Analysis of xx-top500-237-base.sdk
Contents
Original Sudoku
level: medium
position: ...6..2.....23....1........4....8.536......7...........37.5.....2.7...........1.. initial
Autosolve
position: 3..6172..7..23.561162..573.47912865361...3.722.3.76.1..37.51.26.2176.3.55463.21.7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # D3: 4,9 => SOL * DIS # I1: 4,9 => CTR => I1: 8 * PRF # D3: 4,9 => SOL * DIS # I6: 8 => CTR => I6: 4,9 * DIS # D5: 4,9 => CTR => D5: 5 * PRF # D5: 5 => SOL * PRF # D6: 4,9 => SOL * DIS # D6: 5 => CTR => D6: 4,9 * PRF # G5: 4,9 => SOL * DIS # G5: 8 => CTR => G5: 4,9 * PRF # E3: 8 => SOL * PRF # D7: 8,9 => SOL * DIS # D7: 4 => CTR => D7: 8,9 * DIS # G7: 8,9 => CTR => G7: 4 * PRF # G7: 4 => SOL * PRF # H8: 8,9 => SOL * DIS # H8: 4 => CTR => H8: 8,9 * PRF # D7: 8 => SOL * DIS # H8: 8 => CTR => H8: 4,9 * PRF # D7: 8,9 => SOL * DIS # D7: 4 => CTR => D7: 8,9 * DIS # E3: 4 => CTR => E3: 8,9 * DIS # G7: 8,9 => CTR => G7: 4 * PRF # G7: 4 => SOL * PRF # H8: 8,9 => SOL * DIS # H8: 4 => CTR => H8: 8,9 * DIS # H1: 8,9 => CTR => H1: 4 * PRF # H1: 4 => SOL * CNT 28 HDP CHAINS / 39 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # D3: 4,9 => SOL * STA D3: 4,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...6..2.....23....1........4....8.536......7...........37.5.....2.7...........1.. | initial |
| 3..6172..7..23.561162..573.47912865361...3.722.3.76.1..37.51.26.2176.3.55463.21.7 | autosolve |
| 395617248784239561162485739479128653618543972253976814937851426821764395546392187 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) B1: 5,9 C1: 4,5 B2: 8,9 C2: 4,8 F2: 4,9 I3: 4,9 C5: 5,8 B6: 5,8 E5: 4,9 A7: 8,9 A8: 8,9 F8: 4,9 E9: 8,9 H9: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,C2: 4.. / C1 = 4 => 0 pairs (X) / C2 = 4 => 0 pairs (_) D7,F8: 4.. / D7 = 4 => 0 pairs (X) / F8 = 4 => 0 pairs (_) G7,H8: 4.. / G7 = 4 => 0 pairs (*) / H8 = 4 => 0 pairs (X) C2,F2: 4.. / C2 = 4 => 0 pairs (*) / F2 = 4 => 0 pairs (X) D7,G7: 4.. / D7 = 4 => 0 pairs (X) / G7 = 4 => 0 pairs (_) F8,H8: 4.. / F8 = 4 => 0 pairs (*) / H8 = 4 => 0 pairs (X) E3,E5: 4.. / E3 = 4 => 0 pairs (X) / E5 = 4 => 19 pairs (_) F2,F8: 4.. / F2 = 4 => 0 pairs (X) / F8 = 4 => 0 pairs (_) H1,H8: 4.. / H1 = 4 => 0 pairs (*) / H8 = 4 => 0 pairs (X) B1,C1: 5.. / B1 = 5 => 0 pairs (X) / C1 = 5 => 0 pairs (_) C5,B6: 5.. / C5 = 5 => 0 pairs (X) / B6 = 5 => 0 pairs (_) D5,D6: 5.. / D5 = 5 => 0 pairs (*) / D6 = 5 => 0 pairs (X) C5,D5: 5.. / C5 = 5 => 0 pairs (X) / D5 = 5 => 0 pairs (_) B6,D6: 5.. / B6 = 5 => 0 pairs (*) / D6 = 5 => 0 pairs (X) B1,B6: 5.. / B1 = 5 => 0 pairs (X) / B6 = 5 => 0 pairs (_) C1,C5: 5.. / C1 = 5 => 0 pairs (*) / C5 = 5 => 0 pairs (X) B2,C2: 8.. / B2 = 8 => 0 pairs (*) / C2 = 8 => 0 pairs (X) D3,E3: 8.. / D3 = 8 => 18 pairs (_) / E3 = 8 => 0 pairs (*) H1,I1: 8.. / H1 = 8 => 0 pairs (X) / I1 = 8 => 17 pairs (_) C5,B6: 8.. / C5 = 8 => 0 pairs (*) / B6 = 8 => 0 pairs (X) A7,A8: 8.. / A7 = 8 => 0 pairs (X) / A8 = 8 => 17 pairs (_) D7,E9: 8.. / D7 = 8 => 0 pairs (*) / E9 = 8 => 0 pairs (X) C5,G5: 8.. / C5 = 8 => 0 pairs (*) / G5 = 8 => 0 pairs (X) A8,H8: 8.. / A8 = 8 => 17 pairs (_) / H8 = 8 => 0 pairs (X) E9,H9: 8.. / E9 = 8 => 18 pairs (_) / H9 = 8 => 0 pairs (*) B2,B6: 8.. / B2 = 8 => 0 pairs (*) / B6 = 8 => 0 pairs (X) C2,C5: 8.. / C2 = 8 => 0 pairs (X) / C5 = 8 => 0 pairs (_) D3,D7: 8.. / D3 = 8 => 18 pairs (_) / D7 = 8 => 0 pairs (*) E3,E9: 8.. / E3 = 8 => 0 pairs (*) / E9 = 8 => 0 pairs (X) I1,I6: 8.. / I1 = 8 => 17 pairs (_) / I6 = 8 => 0 pairs (X) B1,B2: 9.. / B1 = 9 => 0 pairs (*) / B2 = 9 => 0 pairs (X) A7,A8: 9.. / A7 = 9 => 17 pairs (_) / A8 = 9 => 0 pairs (X) B2,F2: 9.. / B2 = 9 => 0 pairs (X) / F2 = 9 => 0 pairs (_) E9,H9: 9.. / E9 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) F2,F8: 9.. / F2 = 9 => 0 pairs (*) / F8 = 9 => 0 pairs (X) * DURATION: 0:00:58.750667 START: 10:55:16.326998 END: 10:56:15.077665 2017-05-04 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A8,B1,B2,B6,C1,C2,C5,E5,E9,F2,F8,H9,I3) * 3..6172..7..23.561162..573.47912865361...3.722.3.76.1..37.51.26.2176.3.55463.21.7 * PAIR F2: 4,9 BLK 2 D3: 4,9,8 # reduction candidate for 4,9 D3: 4,9 => SOLVED * 395617248784239561162485739479128653618543972253976814937851426821764395546392187 D3: 8 # 18 pairs E3: 4,9,8 # reduction candidate for 4,9 E3: 4,9 # 18 pairs * PAIR I3: 4,9 BLK 3 H1: 4,9,8 # reduction candidate for 4,9 H1: 4,9 # 17 pairs I1: 4,9,8 # reduction candidate for 4,9 I1: 4,9 => CTR * 3..61728.78423.561162..573.47912865361...3.722.3.76.18.37.5182682176.345546382197 I1: 8 # 17 pairs * PAIR I3: 4,9 ROW 3 D3: 4,9,8 # reduction candidate for 4,9 D3: 4,9 => SOLVED * 395617248784239561162485739479128653618543972253976814937851426821764395546392187 D3: 8 # 18 pairs E3: 4,9,8 # reduction candidate for 4,9 E3: 4,9 # 18 pairs * PAIR I3: 4,9 COL I I6: 4,9,8 # reduction candidate for 4,9 I6: 8 => CTR * 3..61728.78423.561162..573.47912865361...3.722.3.76.18.37.5182682176.345546382197 I6: 4,9 # 17 pairs * PAIR E5: 4,9 BLK 5 D5: 4,9,5 # reduction candidate for 4,9 D5: 4,9 => CTR * 3546172.8798234561162..5734479128653615.43872283576419.3745192692176.3.55463.21.7 D5: 5 => SOLVED * 395617248784239561162485739479128653618543972253976814937851426821764395546392187 D6: 4,9,5 # reduction candidate for 4,9 D6: 4,9 => SOLVED * 395617248784239561162485739479128653618543972253976814937851426821764395546392187 D6: 5 => CTR * 3546172..798234561162..5734479128653615.43872283576419.3745192692176.3.55463.21.7 * PAIR E5: 4,9 ROW 5 G5: 4,9,8 # reduction candidate for 4,9 G5: 4,9 => SOLVED * 395617248784239561162485739479128653618543972253976814937851426821764395546392187 G5: 8 => CTR * 3546172.8798234561162..5734479128653615.43872283576419.3745192692176.3.55463.21.7 * PAIR E5: 4,9 COL E E3: 4,9,8 # reduction candidate for 4,9 E3: 8 => SOLVED * 395617248784239561162485739479128653618543972253976814937851426821764395546392187 E3: 4,9 # 18 pairs * PAIR A7: 8,9 ROW 7 D7: 8,9,4 # reduction candidate for 8,9 D7: 8,9 => SOLVED * 395617248784239561162485739479128653618543972253976814937851426821764395546392187 D7: 4 => CTR * 3..61728.7982345611628957344791286536159438722.3.76.1..37451.26.21769345546382197 G7: 8,9,4 # reduction candidate for 8,9 G7: 8,9 => CTR * 3..61728.7982345611628957344791286536159438722.3.76.1..37451.26.21769345546382197 G7: 4 => SOLVED * 395617248784239561162485739479128653618543972253976814937851426821764395546392187 * PAIR A8: 8,9 ROW 8 H8: 8,9,4 # reduction candidate for 8,9 H8: 8,9 => SOLVED * 395617248784239561162485739479128653618543972253976814937851426821764395546392187 H8: 4 => CTR * 3..61728.798234561162895734479128653615.438722.3.76.1..37.51.26821769345546382197 * PAIR F8: 4,9 BLK 8 D7: 4,9,8 # reduction candidate for 4,9 D7: 8 => SOLVED * 395617248784239561162485739479128653618543972253976814937851426821764395546392187 D7: 4,9 # 18 pairs * PAIR F8: 4,9 ROW 8 H8: 4,9,8 # reduction candidate for 4,9 H8: 8 => CTR * 3..6172487.4239561162..57394791286536185.3.72253.76814.37.51426921764385546382197 H8: 4,9 # 17 pairs * PAIR E9: 8,9 BLK 8 D7: 8,9,4 # reduction candidate for 8,9 D7: 8,9 => SOLVED * 395617248784239561162485739479128653618543972253976814937851426821764395546392187 D7: 4 => CTR * 3..61728.7982345611628957344791286536159438722.3.76.1..37451.26.21769345546382197 * PAIR E9: 8,9 COL E E3: 8,9,4 # reduction candidate for 8,9 E3: 4 => CTR * 39561724878.23.56116284573947912865361..93.722.3.7691..37951426921764385546382197 E3: 8,9 # 19 pairs * PAIR H9: 8,9 BLK 9 G7: 8,9,4 # reduction candidate for 8,9 G7: 8,9 => CTR * 3..61728.7982345611628957344791286536159438722.3.76.1..37451.26.21769345546382197 G7: 4 => SOLVED * 395617248784239561162485739479128653618543972253976814937851426821764395546392187 H8: 8,9,4 # reduction candidate for 8,9 H8: 8,9 => SOLVED * 395617248784239561162485739479128653618543972253976814937851426821764395546392187 H8: 4 => CTR * 3..61728.798234561162895734479128653615.438722.3.76.1..37.51.26821769345546382197 * PAIR H9: 8,9 COL H H1: 8,9,4 # reduction candidate for 8,9 H1: 8,9 => CTR * 3.4617289798234561162895734479128653615.43.722.3.7641..37451.26821769345546382197 H1: 4 => SOLVED * 395617248784239561162485739479128653618543972253976814937851426821764395546392187 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-237-base-pr-000.dot * REASONING * PRF # D3: 4,9 => SOL * DIS # I1: 4,9 => CTR => I1: 8 * PRF # D3: 4,9 => SOL * DIS # I6: 8 => CTR => I6: 4,9 * DIS # D5: 4,9 => CTR => D5: 5 * PRF # D5: 5 => SOL * PRF # D6: 4,9 => SOL * DIS # D6: 5 => CTR => D6: 4,9 * PRF # G5: 4,9 => SOL * DIS # G5: 8 => CTR => G5: 4,9 * PRF # E3: 8 => SOL * PRF # D7: 8,9 => SOL * DIS # D7: 4 => CTR => D7: 8,9 * DIS # G7: 8,9 => CTR => G7: 4 * PRF # G7: 4 => SOL * PRF # H8: 8,9 => SOL * DIS # H8: 4 => CTR => H8: 8,9 * PRF # D7: 8 => SOL * DIS # H8: 8 => CTR => H8: 4,9 * PRF # D7: 8,9 => SOL * DIS # D7: 4 => CTR => D7: 8,9 * DIS # E3: 4 => CTR => E3: 8,9 * DIS # G7: 8,9 => CTR => G7: 4 * PRF # G7: 4 => SOL * PRF # H8: 8,9 => SOL * DIS # H8: 4 => CTR => H8: 8,9 * DIS # H1: 8,9 => CTR => H1: 4 * PRF # H1: 4 => SOL * CNT 28 HDP CHAINS / 39 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A8,B1,B2,B6,C1,C2,C5,E5,E9,F2,F8,H9,I3) * 3..6172..7..23.561162..573.47912865361...3.722.3.76.1..37.51.26.2176.3.55463.21.7 * PAIR F2: 4,9 BLK 2 D3: 4,9,8 # reduction candidate for 4,9 D3: 4,9 => SOLVED * 395617248784239561162485739479128653618543972253976814937851426821764395546392187 * DURATION: 0:00:02.095272 START: 10:56:57.892244 END: 10:56:59.987516 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-237-base-pr-001.dot * REASONING * PRF # D3: 4,9 => SOL * STA D3: 4,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 237 solution: 395617248784239561162485739479128653618543972253976814937851426821764395546392187 info: 2068 FNBWXY S8.f 46992 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 395617248784239561162485739479128653618543972253976814937851426821764395546392187 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 # D3: 4,9 => SOL * INC # D3: 8 => UNS * INC # E3: 4,9 => UNS * INC # H1: 4,9 => UNS * DIS # I1: 4,9 => CTR => I1: 8 * INC # I1: 8 => UNS * PRF # D3: 4,9 => SOL * INC # D3: 8 => UNS * INC # E3: 4,9 => UNS * INC # I6: 4,9 => UNS * DIS # I6: 8 => CTR => I6: 4,9 * DIS # D5: 4,9 => CTR => D5: 5 * PRF # D5: 5 => SOL * PRF # D6: 4,9 => SOL * DIS # D6: 5 => CTR => D6: 4,9 * PRF # G5: 4,9 => SOL * DIS # G5: 8 => CTR => G5: 4,9 * INC # E3: 4,9 => UNS * PRF # E3: 8 => SOL * PRF # D7: 8,9 => SOL * DIS # D7: 4 => CTR => D7: 8,9 * DIS # G7: 8,9 => CTR => G7: 4 * PRF # G7: 4 => SOL * PRF # H8: 8,9 => SOL * DIS # H8: 4 => CTR => H8: 8,9 * INC # D7: 4,9 => UNS * PRF # D7: 8 => SOL * INC # H8: 4,9 => UNS * DIS # H8: 8 => CTR => H8: 4,9 * PRF # D7: 8,9 => SOL * DIS # D7: 4 => CTR => D7: 8,9 * INC # E3: 8,9 => UNS * DIS # E3: 4 => CTR => E3: 8,9 * DIS # G7: 8,9 => CTR => G7: 4 * PRF # G7: 4 => SOL * PRF # H8: 8,9 => SOL * DIS # H8: 4 => CTR => H8: 8,9 * DIS # H1: 8,9 => CTR => H1: 4 * PRF # H1: 4 => SOL * CNT 39 HDP CHAINS / 39 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # D3: 4,9 => SOL * STA D3: 4,9 * CNT 1 HDP CHAINS / 1 HYP OPENED