Analysis of zz-www.sudokuoftheday.co.uk-20190126-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019
level: medium
position: ..76.......3.1..89....84..6.6....3..1..7458..5......91...12.....92.....3..1...... initial
Autosolve
position: ..76.....6.3.17.89..5.84..6.6..913..1397458625......91..612.....92.....3..1...... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 2,4 => CTR => A1: 8,9 * PRF # B1: 2,4 => SOL * PRF # G2: 2,4 => SOL * DIS # G2: 5 => CTR => G2: 2,4 * DIS # A1: 2,9 => CTR => A1: 4,8 * PRF # A1: 4,8 => SOL * PRF # D3: 2,9 => SOL * DIS # D3: 3 => CTR => D3: 2,9 * PRF # B1: 1,2 => SOL * DIS # G3: 1,2 => CTR => G3: 7 * PRF # G3: 7 => SOL * DIS # H3: 1,2 => CTR => H3: 3,7 * PRF # H1: 1,2,4 => SOL * DIS # G2: 4 => CTR => G2: 2,5 * DIS # G1: 4,5 => CTR => G1: 1,2 * PRF # H1: 4,5 => SOL * DIS # I7: 4,5 => CTR => I7: 7,8 * PRF # I9: 4,5 => SOL * DIS # D6: 2,8 => CTR => D6: 3 * PRF # D6: 3 => SOL * PRF # F6: 2,8 => SOL * DIS # F6: 3,6 => CTR => F6: 2,8 * DIS # F6: 3,6 => CTR => F6: 2,8 * PRF # F6: 2,8 => SOL * DIS # E9: 3,6 => CTR => E9: 5,7 * DIS # G7: 4,7 => CTR => G7: 5,9 * DIS # G8: 4,7 => CTR => G8: 1,5,6 * DIS # G9: 4,7 => CTR => G9: 2,5,6,9 * DIS # F6: 6,8 => CTR => F6: 2,3 * CNT 29 HDP CHAINS / 52 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 2,4 => CTR => A1: 8,9 * PRF A1: 8,9 # B1: 2,4 => SOL * STA A1: 8,9 + B1: 2,4 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..76.......3.1..89....84..6.6....3..1..7458..5......91...12.....92.....3..1...... | initial |
| ..76.....6.3.17.89..5.84..6.6..913..1397458625......91..612.....92.....3..1...... | autosolve |
| 827639145643517289915284736264891357139745862578362491456123978792458613381976524 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) B2: 2,4 A3: 2,9 B3: 1,2 E1: 3,5 D2: 2,5 I1: 4,5 A4: 2,7 C4: 4,8 B6: 2,7 C6: 4,8 D4: 2,8 E6: 3,6 G6: 4,7 F8: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,B3: 1.. / B1 = 1 => 0 pairs (X) / B3 = 1 => 14 pairs (_) G8,H8: 1.. / G8 = 1 => 0 pairs (X) / H8 = 1 => 14 pairs (_) A4,B6: 2.. / A4 = 2 => 0 pairs (*) / B6 = 2 => 0 pairs (X) G9,H9: 2.. / G9 = 2 => 0 pairs (X) / H9 = 2 => 14 pairs (_) A4,D4: 2.. / A4 = 2 => 0 pairs (*) / D4 = 2 => 0 pairs (X) F1,F6: 2.. / F1 = 2 => 0 pairs (X) / F6 = 2 => 0 pairs (_) H1,H3: 3.. / H1 = 3 => 0 pairs (X) / H3 = 3 => 0 pairs (_) A7,A9: 3.. / A7 = 3 => 15 pairs (_) / A9 = 3 => 15 pairs (_) D3,H3: 3.. / D3 = 3 => 0 pairs (X) / H3 = 3 => 0 pairs (_) A7,F7: 3.. / A7 = 3 => 15 pairs (_) / F7 = 3 => 15 pairs (_) C4,C6: 4.. / C4 = 4 => 0 pairs (*) / C6 = 4 => 0 pairs (X) D8,D9: 4.. / D8 = 4 => 15 pairs (_) / D9 = 4 => 0 pairs (X) B2,G2: 4.. / B2 = 4 => 14 pairs (_) / G2 = 4 => 0 pairs (X) C6,G6: 4.. / C6 = 4 => 0 pairs (X) / G6 = 4 => 0 pairs (_) E1,D2: 5.. / E1 = 5 => 0 pairs (X) / D2 = 5 => 0 pairs (_) H4,I4: 5.. / H4 = 5 => 16 pairs (_) / I4 = 5 => 17 pairs (_) B7,B9: 5.. / B7 = 5 => 15 pairs (_) / B9 = 5 => 14 pairs (_) D2,G2: 5.. / D2 = 5 => 0 pairs (*) / G2 = 5 => 0 pairs (X) E6,F6: 6.. / E6 = 6 => 14 pairs (_) / F6 = 6 => 0 pairs (X) G8,G9: 6.. / G8 = 6 => 17 pairs (_) / G9 = 6 => 15 pairs (_) G3,H3: 7.. / G3 = 7 => 0 pairs (*) / H3 = 7 => 0 pairs (X) A4,B6: 7.. / A4 = 7 => 0 pairs (X) / B6 = 7 => 0 pairs (_) E8,E9: 7.. / E8 = 7 => 15 pairs (_) / E9 = 7 => 15 pairs (_) B6,G6: 7.. / B6 = 7 => 0 pairs (*) / G6 = 7 => 0 pairs (X) A1,B1: 8.. / A1 = 8 => 0 pairs (*) / B1 = 8 => 0 pairs (X) C4,C6: 8.. / C4 = 8 => 0 pairs (X) / C6 = 8 => 0 pairs (_) I7,I9: 8.. / I7 = 8 => 15 pairs (_) / I9 = 8 => 14 pairs (_) C4,D4: 8.. / C4 = 8 => 0 pairs (X) / D4 = 8 => 0 pairs (_) A1,A3: 9.. / A1 = 9 => 0 pairs (X) / A3 = 9 => 0 pairs (_) F1,D3: 9.. / F1 = 9 => 0 pairs (*) / D3 = 9 => 0 pairs (X) G7,G9: 9.. / G7 = 9 => 15 pairs (_) / G9 = 9 => 0 pairs (X) A1,F1: 9.. / A1 = 9 => 0 pairs (X) / F1 = 9 => 0 pairs (_) A3,D3: 9.. / A3 = 9 => 0 pairs (*) / D3 = 9 => 0 pairs (X) F7,G7: 9.. / F7 = 9 => 0 pairs (X) / G7 = 9 => 15 pairs (_) D3,D9: 9.. / D3 = 9 => 0 pairs (X) / D9 = 9 => 0 pairs (_) * DURATION: 0:00:36.371403 START: 03:13:40.823291 END: 03:14:17.194694 2019-05-01 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B2,B3,B6,C4,C6,D2,D4,E1,E6,F8,G6,I1) * ..76.....6.3.17.89..5.84..6.6..913..1397458625......91..612.....92.....3..1...... * PAIR B2: 2,4 BLK 1 A1: 2,4,8,9 # reduction candidate for 2,4 A1: 2,4 => CTR * .876.9...6235174899152847.6.6..913..1397458625....2.91..612.9...92.....3..19..... A1: 8,9 # 15 pairs B1: 2,4,1,8 # reduction candidate for 2,4 B1: 2,4 => SOLVED * 827639145643517289915284736264891357139745862578362491456123978792458613381976524 B1: 1,8 # 15 pairs * PAIR B2: 2,4 ROW 2 G2: 2,4,5 # reduction candidate for 2,4 G2: 2,4 => SOLVED * 827639145643517289915284736264891357139745862578362491456123978792458613381976524 G2: 5 => CTR * ..76.....643217589..5.84..626.8913..139745862578362491..612.....92.....3..1...... * PAIR A3: 2,9 BLK 1 A1: 2,9,4,8 # reduction candidate for 2,9 A1: 2,9 => CTR * .876.2...643517289.15.84..6.6..913..13974586252....791..612.....92.....3..1...... A1: 4,8 => SOLVED * 827639145643517289915284736264891357139745862578362491456123978792458613381976524 * PAIR A3: 2,9 ROW 3 D3: 2,9,3 # reduction candidate for 2,9 D3: 2,9 => SOLVED * 827639145643517289915284736264891357139745862578362491456123978792458613381976524 D3: 3 => CTR * ..76.9...6.32175899.5384..626.8913..1397458625......91..612.....92.....3..1...... * PAIR B3: 1,2 BLK 1 B1: 1,2,4,8 # reduction candidate for 1,2 B1: 1,2 => SOLVED * 827639145643517289915284736264891357139745862578362491456123978792458613381976524 B1: 4,8 # 15 pairs * PAIR B3: 1,2 ROW 3 G3: 1,2,7 # reduction candidate for 1,2 G3: 1,2 => CTR * ..7659.34643217.89..5384.76.6..913..1397458625......91..612.....92....13..19...2. G3: 7 => SOLVED * 827639145643517289915284736264891357139745862578362491456123978792458613381976524 H3: 1,2,3,7 # reduction candidate for 1,2 H3: 1,2 => CTR * ..7659.34643217.89..53847.6.6..913..13974586257....491..612.....92.....3..19..... H3: 3,7 # 15 pairs * PAIR E1: 3,5 ROW 1 H1: 3,5,1,2,4 # reduction candidate for 3,5 H1: 1,2,4 => SOLVED * 827639145643517289915284736264891357139745862578362491456123978792458613381976524 H1: 3,5 # 17 pairs * PAIR E1: 3,5 COL E E9: 3,5,6,7 # reduction candidate for 3,5 E9: 6,7 # 15 pairs E9: 3,5 # 15 pairs * PAIR D2: 2,5 ROW 2 G2: 2,5,4 # reduction candidate for 2,5 G2: 4 => CTR * ..76.....6.3517489..5.84..6.6..913..1397458625.4...791..612.....92.....3..1...... G2: 2,5 # 14 pairs * PAIR I1: 4,5 BLK 3 G1: 4,5,1,2 # reduction candidate for 4,5 G1: 4,5 => CTR * 8276395146435172899152847362648913..1397458625783624913.61289477924561.34.19.362. G1: 1,2 # 15 pairs H1: 4,5,1,2,3 # reduction candidate for 4,5 H1: 4,5 => SOLVED * 827639145643517289915284736264891357139745862578362491456123978792458613381976524 H1: 1,2,3 # 14 pairs G2: 4,5,2 # reduction candidate for 4,5 G2: 4,5 # 16 pairs * PAIR I1: 4,5 COL I I4: 4,5,7 # reduction candidate for 4,5 I4: 4,5 # 18 pairs I7: 4,5,7,8 # reduction candidate for 4,5 I7: 4,5 => CTR * 8.76.9...643.17.899.5.84..6264891357139745862578..2491.861239.5.92458613351976248 I7: 7,8 # 15 pairs I9: 4,5,7,8 # reduction candidate for 4,5 I9: 4,5 => SOLVED * 827639145643517289915284736264891357139745862578362491456123978792458613381976524 I9: 7,8 # 15 pairs * PAIR D4: 2,8 BLK 5 D6: 2,8,3 # reduction candidate for 2,8 D6: 2,8 => CTR * 987632...64351728921598473676..913..1397458625......91..612.....924....3..13...2. D6: 3 => SOLVED * 827639145643517289915284736264891357139745862578362491456123978792458613381976524 F6: 2,8,3,6 # reduction candidate for 2,8 F6: 2,8 => SOLVED * 827639145643517289915284736264891357139745862578362491456123978792458613381976524 F6: 3,6 => CTR * 987632...64351728921598473676..913..1397458625......91..612.....92.....3..1....2. * PAIR E6: 3,6 BLK 5 F6: 3,6,2,8 # reduction candidate for 3,6 F6: 3,6 => CTR * 987632...64351728921598473676..913..1397458625......91..612.....92.....3..1....2. F6: 2,8 => SOLVED * 827639145643517289915284736264891357139745862578362491456123978792458613381976524 * PAIR E6: 3,6 COL E E9: 3,6,5,7 # reduction candidate for 3,6 E9: 3,6 => CTR * ..765...4643217589..5.84..626.8913..139745862578362491..612.....92.7...3..1.3.... E9: 5,7 # 15 pairs * PAIR G6: 4,7 BLK 6 H4: 4,7,5 # reduction candidate for 4,7 H4: 4,7 # 17 pairs I4: 4,7,5 # reduction candidate for 4,7 I4: 4,7 # 16 pairs * PAIR G6: 4,7 COL G G7: 4,7,5,9 # reduction candidate for 4,7 G7: 4,7 => CTR * 9876.....643.17.8921598473676..913..1397458625......91..6129....92.....3..1...92. G7: 5,9 # 15 pairs G8: 4,7,1,5,6 # reduction candidate for 4,7 G8: 4,7 => CTR * ..7659.34643217.89..5384.76.6..913..1397458625......91..612.9...92....13..19..62. G8: 1,5,6 # 14 pairs G9: 4,7,2,5,6,9 # reduction candidate for 4,7 G9: 4,7 => CTR * ..76...34643.17.89..5384.76.6..913..1397458625...36.91..61239...92..86133.19...2. G9: 2,5,6,9 # 14 pairs * PAIR F8: 6,8 BLK 8 F9: 6,8,3,9 # reduction candidate for 6,8 F9: 6,8 # 18 pairs F9: 3,9 # 15 pairs * PAIR F8: 6,8 COL F F6: 6,8,2,3 # reduction candidate for 6,8 F6: 6,8 => CTR * 987632...64351728921598473676..913..1397458625......91..612.....92.....3..1....2. F6: 2,3 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190126-absurd-base-pr-000.dot * REASONING * DIS # A1: 2,4 => CTR => A1: 8,9 * PRF # B1: 2,4 => SOL * PRF # G2: 2,4 => SOL * DIS # G2: 5 => CTR => G2: 2,4 * DIS # A1: 2,9 => CTR => A1: 4,8 * PRF # A1: 4,8 => SOL * PRF # D3: 2,9 => SOL * DIS # D3: 3 => CTR => D3: 2,9 * PRF # B1: 1,2 => SOL * DIS # G3: 1,2 => CTR => G3: 7 * PRF # G3: 7 => SOL * DIS # H3: 1,2 => CTR => H3: 3,7 * PRF # H1: 1,2,4 => SOL * DIS # G2: 4 => CTR => G2: 2,5 * DIS # G1: 4,5 => CTR => G1: 1,2 * PRF # H1: 4,5 => SOL * DIS # I7: 4,5 => CTR => I7: 7,8 * PRF # I9: 4,5 => SOL * DIS # D6: 2,8 => CTR => D6: 3 * PRF # D6: 3 => SOL * PRF # F6: 2,8 => SOL * DIS # F6: 3,6 => CTR => F6: 2,8 * DIS # F6: 3,6 => CTR => F6: 2,8 * PRF # F6: 2,8 => SOL * DIS # E9: 3,6 => CTR => E9: 5,7 * DIS # G7: 4,7 => CTR => G7: 5,9 * DIS # G8: 4,7 => CTR => G8: 1,5,6 * DIS # G9: 4,7 => CTR => G9: 2,5,6,9 * DIS # F6: 6,8 => CTR => F6: 2,3 * CNT 29 HDP CHAINS / 52 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B2,B3,B6,C4,C6,D2,D4,E1,E6,F8,G6,I1) * ..76.....6.3.17.89..5.84..6.6..913..1397458625......91..612.....92.....3..1...... * PAIR B2: 2,4 BLK 1 A1: 2,4,8,9 # reduction candidate for 2,4 A1: 2,4 => CTR * .876.9...6235174899152847.6.6..913..1397458625....2.91..612.9...92.....3..19..... B1: 2,4,1,8 # reduction candidate for 2,4 B1: 2,4 => SOLVED * 827639145643517289915284736264891357139745862578362491456123978792458613381976524 * DURATION: 0:00:02.356243 START: 03:14:49.061092 END: 03:14:51.417335 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190126-absurd-base-pr-001.dot * REASONING * DIS # A1: 2,4 => CTR => A1: 8,9 * PRF A1: 8,9 # B1: 2,4 => SOL * STA A1: 8,9 + B1: 2,4 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190126, absurd
Solution
position: 827639145643517289915284736264891357139745862578362491456123978792458613381976524 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: 2,4 => CTR => A1: 8,9 * INC # A1: 8,9 => UNS * PRF # B1: 2,4 => SOL * INC # B1: 1,8 => UNS * PRF # G2: 2,4 => SOL * DIS # G2: 5 => CTR => G2: 2,4 * DIS # A1: 2,9 => CTR => A1: 4,8 * PRF # A1: 4,8 => SOL * PRF # D3: 2,9 => SOL * DIS # D3: 3 => CTR => D3: 2,9 * PRF # B1: 1,2 => SOL * INC # B1: 4,8 => UNS * DIS # G3: 1,2 => CTR => G3: 7 * PRF # G3: 7 => SOL * DIS # H3: 1,2 => CTR => H3: 3,7 * INC # H3: 3,7 => UNS * INC # H1: 3,5 => UNS * PRF # H1: 1,2,4 => SOL * INC # E9: 3,5 => UNS * INC # E9: 6,7 => UNS * INC # G2: 2,5 => UNS * DIS # G2: 4 => CTR => G2: 2,5 * DIS # G1: 4,5 => CTR => G1: 1,2 * INC # G1: 1,2 => UNS * PRF # H1: 4,5 => SOL * INC # H1: 1,2,3 => UNS * INC # G2: 4,5 => UNS * INC # I4: 4,5 => UNS * DIS # I7: 4,5 => CTR => I7: 7,8 * INC # I7: 7,8 => UNS * PRF # I9: 4,5 => SOL * INC # I9: 7,8 => UNS * DIS # D6: 2,8 => CTR => D6: 3 * PRF # D6: 3 => SOL * PRF # F6: 2,8 => SOL * DIS # F6: 3,6 => CTR => F6: 2,8 * DIS # F6: 3,6 => CTR => F6: 2,8 * PRF # F6: 2,8 => SOL * DIS # E9: 3,6 => CTR => E9: 5,7 * INC # E9: 5,7 => UNS * INC # H4: 4,7 => UNS * INC # I4: 4,7 => UNS * DIS # G7: 4,7 => CTR => G7: 5,9 * INC # G7: 5,9 => UNS * DIS # G8: 4,7 => CTR => G8: 1,5,6 * INC # G8: 1,5,6 => UNS * DIS # G9: 4,7 => CTR => G9: 2,5,6,9 * INC # G9: 2,5,6,9 => UNS * INC # F9: 6,8 => UNS * INC # F9: 3,9 => UNS * DIS # F6: 6,8 => CTR => F6: 2,3 * INC # F6: 2,3 => UNS * CNT 52 HDP CHAINS / 52 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 2,4 => CTR => A1: 8,9 * PRF A1: 8,9 # B1: 2,4 => SOL * STA A1: 8,9 + B1: 2,4 * CNT 2 HDP CHAINS / 2 HYP OPENED