Analysis of xx-top500-148-base.sdk
Contents
Original Sudoku
level: medium
position: .5.....1....2..4...........43....2.....5.1.6.....7....2.....3......3..5...7.....8 initial
Autosolve
position: .524.381717.25843.843.1752.431...2757285419635..3721842.57.4391..4.3.7523.7.25648 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # E4: 6,9 => SOL * DIS # E4: 8 => CTR => E4: 6,9 * DIS # D4: 6,9 => CTR => D4: 8 * PRF # D4: 8 => SOL * DIS # D4: 6,9 => CTR => D4: 8 * PRF # D4: 8 => SOL * PRF # E4: 6,9 => SOL * DIS # E4: 8 => CTR => E4: 6,9 * PRF # E4: 6,8 => SOL * DIS # E4: 9 => CTR => E4: 6,8 * CNT 10 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # E4: 6,9 => SOL * STA E4: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .5.....1....2..4...........43....2.....5.1.6.....7....2.....3......3..5...7.....8 | initial |
| .524.381717.25843.843.1752.431...2757285419635..3721842.57.4391..4.3.7523.7.25648 | autosolve |
| 652493817179258436843617529431869275728541963596372184265784391984136752317925648 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) A1: 6,9 C2: 6,9 E1: 6,9 D3: 6,9 I2: 6,9 I3: 6,9 B6: 6,9 C6: 6,9 F4: 6,9 B7: 6,8 A8: 6,9 B8: 1,8 B9: 1,9 E7: 6,8 D8: 1,8 F8: 6,9 D9: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B8,B9: 1.. / B8 = 1 => 0 pairs (X) / B9 = 1 => 0 pairs (_) D8,D9: 1.. / D8 = 1 => 0 pairs (*) / D9 = 1 => 0 pairs (X) B8,D8: 1.. / B8 = 1 => 0 pairs (X) / D8 = 1 => 0 pairs (_) B9,D9: 1.. / B9 = 1 => 0 pairs (*) / D9 = 1 => 0 pairs (X) A1,C2: 6.. / A1 = 6 => 0 pairs (*) / C2 = 6 => 0 pairs (X) E1,D3: 6.. / E1 = 6 => 0 pairs (X) / D3 = 6 => 0 pairs (_) I2,I3: 6.. / I2 = 6 => 0 pairs (*) / I3 = 6 => 0 pairs (X) B6,C6: 6.. / B6 = 6 => 0 pairs (X) / C6 = 6 => 0 pairs (_) B7,A8: 6.. / B7 = 6 => 0 pairs (*) / A8 = 6 => 0 pairs (X) E7,F8: 6.. / E7 = 6 => 0 pairs (X) / F8 = 6 => 0 pairs (_) A1,E1: 6.. / A1 = 6 => 0 pairs (*) / E1 = 6 => 0 pairs (X) C2,I2: 6.. / C2 = 6 => 0 pairs (X) / I2 = 6 => 0 pairs (_) D3,I3: 6.. / D3 = 6 => 0 pairs (*) / I3 = 6 => 0 pairs (X) B7,E7: 6.. / B7 = 6 => 0 pairs (*) / E7 = 6 => 0 pairs (X) A8,F8: 6.. / A8 = 6 => 0 pairs (X) / F8 = 6 => 0 pairs (_) A1,A8: 6.. / A1 = 6 => 0 pairs (*) / A8 = 6 => 0 pairs (X) B6,B7: 6.. / B6 = 6 => 0 pairs (X) / B7 = 6 => 0 pairs (_) C2,C6: 6.. / C2 = 6 => 0 pairs (X) / C6 = 6 => 0 pairs (_) D3,D4: 6.. / D3 = 6 => 0 pairs (*) / D4 = 6 => 0 pairs (X) F4,F8: 6.. / F4 = 6 => 0 pairs (X) / F8 = 6 => 0 pairs (_) D4,E4: 8.. / D4 = 8 => 0 pairs (*) / E4 = 8 => 0 pairs (X) B7,B8: 8.. / B7 = 8 => 0 pairs (X) / B8 = 8 => 0 pairs (_) E7,D8: 8.. / E7 = 8 => 0 pairs (*) / D8 = 8 => 0 pairs (X) B7,E7: 8.. / B7 = 8 => 0 pairs (X) / E7 = 8 => 0 pairs (_) B8,D8: 8.. / B8 = 8 => 0 pairs (*) / D8 = 8 => 0 pairs (X) D4,D8: 8.. / D4 = 8 => 0 pairs (*) / D8 = 8 => 0 pairs (X) E4,E7: 8.. / E4 = 8 => 0 pairs (X) / E7 = 8 => 0 pairs (_) A1,C2: 9.. / A1 = 9 => 0 pairs (X) / C2 = 9 => 0 pairs (_) E1,D3: 9.. / E1 = 9 => 0 pairs (*) / D3 = 9 => 0 pairs (X) I2,I3: 9.. / I2 = 9 => 0 pairs (X) / I3 = 9 => 0 pairs (_) B6,C6: 9.. / B6 = 9 => 0 pairs (*) / C6 = 9 => 0 pairs (X) A8,B9: 9.. / A8 = 9 => 0 pairs (*) / B9 = 9 => 0 pairs (X) F8,D9: 9.. / F8 = 9 => 0 pairs (X) / D9 = 9 => 0 pairs (_) A1,E1: 9.. / A1 = 9 => 0 pairs (X) / E1 = 9 => 0 pairs (_) C2,I2: 9.. / C2 = 9 => 0 pairs (*) / I2 = 9 => 0 pairs (X) D3,I3: 9.. / D3 = 9 => 0 pairs (X) / I3 = 9 => 0 pairs (_) A8,F8: 9.. / A8 = 9 => 0 pairs (*) / F8 = 9 => 0 pairs (X) B9,D9: 9.. / B9 = 9 => 0 pairs (X) / D9 = 9 => 0 pairs (_) A1,A8: 9.. / A1 = 9 => 0 pairs (X) / A8 = 9 => 0 pairs (_) B6,B9: 9.. / B6 = 9 => 0 pairs (*) / B9 = 9 => 0 pairs (X) C2,C6: 9.. / C2 = 9 => 0 pairs (*) / C6 = 9 => 0 pairs (X) E1,E4: 9.. / E1 = 9 => 0 pairs (*) / E4 = 9 => 0 pairs (X) F4,F8: 9.. / F4 = 9 => 0 pairs (*) / F8 = 9 => 0 pairs (X) * DURATION: 0:01:11.816571 START: 07:48:29.878405 END: 07:49:41.694976 2017-05-04 * CP COUNT: (43) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A8,B6,B7,B8,B9,C2,C6,D3,D8,D9,E1,E7,F4,F8,I2,I3) * .524.381717.25843.843.1752.431...2757285419635..3721842.57.4391..4.3.7523.7.25648 * PAIR E1: 6,9 COL E E4: 6,9,8 # reduction candidate for 6,9 E4: 6,9 => SOLVED * 652493817179258436843617529431869275728541963596372184265784391984136752317925648 E4: 8 => CTR * .52493817179258436843617529431.862757285419635963721842.57.4391..4.3.7523.7.25648 * PAIR D3: 6,9 COL D D4: 6,9,8 # reduction candidate for 6,9 D4: 6,9 => CTR * .524.381717.25843.843.1752.431.8.2757285419635..372184285764391614839752397125648 D4: 8 => SOLVED * 652493817179258436843617529431869275728541963596372184265784391984136752317925648 * PAIR F4: 6,9 BLK 5 D4: 6,9,8 # reduction candidate for 6,9 D4: 6,9 => CTR * .524.381717.25843.843.1752.431.8.2757285419635..372184285764391614839752397125648 D4: 8 => SOLVED * 652493817179258436843617529431869275728541963596372184265784391984136752317925648 E4: 6,9,8 # reduction candidate for 6,9 E4: 6,9 => SOLVED * 652493817179258436843617529431869275728541963596372184265784391984136752317925648 E4: 8 => CTR * .52493817179258436843617529431.862757285419635963721842.57.4391..4.3.7523.7.25648 * PAIR E7: 6,8 COL E E4: 6,8,9 # reduction candidate for 6,8 E4: 6,8 => SOLVED * 652493817179258436843617529431869275728541963596372184265784391984136752317925648 E4: 9 => CTR * .524.381717.25843.843.1752.4318962757285419635..3721842.57.4391..4.3.7523.7.25648 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-148-base-pr-000.dot * REASONING * PRF # E4: 6,9 => SOL * DIS # E4: 8 => CTR => E4: 6,9 * DIS # D4: 6,9 => CTR => D4: 8 * PRF # D4: 8 => SOL * DIS # D4: 6,9 => CTR => D4: 8 * PRF # D4: 8 => SOL * PRF # E4: 6,9 => SOL * DIS # E4: 8 => CTR => E4: 6,9 * PRF # E4: 6,8 => SOL * DIS # E4: 9 => CTR => E4: 6,8 * CNT 10 HDP CHAINS / 10 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A8,B6,B7,B8,B9,C2,C6,D3,D8,D9,E1,E7,F4,F8,I2,I3) * .524.381717.25843.843.1752.431...2757285419635..3721842.57.4391..4.3.7523.7.25648 * PAIR E1: 6,9 COL E E4: 6,9,8 # reduction candidate for 6,9 E4: 6,9 => SOLVED * 652493817179258436843617529431869275728541963596372184265784391984136752317925648 * DURATION: 0:00:01.912057 START: 07:49:54.827011 END: 07:49:56.739068 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-148-base-pr-001.dot * REASONING * PRF # E4: 6,9 => SOL * STA E4: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 148 solution: 652493817179258436843617529431869275728541963596372184265784391984136752317925648 info: 1815 FNTWX S8.f 47281 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 652493817179258436843617529431869275728541963596372184265784391984136752317925648 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 # E4: 6,9 => SOL * DIS # E4: 8 => CTR => E4: 6,9 * DIS # D4: 6,9 => CTR => D4: 8 * PRF # D4: 8 => SOL * DIS # D4: 6,9 => CTR => D4: 8 * PRF # D4: 8 => SOL * PRF # E4: 6,9 => SOL * DIS # E4: 8 => CTR => E4: 6,9 * PRF # E4: 6,8 => SOL * DIS # E4: 9 => CTR => E4: 6,8 * CNT 10 HDP CHAINS / 10 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # E4: 6,9 => SOL * STA E4: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED