X) G9,H9: 5.. / G9 = 5 => 22 pairs (_) / H9 = 5 => 19 pairs (_) C2,I2: 5.. / C2 = 5 => 22 pairs (_) / I2 = 5 => 0 pairs (X) F5,H5: 5.. / F5 = 5 => 15 pairs (_) / H5 = 5 => 0 pairs (X) I2,I6: 5.. / I2 = 5 => 0 pairs (X) / I6 = 5 => 22 pairs (_) B7,B8: 6.. / B7 = 6 => 16 pairs (_) / B8 = 6 => 0 pairs (X) B7,G7: 6.. / B7 = 6 => 16 pairs (_) / G7 = 6 => 0 pairs (X) E4,E6: 7.. / E4 = 7 => 0 pairs (*) / E6 = 7 => 0 pairs (X) H4,H6: 7.. / H4 = 7 => 19 pairs (_) / H6 = 7 => 0 pairs (*) E4,H4: 7.. / E4 = 7 => 0 pairs (*) / H4 = 7 => 0 pairs (X) E6,H6: 7.. / E6 = 7 => 19 pairs (_) / H6 = 7 => 0 pairs (*) C4,A6: 8.. / C4 = 8 => 19 pairs (_) / A6 = 8 => 0 pairs (*) C4,H4: 8.. / C4 = 8 => 19 pairs (_) / H4 = 8 => 0 pairs (*) H1,I1: 9.. / H1 = 9 => 0 pairs (X) / I1 = 9 => 16 pairs (_) G7,I7: 9.. / G7 = 9 => 16 pairs (_) / I7 = 9 => 0 pairs (X) A8,F8: 9.. / A8 = 9 => 16 pairs (_) / F8 = 9 => 0 pairs (*) D6,D9: 9.. / D6 = 9 => 18 pairs (_) / D9 = 9 => 17 pairs (_) * DURATION: 0:00:40.729624 START: 22:27:14.071870 END: 22:27:54.801494 2019-04-30 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B3,B7,B8,B9,C5,D3,E2,E5,G4,H8,I1,I2,I7) * ...75.4...9.3..71.7...9...235.2....667.8..2.4.42......5.3487.2...752.8.3........7 * PAIR B3: 3,8 BLK 1 B1: 3,8,2 # reduction candidate for 3,8 B1: 2 # 25 pairs B1: 3,8 # 17 pairs * PAIR B3: 3,8 ROW 3 H3: 3,8,5,6 # reduction candidate for 3,8 H3: 3,8 # 19 pairs H3: 5,6 # 15 pairs * PAIR E2: 4,6 BLK 2 F2: 4,6,2,8 # reduction candidate for 4,6 F2: 4,6 # 18 pairs F3: 4,6,1,8 # reduction candidate for 4,6 F3: 4,6 # 18 pairs * PAIR E2: 4,6 ROW 2 C2: 4,6,5,8 # reduction candidate for 4,6 C2: 4,6 => CTR * ..675.4...9436.7157.5194..235824..7667183.2.494267....5.3487.2.4.75298.3........7 C2: 5,8 # 19 pairs * PAIR D3: 1,6 BLK 2 F1: 1,6,2,8 # reduction candidate for 1,6 F1: 1,6 => CTR * ...75.4...9.34271.734198..235.2.4..667.8..2.4.42...3..5.3487.2...752.8.3........7 F1: 2,8 # 15 pairs F3: 1,6,4,8 # reduction candidate for 1,6 F3: 1,6 => CTR * .3675849..953..718784.9...235.2....667.8..2.4.42.....55.3487.21.1752.8.3.2......7 F3: 4,8 # 15 pairs * PAIR D3: 1,6 ROW 3 C3: 1,6,4,5,8 # reduction candidate for 1,6 C3: 1,6 => CTR * ...7584.949536271878.194..235824..766798.5234142.73985563487.21.1752.8.3..4.....7 C3: 4,5,8 # 14 pairs * PAIR D3: 1,6 COL D D6: 1,6,9 # reduction candidate for 1,6 D6: 1,6 # 17 pairs D9: 1,6,9 # reduction candidate for 1,6 D9: 1,6 # 18 pairs * PAIR I1: 8,9 BLK 3 H1: 8,9,3,6 # reduction candidate for 8,9 H1: 8,9 => CTR * .3675.4...9436.715785194..235824..7667183.2.494267....5.3487.2.4.75298.382......7 H1: 3,6 # 17 pairs * PAIR I1: 8,9 COL I I6: 8,9,1,5 # reduction candidate for 8,9 I6: 8,9 => CTR * ..675.4...9436.7157.5194..2358249176671835294942671..85634879214175268.3........7 I6: 1,5 # 17 pairs * PAIR I2: 5,8 BLK 3 H3: 5,8,3,6 # reduction candidate for 5,8 H3: 5,8 # 19 pairs H3: 3,6 # 15 pairs * PAIR I2: 5,8 ROW 2 C2: 5,8,4,6 # reduction candidate for 5,8 C2: 4,6 => CTR * ..675.4...9436.7157.5194..235824..7667183.2.494267....5.3487.2.4.75298.3........7 C2: 5,8 # 19 pairs * PAIR I2: 5,8 COL I I6: 5,8,1,9 # reduction candidate for 5,8 I6: 1,9 => CTR * .36752498294368715785194..235824..76671839254942.7..8.5.3487.2...752.8.382......7 I6: 5,8 # 16 pairs * PAIR C5: 1,9 BLK 4 C4: 1,9,8 # reduction candidate for 1,9 C4: 1,9 => SOLVED * 186752439295346718734198652359274186671835294842961375563487921417529863928613547 C4: 8 # 19 pairs A6: 1,9,8 # reduction candidate for 1,9 A6: 1,9 # 19 pairs * PAIR C5: 1,9 ROW 5 F5: 1,9,3,5 # reduction candidate for 1,9 F5: 1,9 => CTR * ...75.4...9.36.7157.5194..235824..7667.83.254.42675...5.3487.2..17526843...913567 F5: 3,5 # 15 pairs * PAIR E5: 1,3 BLK 5 F5: 1,3,5,9 # reduction candidate for 1,3 F5: 1,3 => CTR * ...75.4...9.36.7157.5194..235824..766798..254142675...5.3487.21.1752.8.3..4...5.7 F5: 5,9 # 15 pairs E6: 1,3,6,7 # reduction candidate for 1,3 E6: 1,3 => CTR * ...75.4...953467187.4198..235.274.8667.8..2.48426...755.3487.21.175298.3....63..7 E6: 6,7 # 15 pairs F6: 1,3,5,6,9 # reduction candidate for 1,3 F6: 1,3 # 21 pairs * PAIR E5: 1,3 COL E E9: 1,3,6 # reduction candidate for 1,3 E9: 6 => CTR * ...75.4...953467187.4198..235.2.4..667.8..2.4.426....55.3487.21.175298.3....63..7 E9: 1,3 # 17 pairs * PAIR G4: 1,9 BLK 6 G6: 1,9,3,5 # reduction candidate for 1,9 G6: 1,9 => CTR * .3.75.4...9.3..71.78..9.3.235.2....667.8..2.4.42......5.348762...752.8.3......5.7 G6: 3,5 # 15 pairs I6: 1,9,5,8 # reduction candidate for 1,9 I6: 1,9 => CTR * .36752498294368715785194..235824..76671839254942.7..8.5.3487.2...752.8.382......7 I6: 5,8 # 16 pairs * PAIR G4: 1,9 ROW 4 C4: 1,9,8 # reduction candidate for 1,9 C4: 1,9 => SOLVED * 186752439295346718734198652359274186671835294842961375563487921417529863928613547 C4: 8 # 19 pairs F4: 1,9,4 # reduction candidate for 1,9 F4: 1,9 # 23 pairs * PAIR G4: 1,9 COL G G7: 1,9,6 # reduction candidate for 1,9 G7: 6 => CTR * ...75.498.9.3..7157.519436235.249..667.8..2.4.42......5.3487629.67521843......157 G7: 1,9 # 16 pairs * PAIR B7: 1,6 ROW 7 G7: 1,6,9 # reduction candidate for 1,6 G7: 1,6 => CTR * 136752498294368715785194..23582419766718392549426753815.3487.294175268.3........7 G7: 9 # 16 pairs * PAIR A8: 4,9 BLK 7 A9: 4,9,2,8 # reduction candidate for 4,9 A9: 4,9 => SOLVED * 186752439295346718734198652359274186671835294842961375563487921417529863928613547 A9: 2,8 # 16 pairs C9: 4,9,8 # reduction candidate for 4,9 C9: 4,9 # 16 pairs * PAIR B8: 1,6 ROW 8 F8: 1,6,9 # reduction candidate for 1,6 F8: 9 => SOLVED * 186752439295346718734198652359274186671835294842961375563487921417529863928613547 F8: 1,6 # 16 pairs * PAIR B9: 2,8 BLK 7 A9: 2,8,4,9 # reduction candidate for 2,8 A9: 4,9 => SOLVED * 186752439295346718734198652359274186671835294842961375563487921417529863928613547 A9: 2,8 # 16 pairs * PAIR B9: 2,8 COL B B1: 2,8,3 # reduction candidate for 2,8 B1: 2,8 # 23 pairs B1: 3 # 17 pairs * PAIR I7: 1,9 BLK 9 G7: 1,9,6 # reduction candidate for 1,9 G7: 6 => CTR * ...75.498.9.3..7157.519436235.249..667.8..2.4.42......5.3487629.67521843......157 G7: 1,9 # 16 pairs * PAIR I7: 1,9 COL I I6: 1,9,5,8 # reduction candidate for 1,9 I6: 1,9 => CTR * .36752498294368715785194..235824..76671839254942.7..8.5.3487.2...752.8.382......7 I6: 5,8 # 16 pairs * PAIR H8: 4,6 BLK 9 H9: 4,6,5 # reduction candidate for 4,6 H9: 4,6 # 22 pairs H9: 5 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060417-absurd-base-pr-000.dot * REASONING * DIS # C2: 4,6 => CTR => C2: 5,8 * DIS # F1: 1,6 => CTR => F1: 2,8 * DIS # F3: 1,6 => CTR => F3: 4,8 * DIS # C3: 1,6 => CTR => C3: 4,5,8 * DIS # H1: 8,9 => CTR => H1: 3,6 * DIS # I6: 8,9 => CTR => I6: 1,5 * DIS # C2: 4,6 => CTR => C2: 5,8 * DIS # I6: 1,9 => CTR => I6: 5,8 * PRF # C4: 1,9 => SOL * DIS # F5: 1,9 => CTR => F5: 3,5 * DIS # F5: 1,3 => CTR => F5: 5,9 * DIS # E6: 1,3 => CTR => E6: 6,7 * DIS # E9: 6 => CTR => E9: 1,3 * DIS # G6: 1,9 => CTR => G6: 3,5 * DIS # I6: 1,9 => CTR => I6: 5,8 * PRF # C4: 1,9 => SOL * DIS # G7: 6 => CTR => G7: 1,9 * DIS # G7: 1,6 => CTR => G7: 9 * PRF # A9: 4,9 => SOL * PRF # F8: 9 => SOL * PRF # A9: 4,9 => SOL * DIS # G7: 6 => CTR => G7: 1,9 * DIS # I6: 1,9 => CTR => I6: 5,8 * CNT 23 HDP CHAINS / 64 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B3,B7,B8,B9,C5,D3,E2,E5,G4,H8,I1,I2,I7) * ...75.4...9.3..71.7...9...235.2....667.8..2.4.42......5.3487.2...752.8.3........7 * PAIR B3: 3,8 BLK 1 B1: 3,8,2 # reduction candidate for 3,8 B1: 2 # 25 pairs B1: 3,8 # 17 pairs * PAIR B3: 3,8 ROW 3 H3: 3,8,5,6 # reduction candidate for 3,8 H3: 3,8 # 19 pairs H3: 5,6 # 15 pairs * PAIR E2: 4,6 BLK 2 F2: 4,6,2,8 # reduction candidate for 4,6 F2: 4,6 # 18 pairs F3: 4,6,1,8 # reduction candidate for 4,6 F3: 4,6 # 18 pairs * PAIR E2: 4,6 ROW 2 C2: 4,6,5,8 # reduction candidate for 4,6 C2: 4,6 => CTR * ..675.4...9436.7157.5194..235824..7667183.2.494267....5.3487.2.4.75298.3........7 * PAIR RESTART * PAIR E2: 4,6 BLK 2 F2: 4,6,2 # reduction candidate for 4,6 F2: 2 => CTR * ...7584.949.36271.7..194..235824..766798..2.4142.7..985.34879219175268438249....7 * PAIR A8: 4,9 BLK 7 A9: 4,9,8 # reduction candidate for 4,9 A9: 4,9 => SOLVED * 186752439295346718734198652359274186671835294842961375563487921417529863928613547 * DURATION: 0:00:08.292346 START: 22:28:33.019475 END: 22:28:41.311821 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060417-absurd-base-pr-001.dot * REASONING * DIS # C2: 4,6 => CTR => C2: 5,8 * DIS C2: 5,8 # F2: 2 => CTR => F2: 4,6 * PRF C2: 5,8 + F2: 4,6 # A9: 4,9 => SOL * STA C2: 5,8 + F2: 4,6 + A9: 4,9 * CNT 3 HDP CHAINS / 10 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060417, absurd
Solution
position: 186752439295346718734198652359274186671835294842961375563487921417529863928613547 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 # B1: 3,8 => UNS * INC # B1: 2 => UNS * INC # H3: 3,8 => UNS * INC # H3: 5,6 => UNS * INC # F2: 4,6 => UNS * INC # F3: 4,6 => UNS * DIS # C2: 4,6 => CTR => C2: 5,8 * INC # C2: 5,8 => UNS * DIS # F1: 1,6 => CTR => F1: 2,8 * INC # F1: 2,8 => UNS * DIS # F3: 1,6 => CTR => F3: 4,8 * INC # F3: 4,8 => UNS * DIS # C3: 1,6 => CTR => C3: 4,5,8 * INC # C3: 4,5,8 => UNS * INC # D6: 1,6 => UNS * INC # D9: 1,6 => UNS * DIS # H1: 8,9 => CTR => H1: 3,6 * INC # H1: 3,6 => UNS * DIS # I6: 8,9 => CTR => I6: 1,5 * INC # I6: 1,5 => UNS * INC # H3: 5,8 => UNS * INC # H3: 3,6 => UNS * INC # C2: 5,8 => UNS * DIS # C2: 4,6 => CTR => C2: 5,8 * INC # I6: 5,8 => UNS * DIS # I6: 1,9 => CTR => I6: 5,8 * PRF # C4: 1,9 => SOL * INC # C4: 8 => UNS * INC # A6: 1,9 => UNS * DIS # F5: 1,9 => CTR => F5: 3,5 * INC # F5: 3,5 => UNS * DIS # F5: 1,3 => CTR => F5: 5,9 * INC # F5: 5,9 => UNS * DIS # E6: 1,3 => CTR => E6: 6,7 * INC # E6: 6,7 => UNS * INC # F6: 1,3 => UNS * INC # E9: 1,3 => UNS * DIS # E9: 6 => CTR => E9: 1,3 * DIS # G6: 1,9 => CTR => G6: 3,5 * INC # G6: 3,5 => UNS * DIS # I6: 1,9 => CTR => I6: 5,8 * INC # I6: 5,8 => UNS * PRF # C4: 1,9 => SOL * INC # C4: 8 => UNS * INC # F4: 1,9 => UNS * INC # G7: 1,9 => UNS * DIS # G7: 6 => CTR => G7: 1,9 * DIS # G7: 1,6 => CTR => G7: 9 * INC # G7: 9 => UNS * PRF # A9: 4,9 => SOL * INC # A9: 2,8 => UNS * INC # C9: 4,9 => UNS * INC # F8: 1,6 => UNS * PRF # F8: 9 => SOL * INC # A9: 2,8 => UNS * PRF # A9: 4,9 => SOL * INC # B1: 2,8 => UNS * INC # B1: 3 => UNS * INC # G7: 1,9 => UNS * DIS # G7: 6 => CTR => G7: 1,9 * DIS # I6: 1,9 => CTR => I6: 5,8 * INC # I6: 5,8 => UNS * INC # H9: 4,6 => UNS * INC # H9: 5 => UNS * CNT 64 HDP CHAINS / 64 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 3,8 => UNS * INC # B1: 2 => UNS * INC # H3: 3,8 => UNS * INC # H3: 5,6 => UNS * INC # F2: 4,6 => UNS * INC # F3: 4,6 => UNS * DIS # C2: 4,6 => CTR => C2: 5,8 * INC C2: 5,8 # F2: 4,6 => UNS * DIS C2: 5,8 # F2: 2 => CTR => F2: 4,6 * PRF C2: 5,8 + F2: 4,6 # A9: 4,9 => SOL * STA C2: 5,8 + F2: 4,6 + A9: 4,9 * CNT 10 HDP CHAINS / 10 HYP OPENED