Analysis of xx-top500-203-base.sdk
Contents
Original Sudoku
level: medium
position: ....4..5.....29...3.....8.....8....1.24.......5.......8..6.........5..4....7..3.. initial
Autosolve
position: 2.9.48.5.58..29..43415..8929.38.5421.249..58..584.2..9835694217.1.253948492781365 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G1: 6,7 => CTR => G1: 1 * PRF # G1: 1 => SOL * PRF # G2: 6,7 => SOL * DIS # G2: 1 => CTR => G2: 6,7 * PRF # A5: 6,7 => SOL * DIS # A5: 1 => CTR => A5: 6,7 * DIS # A5: 1,6 => CTR => A5: 7 * PRF # A5: 7 => SOL * PRF # A5: 6,7 => SOL * DIS # A5: 1 => CTR => A5: 6,7 * DIS # G1: 6,7 => CTR => G1: 1 * PRF # G1: 1 => SOL * PRF # G2: 6,7 => SOL * DIS # G2: 1 => CTR => G2: 6,7 * PRF # A5: 6,7 => SOL * DIS # A5: 1 => CTR => A5: 6,7 * CNT 16 HDP CHAINS / 16 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G1: 6,7 => CTR => G1: 1 * PRF G1: 1 => SOL * STA G1: 1 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....4..5.....29...3.....8.....8....1.24.......5.......8..6.........5..4....7..3.. | initial |
| 2.9.48.5.58..29..43415..8929.38.5421.249..58..584.2..9835694217.1.253948492781365 | autosolve |
| 279348156586129734341567892963875421724916583158432679835694217617253948492781365 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) B1: 6,7 C2: 6,7 D1: 1,3 D2: 1,3 E3: 6,7 F3: 6,7 I1: 3,6 H2: 3,7 B4: 6,7 A6: 1,6 E4: 6,7 E5: 1,3 F5: 6,7 E6: 1,3 I5: 3,6 G6: 6,7 H6: 3,7 A8: 6,7 C8: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,D2: 1.. / D1 = 1 => 0 pairs (X) / D2 = 1 => 0 pairs (_) G1,G2: 1.. / G1 = 1 => 0 pairs (*) / G2 = 1 => 0 pairs (X) A5,A6: 1.. / A5 = 1 => 0 pairs (X) / A6 = 1 => 0 pairs (_) E5,E6: 1.. / E5 = 1 => 0 pairs (*) / E6 = 1 => 0 pairs (X) D1,G1: 1.. / D1 = 1 => 0 pairs (X) / G1 = 1 => 0 pairs (_) D2,G2: 1.. / D2 = 1 => 0 pairs (*) / G2 = 1 => 0 pairs (X) A5,E5: 1.. / A5 = 1 => 0 pairs (X) / E5 = 1 => 0 pairs (_) A6,E6: 1.. / A6 = 1 => 0 pairs (*) / E6 = 1 => 0 pairs (X) D1,D2: 3.. / D1 = 3 => 0 pairs (*) / D2 = 3 => 0 pairs (X) I1,H2: 3.. / I1 = 3 => 0 pairs (X) / H2 = 3 => 0 pairs (_) E5,E6: 3.. / E5 = 3 => 0 pairs (X) / E6 = 3 => 0 pairs (_) I5,H6: 3.. / I5 = 3 => 0 pairs (*) / H6 = 3 => 0 pairs (X) D1,I1: 3.. / D1 = 3 => 0 pairs (*) / I1 = 3 => 0 pairs (X) D2,H2: 3.. / D2 = 3 => 0 pairs (X) / H2 = 3 => 0 pairs (_) E5,I5: 3.. / E5 = 3 => 0 pairs (X) / I5 = 3 => 0 pairs (_) E6,H6: 3.. / E6 = 3 => 0 pairs (*) / H6 = 3 => 0 pairs (X) H2,H6: 3.. / H2 = 3 => 0 pairs (*) / H6 = 3 => 0 pairs (X) I1,I5: 3.. / I1 = 3 => 0 pairs (X) / I5 = 3 => 0 pairs (_) B1,C2: 6.. / B1 = 6 => 0 pairs (X) / C2 = 6 => 0 pairs (_) E3,F3: 6.. / E3 = 6 => 0 pairs (*) / F3 = 6 => 0 pairs (X) E4,F5: 6.. / E4 = 6 => 0 pairs (X) / F5 = 6 => 0 pairs (_) I5,G6: 6.. / I5 = 6 => 0 pairs (X) / G6 = 6 => 0 pairs (_) A8,C8: 6.. / A8 = 6 => 0 pairs (*) / C8 = 6 => 0 pairs (X) C2,G2: 6.. / C2 = 6 => 0 pairs (*) / G2 = 6 => 0 pairs (X) B4,E4: 6.. / B4 = 6 => 0 pairs (*) / E4 = 6 => 0 pairs (X) A6,G6: 6.. / A6 = 6 => 0 pairs (X) / G6 = 6 => 0 pairs (_) B1,B4: 6.. / B1 = 6 => 0 pairs (X) / B4 = 6 => 0 pairs (_) C2,C8: 6.. / C2 = 6 => 0 pairs (*) / C8 = 6 => 0 pairs (X) E3,E4: 6.. / E3 = 6 => 0 pairs (*) / E4 = 6 => 0 pairs (X) F3,F5: 6.. / F3 = 6 => 0 pairs (X) / F5 = 6 => 0 pairs (_) I1,I5: 6.. / I1 = 6 => 0 pairs (*) / I5 = 6 => 0 pairs (X) B1,C2: 7.. / B1 = 7 => 0 pairs (*) / C2 = 7 => 0 pairs (X) E3,F3: 7.. / E3 = 7 => 0 pairs (X) / F3 = 7 => 0 pairs (_) B4,A5: 7.. / B4 = 7 => 0 pairs (X) / A5 = 7 => 0 pairs (_) E4,F5: 7.. / E4 = 7 => 0 pairs (*) / F5 = 7 => 0 pairs (X) G6,H6: 7.. / G6 = 7 => 0 pairs (X) / H6 = 7 => 0 pairs (_) A8,C8: 7.. / A8 = 7 => 0 pairs (X) / C8 = 7 => 0 pairs (_) B1,G1: 7.. / B1 = 7 => 0 pairs (*) / G1 = 7 => 0 pairs (X) B4,E4: 7.. / B4 = 7 => 0 pairs (X) / E4 = 7 => 0 pairs (_) A5,F5: 7.. / A5 = 7 => 0 pairs (*) / F5 = 7 => 0 pairs (X) A5,A8: 7.. / A5 = 7 => 0 pairs (*) / A8 = 7 => 0 pairs (X) B1,B4: 7.. / B1 = 7 => 0 pairs (*) / B4 = 7 => 0 pairs (X) C2,C8: 7.. / C2 = 7 => 0 pairs (X) / C8 = 7 => 0 pairs (_) E3,E4: 7.. / E3 = 7 => 0 pairs (X) / E4 = 7 => 0 pairs (_) F3,F5: 7.. / F3 = 7 => 0 pairs (*) / F5 = 7 => 0 pairs (X) H2,H6: 7.. / H2 = 7 => 0 pairs (X) / H6 = 7 => 0 pairs (_) * DURATION: 0:01:40.846847 START: 09:43:51.332681 END: 09:45:32.179528 2017-05-04 * CP COUNT: (46) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A8,B1,B4,C2,C8,D1,D2,E3,E4,E5,E6,F3,F5,G6,H2,H6,I1,I5) * 2.9.48.5.58..29..43415..8929.38.5421.249..58..584.2..9835694217.1.253948492781365 * PAIR B1: 6,7 ROW 1 G1: 6,7,1 # reduction candidate for 6,7 G1: 6,7 => CTR * 2.9148.5358.3291743415..8929.38.5421.2493.58665841273983569421771.253948492781365 G1: 1 => SOLVED * 279348156586129734341567892963875421724916583158432679835694217617253948492781365 * PAIR C2: 6,7 ROW 2 G2: 6,7,1 # reduction candidate for 6,7 G2: 6,7 => SOLVED * 279348156586129734341567892963875421724916583158432679835694217617253948492781365 G2: 1 => CTR * 2.9.48.5.586.291743415..892963875421724916583.584.2..9835694217.1.253948492781365 * PAIR B4: 6,7 BLK 4 A5: 6,7,1 # reduction candidate for 6,7 A5: 6,7 => SOLVED * 279348156586129734341567892963875421724916583158432679835694217617253948492781365 A5: 1 => CTR * 2.9.48.5.58..29..43415..892973865421124937586658412739835694217716253948492781365 * PAIR A6: 1,6 BLK 4 A5: 1,6,7 # reduction candidate for 1,6 A5: 1,6 => CTR * 269.4875358..29..43415..892973865421.249.758..584.2..9835694217716253948492781365 A5: 7 => SOLVED * 279348156586129734341567892963875421724916583158432679835694217617253948492781365 * PAIR F5: 6,7 ROW 5 A5: 6,7,1 # reduction candidate for 6,7 A5: 6,7 => SOLVED * 279348156586129734341567892963875421724916583158432679835694217617253948492781365 A5: 1 => CTR * 2.9.48.5.58..29..43415..892973865421124937586658412739835694217716253948492781365 * PAIR G6: 6,7 COL G G1: 6,7,1 # reduction candidate for 6,7 G1: 6,7 => CTR * 2.9148.5358.3291743415..8929.38.5421.2493.58665841273983569421771.253948492781365 G1: 1 => SOLVED * 279348156586129734341567892963875421724916583158432679835694217617253948492781365 G2: 6,7,1 # reduction candidate for 6,7 G2: 6,7 => SOLVED * 279348156586129734341567892963875421724916583158432679835694217617253948492781365 G2: 1 => CTR * 2.9.48.5.586.291743415..892963875421724916583.584.2..9835694217.1.253948492781365 * PAIR A8: 6,7 COL A A5: 6,7,1 # reduction candidate for 6,7 A5: 6,7 => SOLVED * 279348156586129734341567892963875421724916583158432679835694217617253948492781365 A5: 1 => CTR * 2.9.48.5.58..29..43415..892973865421124937586658412739835694217716253948492781365 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-203-base-pr-000.dot * REASONING * DIS # G1: 6,7 => CTR => G1: 1 * PRF # G1: 1 => SOL * PRF # G2: 6,7 => SOL * DIS # G2: 1 => CTR => G2: 6,7 * PRF # A5: 6,7 => SOL * DIS # A5: 1 => CTR => A5: 6,7 * DIS # A5: 1,6 => CTR => A5: 7 * PRF # A5: 7 => SOL * PRF # A5: 6,7 => SOL * DIS # A5: 1 => CTR => A5: 6,7 * DIS # G1: 6,7 => CTR => G1: 1 * PRF # G1: 1 => SOL * PRF # G2: 6,7 => SOL * DIS # G2: 1 => CTR => G2: 6,7 * PRF # A5: 6,7 => SOL * DIS # A5: 1 => CTR => A5: 6,7 * CNT 16 HDP CHAINS / 16 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A8,B1,B4,C2,C8,D1,D2,E3,E4,E5,E6,F3,F5,G6,H2,H6,I1,I5) * 2.9.48.5.58..29..43415..8929.38.5421.249..58..584.2..9835694217.1.253948492781365 * PAIR B1: 6,7 ROW 1 G1: 6,7,1 # reduction candidate for 6,7 G1: 6,7 => CTR * 2.9148.5358.3291743415..8929.38.5421.2493.58665841273983569421771.253948492781365 G1: 1 => SOLVED * 279348156586129734341567892963875421724916583158432679835694217617253948492781365 * DURATION: 0:00:03.608819 START: 09:45:57.594841 END: 09:46:01.203660 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-203-base-pr-001.dot * REASONING * DIS # G1: 6,7 => CTR => G1: 1 * PRF G1: 1 => SOL * STA G1: 1 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 203 solution: 279348156586129734341567892963875421724916583158432679835694217617253948492781365 info: 1892 FNBTHWY S8.f 4223 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 279348156586129734341567892963875421724916583158432679835694217617253948492781365 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 # G1: 6,7 => CTR => G1: 1 * PRF # G1: 1 => SOL * PRF # G2: 6,7 => SOL * DIS # G2: 1 => CTR => G2: 6,7 * PRF # A5: 6,7 => SOL * DIS # A5: 1 => CTR => A5: 6,7 * DIS # A5: 1,6 => CTR => A5: 7 * PRF # A5: 7 => SOL * PRF # A5: 6,7 => SOL * DIS # A5: 1 => CTR => A5: 6,7 * DIS # G1: 6,7 => CTR => G1: 1 * PRF # G1: 1 => SOL * PRF # G2: 6,7 => SOL * DIS # G2: 1 => CTR => G2: 6,7 * PRF # A5: 6,7 => SOL * DIS # A5: 1 => CTR => A5: 6,7 * CNT 16 HDP CHAINS / 16 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # G1: 6,7 => CTR => G1: 1 * PRF G1: 1 => SOL * STA G1: 1 * CNT 2 HDP CHAINS / 1 HYP OPENED