Analysis of zz-www.sudokuoftheday.co.uk-20060624-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006
level: medium
position: .79.1......86..3.14....86......7...4.3..4.......8...6.98.5.......1...5.23.5....4. initial
Autosolve
position: 679.1.4..2586943714137.86...9..7...4.3..4.....4.8...6.9845.....7614..5.2325....4. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # F1: 5 => SOL * DIS # D4: 1 => CTR => D4: 2,3 * DIS # F1: 3 => CTR => F1: 2,5 * PRF # H3: 9 => SOL * PRF # E6: 2,5 => SOL * DIS # E6: 3 => CTR => E6: 2,5 * PRF # H1: 2 => SOL * PRF # H3: 5,9 => SOL * PRF # I6: 5,9 => SOL * DIS # F6: 1,5 => CTR => F6: 2,3,9 * PRF # H8: 3,8 => SOL * DIS # H8: 9 => CTR => H8: 3,8 * DIS # H8: 3,9 => CTR => H8: 8 * PRF # H8: 8 => SOL * PRF # F6: 3,9 => SOL * DIS # F9: 1,9 => CTR => F9: 7 * DIS # D5: 2 => CTR => D5: 1,9 * DIS # I9: 7,9 => CTR => I9: 6,8 * DIS # G9: 1,7 => CTR => G9: 8,9 * DIS # F7: 1,7 => CTR => F7: 2,3 * PRF # F7: 2,3 => SOL * DIS # F7: 1,3 => CTR => F7: 2,7 * DIS # H4: 5,8 => CTR => H4: 1,3 * CNT 23 HDP CHAINS / 55 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # F1: 5 => SOL * STA F1: 5 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .79.1......86..3.14....86......7...4.3..4.......8...6.98.5.......1...5.23.5....4. | initial |
| 679.1.4..2586943714137.86...9..7...4.3..4.....4.8...6.9845.....7614..5.2325....4. | autosolve |
| 679315428258694371413728695596271834832946157147853269984562713761439582325187946 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) D1: 2,3 E3: 2,5 I1: 5,8 I3: 5,9 C4: 2,6 A6: 1,5 C6: 2,7 E8: 3,8 F8: 3,9 D9: 1,9 E9: 6,8 G7: 1,7 H7: 1,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H1,H3: 2.. / H1 = 2 => 0 pairs (*) / H3 = 2 => 0 pairs (X) E7,F7: 2.. / E7 = 2 => 0 pairs (X) / F7 = 2 => 0 pairs (_) E3,H3: 2.. / E3 = 2 => 0 pairs (*) / H3 = 2 => 0 pairs (X) D1,F1: 3.. / D1 = 3 => 15 pairs (_) / F1 = 3 => 0 pairs (X) H4,I6: 3.. / H4 = 3 => 0 pairs (*) / I6 = 3 => 0 pairs (X) D1,D4: 3.. / D1 = 3 => 15 pairs (_) / D4 = 3 => 0 pairs (X) I6,I7: 3.. / I6 = 3 => 0 pairs (X) / I7 = 3 => 0 pairs (_) F1,E3: 5.. / F1 = 5 => 0 pairs (*) / E3 = 5 => 0 pairs (X) E3,E6: 5.. / E3 = 5 => 14 pairs (_) / E6 = 5 => 0 pairs (*) C4,C5: 6.. / C4 = 6 => 13 pairs (_) / C5 = 6 => 13 pairs (_) F4,F5: 6.. / F4 = 6 => 13 pairs (_) / F5 = 6 => 13 pairs (_) E7,E9: 6.. / E7 = 6 => 0 pairs (*) / E9 = 6 => 0 pairs (X) I7,I9: 6.. / I7 = 6 => 0 pairs (X) / I9 = 6 => 0 pairs (_) C4,F4: 6.. / C4 = 6 => 13 pairs (_) / F4 = 6 => 13 pairs (_) C5,F5: 6.. / C5 = 6 => 13 pairs (_) / F5 = 6 => 13 pairs (_) E7,I7: 6.. / E7 = 6 => 0 pairs (*) / I7 = 6 => 0 pairs (X) E9,I9: 6.. / E9 = 6 => 0 pairs (X) / I9 = 6 => 0 pairs (_) C5,C6: 7.. / C5 = 7 => 18 pairs (_) / C6 = 7 => 13 pairs (_) F7,F9: 7.. / F7 = 7 => 0 pairs (X) / F9 = 7 => 13 pairs (_) H1,I1: 8.. / H1 = 8 => 0 pairs (X) / I1 = 8 => 13 pairs (_) A4,A5: 8.. / A4 = 8 => 15 pairs (_) / A5 = 8 => 14 pairs (_) E8,E9: 8.. / E8 = 8 => 0 pairs (X) / E9 = 8 => 0 pairs (_) E8,H8: 8.. / E8 = 8 => 0 pairs (X) / H8 = 8 => 0 pairs (_) H3,I3: 9.. / H3 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) F8,H8: 9.. / F8 = 9 => 0 pairs (*) / H8 = 9 => 0 pairs (X) D5,D9: 9.. / D5 = 9 => 14 pairs (_) / D9 = 9 => 0 pairs (X) * DURATION: 0:00:29.401985 START: 00:04:00.923889 END: 00:04:30.325874 2019-05-01 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,C4,C6,D1,D9,E3,E8,E9,F8,G7,H7,I1,I3) * 679.1.4..2586943714137.86...9..7...4.3..4.....4.8...6.9845.....7614..5.2325....4. * PAIR D1: 2,3 BLK 2 F1: 2,3,5 # reduction candidate for 2,3 F1: 5 => SOLVED * 679315428258694371413728695596271834832946157147853269984562713761439582325187946 F1: 2,3 # 14 pairs * PAIR D1: 2,3 COL D D4: 2,3,1 # reduction candidate for 2,3 D4: 1 => CTR * 67931.4..2586943714137.86.9.9.17..34.3.24.....4.83..6.9845...13761483592325961.4. D4: 2,3 # 15 pairs * PAIR E3: 2,5 BLK 2 F1: 2,5,3 # reduction candidate for 2,5 F1: 3 => CTR * 679.134..258694371413758629.9.37...4.3..4.....4.82..639845.2...7614.95.23251.794. F1: 2,5 # 15 pairs * PAIR E3: 2,5 ROW 3 H3: 2,5,9 # reduction candidate for 2,5 H3: 9 => SOLVED * 679315428258694371413728695596271834832946157147853269984562713761439582325187946 H3: 2,5 # 13 pairs * PAIR E3: 2,5 COL E E6: 2,5,3 # reduction candidate for 2,5 E6: 2,5 => SOLVED * 679315428258694371413728695596271834832946157147853269984562713761439582325187946 E6: 3 => CTR * 679.1.4..258694371413758629.9..7...4.3..4.....4.83..6.98452....7614..5.2325....4. * PAIR I1: 5,8 BLK 3 H1: 5,8,2 # reduction candidate for 5,8 H1: 2 => SOLVED * 679315428258694371413728695596271834832946157147853269984562713761439582325187946 H1: 5,8 # 14 pairs * PAIR I1: 5,8 COL I I5: 5,8,7,9 # reduction candidate for 5,8 I5: 5,8 # 20 pairs I5: 7,9 # 14 pairs * PAIR I3: 5,9 BLK 3 H3: 5,9,2 # reduction candidate for 5,9 H3: 5,9 => SOLVED * 679315428258694371413728695596271834832946157147853269984562713761439582325187946 H3: 2 # 14 pairs * PAIR I3: 5,9 COL I I5: 5,9,7,8 # reduction candidate for 5,9 I5: 5,9 # 20 pairs I6: 5,9,3,7 # reduction candidate for 5,9 I6: 5,9 => SOLVED * 679315428258694371413728695596271834832946157147853269984562713761439582325187946 I6: 3,7 # 14 pairs * PAIR C4: 2,6 BLK 4 C5: 2,6,7 # reduction candidate for 2,6 C5: 7 # 18 pairs C5: 2,6 # 13 pairs * PAIR C4: 2,6 ROW 4 F4: 2,6,1,3,5 # reduction candidate for 2,6 F4: 2,6 # 16 pairs F4: 1,3,5 # 13 pairs * PAIR A6: 1,5 BLK 4 A4: 1,5,8 # reduction candidate for 1,5 A4: 1,5 # 14 pairs A5: 1,5,8 # reduction candidate for 1,5 A5: 1,5 # 15 pairs * PAIR A6: 1,5 ROW 6 F6: 1,5,2,3,9 # reduction candidate for 1,5 F6: 1,5 => CTR * 6793124..258694371413758629.9..7..34.3..4.....4.83.9679845.....761483592325.6..4. F6: 2,3,9 # 13 pairs * PAIR C6: 2,7 BLK 4 C5: 2,7,6 # reduction candidate for 2,7 C5: 6 # 13 pairs C5: 2,7 # 13 pairs * PAIR C6: 2,7 ROW 6 G6: 2,7,1,9 # reduction candidate for 2,7 G6: 2,7 # 15 pairs G6: 1,9 # 14 pairs * PAIR E8: 3,8 ROW 8 H8: 3,8,9 # reduction candidate for 3,8 H8: 3,8 => SOLVED * 679315428258694371413728695596271834832946157147853269984562713761439582325187946 H8: 9 => CTR * 67931.4..2586943714137.86.9.9..7..34.3..4.....4.83..6.98452....761483592325.6..4. * PAIR F8: 3,9 ROW 8 H8: 3,9,8 # reduction candidate for 3,9 H8: 3,9 => CTR * 679.1.4.82586943714137.8695.9..7...4.3.94...7.478..963984532716761489532325167849 H8: 8 => SOLVED * 679315428258694371413728695596271834832946157147853269984562713761439582325187946 * PAIR F8: 3,9 COL F F6: 3,9,1,2,5 # reduction candidate for 3,9 F6: 3,9 => SOLVED * 679315428258694371413728695596271834832946157147853269984562713761439582325187946 F6: 1,2,5 # 13 pairs * PAIR D9: 1,9 BLK 8 F9: 1,9,7 # reduction candidate for 1,9 F9: 1,9 => CTR * 679.1.4..2586943714137.86...9..7...4.3..4.....4.8...639845271367614..5.2325.6..4. F9: 7 # 13 pairs * PAIR D9: 1,9 ROW 9 G9: 1,9,7,8 # reduction candidate for 1,9 G9: 1,9 # 15 pairs G9: 7,8 # 14 pairs * PAIR D9: 1,9 COL D D5: 1,9,2 # reduction candidate for 1,9 D5: 2 => CTR * 67931.4..2586943714137.86.9.9.17..34.3.24.....4.83..6.9845...13761483592325961.4. D5: 1,9 # 15 pairs * PAIR E9: 6,8 ROW 9 I9: 6,8,7,9 # reduction candidate for 6,8 I9: 7,9 => CTR * 679.1.4..2586943714137.8695.9..7...4.3.94...7.47851.63984532716761489532325167849 I9: 6,8 # 14 pairs * PAIR G7: 1,7 BLK 9 G9: 1,7,8,9 # reduction candidate for 1,7 G9: 1,7 => CTR * 679.1.4..2586943714137.86...9..7...4.3..4.....4.8...6398452..367614395.2325....4. G9: 8,9 # 14 pairs * PAIR G7: 1,7 ROW 7 F7: 1,7,2,3 # reduction candidate for 1,7 F7: 1,7 => CTR * 679.1.4..258694371413758629.9..7...4.3..4.....4.83..6.98452..36761483592325.6..4. F7: 2,3 => SOLVED * 679315428258694371413728695596271834832946157147853269984562713761439582325187946 * PAIR G7: 1,7 COL G G5: 1,7,2,8,9 # reduction candidate for 1,7 G5: 1,7 # 17 pairs G6: 1,7,2,9 # reduction candidate for 1,7 G6: 1,7 # 16 pairs * PAIR H7: 1,3 ROW 7 F7: 1,3,2,7 # reduction candidate for 1,3 F7: 1,3 => CTR * 679.1.4..258694371413758629.9..7...4.3..4.....4.83..6.98452.7.676148.5.2325.67.48 F7: 2,7 # 14 pairs * PAIR H7: 1,3 COL H H4: 1,3,5,8 # reduction candidate for 1,3 H4: 5,8 => CTR * 679.1.4..2586943714137.8695.9..7...4.3.94.....478..9639845.2...7614.95.23251.7849 H4: 1,3 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060624-absurd-base-pr-000.dot * REASONING * PRF # F1: 5 => SOL * DIS # D4: 1 => CTR => D4: 2,3 * DIS # F1: 3 => CTR => F1: 2,5 * PRF # H3: 9 => SOL * PRF # E6: 2,5 => SOL * DIS # E6: 3 => CTR => E6: 2,5 * PRF # H1: 2 => SOL * PRF # H3: 5,9 => SOL * PRF # I6: 5,9 => SOL * DIS # F6: 1,5 => CTR => F6: 2,3,9 * PRF # H8: 3,8 => SOL * DIS # H8: 9 => CTR => H8: 3,8 * DIS # H8: 3,9 => CTR => H8: 8 * PRF # H8: 8 => SOL * PRF # F6: 3,9 => SOL * DIS # F9: 1,9 => CTR => F9: 7 * DIS # D5: 2 => CTR => D5: 1,9 * DIS # I9: 7,9 => CTR => I9: 6,8 * DIS # G9: 1,7 => CTR => G9: 8,9 * DIS # F7: 1,7 => CTR => F7: 2,3 * PRF # F7: 2,3 => SOL * DIS # F7: 1,3 => CTR => F7: 2,7 * DIS # H4: 5,8 => CTR => H4: 1,3 * CNT 23 HDP CHAINS / 55 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,C4,C6,D1,D9,E3,E8,E9,F8,G7,H7,I1,I3) * 679.1.4..2586943714137.86...9..7...4.3..4.....4.8...6.9845.....7614..5.2325....4. * PAIR D1: 2,3 BLK 2 F1: 2,3,5 # reduction candidate for 2,3 F1: 5 => SOLVED * 679315428258694371413728695596271834832946157147853269984562713761439582325187946 * DURATION: 0:00:02.157461 START: 00:05:05.360312 END: 00:05:07.517773 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060624-absurd-base-pr-001.dot * REASONING * PRF # F1: 5 => SOL * STA F1: 5 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060624, absurd
Solution
position: 679315428258694371413728695596271834832946157147853269984562713761439582325187946 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 # F1: 2,3 => UNS * PRF # F1: 5 => SOL * INC # D4: 2,3 => UNS * DIS # D4: 1 => CTR => D4: 2,3 * INC # F1: 2,5 => UNS * DIS # F1: 3 => CTR => F1: 2,5 * INC # H3: 2,5 => UNS * PRF # H3: 9 => SOL * PRF # E6: 2,5 => SOL * DIS # E6: 3 => CTR => E6: 2,5 * INC # H1: 5,8 => UNS * PRF # H1: 2 => SOL * INC # I5: 5,8 => UNS * INC # I5: 7,9 => UNS * PRF # H3: 5,9 => SOL * INC # H3: 2 => UNS * INC # I5: 5,9 => UNS * PRF # I6: 5,9 => SOL * INC # I6: 3,7 => UNS * INC # C5: 2,6 => UNS * INC # C5: 7 => UNS * INC # F4: 2,6 => UNS * INC # F4: 1,3,5 => UNS * INC # A4: 1,5 => UNS * INC # A5: 1,5 => UNS * DIS # F6: 1,5 => CTR => F6: 2,3,9 * INC # F6: 2,3,9 => UNS * INC # C5: 2,7 => UNS * INC # C5: 6 => UNS * INC # G6: 2,7 => UNS * INC # G6: 1,9 => UNS * PRF # H8: 3,8 => SOL * DIS # H8: 9 => CTR => H8: 3,8 * DIS # H8: 3,9 => CTR => H8: 8 * PRF # H8: 8 => SOL * PRF # F6: 3,9 => SOL * INC # F6: 1,2,5 => UNS * DIS # F9: 1,9 => CTR => F9: 7 * INC # F9: 7 => UNS * INC # G9: 1,9 => UNS * INC # G9: 7,8 => UNS * INC # D5: 1,9 => UNS * DIS # D5: 2 => CTR => D5: 1,9 * INC # I9: 6,8 => UNS * DIS # I9: 7,9 => CTR => I9: 6,8 * DIS # G9: 1,7 => CTR => G9: 8,9 * INC # G9: 8,9 => UNS * DIS # F7: 1,7 => CTR => F7: 2,3 * PRF # F7: 2,3 => SOL * INC # G5: 1,7 => UNS * INC # G6: 1,7 => UNS * DIS # F7: 1,3 => CTR => F7: 2,7 * INC # F7: 2,7 => UNS * INC # H4: 1,3 => UNS * DIS # H4: 5,8 => CTR => H4: 1,3 * CNT 55 HDP CHAINS / 55 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F1: 2,3 => UNS * PRF # F1: 5 => SOL * STA F1: 5 * CNT 2 HDP CHAINS / 2 HYP OPENED