Analysis of xx-top500-134-base.sdk
Contents
Original Sudoku
level: medium
position: ..72..5...4......6.......1.62....3......47.......6....1..8...5.........49........ initial
Autosolve
position: .672145...41...72629.7.641.62.1..347.1..4726.47..62...1348796527.26....49.642..7. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A2: 3,8 => SOL * DIS # A2: 5 => CTR => A2: 3,8 * DIS # C3: 3,8 => CTR => C3: 5 * PRF # C3: 5 => SOL * PRF # I1: 3,8 => SOL * DIS # A5: 3,8 => CTR => A5: 5 * PRF # A5: 5 => SOL * PRF # E2: 5,9 => SOL * DIS # E2: 3,8 => CTR => E2: 5,9 * PRF # I1: 3,8 => SOL * DIS # C3: 3,8 => CTR => C3: 5 * PRF # C3: 5 => SOL * PRF # E3: 3,8 => SOL * DIS # E3: 5 => CTR => E3: 3,8 * DIS # I9: 3,8 => CTR => I9: 1 * PRF # I9: 1 => SOL * DIS # C5: 5,9 => CTR => C5: 3,8 * DIS # C6: 5,9 => CTR => C6: 3,8 * PRF # E4: 8 => SOL * PRF # E4: 5,8 => SOL * DIS # E4: 9 => CTR => E4: 5,8 * PRF # F2: 5,8 => SOL * DIS # F2: 3 => CTR => F2: 5,8 * PRF # I5: 8,9 => SOL * DIS # I5: 5 => CTR => I5: 8,9 * DIS # G6: 8,9 => CTR => G6: 1 * PRF # G6: 1 => SOL * DIS # I6: 8,9 => CTR => I6: 1,5 * DIS # C6: 8,9 => CTR => C6: 3,5 * PRF # H1: 8,9 => SOL * DIS # H1: 3 => CTR => H1: 8,9 * DIS # H8: 8,9 => CTR => H8: 3 * PRF # H8: 3 => SOL * DIS # F8: 3,5 => CTR => F8: 1 * DIS # E2: 3,5 => CTR => E2: 8,9 * DIS # G8: 1,8 => CTR => G8: 9 * PRF # I9: 1,8 => SOL * DIS # I9: 3 => CTR => I9: 1,8 * DIS # G6: 9 => CTR => G6: 1,8 * CNT 39 HDP CHAINS / 56 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A2: 3,8 => SOL * STA A2: 3,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..72..5...4......6.......1.62....3......47.......6....1..8...5.........49........ | initial |
| .672145...41...72629.7.641.62.1..347.1..4726.47..62...1348796527.26....49.642..7. | autosolve |
| 867214593341598726295736418629185347518347269473962185134879652782651934956423871 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) A1: 3,8 D2: 5,9 I3: 3,8 C4: 5,9 F4: 5,8 H6: 8,9 B8: 5,8 B9: 5,8 E8: 3,5 G9: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G6,I6: 1.. / G6 = 1 => 0 pairs (*) / I6 = 1 => 0 pairs (X) F8,F9: 1.. / F8 = 1 => 12 pairs (_) / F9 = 1 => 0 pairs (X) F8,G8: 1.. / F8 = 1 => 12 pairs (_) / G8 = 1 => 0 pairs (X) I6,I9: 1.. / I6 = 1 => 0 pairs (X) / I9 = 1 => 0 pairs (_) D5,D6: 3.. / D5 = 3 => 14 pairs (_) / D6 = 3 => 11 pairs (_) H8,I9: 3.. / H8 = 3 => 0 pairs (*) / I9 = 3 => 0 pairs (X) C6,D6: 3.. / C6 = 3 => 14 pairs (_) / D6 = 3 => 11 pairs (_) F9,I9: 3.. / F9 = 3 => 0 pairs (*) / I9 = 3 => 0 pairs (X) H1,H8: 3.. / H1 = 3 => 0 pairs (X) / H8 = 3 => 0 pairs (_) A2,C3: 5.. / A2 = 5 => 0 pairs (X) / C3 = 5 => 0 pairs (_) I5,I6: 5.. / I5 = 5 => 0 pairs (X) / I6 = 5 => 0 pairs (_) B8,B9: 5.. / B8 = 5 => 0 pairs (X) / B9 = 5 => 11 pairs (_) C3,E3: 5.. / C3 = 5 => 0 pairs (*) / E3 = 5 => 0 pairs (X) B9,F9: 5.. / B9 = 5 => 11 pairs (_) / F9 = 5 => 0 pairs (X) A2,A5: 5.. / A2 = 5 => 0 pairs (X) / A5 = 5 => 0 pairs (_) E4,F4: 8.. / E4 = 8 => 0 pairs (*) / F4 = 8 => 0 pairs (X) B8,B9: 8.. / B8 = 8 => 11 pairs (_) / B9 = 8 => 0 pairs (X) F2,F4: 8.. / F2 = 8 => 0 pairs (*) / F4 = 8 => 0 pairs (X) D2,E2: 9.. / D2 = 9 => 0 pairs (X) / E2 = 9 => 0 pairs (_) H1,I1: 9.. / H1 = 9 => 0 pairs (*) / I1 = 9 => 0 pairs (X) G8,H8: 9.. / G8 = 9 => 13 pairs (_) / H8 = 9 => 0 pairs (X) C4,E4: 9.. / C4 = 9 => 0 pairs (*) / E4 = 9 => 0 pairs (X) E2,E4: 9.. / E2 = 9 => 0 pairs (*) / E4 = 9 => 0 pairs (X) G6,G8: 9.. / G6 = 9 => 0 pairs (X) / G8 = 9 => 13 pairs (_) * DURATION: 0:00:43.434591 START: 07:19:36.795413 END: 07:20:20.230004 2017-05-04 * CP COUNT: (24) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B8,B9,C4,D2,E8,F4,G9,H6,I3) * .672145...41...72629.7.641.62.1..347.1..4726.47..62...1348796527.26....49.642..7. * PAIR A1: 3,8 BLK 1 A2: 3,8,5 # reduction candidate for 3,8 A2: 3,8 => SOLVED * 867214593341598726295736418629185347518347269473962185134879652782651934956423871 A2: 5 => CTR * .6721453954198372629375641862519834731..4726.47..62...1348796527.263...49.642..73 C3: 3,8,5 # reduction candidate for 3,8 C3: 3,8 => CTR * .6721453954198372629375641862519834731..4726.47..62...1348796527.263...49.642..73 C3: 5 => SOLVED * 867214593341598726295736418629185347518347269473962185134879652782651934956423871 * PAIR A1: 3,8 ROW 1 H1: 3,8,9 # reduction candidate for 3,8 H1: 3,8 # 13 pairs I1: 3,8,9 # reduction candidate for 3,8 I1: 3,8 => SOLVED * 867214593341598726295736418629185347518347269473962185134879652782651934956423871 I1: 9 # 13 pairs * PAIR A1: 3,8 COL A A5: 3,8,5 # reduction candidate for 3,8 A5: 3,8 => CTR * .6721453954198372629375641862519834731..4726.47..62...1348796527.263...49.642..73 A5: 5 => SOLVED * 867214593341598726295736418629185347518347269473962185134879652782651934956423871 * PAIR D2: 5,9 BLK 2 E2: 5,9,3,8 # reduction candidate for 5,9 E2: 5,9 => SOLVED * 867214593341598726295736418629185347518347269473962185134879652782651934956423871 E2: 3,8 => CTR * .6721453954198372629375641862519834731..4726.47..62...1348796527.263...49.642..73 * PAIR D2: 5,9 COL D D5: 5,9,3 # reduction candidate for 5,9 D5: 5,9 # 11 pairs D6: 5,9,3 # reduction candidate for 5,9 D6: 5,9 # 14 pairs * PAIR I3: 3,8 BLK 3 H1: 3,8,9 # reduction candidate for 3,8 H1: 3,8 # 13 pairs I1: 3,8,9 # reduction candidate for 3,8 I1: 3,8 => SOLVED * 867214593341598726295736418629185347518347269473962185134879652782651934956423871 I1: 9 # 13 pairs * PAIR I3: 3,8 ROW 3 C3: 3,8,5 # reduction candidate for 3,8 C3: 3,8 => CTR * .6721453954198372629375641862519834731..4726.47..62...1348796527.263...49.642..73 C3: 5 => SOLVED * 867214593341598726295736418629185347518347269473962185134879652782651934956423871 E3: 3,8,5 # reduction candidate for 3,8 E3: 3,8 => SOLVED * 867214593341598726295736418629185347518347269473962185134879652782651934956423871 E3: 5 => CTR * .6721453954198372629375641862.19834731..4726.47..62...1348796527.263...49.642..73 * PAIR I3: 3,8 COL I I9: 3,8,1 # reduction candidate for 3,8 I9: 3,8 => CTR * .672145.95419..72629.75641.62.198347.19347265473562..11348796527.263...49.642..73 I9: 1 => SOLVED * 867214593341598726295736418629185347518347269473962185134879652782651934956423871 * PAIR C4: 5,9 BLK 4 C5: 5,9,3,8 # reduction candidate for 5,9 C5: 5,9 => CTR * .67214539541983726293756418625198347.19.4726.47..62...1348796527.263...49.642..73 C5: 3,8 # 11 pairs C6: 5,9,3,8 # reduction candidate for 5,9 C6: 5,9 => CTR * .672145..5419..72629.75641.62.198347.1.547269479362.851348796527.263.9.49.642..7. C6: 3,8 # 11 pairs * PAIR C4: 5,9 ROW 4 E4: 5,9,8 # reduction candidate for 5,9 E4: 8 => SOLVED * 867214593341598726295736418629185347518347269473962185134879652782651934956423871 E4: 5,9 # 11 pairs * PAIR F4: 5,8 BLK 5 E4: 5,8,9 # reduction candidate for 5,8 E4: 5,8 => SOLVED * 867214593341598726295736418629185347518347269473962185134879652782651934956423871 E4: 9 => CTR * .6721453954198372629375641862519834731..4726.47..62...1348796527.263...49.642..73 * PAIR F4: 5,8 COL F F2: 5,8,3 # reduction candidate for 5,8 F2: 5,8 => SOLVED * 867214593341598726295736418629185347518347269473962185134879652782651934956423871 F2: 3 => CTR * .67214539.41..372629375641862519834731..4726.47..62...1348796527.263...49.642..73 * PAIR H6: 8,9 BLK 6 I5: 8,9,5 # reduction candidate for 8,9 I5: 8,9 => SOLVED * 867214593341598726295736418629185347518347269473962185134879652782651934956423871 I5: 5 => CTR * .672145..5419..72629.75641.62.198347.19347265473562...1348796527.263...49.642..73 G6: 8,9,1 # reduction candidate for 8,9 G6: 8,9 => CTR * .672145.95419..72629.75641.62.198347.19347265473562..11348796527.263...49.642..73 G6: 1 => SOLVED * 867214593341598726295736418629185347518347269473962185134879652782651934956423871 I6: 8,9,1,5 # reduction candidate for 8,9 I6: 8,9 => CTR * .672145..5419..72629.75641.62.198347.1..4726547..621..1348796527.26.19.49.642.871 I6: 1,5 # 11 pairs * PAIR H6: 8,9 ROW 6 C6: 8,9,3,5 # reduction candidate for 8,9 C6: 8,9 => CTR * .672145...41...7262957.641.629185347513947268478362195134879652782651934956423871 C6: 3,5 # 12 pairs * PAIR H6: 8,9 COL H H1: 8,9,3 # reduction candidate for 8,9 H1: 8,9 => SOLVED * 867214593341598726295736418629185347518347269473962185134879652782651934956423871 H1: 3 => CTR * 8672145395419..7262937.641862.1..347.1..4726547..62..11348796527.26....49.642..73 H8: 8,9,3 # reduction candidate for 8,9 H8: 8,9 => CTR * 8672145395419..7262937.641862.1..347.1..4726547..62..11348796527.26....49.642..73 H8: 3 => SOLVED * 867214593341598726295736418629185347518347269473962185134879652782651934956423871 * PAIR E8: 3,5 BLK 8 F8: 3,5,1 # reduction candidate for 3,5 F8: 3,5 => CTR * 8672145395419..7262937.641862.1..347.1..4726547..629811348796527826..194956421873 F8: 1 # 12 pairs F9: 3,5,1 # reduction candidate for 3,5 F9: 3,5 # 12 pairs * PAIR E8: 3,5 COL E E2: 3,5,8,9 # reduction candidate for 3,5 E2: 3,5 => CTR * .672145..8419..7262957.641.62.198347.1..4726.47..62...1348796527.26....49.642..7. E2: 8,9 # 11 pairs E3: 3,5,8 # reduction candidate for 3,5 E3: 3,5 # 14 pairs * PAIR G9: 1,8 BLK 9 G8: 1,8,9 # reduction candidate for 1,8 G8: 1,8 => CTR * 867214539541...72629.7.641862.1..347.1894726547.3629811348796527.26...949.642..73 G8: 9 # 13 pairs I9: 1,8,3 # reduction candidate for 1,8 I9: 1,8 => SOLVED * 867214593341598726295736418629185347518347269473962185134879652782651934956423871 I9: 3 => CTR * 8672145395419..7262937.641862.1..347.1..4726547..62..11348796527.26....49.642..73 * PAIR G9: 1,8 COL G G6: 1,8,9 # reduction candidate for 1,8 G6: 9 => CTR * 867214539541...72629.7.641862.1..347.1894726547.3629811348796527.26...949.642..73 G6: 1,8 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-134-base-pr-000.dot * REASONING * PRF # A2: 3,8 => SOL * DIS # A2: 5 => CTR => A2: 3,8 * DIS # C3: 3,8 => CTR => C3: 5 * PRF # C3: 5 => SOL * PRF # I1: 3,8 => SOL * DIS # A5: 3,8 => CTR => A5: 5 * PRF # A5: 5 => SOL * PRF # E2: 5,9 => SOL * DIS # E2: 3,8 => CTR => E2: 5,9 * PRF # I1: 3,8 => SOL * DIS # C3: 3,8 => CTR => C3: 5 * PRF # C3: 5 => SOL * PRF # E3: 3,8 => SOL * DIS # E3: 5 => CTR => E3: 3,8 * DIS # I9: 3,8 => CTR => I9: 1 * PRF # I9: 1 => SOL * DIS # C5: 5,9 => CTR => C5: 3,8 * DIS # C6: 5,9 => CTR => C6: 3,8 * PRF # E4: 8 => SOL * PRF # E4: 5,8 => SOL * DIS # E4: 9 => CTR => E4: 5,8 * PRF # F2: 5,8 => SOL * DIS # F2: 3 => CTR => F2: 5,8 * PRF # I5: 8,9 => SOL * DIS # I5: 5 => CTR => I5: 8,9 * DIS # G6: 8,9 => CTR => G6: 1 * PRF # G6: 1 => SOL * DIS # I6: 8,9 => CTR => I6: 1,5 * DIS # C6: 8,9 => CTR => C6: 3,5 * PRF # H1: 8,9 => SOL * DIS # H1: 3 => CTR => H1: 8,9 * DIS # H8: 8,9 => CTR => H8: 3 * PRF # H8: 3 => SOL * DIS # F8: 3,5 => CTR => F8: 1 * DIS # E2: 3,5 => CTR => E2: 8,9 * DIS # G8: 1,8 => CTR => G8: 9 * PRF # I9: 1,8 => SOL * DIS # I9: 3 => CTR => I9: 1,8 * DIS # G6: 9 => CTR => G6: 1,8 * CNT 39 HDP CHAINS / 56 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B8,B9,C4,D2,E8,F4,G9,H6,I3) * .672145...41...72629.7.641.62.1..347.1..4726.47..62...1348796527.26....49.642..7. * PAIR A1: 3,8 BLK 1 A2: 3,8,5 # reduction candidate for 3,8 A2: 3,8 => SOLVED * 867214593341598726295736418629185347518347269473962185134879652782651934956423871 * DURATION: 0:00:02.178265 START: 07:21:24.123510 END: 07:21:26.301775 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-134-base-pr-001.dot * REASONING * PRF # A2: 3,8 => SOL * STA A2: 3,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 134 solution: 867214593341598726295736418629185347518347269473962185134879652782651934956423871 info: 1811 FNBWY S8.f 45892 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 867214593341598726295736418629185347518347269473962185134879652782651934956423871 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 # A2: 3,8 => SOL * DIS # A2: 5 => CTR => A2: 3,8 * DIS # C3: 3,8 => CTR => C3: 5 * PRF # C3: 5 => SOL * INC # H1: 3,8 => UNS * PRF # I1: 3,8 => SOL * INC # I1: 9 => UNS * DIS # A5: 3,8 => CTR => A5: 5 * PRF # A5: 5 => SOL * PRF # E2: 5,9 => SOL * DIS # E2: 3,8 => CTR => E2: 5,9 * INC # D5: 5,9 => UNS * INC # D6: 5,9 => UNS * INC # H1: 3,8 => UNS * PRF # I1: 3,8 => SOL * INC # I1: 9 => UNS * DIS # C3: 3,8 => CTR => C3: 5 * PRF # C3: 5 => SOL * PRF # E3: 3,8 => SOL * DIS # E3: 5 => CTR => E3: 3,8 * DIS # I9: 3,8 => CTR => I9: 1 * PRF # I9: 1 => SOL * DIS # C5: 5,9 => CTR => C5: 3,8 * INC # C5: 3,8 => UNS * DIS # C6: 5,9 => CTR => C6: 3,8 * INC # C6: 3,8 => UNS * INC # E4: 5,9 => UNS * PRF # E4: 8 => SOL * PRF # E4: 5,8 => SOL * DIS # E4: 9 => CTR => E4: 5,8 * PRF # F2: 5,8 => SOL * DIS # F2: 3 => CTR => F2: 5,8 * PRF # I5: 8,9 => SOL * DIS # I5: 5 => CTR => I5: 8,9 * DIS # G6: 8,9 => CTR => G6: 1 * PRF # G6: 1 => SOL * DIS # I6: 8,9 => CTR => I6: 1,5 * INC # I6: 1,5 => UNS * DIS # C6: 8,9 => CTR => C6: 3,5 * INC # C6: 3,5 => UNS * PRF # H1: 8,9 => SOL * DIS # H1: 3 => CTR => H1: 8,9 * DIS # H8: 8,9 => CTR => H8: 3 * PRF # H8: 3 => SOL * DIS # F8: 3,5 => CTR => F8: 1 * INC # F8: 1 => UNS * INC # F9: 3,5 => UNS * DIS # E2: 3,5 => CTR => E2: 8,9 * INC # E2: 8,9 => UNS * INC # E3: 3,5 => UNS * DIS # G8: 1,8 => CTR => G8: 9 * INC # G8: 9 => UNS * PRF # I9: 1,8 => SOL * DIS # I9: 3 => CTR => I9: 1,8 * INC # G6: 1,8 => UNS * DIS # G6: 9 => CTR => G6: 1,8 * CNT 56 HDP CHAINS / 56 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A2: 3,8 => SOL * STA A2: 3,8 * CNT 1 HDP CHAINS / 1 HYP OPENED