Analysis of xx-top500-014-base.sdk
Contents
Original Sudoku
level: medium
position: ....85...9.....3......4.....81....4....2...7.........82..9..6........5.3.4....... initial
Autosolve
position: ....854699547..3818...49752.8159.2464..2.8.75...4...382.895.614...8.45.3.4.6..8.7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 1,3 => CTR => B1: 2,7 * DIS # E6: 1,6 => CTR => E6: 7 * DIS # E9: 1,2 => CTR => E9: 3 * CNT 3 HDP CHAINS / 19 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 1,3 => CTR => B1: 2,7 * DIS B1: 2,7 # A1: 7 => CTR => A1: 1,3 * DIS B1: 2,7 + A1: 1,3 # E6: 1,6 => CTR => E6: 7 * PRF B1: 2,7 + A1: 1,3 + E6: 7 # B6: 6,9 => SOL * STA B1: 2,7 + A1: 1,3 + E6: 7 + B6: 6,9 * CNT 4 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....85...9.....3......4.....81....4....2...7.........82..9..6........5.3.4....... | initial |
| ....854699547..3818...49752.8159.2464..2.8.75...4...382.895.614...8.45.3.4.6..8.7 | autosolve |
| 327185469954726381816349752781593246493268175562471938238957614679814523145632897 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) C3: 3,6 D1: 1,3 E2: 2,6 F2: 2,6 D3: 1,3 A4: 3,7 F4: 3,7 F6: 1,6 G5: 1,9 G6: 1,9 B7: 3,7 F7: 3,7 F9: 1,2 H8: 2,9 H9: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,D3: 1.. / D1 = 1 => 18 pairs (_) / D3 = 1 => 16 pairs (_) G5,G6: 1.. / G5 = 1 => 14 pairs (_) / G6 = 1 => 0 pairs (X) B3,D3: 1.. / B3 = 1 => 18 pairs (_) / D3 = 1 => 16 pairs (_) E5,G5: 1.. / E5 = 1 => 0 pairs (X) / G5 = 1 => 14 pairs (_) F6,F9: 1.. / F6 = 1 => 12 pairs (_) / F9 = 1 => 23 pairs (_) B1,C1: 2.. / B1 = 2 => 17 pairs (_) / C1 = 2 => 15 pairs (_) E2,F2: 2.. / E2 = 2 => 12 pairs (_) / F2 = 2 => 23 pairs (_) B6,C6: 2.. / B6 = 2 => 15 pairs (_) / C6 = 2 => 17 pairs (_) H8,H9: 2.. / H8 = 2 => 15 pairs (_) / H9 = 2 => 0 pairs (X) E8,H8: 2.. / E8 = 2 => 0 pairs (X) / H8 = 2 => 15 pairs (_) B1,B6: 2.. / B1 = 2 => 17 pairs (_) / B6 = 2 => 15 pairs (_) C1,C6: 2.. / C1 = 2 => 15 pairs (_) / C6 = 2 => 17 pairs (_) F2,F9: 2.. / F2 = 2 => 23 pairs (_) / F9 = 2 => 12 pairs (_) D1,D3: 3.. / D1 = 3 => 16 pairs (_) / D3 = 3 => 18 pairs (_) F4,E5: 3.. / F4 = 3 => 18 pairs (_) / E5 = 3 => 0 pairs (X) F7,E9: 3.. / F7 = 3 => 0 pairs (X) / E9 = 3 => 18 pairs (_) A4,F4: 3.. / A4 = 3 => 0 pairs (X) / F4 = 3 => 18 pairs (_) B7,F7: 3.. / B7 = 3 => 18 pairs (_) / F7 = 3 => 0 pairs (X) E5,E9: 3.. / E5 = 3 => 0 pairs (X) / E9 = 3 => 18 pairs (_) F4,F7: 3.. / F4 = 3 => 18 pairs (_) / F7 = 3 => 0 pairs (X) A6,C6: 5.. / A6 = 5 => 16 pairs (_) / C6 = 5 => 0 pairs (X) A9,C9: 5.. / A9 = 5 => 0 pairs (X) / C9 = 5 => 16 pairs (_) A6,A9: 5.. / A6 = 5 => 16 pairs (_) / A9 = 5 => 0 pairs (X) C6,C9: 5.. / C6 = 5 => 0 pairs (X) / C9 = 5 => 16 pairs (_) B3,C3: 6.. / B3 = 6 => 17 pairs (_) / C3 = 6 => 17 pairs (_) E2,F2: 6.. / E2 = 6 => 23 pairs (_) / F2 = 6 => 12 pairs (_) A6,A8: 6.. / A6 = 6 => 0 pairs (X) / A8 = 6 => 17 pairs (_) F2,F6: 6.. / F2 = 6 => 12 pairs (_) / F6 = 6 => 23 pairs (_) F4,E6: 7.. / F4 = 7 => 0 pairs (X) / E6 = 7 => 18 pairs (_) F7,E8: 7.. / F7 = 7 => 18 pairs (_) / E8 = 7 => 0 pairs (X) A4,F4: 7.. / A4 = 7 => 18 pairs (_) / F4 = 7 => 0 pairs (X) B7,F7: 7.. / B7 = 7 => 0 pairs (X) / F7 = 7 => 18 pairs (_) E6,E8: 7.. / E6 = 7 => 18 pairs (_) / E8 = 7 => 0 pairs (X) F4,F7: 7.. / F4 = 7 => 0 pairs (X) / F7 = 7 => 18 pairs (_) G5,G6: 9.. / G5 = 9 => 0 pairs (X) / G6 = 9 => 14 pairs (_) H8,H9: 9.. / H8 = 9 => 0 pairs (X) / H9 = 9 => 15 pairs (_) C9,H9: 9.. / C9 = 9 => 0 pairs (X) / H9 = 9 => 15 pairs (_) * DURATION: 0:01:03.261360 START: 03:04:06.440776 END: 03:05:09.702136 2017-05-04 * CP COUNT: (37) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B7,C3,D1,D3,E2,F2,F4,F6,F7,F9,G5,G6,H8,H9) * ....854699547..3818...49752.8159.2464..2.8.75...4...382.895.614...8.45.3.4.6..8.7 * PAIR C3: 3,6 BLK 1 B3: 3,6,1 # reduction candidate for 3,6 B3: 1 # 18 pairs B3: 3,6 # 16 pairs * PAIR C3: 3,6 COL C C5: 3,6,9 # reduction candidate for 3,6 C5: 9 # 20 pairs C5: 3,6 # 19 pairs * PAIR D1: 1,3 ROW 1 A1: 1,3,7 # reduction candidate for 1,3 A1: 1,3 # 18 pairs B1: 1,3,2,7 # reduction candidate for 1,3 B1: 1,3 => CTR * 7.2.854699547..3818...497523815972464..238175.274..93827895.614...8.45.3.4.6..8.7 B1: 2,7 # 16 pairs * PAIR D3: 1,3 ROW 3 B3: 1,3,6 # reduction candidate for 1,3 B3: 6 # 17 pairs B3: 1,3 # 17 pairs * PAIR A4: 3,7 COL A A1: 3,7,1 # reduction candidate for 3,7 A1: 1 # 23 pairs A1: 3,7 # 19 pairs * PAIR F6: 1,6 BLK 5 E5: 1,6,3 # reduction candidate for 1,6 E5: 1,6 # 18 pairs E6: 1,6,7 # reduction candidate for 1,6 E6: 1,6 => CTR * ....854699547..3818.6.49752381597246469238175...4..938278953614...874523.436..897 E6: 7 # 18 pairs * PAIR B7: 3,7 COL B B1: 3,7,1,2 # reduction candidate for 3,7 B1: 3,7 # 18 pairs B1: 1,2 # 16 pairs * PAIR F9: 1,2 BLK 8 E8: 1,2,7 # reduction candidate for 1,2 E8: 1,2 # 18 pairs E9: 1,2,3 # reduction candidate for 1,2 E9: 1,2 => CTR * ....854699547..3818.6.49752381597246469238175...4..938278953614...874523.436..897 E9: 3 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-014-base-pr-000.dot * REASONING * DIS # B1: 1,3 => CTR => B1: 2,7 * DIS # E6: 1,6 => CTR => E6: 7 * DIS # E9: 1,2 => CTR => E9: 3 * CNT 3 HDP CHAINS / 19 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B7,C3,D1,D3,E2,F2,F4,F6,F7,F9,G5,G6,H8,H9) * ....854699547..3818...49752.8159.2464..2.8.75...4...382.895.614...8.45.3.4.6..8.7 * PAIR C3: 3,6 BLK 1 B3: 3,6,1 # reduction candidate for 3,6 B3: 1 # 18 pairs B3: 3,6 # 16 pairs * PAIR C3: 3,6 COL C C5: 3,6,9 # reduction candidate for 3,6 C5: 9 # 20 pairs C5: 3,6 # 19 pairs * PAIR D1: 1,3 ROW 1 A1: 1,3,7 # reduction candidate for 1,3 A1: 1,3 # 18 pairs B1: 1,3,2,7 # reduction candidate for 1,3 B1: 1,3 => CTR * 7.2.854699547..3818...497523815972464..238175.274..93827895.614...8.45.3.4.6..8.7 * RESTART * PAIR D1: 1,3 ROW 1 A1: 1,3,7 # reduction candidate for 1,3 A1: 7 => CTR * 7231854699547..3818163497523815972464.9238175..24..9382.895.614...8.45.3.4.6..8.7 * PAIR RESTART * PAIR D3: 1,3 ROW 3 B3: 1,3,6 # reduction candidate for 1,3 B3: 6 # 23 pairs B3: 1,3 # 20 pairs * PAIR F6: 1,6 BLK 5 E5: 1,6,3 # reduction candidate for 1,6 E5: 1,6 # 18 pairs E6: 1,6,7 # reduction candidate for 1,6 E6: 1,6 => CTR * .27.854699547..38183614975238159724646.238175...4..938278953614...874523.4.6..897 * RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A6,A8,A9,B1,B5,C1,C8,C9,E2,E5,E8,F2,F6,F9,G5,G6,H8,H9) * 3..1854699547..3818163497527815932464.32.8.75...47..38238957614...8.45.3.4.63.8.7 * PAIR B5: 6,9 BLK 4 B6: 6,9,2 # reduction candidate for 6,9 B6: 6,9 => SOLVED * 327185469954726381816349752781593246493268175562471938238957614679814523145632897 * DURATION: 0:00:13.845308 START: 03:05:27.718802 END: 03:05:41.564110 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-014-base-pr-001.dot * REASONING * DIS # B1: 1,3 => CTR => B1: 2,7 * DIS B1: 2,7 # A1: 7 => CTR => A1: 1,3 * DIS B1: 2,7 + A1: 1,3 # E6: 1,6 => CTR => E6: 7 * PRF B1: 2,7 + A1: 1,3 + E6: 7 # B6: 6,9 => SOL * STA B1: 2,7 + A1: 1,3 + E6: 7 + B6: 6,9 * CNT 4 HDP CHAINS / 13 HYP OPENED
Header Info
Top 500 Minimum 17 014 solution: 327185469954726381816349752781593246493268175562471938238957614679814523145632897 info: 1310 FNBTWXY S8.f 6482 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 327185469954726381816349752781593246493268175562471938238957614679814523145632897 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:
* INC # B3: 3,6 => UNS * INC # B3: 1 => UNS * INC # C5: 3,6 => UNS * INC # C5: 9 => UNS * INC # A1: 1,3 => UNS * DIS # B1: 1,3 => CTR => B1: 2,7 * INC # B1: 2,7 => UNS * INC # B3: 1,3 => UNS * INC # B3: 6 => UNS * INC # A1: 3,7 => UNS * INC # A1: 1 => UNS * INC # E5: 1,6 => UNS * DIS # E6: 1,6 => CTR => E6: 7 * INC # E6: 7 => UNS * INC # B1: 3,7 => UNS * INC # B1: 1,2 => UNS * INC # E8: 1,2 => UNS * DIS # E9: 1,2 => CTR => E9: 3 * INC # E9: 3 => UNS * CNT 19 HDP CHAINS / 19 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B3: 3,6 => UNS * INC # B3: 1 => UNS * INC # C5: 3,6 => UNS * INC # C5: 9 => UNS * INC # A1: 1,3 => UNS * DIS # B1: 1,3 => CTR => B1: 2,7 * INC B1: 2,7 # A1: 1,3 => UNS * DIS B1: 2,7 # A1: 7 => CTR => A1: 1,3 * INC B1: 2,7 + A1: 1,3 # B3: 1,3 => UNS * INC B1: 2,7 + A1: 1,3 # B3: 6 => UNS * INC B1: 2,7 + A1: 1,3 # E5: 1,6 => UNS * DIS B1: 2,7 + A1: 1,3 # E6: 1,6 => CTR => E6: 7 * PRF B1: 2,7 + A1: 1,3 + E6: 7 # B6: 6,9 => SOL * STA B1: 2,7 + A1: 1,3 + E6: 7 + B6: 6,9 * CNT 13 HDP CHAINS / 13 HYP OPENED