Analysis of zz-www.sudokuoftheday.co.uk-20060616-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: 32.....8....6.279...9....1......1...143....5..5..8.....8.7.6.23...15..6.5.6.2.... initial
Autosolve
position: 32..1..8..1.63279...98.5312...5.1.3.143....5..5..8.....817.6523...15..6.5.6.2.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C2: 4,8 => SOL * PRF # A3: 6,7 => SOL * DIS # A3: 4 => CTR => A3: 6,7 * PRF # B4: 6,7 => SOL * DIS # F1: 4,9 => CTR => F1: 7 * PRF # F1: 7 => SOL * DIS # F1: 9 => CTR => F1: 4,7 * DIS # A3: 6 => CTR => A3: 4,7 * DIS # E4: 4,7 => CTR => E4: 6,9 * PRF # E4: 6,9 => SOL * PRF # I1: 4,6 => SOL * DIS # G4: 4,6 => CTR => G4: 2,9 * PRF # I1: 6 => SOL * DIS # C2: 8 => CTR => C2: 4,5 * DIS # C4: 2,7 => CTR => C4: 8 * DIS # A6: 2,7 => CTR => A6: 6,9 * PRF # C8: 2,7 => SOL * DIS # C8: 4 => CTR => C8: 2,7 * DIS # D6: 2,9 => CTR => D6: 3,4 * DIS # G5: 2,9 => CTR => G5: 6,8 * DIS # E4: 7,9 => CTR => E4: 4,6 * PRF # E5: 7,9 => SOL * DIS # F6: 7,9 => CTR => F6: 3,4 * DIS # F1: 4 => CTR => F1: 7,9 * DIS # I6: 4,7 => CTR => I6: 1,6,9 * DIS # A8: 4,9 => CTR => A8: 2,7 * DIS # E4: 4,9 => CTR => E4: 6,7 * PRF # E4: 6,7 => SOL * CNT 28 HDP CHAINS / 60 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C2: 4,8 => SOL * STA C2: 4,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 32.....8....6.279...9....1......1...143....5..5..8.....8.7.6.23...15..6.5.6.2.... | initial |
| 32..1..8..1.63279...98.5312...5.1.3.143....5..5..8.....817.6523...15..6.5.6.2.... | autosolve |
| 325917486814632795769845312978561234143279658652483971481796523237154869596328147 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A2: 4,8 B3: 6,7 D1: 4,9 E3: 4,7 G1: 4,6 I2: 4,5 C6: 2,7 D5: 2,9 F5: 7,9 H6: 4,7 A7: 4,9 E7: 4,9 H9: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G6,I6: 1.. / G6 = 1 => 13 pairs (_) / I6 = 1 => 13 pairs (_) G9,I9: 1.. / G9 = 1 => 13 pairs (_) / I9 = 1 => 13 pairs (_) G6,G9: 1.. / G6 = 1 => 13 pairs (_) / G9 = 1 => 13 pairs (_) I6,I9: 1.. / I6 = 1 => 13 pairs (_) / I9 = 1 => 13 pairs (_) D5,D6: 2.. / D5 = 2 => 12 pairs (_) / D6 = 2 => 0 pairs (X) A8,C8: 2.. / A8 = 2 => 14 pairs (_) / C8 = 2 => 0 pairs (X) D5,G5: 2.. / D5 = 2 => 12 pairs (_) / G5 = 2 => 0 pairs (X) D6,F6: 3.. / D6 = 3 => 15 pairs (_) / F6 = 3 => 14 pairs (_) B8,B9: 3.. / B8 = 3 => 14 pairs (_) / B9 = 3 => 14 pairs (_) B8,F8: 3.. / B8 = 3 => 14 pairs (_) / F8 = 3 => 14 pairs (_) D6,D9: 3.. / D6 = 3 => 15 pairs (_) / D9 = 3 => 14 pairs (_) A3,E3: 4.. / A3 = 4 => 0 pairs (X) / E3 = 4 => 0 pairs (_) A7,E7: 4.. / A7 = 4 => 0 pairs (*) / E7 = 4 => 0 pairs (X) H6,H9: 4.. / H6 = 4 => 0 pairs (X) / H9 = 4 => 14 pairs (_) C1,C2: 5.. / C1 = 5 => 0 pairs (*) / C2 = 5 => 0 pairs (X) I1,I2: 5.. / I1 = 5 => 11 pairs (_) / I2 = 5 => 0 pairs (*) C1,I1: 5.. / C1 = 5 => 0 pairs (*) / I1 = 5 => 0 pairs (X) C2,I2: 5.. / C2 = 5 => 11 pairs (_) / I2 = 5 => 0 pairs (*) A3,B3: 6.. / A3 = 6 => 0 pairs (X) / B3 = 6 => 14 pairs (_) G1,I1: 6.. / G1 = 6 => 13 pairs (_) / I1 = 6 => 0 pairs (*) E4,E5: 6.. / E4 = 6 => 0 pairs (*) / E5 = 6 => 0 pairs (X) B3,B4: 6.. / B3 = 6 => 14 pairs (_) / B4 = 6 => 0 pairs (X) F1,E3: 7.. / F1 = 7 => 0 pairs (*) / E3 = 7 => 0 pairs (X) C1,F1: 7.. / C1 = 7 => 0 pairs (X) / F1 = 7 => 0 pairs (_) H6,H9: 7.. / H6 = 7 => 14 pairs (_) / H9 = 7 => 0 pairs (X) A2,C2: 8.. / A2 = 8 => 13 pairs (_) / C2 = 8 => 0 pairs (X) A4,C4: 8.. / A4 = 8 => 0 pairs (X) / C4 = 8 => 13 pairs (_) G5,I5: 8.. / G5 = 8 => 13 pairs (_) / I5 = 8 => 13 pairs (_) F8,F9: 8.. / F8 = 8 => 17 pairs (_) / F9 = 8 => 13 pairs (_) A2,A4: 8.. / A2 = 8 => 13 pairs (_) / A4 = 8 => 0 pairs (X) C2,C4: 8.. / C2 = 8 => 0 pairs (X) / C4 = 8 => 13 pairs (_) D1,F1: 9.. / D1 = 9 => 14 pairs (_) / F1 = 9 => 0 pairs (X) A7,E7: 9.. / A7 = 9 => 0 pairs (X) / E7 = 9 => 0 pairs (_) * DURATION: 0:00:33.808066 START: 23:53:21.160910 END: 23:53:54.968976 2019-04-30 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,B3,C6,D1,D5,E3,E7,F5,G1,H6,H9,I2) * 32..1..8..1.63279...98.5312...5.1.3.143....5..5..8.....817.6523...15..6.5.6.2.... * PAIR A2: 4,8 BLK 1 C2: 4,8,5 # reduction candidate for 4,8 C2: 4,8 => SOLVED * 325917486814632795769845312978561234143279658652483971481796523237154869596328147 C2: 5 # 11 pairs * PAIR B3: 6,7 BLK 1 A3: 6,7,4 # reduction candidate for 6,7 A3: 6,7 => SOLVED * 325917486814632795769845312978561234143279658652483971481796523237154869596328147 A3: 4 => CTR * 327.1..85815632794469875312.98561437143....5..5..8....981746523..415..6.5.6.2.... * PAIR B3: 6,7 COL B B4: 6,7,9 # reduction candidate for 6,7 B4: 6,7 => SOLVED * 325917486814632795769845312978561234143279658652483971481796523237154869596328147 B4: 9 # 16 pairs * PAIR D1: 4,9 BLK 2 F1: 4,9,7 # reduction candidate for 4,9 F1: 4,9 => CTR * 327.1..85.15632794469875312..85.1.3.143....5..52.8....9817465232.415..6.5.6.2.... F1: 7 => SOLVED * 325917486814632795769845312978561234143279658652483971481796523237154869596328147 * PAIR D1: 4,9 COL D D6: 4,9,2,3 # reduction candidate for 4,9 D6: 4,9 # 14 pairs D9: 4,9,3 # reduction candidate for 4,9 D9: 4,9 # 15 pairs * PAIR E3: 4,7 BLK 2 F1: 4,7,9 # reduction candidate for 4,7 F1: 9 => CTR * 327.19.85.15632794469875312..85.1.3.143..7.5..52.8....9817465232.415..6.5.692.... F1: 4,7 # 14 pairs * PAIR E3: 4,7 ROW 3 A3: 4,7,6 # reduction candidate for 4,7 A3: 6 => CTR * 32.917.8.81.63279.679845312.68571.3.143269857.5..8..4.481796523...15..6.5.642..7. A3: 4,7 # 14 pairs * PAIR E3: 4,7 COL E E4: 4,7,6,9 # reduction candidate for 4,7 E4: 4,7 => CTR * 32..1..8.81.63279...9845312..8571.3.143.69.57.5..8..4.481796523...15..6.5.642..7. E4: 6,9 => SOLVED * 325917486814632795769845312978561234143279658652483971481796523237154869596328147 * PAIR G1: 4,6 BLK 3 I1: 4,6,5 # reduction candidate for 4,6 I1: 4,6 => SOLVED * 325917486814632795769845312978561234143279658652483971481796523237154869596328147 I1: 5 # 11 pairs * PAIR G1: 4,6 COL G G4: 4,6,2,9 # reduction candidate for 4,6 G4: 4,6 => CTR * 32..17.8..1.63279...9845312...5.163.143.69.57657.83.4.481796523...15..6.5.6.2..7. G4: 2,9 # 14 pairs G6: 4,6,1,2,9 # reduction candidate for 4,6 G6: 4,6 # 16 pairs * PAIR I2: 4,5 BLK 3 I1: 4,5,6 # reduction candidate for 4,5 I1: 6 => SOLVED * 325917486814632795769845312978561234143279658652483971481796523237154869596328147 I1: 4,5 # 13 pairs * PAIR I2: 4,5 ROW 2 C2: 4,5,8 # reduction candidate for 4,5 C2: 8 => CTR * 325.17.8..18632795..98453128..5.1.3.143..9.5..5..8....4817.6523...15..6.5.6.2.... C2: 4,5 # 13 pairs * PAIR C6: 2,7 BLK 4 A4: 2,7,6,8,9 # reduction candidate for 2,7 A4: 2,7 # 16 pairs C4: 2,7,8 # reduction candidate for 2,7 C4: 2,7 => CTR * 325.17.8.418632795..98453128..5.1.3.143..9.5..5..8....9817.6523...15..6.5.6.2.... C4: 8 # 13 pairs A6: 2,7,6,9 # reduction candidate for 2,7 A6: 2,7 => CTR * 32..1..8.81.63279...9845312..8571.34143.69.57.5..8....481796523...15..6.5.6.2.... A6: 6,9 # 14 pairs * PAIR C6: 2,7 COL C C8: 2,7,4 # reduction candidate for 2,7 C8: 2,7 => SOLVED * 325917486814632795769845312978561234143279658652483971481796523237154869596328147 C8: 4 => CTR * 327.1..8581563279446987531279.561.3.143.97.5.65..8....9817465232.415..6.5.6.2.... * PAIR D5: 2,9 BLK 5 D6: 2,9,3,4 # reduction candidate for 2,9 D6: 2,9 => CTR * 32.419685.15632794469875312...5.1.3.143....5..5..83....817.6523.3.15..6.5.632.... D6: 3,4 # 13 pairs * PAIR D5: 2,9 ROW 5 G5: 2,9,6,8 # reduction candidate for 2,9 G5: 2,9 => CTR * 327.1..85.15632794469875312..85.1.3.143.67.58.52.8....9817465232.415..6.5.6.2.... G5: 6,8 # 13 pairs * PAIR F5: 7,9 BLK 5 E4: 7,9,4,6 # reduction candidate for 7,9 E4: 7,9 => CTR * 327.1..85.156327944698753127..5.1.3.143.67.5..52.8..7..817.65232..15..6.5.6.2..4. E4: 4,6 # 14 pairs E5: 7,9,6 # reduction candidate for 7,9 E5: 7,9 => SOLVED * 325917486814632795769845312978561234143279658652483971481796523237154869596328147 E5: 6 # 13 pairs F6: 7,9,3,4 # reduction candidate for 7,9 F6: 7,9 => CTR * 32..1..8..1.63279...98.5312...541.3.14326..5..5.38....481796523...15..6.5.642..7. F6: 3,4 # 14 pairs * PAIR F5: 7,9 ROW 5 I5: 7,9,6,8 # reduction candidate for 7,9 I5: 7,9 # 14 pairs I5: 6,8 # 14 pairs * PAIR F5: 7,9 COL F F1: 7,9,4 # reduction candidate for 7,9 F1: 4 => CTR * 327914685.15632794469875312..85.1.3.1432...5..52.8....9817465232.415..6.5.632.... F1: 7,9 # 15 pairs * PAIR H6: 4,7 BLK 6 I4: 4,7,6,9 # reduction candidate for 4,7 I4: 4,7 # 14 pairs I6: 4,7,1,6,9 # reduction candidate for 4,7 I6: 4,7 => CTR * 327.1..85.156327944698.5312...5.1.3.1432.7.5.652.8.1...817965232..15..6.5.6.2...1 I6: 1,6,9 # 13 pairs * PAIR H6: 4,7 ROW 6 F6: 4,7,3,9 # reduction candidate for 4,7 F6: 4,7 # 18 pairs F6: 3,9 # 14 pairs * PAIR A7: 4,9 BLK 7 A8: 4,9,2,7 # reduction candidate for 4,9 A8: 4,9 => CTR * 32..17.8..1.63279.769845312.985.1.3.143..9.5..57.83.4.4817.6523..215..6.5.6.2..7. A8: 2,7 # 14 pairs * PAIR E7: 4,9 BLK 8 F8: 4,9,3,8 # reduction candidate for 4,9 F8: 4,9 # 16 pairs D9: 4,9,3 # reduction candidate for 4,9 D9: 4,9 # 15 pairs F9: 4,9,3,8 # reduction candidate for 4,9 F9: 4,9 # 18 pairs * PAIR E7: 4,9 COL E E4: 4,9,6,7 # reduction candidate for 4,9 E4: 4,9 => CTR * 327.1..85.15632794469875312..85.1.3.143.6..5..52.8....9817465232.415..6.5.6.2.... E4: 6,7 => SOLVED * 325917486814632795769845312978561234143279658652483971481796523237154869596328147 * PAIR H9: 4,7 BLK 9 I8: 4,7,8,9 # reduction candidate for 4,7 I8: 4,7 # 15 pairs I9: 4,7,1,8,9 # reduction candidate for 4,7 I9: 4,7 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060616-absurd-base-pr-000.dot * REASONING * PRF # C2: 4,8 => SOL * PRF # A3: 6,7 => SOL * DIS # A3: 4 => CTR => A3: 6,7 * PRF # B4: 6,7 => SOL * DIS # F1: 4,9 => CTR => F1: 7 * PRF # F1: 7 => SOL * DIS # F1: 9 => CTR => F1: 4,7 * DIS # A3: 6 => CTR => A3: 4,7 * DIS # E4: 4,7 => CTR => E4: 6,9 * PRF # E4: 6,9 => SOL * PRF # I1: 4,6 => SOL * DIS # G4: 4,6 => CTR => G4: 2,9 * PRF # I1: 6 => SOL * DIS # C2: 8 => CTR => C2: 4,5 * DIS # C4: 2,7 => CTR => C4: 8 * DIS # A6: 2,7 => CTR => A6: 6,9 * PRF # C8: 2,7 => SOL * DIS # C8: 4 => CTR => C8: 2,7 * DIS # D6: 2,9 => CTR => D6: 3,4 * DIS # G5: 2,9 => CTR => G5: 6,8 * DIS # E4: 7,9 => CTR => E4: 4,6 * PRF # E5: 7,9 => SOL * DIS # F6: 7,9 => CTR => F6: 3,4 * DIS # F1: 4 => CTR => F1: 7,9 * DIS # I6: 4,7 => CTR => I6: 1,6,9 * DIS # A8: 4,9 => CTR => A8: 2,7 * DIS # E4: 4,9 => CTR => E4: 6,7 * PRF # E4: 6,7 => SOL * CNT 28 HDP CHAINS / 60 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,B3,C6,D1,D5,E3,E7,F5,G1,H6,H9,I2) * 32..1..8..1.63279...98.5312...5.1.3.143....5..5..8.....817.6523...15..6.5.6.2.... * PAIR A2: 4,8 BLK 1 C2: 4,8,5 # reduction candidate for 4,8 C2: 4,8 => SOLVED * 325917486814632795769845312978561234143279658652483971481796523237154869596328147 * DURATION: 0:00:01.776139 START: 23:54:31.250906 END: 23:54:33.027045 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060616-absurd-base-pr-001.dot * REASONING * PRF # C2: 4,8 => SOL * STA C2: 4,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060616, absurd
Solution
position: 325917486814632795769845312978561234143279658652483971481796523237154869596328147 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:
* PRF # C2: 4,8 => SOL * INC # C2: 5 => UNS * PRF # A3: 6,7 => SOL * DIS # A3: 4 => CTR => A3: 6,7 * PRF # B4: 6,7 => SOL * INC # B4: 9 => UNS * DIS # F1: 4,9 => CTR => F1: 7 * PRF # F1: 7 => SOL * INC # D6: 4,9 => UNS * INC # D9: 4,9 => UNS * INC # F1: 4,7 => UNS * DIS # F1: 9 => CTR => F1: 4,7 * INC # A3: 4,7 => UNS * DIS # A3: 6 => CTR => A3: 4,7 * DIS # E4: 4,7 => CTR => E4: 6,9 * PRF # E4: 6,9 => SOL * PRF # I1: 4,6 => SOL * INC # I1: 5 => UNS * DIS # G4: 4,6 => CTR => G4: 2,9 * INC # G4: 2,9 => UNS * INC # G6: 4,6 => UNS * INC # I1: 4,5 => UNS * PRF # I1: 6 => SOL * INC # C2: 4,5 => UNS * DIS # C2: 8 => CTR => C2: 4,5 * INC # A4: 2,7 => UNS * DIS # C4: 2,7 => CTR => C4: 8 * INC # C4: 8 => UNS * DIS # A6: 2,7 => CTR => A6: 6,9 * INC # A6: 6,9 => UNS * PRF # C8: 2,7 => SOL * DIS # C8: 4 => CTR => C8: 2,7 * DIS # D6: 2,9 => CTR => D6: 3,4 * INC # D6: 3,4 => UNS * DIS # G5: 2,9 => CTR => G5: 6,8 * INC # G5: 6,8 => UNS * DIS # E4: 7,9 => CTR => E4: 4,6 * INC # E4: 4,6 => UNS * PRF # E5: 7,9 => SOL * INC # E5: 6 => UNS * DIS # F6: 7,9 => CTR => F6: 3,4 * INC # F6: 3,4 => UNS * INC # I5: 7,9 => UNS * INC # I5: 6,8 => UNS * INC # F1: 7,9 => UNS * DIS # F1: 4 => CTR => F1: 7,9 * INC # I4: 4,7 => UNS * DIS # I6: 4,7 => CTR => I6: 1,6,9 * INC # I6: 1,6,9 => UNS * INC # F6: 4,7 => UNS * INC # F6: 3,9 => UNS * DIS # A8: 4,9 => CTR => A8: 2,7 * INC # A8: 2,7 => UNS * INC # F8: 4,9 => UNS * INC # D9: 4,9 => UNS * INC # F9: 4,9 => UNS * DIS # E4: 4,9 => CTR => E4: 6,7 * PRF # E4: 6,7 => SOL * INC # I8: 4,7 => UNS * INC # I9: 4,7 => UNS * CNT 60 HDP CHAINS / 60 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C2: 4,8 => SOL * STA C2: 4,8 * CNT 1 HDP CHAINS / 1 HYP OPENED