Analysis of zz-www.sudokuoftheday.co.uk-20060425-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: ........9....485.....6..817.9....6..67.9.5.....2..6.93.....7..14135.2.......1.... initial
Autosolve
position: ........9....485.....6..81739....6..67.935.....2..6.93.....7..14135.2.......1.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 2,5 => CTR => A1: 1,7,8 * DIS # B1: 2,5 => CTR => B1: 3,6,8 * DIS # B3: 2,5 => CTR => B3: 3,4 * DIS # E3: 9 => CTR => E3: 2,5 * DIS # A7: 2,5 => CTR => A7: 8,9 * DIS # A9: 2,5 => CTR => A9: 7,8,9 * DIS # B3: 4,5 => CTR => B3: 2,3 * PRF # D1: 1,3 => SOL * DIS # D1: 1,7 => CTR => D1: 2,3 * DIS # F9: 4 => CTR => F9: 3,9 * DIS # H2: 2,6 => CTR => H2: 3 * DIS # B2: 3 => CTR => B2: 2,6 * DIS # D4: 1,4 => CTR => D4: 2,7,8 * PRF # E4: 7,8 => SOL * DIS # D6: 7,8 => CTR => D6: 1,4 * DIS # H7: 6,8 => CTR => H7: 2,3,4,5 * DIS # H8: 6,8 => CTR => H8: 7 * PRF # H8: 7 => SOL * DIS # H9: 6,8 => CTR => H9: 2,3,4,5 * PRF # I9: 6,8 => SOL * PRF # E8: 6,8 => SOL * DIS # E8: 9 => CTR => E8: 6,8 * CNT 22 HDP CHAINS / 51 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 2,5 => CTR => A1: 1,7,8 * DIS A1: 1,7,8 # B1: 2,5 => CTR => B1: 3,6,8 * DIS A1: 1,7,8 + B1: 3,6,8 # B3: 2,5 => CTR => B3: 3,4 * DIS A1: 1,7,8 + B1: 3,6,8 + B3: 3,4 # E3: 9 => CTR => E3: 2,5 * PRF A1: 1,7,8 + B1: 3,6,8 + B3: 3,4 + E3: 2,5 # A2: 1,7 => SOL * STA A1: 1,7,8 + B1: 3,6,8 + B3: 3,4 + E3: 2,5 + A2: 1,7 * CNT 5 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ........9....485.....6..817.9....6..67.9.5.....2..6.93.....7..14135.2.......1.... | initial |
| ........9....485.....6..81739....6..67.935.....2..6.93.....7..14135.2.......1.... | autosolve |
| 785321469169748532234659817391274685678935124542186793826497351413562978957813246 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) A3: 2,5 C3: 4,5 F1: 1,3 D2: 1,7 F3: 3,9 I2: 2,6 F4: 1,4 E6: 7,8 G8: 7,9 I8: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G5,G6: 1.. / G5 = 1 => 12 pairs (_) / G6 = 1 => 0 pairs (X) C5,G5: 1.. / C5 = 1 => 0 pairs (X) / G5 = 1 => 12 pairs (_) F1,F4: 1.. / F1 = 1 => 15 pairs (_) / F4 = 1 => 0 pairs (X) D4,E4: 2.. / D4 = 2 => 0 pairs (*) / E4 = 2 => 0 pairs (X) D1,D4: 2.. / D1 = 2 => 15 pairs (_) / D4 = 2 => 0 pairs (*) B2,H2: 3.. / B2 = 3 => 0 pairs (X) / H2 = 3 => 12 pairs (_) B3,F3: 3.. / B3 = 3 => 24 pairs (_) / F3 = 3 => 0 pairs (X) B3,C3: 4.. / B3 = 4 => 0 pairs (X) / C3 = 4 => 19 pairs (_) G1,H1: 4.. / G1 = 4 => 12 pairs (_) / H1 = 4 => 13 pairs (_) B3,B6: 4.. / B3 = 4 => 0 pairs (X) / B6 = 4 => 19 pairs (_) F4,F9: 4.. / F4 = 4 => 15 pairs (_) / F9 = 4 => 0 pairs (X) E1,E3: 5.. / E1 = 5 => 11 pairs (_) / E3 = 5 => 24 pairs (_) A6,B6: 5.. / A6 = 5 => 15 pairs (_) / B6 = 5 => 0 pairs (X) H4,I4: 5.. / H4 = 5 => 0 pairs (X) / I4 = 5 => 10 pairs (_) I4,I9: 5.. / I4 = 5 => 10 pairs (_) / I9 = 5 => 0 pairs (X) E7,E8: 6.. / E7 = 6 => 11 pairs (_) / E8 = 6 => 0 pairs (*) H4,G6: 7.. / H4 = 7 => 0 pairs (X) / G6 = 7 => 0 pairs (_) A9,C9: 7.. / A9 = 7 => 11 pairs (_) / C9 = 7 => 11 pairs (_) G8,H8: 7.. / G8 = 7 => 0 pairs (X) / H8 = 7 => 0 pairs (_) G6,G8: 7.. / G6 = 7 => 0 pairs (*) / G8 = 7 => 0 pairs (X) H4,H8: 7.. / H4 = 7 => 0 pairs (X) / H8 = 7 => 0 pairs (_) A2,C2: 9.. / A2 = 9 => 11 pairs (_) / C2 = 9 => 11 pairs (_) E3,F3: 9.. / E3 = 9 => 0 pairs (X) / F3 = 9 => 24 pairs (_) E8,G8: 9.. / E8 = 9 => 0 pairs (X) / G8 = 9 => 0 pairs (_) F3,F9: 9.. / F3 = 9 => 24 pairs (_) / F9 = 9 => 0 pairs (X) * DURATION: 0:00:28.754321 START: 22:39:13.186033 END: 22:39:41.940354 2019-04-30 * CP COUNT: (25) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,C3,D2,E6,F1,F3,F4,G8,I2,I8) * ........9....485.....6..81739....6..67.935.....2..6.93.....7..14135.2.......1.... * PAIR A3: 2,5 BLK 1 A1: 2,5,1,7,8 # reduction candidate for 2,5 A1: 2,5 => CTR * .87....69169748532.346.981739....6..67.935...8.2..6.93.....7..14135.2.......1.... A1: 1,7,8 # 10 pairs B1: 2,5,3,6,8 # reduction candidate for 2,5 B1: 2,5 => CTR * 857.2.46916974853223465981739.2.46..67.935...542186793.....7..14135.2...7...1.9.. B1: 3,6,8 # 10 pairs B3: 2,5,3,4 # reduction candidate for 2,5 B3: 2,5 => CTR * ...251..9...7485....469381739...46..67.935...542..6.93.....7..14135.297.....19... B3: 3,4 # 11 pairs * PAIR A3: 2,5 ROW 3 E3: 2,5,9 # reduction candidate for 2,5 E3: 9 => CTR * ....5...9....485.....69381739..2.6..67.935.....2.76.93.....7..14135.2.......1.... E3: 2,5 # 24 pairs * PAIR A3: 2,5 COL A A7: 2,5,8,9 # reduction candidate for 2,5 A7: 2,5 => CTR * ....51..99.17485..24569381739.1246756749351...52..6.935....7..14135.2.......19... A7: 8,9 # 11 pairs A9: 2,5,7,8,9 # reduction candidate for 2,5 A9: 2,5 => CTR * ....51..9...7485..24569381739..246756749351...52..6.93.....7.514135.2...5.7.19... A9: 7,8,9 # 10 pairs * PAIR C3: 4,5 BLK 1 B3: 4,5,2,3 # reduction candidate for 4,5 B3: 4,5 => CTR * ...251..9...7485.....69381739...46..67.935.....2..6.93.....7..14135.297.....19... B3: 2,3 # 24 pairs * PAIR F1: 1,3 BLK 2 D1: 1,3,2,7 # reduction candidate for 1,3 D1: 1,3 => SOLVED * 785321469169748532234659817391274685678935124542186793826497351413562978957813246 D1: 2,7 # 12 pairs * PAIR D2: 1,7 BLK 2 D1: 1,7,2,3 # reduction candidate for 1,7 D1: 1,7 => CTR * .....3..9....4853..346.981739.2.16..671935....42..6.93.....7..14135.2.......1.... D1: 2,3 # 11 pairs * PAIR D2: 1,7 ROW 2 A2: 1,7,9 # reduction candidate for 1,7 A2: 1,7 # 11 pairs C2: 1,7,9 # reduction candidate for 1,7 C2: 1,7 # 11 pairs * PAIR D2: 1,7 COL D D4: 1,7,2,4,8 # reduction candidate for 1,7 D4: 1,7 # 20 pairs D6: 1,7,4,8 # reduction candidate for 1,7 D6: 1,7 # 14 pairs * PAIR F3: 3,9 COL F F9: 3,9,4 # reduction candidate for 3,9 F9: 4 => CTR * ...2.3469.6.148532234659817398421675671935284542..6193.....7..14135.27......14... F9: 3,9 # 15 pairs * PAIR I2: 2,6 BLK 3 H1: 2,6,3,4 # reduction candidate for 2,6 H1: 2,6 # 14 pairs H2: 2,6,3 # reduction candidate for 2,6 H2: 2,6 => CTR * ...251..9.3.7485.....69381739...46..67.935.....2..6.93.....7..14135.297.....19... H2: 3 # 12 pairs * PAIR I2: 2,6 ROW 2 B2: 2,6,3 # reduction candidate for 2,6 B2: 3 => CTR * ...251..9.3.7485.....69381739...46..67.935.....2..6.93.....7..14135.297.....19... B2: 2,6 # 12 pairs * PAIR I2: 2,6 COL I I9: 2,6,4,5,8 # reduction candidate for 2,6 I9: 2,6 # 17 pairs I9: 4,5,8 # 10 pairs * PAIR F4: 1,4 BLK 5 D4: 1,4,2,7,8 # reduction candidate for 1,4 D4: 1,4 => CTR * ...273469.6.1485322346598173984216756719352..542786193....67.4141359278.....1.... D4: 2,7,8 # 11 pairs D6: 1,4,7,8 # reduction candidate for 1,4 D6: 1,4 # 11 pairs * PAIR F4: 1,4 ROW 4 C4: 1,4,8 # reduction candidate for 1,4 C4: 8 # 15 pairs C4: 1,4 # 13 pairs * PAIR E6: 7,8 BLK 5 D4: 7,8,1,2,4 # reduction candidate for 7,8 D4: 7,8 # 17 pairs E4: 7,8,2 # reduction candidate for 7,8 E4: 7,8 => SOLVED * 785321469169748532234659817391274685678935124542186793826497351413562978957813246 E4: 2 # 15 pairs D6: 7,8,1,4 # reduction candidate for 7,8 D6: 7,8 => CTR * ...273469.6.1485322346598173984216756719352..542786193....67.4141359278.....1.... D6: 1,4 # 11 pairs * PAIR I8: 6,8 BLK 9 H7: 6,8,2,3,4,5 # reduction candidate for 6,8 H7: 6,8 => CTR * .56..1..912..485.6.346.981739....6..6789351...42186793..5.97.61413562978...81.... H7: 2,3,4,5 # 10 pairs H8: 6,8,7 # reduction candidate for 6,8 H8: 6,8 => CTR * ...273469.6.1485322346598173984216756719352..542786193....67.4141359278.....1.... H8: 7 => SOLVED * 785321469169748532234659817391274685678935124542186793826497351413562978957813246 H9: 6,8,2,3,4,5 # reduction candidate for 6,8 H9: 6,8 => CTR * .....1..91297485365346.981739....6..6789351...42186793....97..1413562978....1..6. H9: 2,3,4,5 # 10 pairs I9: 6,8,2,4,5 # reduction candidate for 6,8 I9: 6,8 => SOLVED * 785321469169748532234659817391274685678935124542186793826497351413562978957813246 I9: 2,4,5 # 10 pairs * PAIR I8: 6,8 ROW 8 E8: 6,8,9 # reduction candidate for 6,8 E8: 6,8 => SOLVED * 785321469169748532234659817391274685678935124542186793826497351413562978957813246 E8: 9 => CTR * ...273469.6.1485322346598173984216756719352..542786193....67.4141359278.....1.... * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060425-absurd-base-pr-000.dot * REASONING * DIS # A1: 2,5 => CTR => A1: 1,7,8 * DIS # B1: 2,5 => CTR => B1: 3,6,8 * DIS # B3: 2,5 => CTR => B3: 3,4 * DIS # E3: 9 => CTR => E3: 2,5 * DIS # A7: 2,5 => CTR => A7: 8,9 * DIS # A9: 2,5 => CTR => A9: 7,8,9 * DIS # B3: 4,5 => CTR => B3: 2,3 * PRF # D1: 1,3 => SOL * DIS # D1: 1,7 => CTR => D1: 2,3 * DIS # F9: 4 => CTR => F9: 3,9 * DIS # H2: 2,6 => CTR => H2: 3 * DIS # B2: 3 => CTR => B2: 2,6 * DIS # D4: 1,4 => CTR => D4: 2,7,8 * PRF # E4: 7,8 => SOL * DIS # D6: 7,8 => CTR => D6: 1,4 * DIS # H7: 6,8 => CTR => H7: 2,3,4,5 * DIS # H8: 6,8 => CTR => H8: 7 * PRF # H8: 7 => SOL * DIS # H9: 6,8 => CTR => H9: 2,3,4,5 * PRF # I9: 6,8 => SOL * PRF # E8: 6,8 => SOL * DIS # E8: 9 => CTR => E8: 6,8 * CNT 22 HDP CHAINS / 51 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,C3,D2,E6,F1,F3,F4,G8,I2,I8) * ........9....485.....6..81739....6..67.935.....2..6.93.....7..14135.2.......1.... * PAIR A3: 2,5 BLK 1 A1: 2,5,1,7,8 # reduction candidate for 2,5 A1: 2,5 => CTR * .87....69169748532.346.981739....6..67.935...8.2..6.93.....7..14135.2.......1.... B1: 2,5,3,6,8 # reduction candidate for 2,5 B1: 2,5 => CTR * 857.2.46916974853223465981739.2.46..67.935...542186793.....7..14135.2...7...1.9.. B3: 2,5,3,4 # reduction candidate for 2,5 B3: 2,5 => CTR * ...251..9...7485....469381739...46..67.935...542..6.93.....7..14135.297.....19... * RESTART * PAIR A3: 2,5 ROW 3 E3: 2,5,9 # reduction candidate for 2,5 E3: 9 => CTR * ....5...9....485..2.569381739..2.6..67.935.....2.76.93.....7..14135.2.......1.... * PAIR RESTART * PAIR D2: 1,7 ROW 2 A2: 1,7,9 # reduction candidate for 1,7 A2: 1,7 => SOLVED * 785321469169748532234659817391274685678935124542186793826497351413562978957813246 * DURATION: 0:00:05.424977 START: 22:40:11.433146 END: 22:40:16.858123 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060425-absurd-base-pr-001.dot * REASONING * DIS # A1: 2,5 => CTR => A1: 1,7,8 * DIS A1: 1,7,8 # B1: 2,5 => CTR => B1: 3,6,8 * DIS A1: 1,7,8 + B1: 3,6,8 # B3: 2,5 => CTR => B3: 3,4 * DIS A1: 1,7,8 + B1: 3,6,8 + B3: 3,4 # E3: 9 => CTR => E3: 2,5 * PRF A1: 1,7,8 + B1: 3,6,8 + B3: 3,4 + E3: 2,5 # A2: 1,7 => SOL * STA A1: 1,7,8 + B1: 3,6,8 + B3: 3,4 + E3: 2,5 + A2: 1,7 * CNT 5 HDP CHAINS / 6 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060425, absurd
Solution
position: 785321469169748532234659817391274685678935124542186793826497351413562978957813246 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 # A1: 2,5 => CTR => A1: 1,7,8 * INC # A1: 1,7,8 => UNS * DIS # B1: 2,5 => CTR => B1: 3,6,8 * INC # B1: 3,6,8 => UNS * DIS # B3: 2,5 => CTR => B3: 3,4 * INC # B3: 3,4 => UNS * INC # E3: 2,5 => UNS * DIS # E3: 9 => CTR => E3: 2,5 * DIS # A7: 2,5 => CTR => A7: 8,9 * INC # A7: 8,9 => UNS * DIS # A9: 2,5 => CTR => A9: 7,8,9 * INC # A9: 7,8,9 => UNS * DIS # B3: 4,5 => CTR => B3: 2,3 * INC # B3: 2,3 => UNS * PRF # D1: 1,3 => SOL * INC # D1: 2,7 => UNS * DIS # D1: 1,7 => CTR => D1: 2,3 * INC # D1: 2,3 => UNS * INC # A2: 1,7 => UNS * INC # C2: 1,7 => UNS * INC # D4: 1,7 => UNS * INC # D6: 1,7 => UNS * INC # F9: 3,9 => UNS * DIS # F9: 4 => CTR => F9: 3,9 * INC # H1: 2,6 => UNS * DIS # H2: 2,6 => CTR => H2: 3 * INC # H2: 3 => UNS * INC # B2: 2,6 => UNS * DIS # B2: 3 => CTR => B2: 2,6 * INC # I9: 2,6 => UNS * INC # I9: 4,5,8 => UNS * DIS # D4: 1,4 => CTR => D4: 2,7,8 * INC # D4: 2,7,8 => UNS * INC # D6: 1,4 => UNS * INC # C4: 1,4 => UNS * INC # C4: 8 => UNS * INC # D4: 7,8 => UNS * PRF # E4: 7,8 => SOL * INC # E4: 2 => UNS * DIS # D6: 7,8 => CTR => D6: 1,4 * INC # D6: 1,4 => UNS * DIS # H7: 6,8 => CTR => H7: 2,3,4,5 * INC # H7: 2,3,4,5 => UNS * DIS # H8: 6,8 => CTR => H8: 7 * PRF # H8: 7 => SOL * DIS # H9: 6,8 => CTR => H9: 2,3,4,5 * INC # H9: 2,3,4,5 => UNS * PRF # I9: 6,8 => SOL * INC # I9: 2,4,5 => UNS * PRF # E8: 6,8 => SOL * DIS # E8: 9 => CTR => E8: 6,8 * CNT 51 HDP CHAINS / 51 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 2,5 => CTR => A1: 1,7,8 * DIS A1: 1,7,8 # B1: 2,5 => CTR => B1: 3,6,8 * DIS A1: 1,7,8 + B1: 3,6,8 # B3: 2,5 => CTR => B3: 3,4 * INC A1: 1,7,8 + B1: 3,6,8 + B3: 3,4 # E3: 2,5 => UNS * DIS A1: 1,7,8 + B1: 3,6,8 + B3: 3,4 # E3: 9 => CTR => E3: 2,5 * PRF A1: 1,7,8 + B1: 3,6,8 + B3: 3,4 + E3: 2,5 # A2: 1,7 => SOL * STA A1: 1,7,8 + B1: 3,6,8 + B3: 3,4 + E3: 2,5 + A2: 1,7 * CNT 6 HDP CHAINS / 6 HYP OPENED