Analysis of xx-top500-064-base.sdk
Contents
Original Sudoku
level: medium
position: 16..4.......5..8.2.........2.83..........9.4...5.......4.....6....2..5..7........ initial
Autosolve
position: 162.48.53..45.68.285..324.62.83546.....829.454.56...2854..83267.8.2..534723465.8. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B5: 3,7 => CTR => B5: 1 * PRF # D3: 7,9 => SOL * DIS # D3: 1 => CTR => D3: 7,9 * DIS # H3: 7,9 => CTR => H3: 1 * PRF # H3: 1 => SOL * PRF # D3: 7,9 => SOL * DIS # D3: 1 => CTR => D3: 7,9 * PRF # D3: 1,9 => SOL * DIS # D3: 7 => CTR => D3: 1,9 * DIS # H2: 1,9 => CTR => H2: 7 * PRF # H2: 7 => SOL * DIS # E8: 7 => CTR => E8: 1,9 * PRF # H2: 7,9 => SOL * DIS # H2: 1 => CTR => H2: 7,9 * DIS # H3: 7,9 => CTR => H3: 1 * PRF # H3: 1 => SOL * DIS # E8: 1,7 => CTR => E8: 9 * PRF # E8: 9 => SOL * DIS # B4: 1 => CTR => B4: 7,9 * PRF # H2: 7,9 => SOL * DIS # H2: 1 => CTR => H2: 7,9 * DIS # H3: 7,9 => CTR => H3: 1 * PRF # H3: 1 => SOL * DIS # B4: 1,9 => CTR => B4: 7 * PRF # B4: 7 => SOL * PRF # C8: 1,9 => SOL * DIS # C8: 6 => CTR => C8: 1,9 * DIS # C8: 6,9 => CTR => C8: 1 * PRF # C8: 1 => SOL * DIS # E8: 7 => CTR => E8: 1,9 * PRF # D3: 1,9 => SOL * DIS # D3: 7 => CTR => D3: 1,9 * DIS # E8: 1,7 => CTR => E8: 9 * PRF # E8: 9 => SOL * CNT 34 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B5: 3,7 => CTR => B5: 1 * PRF B5: 1 # D3: 7,9 => SOL * STA B5: 1 + D3: 7,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 16..4.......5..8.2.........2.83..........9.4...5.......4.....6....2..5..7........ | initial |
| 162.48.53..45.68.285..324.62.83546.....829.454.56...2854..83267.8.2..534723465.8. | autosolve |
| 162748953934516872857932416278354691316829745495671328549183267681297534723465189 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) A2: 3,9 B2: 3,7 C3: 7,9 D1: 7,9 E2: 1,9 G1: 7,9 A5: 3,6 C5: 6,7 B6: 3,9 E6: 1,7 F6: 1,7 H4: 7,9 I4: 1,9 G6: 3,9 C7: 1,9 A8: 6,9 D7: 1,9 F8: 1,7 G9: 1,9 I9: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,D3: 1.. / E2 = 1 => 0 pairs (*) / D3 = 1 => 0 pairs (X) H2,H3: 1.. / H2 = 1 => 0 pairs (X) / H3 = 1 => 0 pairs (_) B4,B5: 1.. / B4 = 1 => 0 pairs (X) / B5 = 1 => 19 pairs (_) E6,F6: 1.. / E6 = 1 => 0 pairs (X) / F6 = 1 => 18 pairs (_) I4,G5: 1.. / I4 = 1 => 19 pairs (_) / G5 = 1 => 0 pairs (X) C7,C8: 1.. / C7 = 1 => 0 pairs (X) / C8 = 1 => 0 pairs (_) G9,I9: 1.. / G9 = 1 => 19 pairs (_) / I9 = 1 => 0 pairs (X) E2,H2: 1.. / E2 = 1 => 0 pairs (*) / H2 = 1 => 0 pairs (X) D3,H3: 1.. / D3 = 1 => 0 pairs (X) / H3 = 1 => 0 pairs (_) B4,I4: 1.. / B4 = 1 => 0 pairs (X) / I4 = 1 => 19 pairs (_) B5,G5: 1.. / B5 = 1 => 19 pairs (_) / G5 = 1 => 0 pairs (X) C7,D7: 1.. / C7 = 1 => 0 pairs (X) / D7 = 1 => 0 pairs (_) D3,D7: 1.. / D3 = 1 => 0 pairs (X) / D7 = 1 => 0 pairs (_) F6,F8: 1.. / F6 = 1 => 18 pairs (_) / F8 = 1 => 0 pairs (X) G5,G9: 1.. / G5 = 1 => 0 pairs (X) / G9 = 1 => 19 pairs (_) I4,I9: 1.. / I4 = 1 => 19 pairs (_) / I9 = 1 => 0 pairs (X) A2,B2: 3.. / A2 = 3 => 0 pairs (X) / B2 = 3 => 0 pairs (_) G5,G6: 3.. / G5 = 3 => 0 pairs (X) / G6 = 3 => 20 pairs (_) B6,G6: 3.. / B6 = 3 => 0 pairs (X) / G6 = 3 => 20 pairs (_) A2,A5: 3.. / A2 = 3 => 0 pairs (X) / A5 = 3 => 0 pairs (_) A5,C5: 6.. / A5 = 6 => 0 pairs (X) / C5 = 6 => 0 pairs (_) A8,C8: 6.. / A8 = 6 => 0 pairs (*) / C8 = 6 => 0 pairs (X) A5,A8: 6.. / A5 = 6 => 0 pairs (X) / A8 = 6 => 0 pairs (_) C5,C8: 6.. / C5 = 6 => 0 pairs (*) / C8 = 6 => 0 pairs (X) B2,C3: 7.. / B2 = 7 => 0 pairs (X) / C3 = 7 => 0 pairs (_) D1,D3: 7.. / D1 = 7 => 0 pairs (*) / D3 = 7 => 0 pairs (X) E6,F6: 7.. / E6 = 7 => 18 pairs (_) / F6 = 7 => 0 pairs (X) H4,G5: 7.. / H4 = 7 => 0 pairs (X) / G5 = 7 => 0 pairs (_) E8,F8: 7.. / E8 = 7 => 0 pairs (X) / F8 = 7 => 18 pairs (_) D1,G1: 7.. / D1 = 7 => 0 pairs (*) / G1 = 7 => 0 pairs (X) B2,H2: 7.. / B2 = 7 => 0 pairs (X) / H2 = 7 => 0 pairs (_) B4,H4: 7.. / B4 = 7 => 0 pairs (*) / H4 = 7 => 0 pairs (X) C3,C5: 7.. / C3 = 7 => 0 pairs (*) / C5 = 7 => 0 pairs (X) E6,E8: 7.. / E6 = 7 => 18 pairs (_) / E8 = 7 => 0 pairs (X) F6,F8: 7.. / F6 = 7 => 0 pairs (X) / F8 = 7 => 18 pairs (_) G1,G5: 7.. / G1 = 7 => 0 pairs (X) / G5 = 7 => 0 pairs (_) A2,C3: 9.. / A2 = 9 => 0 pairs (*) / C3 = 9 => 0 pairs (X) B4,B6: 9.. / B4 = 9 => 0 pairs (X) / B6 = 9 => 20 pairs (_) D7,E8: 9.. / D7 = 9 => 0 pairs (X) / E8 = 9 => 0 pairs (_) G9,I9: 9.. / G9 = 9 => 0 pairs (X) / I9 = 9 => 19 pairs (_) D1,G1: 9.. / D1 = 9 => 0 pairs (X) / G1 = 9 => 0 pairs (_) B6,G6: 9.. / B6 = 9 => 20 pairs (_) / G6 = 9 => 0 pairs (X) C7,D7: 9.. / C7 = 9 => 0 pairs (*) / D7 = 9 => 0 pairs (X) A2,A8: 9.. / A2 = 9 => 0 pairs (*) / A8 = 9 => 0 pairs (X) E2,E8: 9.. / E2 = 9 => 0 pairs (X) / E8 = 9 => 0 pairs (_) I4,I9: 9.. / I4 = 9 => 0 pairs (X) / I9 = 9 => 19 pairs (_) * DURATION: 0:01:59.527237 START: 04:48:29.235561 END: 04:50:28.762798 2017-05-04 * CP COUNT: (46) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,A8,B2,B6,C3,C5,C7,D1,D7,E2,E6,F6,F8,G1,G6,G9,H4,I4,I9) * 162.48.53..45.68.285..324.62.83546.....829.454.56...2854..83267.8.2..534723465.8. * PAIR B2: 3,7 COL B B5: 3,7,1 # reduction candidate for 3,7 B5: 3,7 => CTR * 162948753.74516892859732416218354679.37829145495671328541.83267.8.2..534723465981 B5: 1 # 19 pairs * PAIR C3: 7,9 ROW 3 D3: 7,9,1 # reduction candidate for 7,9 D3: 7,9 => SOLVED * 162748953934516872857932416278354691316829745495671328549183267681297534723465189 D3: 1 => CTR * 162748953..4596812859132476278354691.168297454956..328541.83267.8.2..534723465.8. H3: 7,9,1 # reduction candidate for 7,9 H3: 7,9 => CTR * 162748953.745968128591324762.83546.....829.454.56...28541983267.8.2..534723465.8. H3: 1 => SOLVED * 162748953934516872857932416278354691316829745495671328549183267681297534723465189 * PAIR D1: 7,9 BLK 2 D3: 7,9,1 # reduction candidate for 7,9 D3: 7,9 => SOLVED * 162748953934516872857932416278354691316829745495671328549183267681297534723465189 D3: 1 => CTR * 162748953..4596812859132476278354691.168297454956..328541.83267.8.2..534723465.8. * PAIR E2: 1,9 BLK 2 D3: 1,9,7 # reduction candidate for 1,9 D3: 1,9 => SOLVED * 162748953934516872857932416278354691316829745495671328549183267681297534723465189 D3: 7 => CTR * 162.48.53..45168.285.7324162.83546....7829.454.5671.2854.183267.8.2..534723465.8. * PAIR E2: 1,9 ROW 2 H2: 1,9,7 # reduction candidate for 1,9 H2: 1,9 => CTR * 162.48.53.745.68.2859.324.62.835467...7829.454.56...28541983267.8.2..534723465.8. H2: 7 => SOLVED * 162748953934516872857932416278354691316829745495671328549183267681297534723465189 * PAIR E2: 1,9 COL E E8: 1,9,7 # reduction candidate for 1,9 E8: 7 => CTR * 162.48.53..4596812859132476278354691.16829745495617328541.83267.8.2..534723465.8. E8: 1,9 # 18 pairs * PAIR G1: 7,9 BLK 3 H2: 7,9,1 # reduction candidate for 7,9 H2: 7,9 => SOLVED * 162748953934516872857932416278354691316829745495671328549183267681297534723465189 H2: 1 => CTR * 162.48.53.745.68128591324762.83546.....829.454.56...2854..83267.8.2..534723465.8. H3: 7,9,1 # reduction candidate for 7,9 H3: 7,9 => CTR * 162748953.745968128591324762.83546.....829.454.56...28541983267.8.2..534723465.8. H3: 1 => SOLVED * 162748953934516872857932416278354691316829745495671328549183267681297534723465189 * PAIR E6: 1,7 COL E E8: 1,7,9 # reduction candidate for 1,7 E8: 1,7 => CTR * 162.48.53..4596812859132476278354691.168297454956..328541.83267.8.2..534723465.8. E8: 9 => SOLVED * 162748953934516872857932416278354691316829745495671328549183267681297534723465189 * PAIR H4: 7,9 ROW 4 B4: 7,9,1 # reduction candidate for 7,9 B4: 1 => CTR * 162948753.74516892859732416218354679.37829145495671328541.83267.8.2..534723465981 B4: 7,9 # 19 pairs * PAIR H4: 7,9 COL H H2: 7,9,1 # reduction candidate for 7,9 H2: 7,9 => SOLVED * 162748953934516872857932416278354691316829745495671328549183267681297534723465189 H2: 1 => CTR * 162.48.53.745.68128591324762.83546.....829.454.56...2854..83267.8.2..534723465.8. H3: 7,9,1 # reduction candidate for 7,9 H3: 7,9 => CTR * 162748953.745968128591324762.83546.....829.454.56...28541983267.8.2..534723465.8. H3: 1 => SOLVED * 162748953934516872857932416278354691316829745495671328549183267681297534723465189 * PAIR I4: 1,9 ROW 4 B4: 1,9,7 # reduction candidate for 1,9 B4: 1,9 => CTR * 162.48753.745.68.28597324162.835467...7829.454.56...28541.83267.8.2..534723465.8. B4: 7 => SOLVED * 162748953934516872857932416278354691316829745495671328549183267681297534723465189 * PAIR C7: 1,9 BLK 7 C8: 1,9,6 # reduction candidate for 1,9 C8: 1,9 => SOLVED * 162748953934516872857932416278354691316829745495671328549183267681297534723465189 C8: 6 => CTR * 16274895337459681285..324.62.83546.....829.454.56...285419832679862..534723465.8. * PAIR A8: 6,9 BLK 7 C8: 6,9,1 # reduction candidate for 6,9 C8: 6,9 => CTR * 162748953..4596812859132476278354691.16829.454.56...28541983267.8.2..534723465.8. C8: 1 => SOLVED * 162748953934516872857932416278354691316829745495671328549183267681297534723465189 * PAIR D7: 1,9 BLK 8 E8: 1,9,7 # reduction candidate for 1,9 E8: 7 => CTR * 162.48.53..4596812859132476278354691.16829745495617328541.83267.8.2..534723465.8. E8: 1,9 # 18 pairs * PAIR D7: 1,9 COL D D3: 1,9,7 # reduction candidate for 1,9 D3: 1,9 => SOLVED * 162748953934516872857932416278354691316829745495671328549183267681297534723465189 D3: 7 => CTR * 162.48.53..45168.285.7324162.83546....7829.454.5671.2854.183267.8.2..534723465.8. * PAIR F8: 1,7 BLK 8 E8: 1,7,9 # reduction candidate for 1,7 E8: 1,7 => CTR * 162.48.53..4596812859132476278354691.168297454956..328541.83267.8.2..534723465.8. E8: 9 => SOLVED * 162748953934516872857932416278354691316829745495671328549183267681297534723465189 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-064-base-pr-000.dot * REASONING * DIS # B5: 3,7 => CTR => B5: 1 * PRF # D3: 7,9 => SOL * DIS # D3: 1 => CTR => D3: 7,9 * DIS # H3: 7,9 => CTR => H3: 1 * PRF # H3: 1 => SOL * PRF # D3: 7,9 => SOL * DIS # D3: 1 => CTR => D3: 7,9 * PRF # D3: 1,9 => SOL * DIS # D3: 7 => CTR => D3: 1,9 * DIS # H2: 1,9 => CTR => H2: 7 * PRF # H2: 7 => SOL * DIS # E8: 7 => CTR => E8: 1,9 * PRF # H2: 7,9 => SOL * DIS # H2: 1 => CTR => H2: 7,9 * DIS # H3: 7,9 => CTR => H3: 1 * PRF # H3: 1 => SOL * DIS # E8: 1,7 => CTR => E8: 9 * PRF # E8: 9 => SOL * DIS # B4: 1 => CTR => B4: 7,9 * PRF # H2: 7,9 => SOL * DIS # H2: 1 => CTR => H2: 7,9 * DIS # H3: 7,9 => CTR => H3: 1 * PRF # H3: 1 => SOL * DIS # B4: 1,9 => CTR => B4: 7 * PRF # B4: 7 => SOL * PRF # C8: 1,9 => SOL * DIS # C8: 6 => CTR => C8: 1,9 * DIS # C8: 6,9 => CTR => C8: 1 * PRF # C8: 1 => SOL * DIS # E8: 7 => CTR => E8: 1,9 * PRF # D3: 1,9 => SOL * DIS # D3: 7 => CTR => D3: 1,9 * DIS # E8: 1,7 => CTR => E8: 9 * PRF # E8: 9 => SOL * CNT 34 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,A8,B2,B6,C3,C5,C7,D1,D7,E2,E6,F6,F8,G1,G6,G9,H4,I4,I9) * 162.48.53..45.68.285..324.62.83546.....829.454.56...2854..83267.8.2..534723465.8. * PAIR B2: 3,7 COL B B5: 3,7,1 # reduction candidate for 3,7 B5: 3,7 => CTR * 162948753.74516892859732416218354679.37829145495671328541.83267.8.2..534723465981 * PAIR RESTART * PAIR C3: 7,9 ROW 3 D3: 7,9,1 # reduction candidate for 7,9 D3: 7,9 => SOLVED * 162748953934516872857932416278354691316829745495671328549183267681297534723465189 * DURATION: 0:00:06.274717 START: 04:51:28.638002 END: 04:51:34.912719 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-064-base-pr-001.dot * REASONING * DIS # B5: 3,7 => CTR => B5: 1 * PRF B5: 1 # D3: 7,9 => SOL * STA B5: 1 + D3: 7,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 064 solution: 162748953934516872857932416278354691316829745495671328549183267681297534723465189 info: 1440 FNBHWY S8.f 26529 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 162748953934516872857932416278354691316829745495671328549183267681297534723465189 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 # B5: 3,7 => CTR => B5: 1 * INC # B5: 1 => UNS * PRF # D3: 7,9 => SOL * DIS # D3: 1 => CTR => D3: 7,9 * DIS # H3: 7,9 => CTR => H3: 1 * PRF # H3: 1 => SOL * PRF # D3: 7,9 => SOL * DIS # D3: 1 => CTR => D3: 7,9 * PRF # D3: 1,9 => SOL * DIS # D3: 7 => CTR => D3: 1,9 * DIS # H2: 1,9 => CTR => H2: 7 * PRF # H2: 7 => SOL * INC # E8: 1,9 => UNS * DIS # E8: 7 => CTR => E8: 1,9 * PRF # H2: 7,9 => SOL * DIS # H2: 1 => CTR => H2: 7,9 * DIS # H3: 7,9 => CTR => H3: 1 * PRF # H3: 1 => SOL * DIS # E8: 1,7 => CTR => E8: 9 * PRF # E8: 9 => SOL * INC # B4: 7,9 => UNS * DIS # B4: 1 => CTR => B4: 7,9 * PRF # H2: 7,9 => SOL * DIS # H2: 1 => CTR => H2: 7,9 * DIS # H3: 7,9 => CTR => H3: 1 * PRF # H3: 1 => SOL * DIS # B4: 1,9 => CTR => B4: 7 * PRF # B4: 7 => SOL * PRF # C8: 1,9 => SOL * DIS # C8: 6 => CTR => C8: 1,9 * DIS # C8: 6,9 => CTR => C8: 1 * PRF # C8: 1 => SOL * INC # E8: 1,9 => UNS * DIS # E8: 7 => CTR => E8: 1,9 * PRF # D3: 1,9 => SOL * DIS # D3: 7 => CTR => D3: 1,9 * DIS # E8: 1,7 => CTR => E8: 9 * PRF # E8: 9 => SOL * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B5: 3,7 => CTR => B5: 1 * PRF B5: 1 # D3: 7,9 => SOL * STA B5: 1 + D3: 7,9 * CNT 2 HDP CHAINS / 2 HYP OPENED