Analysis of zz-www.sudokuoftheday.co.uk-20190111-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: ..318....7.5...6......2..51.4.91....5.2...7..........4.69...2.....3...8.........7 initial
Autosolve
position: 6231854797154..628984.2.351.4.91.5.2592...71.......894.69...2.....3...8.........7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D6: 6,7 => CTR => D6: 2,5 * DIS # F6: 6,7 => CTR => F6: 2,3 * DIS # A9: 1,3 => CTR => A9: 2,4,8 * PRF # F6: 3,7 => SOL * DIS # F5: 3,4 => CTR => F5: 6,8 * DIS # D9: 6,8 => CTR => D9: 2,5 * DIS # F4: 3,6 => CTR => F4: 7 * DIS # E5: 3,6 => CTR => E5: 4 * DIS # F5: 3,6 => CTR => F5: 4,8 * DIS # C6: 1,7 => CTR => C6: 6 * DIS # A7: 1,8 => CTR => A7: 3,4 * PRF # A9: 1,8 => SOL * DIS # F9: 1,8 => CTR => F9: 2,4,6,9 * DIS # H9: 6 => CTR => H9: 3,4 * DIS # A7: 1,8 => CTR => A7: 3,4 * DIS # F8: 1,9 => CTR => F8: 2,4,6 * DIS # E8: 5,6 => CTR => E8: 4,9 * CNT 17 HDP CHAINS / 43 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D6: 6,7 => CTR => D6: 2,5 * DIS D6: 2,5 # F6: 6,7 => CTR => F6: 2,3 * DIS D6: 2,5 + F6: 2,3 # F4: 3 => CTR => F4: 6,7 * PRF D6: 2,5 + F6: 2,3 + F4: 6,7 # A9: 3,8 => SOL * STA D6: 2,5 + F6: 2,3 + F4: 6,7 + A9: 3,8 * CNT 4 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..318....7.5...6......2..51.4.91....5.2...7..........4.69...2.....3...8.........7 | initial |
| 6231854797154..628984.2.351.4.91.5.2592...71.......894.69...2.....3...8.........7 | autosolve |
| 623185479715439628984726351348917562592648713176253894469871235257394186831562947 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) E2: 3,9 F2: 3,9 D3: 6,7 F3: 6,7 A4: 3,8 A6: 1,3 B6: 3,7 D5: 6,8 H4: 3,6 I5: 3,6 B8: 5,7 C8: 1,7 B9: 3,5 C9: 1,8 H7: 3,4 I7: 3,5 G8: 1,9 I8: 5,6 G9: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A6,C6: 1.. / A6 = 1 => 20 pairs (_) / C6 = 1 => 0 pairs (X) G8,G9: 1.. / G8 = 1 => 0 pairs (*) / G9 = 1 => 0 pairs (X) A7,F7: 1.. / A7 = 1 => 0 pairs (X) / F7 = 1 => 19 pairs (_) D6,F6: 2.. / D6 = 2 => 0 pairs (*) / F6 = 2 => 0 pairs (X) A8,A9: 2.. / A8 = 2 => 20 pairs (_) / A9 = 2 => 0 pairs (X) A8,F8: 2.. / A8 = 2 => 20 pairs (_) / F8 = 2 => 0 pairs (X) D6,D9: 2.. / D6 = 2 => 0 pairs (*) / D9 = 2 => 0 pairs (X) E2,F2: 3.. / E2 = 3 => 18 pairs (_) / F2 = 3 => 23 pairs (_) H4,I5: 3.. / H4 = 3 => 0 pairs (X) / I5 = 3 => 23 pairs (_) B6,B9: 3.. / B6 = 3 => 0 pairs (X) / B9 = 3 => 0 pairs (_) I5,I7: 3.. / I5 = 3 => 23 pairs (_) / I7 = 3 => 0 pairs (X) E5,F5: 4.. / E5 = 4 => 22 pairs (_) / F5 = 4 => 0 pairs (X) H7,H9: 4.. / H7 = 4 => 22 pairs (_) / H9 = 4 => 22 pairs (_) D6,E6: 5.. / D6 = 5 => 21 pairs (_) / E6 = 5 => 20 pairs (_) B8,B9: 5.. / B8 = 5 => 0 pairs (*) / B9 = 5 => 0 pairs (X) I7,I8: 5.. / I7 = 5 => 23 pairs (_) / I8 = 5 => 0 pairs (X) D3,F3: 6.. / D3 = 6 => 0 pairs (X) / F3 = 6 => 19 pairs (_) C4,C6: 6.. / C4 = 6 => 0 pairs (X) / C6 = 6 => 20 pairs (_) H4,I5: 6.. / H4 = 6 => 23 pairs (_) / I5 = 6 => 0 pairs (X) I8,H9: 6.. / I8 = 6 => 23 pairs (_) / H9 = 6 => 0 pairs (X) H4,H9: 6.. / H4 = 6 => 23 pairs (_) / H9 = 6 => 0 pairs (X) I5,I8: 6.. / I5 = 6 => 0 pairs (X) / I8 = 6 => 23 pairs (_) D3,F3: 7.. / D3 = 7 => 19 pairs (_) / F3 = 7 => 0 pairs (X) B8,C8: 7.. / B8 = 7 => 0 pairs (X) / C8 = 7 => 0 pairs (_) C4,F4: 7.. / C4 = 7 => 0 pairs (X) / F4 = 7 => 20 pairs (_) B6,B8: 7.. / B6 = 7 => 0 pairs (*) / B8 = 7 => 0 pairs (X) E6,E7: 7.. / E6 = 7 => 0 pairs (X) / E7 = 7 => 20 pairs (_) A4,C4: 8.. / A4 = 8 => 18 pairs (_) / C4 = 8 => 0 pairs (*) D5,F5: 8.. / D5 = 8 => 0 pairs (X) / F5 = 8 => 21 pairs (_) C4,C9: 8.. / C4 = 8 => 0 pairs (*) / C9 = 8 => 0 pairs (X) E2,F2: 9.. / E2 = 9 => 23 pairs (_) / F2 = 9 => 18 pairs (_) G8,G9: 9.. / G8 = 9 => 16 pairs (_) / G9 = 9 => 0 pairs (*) * DURATION: 0:00:34.148890 START: 02:51:55.446579 END: 02:52:29.595469 2019-05-01 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B6,B8,B9,C8,C9,D3,D5,E2,F2,F3,G8,G9,H4,H7,I5,I7,I8) * 6231854797154..628984.2.351.4.91.5.2592...71.......894.69...2.....3...8.........7 * PAIR D3: 6,7 COL D D6: 6,7,2,5 # reduction candidate for 6,7 D6: 6,7 => CTR * 6231854797154..628984.2.351.4.91.5325928..716.3..52894.6957.24327.3...85.5.2...67 D6: 2,5 # 20 pairs * PAIR F3: 6,7 COL F F4: 6,7,3 # reduction candidate for 6,7 F4: 6,7 # 21 pairs F6: 6,7,2,3 # reduction candidate for 6,7 F6: 6,7 => CTR * 6231854797154..628984726351.4.91.5.2592...71...6257894.69.7.2...713..985.586..1.7 F6: 2,3 # 20 pairs * PAIR A4: 3,8 COL A A7: 3,8,1,4 # reduction candidate for 3,8 A7: 3,8 # 22 pairs A9: 3,8,1,2,4 # reduction candidate for 3,8 A9: 3,8 # 18 pairs * PAIR A6: 1,3 COL A A7: 1,3,4,8 # reduction candidate for 1,3 A7: 1,3 # 21 pairs A9: 1,3,2,4,8 # reduction candidate for 1,3 A9: 1,3 => CTR * 6231854797154..628984.2.35184.913562592..8713..6...8944698712352.13.4986358...147 A9: 2,4,8 # 19 pairs * PAIR B6: 3,7 ROW 6 E6: 3,7,5,6 # reduction candidate for 3,7 E6: 3,7 # 22 pairs F6: 3,7,2,6 # reduction candidate for 3,7 F6: 3,7 => SOLVED * 623185479715439628984726351348917562592648713176253894469871235257394186831562947 F6: 2,6 # 20 pairs * PAIR D5: 6,8 BLK 5 F5: 6,8,3,4 # reduction candidate for 6,8 F5: 3,4 => CTR * 6231854797154..628984.2.351.4.91.5.25928..71..7....894.69.7.243.573...86.3......7 F5: 6,8 # 21 pairs * PAIR D5: 6,8 COL D D9: 6,8,2,5 # reduction candidate for 6,8 D9: 6,8 => CTR * 6231854797154..628984726351.469175325926..71....25.894.6957.2.3...3...85.5.....67 D9: 2,5 # 20 pairs * PAIR H4: 3,6 ROW 4 F4: 3,6,7 # reduction candidate for 3,6 F4: 3,6 => CTR * 6231854797154..628984.2.35184791.5.2592..871.136...894.698712.5.7135.98..58...1.7 F4: 7 # 20 pairs * PAIR H4: 3,6 COL H H9: 3,6,4 # reduction candidate for 3,6 H9: 4 # 22 pairs H9: 3,6 # 22 pairs * PAIR I5: 3,6 ROW 5 E5: 3,6,4 # reduction candidate for 3,6 E5: 3,6 => CTR * 6231854797154..628984.2.351.4.91.5.25928.471..7....894.69.7.243.573...86.3......7 E5: 4 # 22 pairs F5: 3,6,4,8 # reduction candidate for 3,6 F5: 3,6 => CTR * 6231854797154..628984.2.351.4.91.5.259284.71.......894.69...2.....3...8.........7 F5: 4,8 # 20 pairs * PAIR C8: 1,7 COL C C6: 1,7,6 # reduction candidate for 1,7 C6: 1,7 => CTR * 6231854797154..6289847263518469175325928..716.37652894169.7.243...3...85.58....67 C6: 6 # 20 pairs * PAIR C9: 1,8 BLK 7 A7: 1,8,3,4 # reduction candidate for 1,8 A7: 1,8 => CTR * 6231854797154..628984726351.4.917562592...713.76...894.69.74235457392186231..8.47 A7: 3,4 # 21 pairs A9: 1,8,2,3,4 # reduction candidate for 1,8 A9: 1,8 => SOLVED * 623185479715439628984726351348917562592648713176253894469871235257394186831562947 A9: 2,3,4 # 19 pairs * PAIR C9: 1,8 ROW 9 F9: 1,8,2,4,6,9 # reduction candidate for 1,8 F9: 1,8 => CTR * 6231854797154..628984726351.4.917562592...713.76...894.69.7.235.573..186231..8947 F9: 2,4,6,9 # 19 pairs * PAIR H7: 3,4 BLK 9 H9: 3,4,6 # reduction candidate for 3,4 H9: 6 => CTR * 6231854797154..628984.2.351.4.91.532592...716.3....894.69...243.713..985358....67 H9: 3,4 # 23 pairs * PAIR H7: 3,4 ROW 7 A7: 3,4,1,8 # reduction candidate for 3,4 A7: 1,8 => CTR * 6231854797154..628984726351.4.917562592...713.76...894.69.74235457392186231..8.47 A7: 3,4 # 21 pairs * PAIR G8: 1,9 ROW 8 F8: 1,9,2,4,6 # reduction candidate for 1,9 F8: 1,9 => CTR * 623185479715493628984.2.351348917562592864713176.328944697..2.525734..86.31...947 F8: 2,4,6 # 19 pairs * PAIR I8: 5,6 ROW 8 E8: 5,6,4,9 # reduction candidate for 5,6 E8: 5,6 => CTR * 6231854797154..628984.2.35184.91.5.2592..871.13....894.698712.5.7135.986.58...1.7 E8: 4,9 # 20 pairs * PAIR G9: 1,9 ROW 9 F9: 1,9,2,4,6,8 # reduction candidate for 1,9 F9: 2,4,6,8 # 19 pairs F9: 1,9 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190111-absurd-base-pr-000.dot * REASONING * DIS # D6: 6,7 => CTR => D6: 2,5 * DIS # F6: 6,7 => CTR => F6: 2,3 * DIS # A9: 1,3 => CTR => A9: 2,4,8 * PRF # F6: 3,7 => SOL * DIS # F5: 3,4 => CTR => F5: 6,8 * DIS # D9: 6,8 => CTR => D9: 2,5 * DIS # F4: 3,6 => CTR => F4: 7 * DIS # E5: 3,6 => CTR => E5: 4 * DIS # F5: 3,6 => CTR => F5: 4,8 * DIS # C6: 1,7 => CTR => C6: 6 * DIS # A7: 1,8 => CTR => A7: 3,4 * PRF # A9: 1,8 => SOL * DIS # F9: 1,8 => CTR => F9: 2,4,6,9 * DIS # H9: 6 => CTR => H9: 3,4 * DIS # A7: 1,8 => CTR => A7: 3,4 * DIS # F8: 1,9 => CTR => F8: 2,4,6 * DIS # E8: 5,6 => CTR => E8: 4,9 * CNT 17 HDP CHAINS / 43 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B6,B8,B9,C8,C9,D3,D5,E2,F2,F3,G8,G9,H4,H7,I5,I7,I8) * 6231854797154..628984.2.351.4.91.5.2592...71.......894.69...2.....3...8.........7 * PAIR D3: 6,7 COL D D6: 6,7,2,5 # reduction candidate for 6,7 D6: 6,7 => CTR * 6231854797154..628984.2.351.4.91.5325928..716.3..52894.6957.24327.3...85.5.2...67 * PAIR RESTART * PAIR F3: 6,7 COL F F4: 6,7,3 # reduction candidate for 6,7 F4: 6,7 # 22 pairs F6: 6,7,2,3 # reduction candidate for 6,7 F6: 6,7 => CTR * 6231854797154..628984726351.4.91.5.2592...71...6257894.69.7.2...713..985.586..1.7 * RESTART * PAIR F3: 6,7 COL F F4: 6,7,3 # reduction candidate for 6,7 F4: 3 => CTR * 6231854797154..628984.2.351.47913562592...713.36.72894.69...2.5271354.8.........7 * PAIR RESTART * PAIR A4: 3,8 COL A A7: 3,8,1,4 # reduction candidate for 3,8 A7: 3,8 # 25 pairs A9: 3,8,1,2,4 # reduction candidate for 3,8 A9: 3,8 => SOLVED * 623185479715439628984726351348917562592648713176253894469871235257394186831562947 * DURATION: 0:00:06.006351 START: 02:52:55.807244 END: 02:53:01.813595 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190111-absurd-base-pr-001.dot * REASONING * DIS # D6: 6,7 => CTR => D6: 2,5 * DIS D6: 2,5 # F6: 6,7 => CTR => F6: 2,3 * DIS D6: 2,5 + F6: 2,3 # F4: 3 => CTR => F4: 6,7 * PRF D6: 2,5 + F6: 2,3 + F4: 6,7 # A9: 3,8 => SOL * STA D6: 2,5 + F6: 2,3 + F4: 6,7 + A9: 3,8 * CNT 4 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190111, absurd
Solution
position: 623185479715439628984726351348917562592648713176253894469871235257394186831562947 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 # D6: 6,7 => CTR => D6: 2,5 * INC # D6: 2,5 => UNS * INC # F4: 6,7 => UNS * DIS # F6: 6,7 => CTR => F6: 2,3 * INC # F6: 2,3 => UNS * INC # A7: 3,8 => UNS * INC # A9: 3,8 => UNS * INC # A7: 1,3 => UNS * DIS # A9: 1,3 => CTR => A9: 2,4,8 * INC # A9: 2,4,8 => UNS * INC # E6: 3,7 => UNS * PRF # F6: 3,7 => SOL * INC # F6: 2,6 => UNS * INC # F5: 6,8 => UNS * DIS # F5: 3,4 => CTR => F5: 6,8 * DIS # D9: 6,8 => CTR => D9: 2,5 * INC # D9: 2,5 => UNS * DIS # F4: 3,6 => CTR => F4: 7 * INC # F4: 7 => UNS * INC # H9: 3,6 => UNS * INC # H9: 4 => UNS * DIS # E5: 3,6 => CTR => E5: 4 * INC # E5: 4 => UNS * DIS # F5: 3,6 => CTR => F5: 4,8 * INC # F5: 4,8 => UNS * DIS # C6: 1,7 => CTR => C6: 6 * INC # C6: 6 => UNS * DIS # A7: 1,8 => CTR => A7: 3,4 * INC # A7: 3,4 => UNS * PRF # A9: 1,8 => SOL * INC # A9: 2,3,4 => UNS * DIS # F9: 1,8 => CTR => F9: 2,4,6,9 * INC # F9: 2,4,6,9 => UNS * INC # H9: 3,4 => UNS * DIS # H9: 6 => CTR => H9: 3,4 * INC # A7: 3,4 => UNS * DIS # A7: 1,8 => CTR => A7: 3,4 * DIS # F8: 1,9 => CTR => F8: 2,4,6 * INC # F8: 2,4,6 => UNS * DIS # E8: 5,6 => CTR => E8: 4,9 * INC # E8: 4,9 => UNS * INC # F9: 1,9 => UNS * INC # F9: 2,4,6,8 => UNS * CNT 43 HDP CHAINS / 43 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D6: 6,7 => CTR => D6: 2,5 * INC D6: 2,5 # F4: 6,7 => UNS * DIS D6: 2,5 # F6: 6,7 => CTR => F6: 2,3 * INC D6: 2,5 + F6: 2,3 # F4: 6,7 => UNS * DIS D6: 2,5 + F6: 2,3 # F4: 3 => CTR => F4: 6,7 * INC D6: 2,5 + F6: 2,3 + F4: 6,7 # A7: 3,8 => UNS * PRF D6: 2,5 + F6: 2,3 + F4: 6,7 # A9: 3,8 => SOL * STA D6: 2,5 + F6: 2,3 + F4: 6,7 + A9: 3,8 * CNT 7 HDP CHAINS / 7 HYP OPENED