Analysis of xx-top500-015-base.sdk
Contents
Original Sudoku
level: medium
position: .358.........2.7...........4...7...17......6........5.28....4.....3.5......6..... initial
Autosolve
position: .35867.4.6..52.7838...345.6458.763.17...5386436.4.8.572867..435...3.56..5.36.2... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # G1: 1,9 => SOL * DIS # G1: 2 => CTR => G1: 1,9 * PRF # D5: 1,9 => SOL * DIS # D5: 2 => CTR => D5: 1,9 * PRF # G1: 2,9 => SOL * DIS # G1: 1 => CTR => G1: 2,9 * PRF # I8: 8 => SOL * PRF # G1: 1,9 => SOL * DIS # G1: 2 => CTR => G1: 1,9 * DIS # H8: 1,9 => CTR => H8: 2,7 * DIS # H9: 1,9 => CTR => H9: 7 * DIS # D5: 2,9 => CTR => D5: 1 * PRF # D5: 1 => SOL * PRF # D5: 1,9 => SOL * DIS # D5: 2 => CTR => D5: 1,9 * PRF # C6: 1,9 => SOL * DIS # C6: 2 => CTR => C6: 1,9 * PRF # H8: 2,9 => SOL * DIS # H8: 1,7 => CTR => H8: 2,9 * DIS # C6: 2,9 => CTR => C6: 1 * PRF # C6: 1 => SOL * PRF # G1: 2,9 => SOL * DIS # G1: 1 => CTR => G1: 2,9 * DIS # H8: 1,9 => CTR => H8: 2,7 * DIS # H8: 1,9 => CTR => H8: 2,7 * DIS # H9: 1,9 => CTR => H9: 7 * PRF # G1: 1,9 => SOL * DIS # G1: 2 => CTR => G1: 1,9 * PRF # I8: 8,9 => SOL * DIS # I8: 2 => CTR => I8: 8,9 * CNT 30 HDP CHAINS / 45 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # G1: 1,9 => SOL * STA G1: 1,9 * CNT 1 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .358.........2.7...........4...7...17......6........5.28....4.....3.5......6..... | initial |
| .35867.4.6..52.7838...345.6458.763.17...5386436.4.8.572867..435...3.56..5.36.2... | autosolve |
| 135867942694521783872934516458276391729153864361498257286719435917345628543682179 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) A1: 1,9 B3: 2,7 C3: 2,7 F2: 1,9 D3: 1,9 I1: 2,9 H3: 1,9 D4: 2,9 E6: 1,9 H4: 2,9 G6: 2,9 A8: 1,9 E7: 1,9 F7: 1,9 E8: 4,8 E9: 4,8 G9: 1,9 I9: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F2,D3: 1.. / F2 = 1 => 0 pairs (*) / D3 = 1 => 0 pairs (X) G1,H3: 1.. / G1 = 1 => 0 pairs (X) / H3 = 1 => 0 pairs (_) D5,E6: 1.. / D5 = 1 => 0 pairs (*) / E6 = 1 => 0 pairs (X) E7,F7: 1.. / E7 = 1 => 0 pairs (*) / F7 = 1 => 0 pairs (X) A1,G1: 1.. / A1 = 1 => 0 pairs (*) / G1 = 1 => 0 pairs (X) D3,H3: 1.. / D3 = 1 => 0 pairs (X) / H3 = 1 => 0 pairs (_) C6,E6: 1.. / C6 = 1 => 0 pairs (*) / E6 = 1 => 0 pairs (X) A1,A8: 1.. / A1 = 1 => 0 pairs (*) / A8 = 1 => 0 pairs (X) D3,D5: 1.. / D3 = 1 => 0 pairs (X) / D5 = 1 => 0 pairs (_) E6,E7: 1.. / E6 = 1 => 0 pairs (X) / E7 = 1 => 0 pairs (_) F2,F7: 1.. / F2 = 1 => 0 pairs (*) / F7 = 1 => 0 pairs (X) G1,G9: 1.. / G1 = 1 => 0 pairs (X) / G9 = 1 => 0 pairs (_) B3,C3: 2.. / B3 = 2 => 17 pairs (_) / C3 = 2 => 0 pairs (*) G1,I1: 2.. / G1 = 2 => 0 pairs (X) / I1 = 2 => 0 pairs (_) D4,D5: 2.. / D4 = 2 => 0 pairs (*) / D5 = 2 => 0 pairs (X) H4,G6: 2.. / H4 = 2 => 0 pairs (X) / G6 = 2 => 0 pairs (_) H8,I8: 2.. / H8 = 2 => 0 pairs (*) / I8 = 2 => 0 pairs (X) D4,H4: 2.. / D4 = 2 => 0 pairs (*) / H4 = 2 => 0 pairs (X) C6,G6: 2.. / C6 = 2 => 0 pairs (X) / G6 = 2 => 0 pairs (_) B3,B5: 2.. / B3 = 2 => 17 pairs (_) / B5 = 2 => 0 pairs (*) G1,G6: 2.. / G1 = 2 => 0 pairs (X) / G6 = 2 => 0 pairs (_) H4,H8: 2.. / H4 = 2 => 0 pairs (X) / H8 = 2 => 0 pairs (_) I1,I8: 2.. / I1 = 2 => 0 pairs (*) / I8 = 2 => 0 pairs (X) B2,C2: 4.. / B2 = 4 => 16 pairs (_) / C2 = 4 => 19 pairs (_) E8,E9: 4.. / E8 = 4 => 0 pairs (*) / E9 = 4 => 0 pairs (X) B9,E9: 4.. / B9 = 4 => 0 pairs (*) / E9 = 4 => 0 pairs (X) C2,C8: 4.. / C2 = 4 => 19 pairs (_) / C8 = 4 => 16 pairs (_) B3,C3: 7.. / B3 = 7 => 0 pairs (*) / C3 = 7 => 0 pairs (X) H8,H9: 7.. / H8 = 7 => 0 pairs (X) / H9 = 7 => 18 pairs (_) B9,H9: 7.. / B9 = 7 => 0 pairs (X) / H9 = 7 => 18 pairs (_) C3,C8: 7.. / C3 = 7 => 17 pairs (_) / C8 = 7 => 0 pairs (*) E8,E9: 8.. / E8 = 8 => 16 pairs (_) / E9 = 8 => 0 pairs (*) I8,I9: 8.. / I8 = 8 => 0 pairs (*) / I9 = 8 => 0 pairs (X) E8,I8: 8.. / E8 = 8 => 16 pairs (_) / I8 = 8 => 0 pairs (*) E9,I9: 8.. / E9 = 8 => 0 pairs (*) / I9 = 8 => 0 pairs (X) F2,D3: 9.. / F2 = 9 => 0 pairs (X) / D3 = 9 => 0 pairs (_) H4,G6: 9.. / H4 = 9 => 0 pairs (*) / G6 = 9 => 0 pairs (X) E7,F7: 9.. / E7 = 9 => 0 pairs (X) / F7 = 9 => 0 pairs (_) D3,H3: 9.. / D3 = 9 => 0 pairs (*) / H3 = 9 => 0 pairs (X) D4,H4: 9.. / D4 = 9 => 0 pairs (X) / H4 = 9 => 0 pairs (_) A1,A8: 9.. / A1 = 9 => 0 pairs (X) / A8 = 9 => 0 pairs (_) E6,E7: 9.. / E6 = 9 => 0 pairs (*) / E7 = 9 => 0 pairs (X) F2,F7: 9.. / F2 = 9 => 0 pairs (X) / F7 = 9 => 0 pairs (_) * DURATION: 0:01:18.071924 START: 03:05:56.605297 END: 03:07:14.677221 2017-05-04 * CP COUNT: (43) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A8,B3,C3,D3,D4,E6,E7,E8,E9,F2,F7,G6,G9,H3,H4,I1,I9) * .35867.4.6..52.7838...345.6458.763.17...5386436.4.8.572867..435...3.56..5.36.2... * PAIR A1: 1,9 BLK 1 B2: 1,9,4 # reduction candidate for 1,9 B2: 1,9 # 19 pairs C2: 1,9,4 # reduction candidate for 1,9 C2: 1,9 # 16 pairs * PAIR A1: 1,9 ROW 1 G1: 1,9,2 # reduction candidate for 1,9 G1: 1,9 => SOLVED * 135867942694521783872934516458276391729153864361498257286719435917345628543682179 G1: 2 => CTR * 1358672496..5217838..934516458.763.17...5386436.4.8.572867..435...3.56..5.36.2... * PAIR F2: 1,9 ROW 2 B2: 1,9,4 # reduction candidate for 1,9 B2: 1,9 # 19 pairs C2: 1,9,4 # reduction candidate for 1,9 C2: 1,9 # 16 pairs * PAIR D3: 1,9 COL D D5: 1,9,2 # reduction candidate for 1,9 D5: 1,9 => SOLVED * 135867942694521783872934516458276391729153864361498257286719435917345628543682179 D5: 2 => CTR * .35867.4.6..52.7838..1345964589763217..2538643624189572867..435...3.56..5.36.2... * PAIR I1: 2,9 BLK 3 G1: 2,9,1 # reduction candidate for 2,9 G1: 2,9 => SOLVED * 135867942694521783872934516458276391729153864361498257286719435917345628543682179 G1: 1 => CTR * .358671426..52.7838..1345964589763217...5386436.4.8.572867..435...3.56..5.36.2... * PAIR I1: 2,9 COL I I8: 2,9,8 # reduction candidate for 2,9 I8: 8 => SOLVED * 135867942694521783872934516458276391729153864361498257286719435917345628543682179 I8: 2,9 # 16 pairs * PAIR H3: 1,9 BLK 3 G1: 1,9,2 # reduction candidate for 1,9 G1: 1,9 => SOLVED * 135867942694521783872934516458276391729153864361498257286719435917345628543682179 G1: 2 => CTR * 1358672496..5217838..934516458.763.17...5386436.4.8.572867..435...3.56..5.36.2... * PAIR H3: 1,9 COL H H8: 1,9,2,7 # reduction candidate for 1,9 H8: 1,9 => CTR * 1358672496..5297838...345.6458.763217..253864362418957286791435...3.56.25.36.2178 H8: 2,7 # 19 pairs H9: 1,9,7 # reduction candidate for 1,9 H9: 1,9 => CTR * .358672496..52.783827934516458.763.17...5386436.4.8.572867..435...3.5672573642..8 H9: 7 # 18 pairs * PAIR D4: 2,9 BLK 5 D5: 2,9,1 # reduction candidate for 2,9 D5: 2,9 => CTR * .35867.4.6..52.7838..1345964589763217..2538643624189572867..435...3.56..5.36.2... D5: 1 => SOLVED * 135867942694521783872934516458276391729153864361498257286719435917345628543682179 * PAIR E6: 1,9 BLK 5 D5: 1,9,2 # reduction candidate for 1,9 D5: 1,9 => SOLVED * 135867942694521783872934516458276391729153864361498257286719435917345628543682179 D5: 2 => CTR * .35867.4.6..52.7838..1345964589763217..2538643624189572867..435...3.56..5.36.2... * PAIR E6: 1,9 ROW 6 C6: 1,9,2 # reduction candidate for 1,9 C6: 1,9 => SOLVED * 135867942694521783872934516458276391729153864361498257286719435917345628543682179 C6: 2 => CTR * 1358672496..5297838...345.6458.763.17...53864362418957286791435...3.56..5.36.21.. * PAIR H4: 2,9 COL H H8: 2,9,1,7 # reduction candidate for 2,9 H8: 2,9 => SOLVED * 135867942694521783872934516458276391729153864361498257286719435917345628543682179 H8: 1,7 => CTR * 1358672496..5297838...345.6458.763217..253864362418957286791435...3.56.25.36.21.8 * PAIR G6: 2,9 ROW 6 C6: 2,9,1 # reduction candidate for 2,9 C6: 2,9 => CTR * .35867.4.6..5297838..1345964589763217..253864362418957286791435...3.56..5.36.2... C6: 1 => SOLVED * 135867942694521783872934516458276391729153864361498257286719435917345628543682179 * PAIR G6: 2,9 COL G G1: 2,9,1 # reduction candidate for 2,9 G1: 2,9 => SOLVED * 135867942694521783872934516458276391729153864361498257286719435917345628543682179 G1: 1 => CTR * .358671426..52.7838..1345964589763217...5386436.4.8.572867..435...3.56..5.36.2... * PAIR A8: 1,9 BLK 7 B8: 1,9,4,7 # reduction candidate for 1,9 B8: 1,9 # 23 pairs C8: 1,9,4,7 # reduction candidate for 1,9 C8: 1,9 # 23 pairs B9: 1,9,4,7 # reduction candidate for 1,9 B9: 1,9 # 19 pairs * PAIR A8: 1,9 ROW 8 H8: 1,9,2,7 # reduction candidate for 1,9 H8: 1,9 => CTR * 1358672496..5297838...345.6458.763217..253864362418957286791435...3.56.25.36.2178 H8: 2,7 # 19 pairs * PAIR G9: 1,9 BLK 9 H8: 1,9,2,7 # reduction candidate for 1,9 H8: 1,9 => CTR * 1358672496..5297838...345.6458.763217..253864362418957286791435...3.56.25.36.2178 H8: 2,7 # 19 pairs H9: 1,9,7 # reduction candidate for 1,9 H9: 1,9 => CTR * .358672496..52.783827934516458.763.17...5386436.4.8.572867..435...3.5672573642..8 H9: 7 # 18 pairs * PAIR G9: 1,9 ROW 9 B9: 1,9,4,7 # reduction candidate for 1,9 B9: 4,7 # 21 pairs B9: 1,9 # 19 pairs * PAIR G9: 1,9 COL G G1: 1,9,2 # reduction candidate for 1,9 G1: 1,9 => SOLVED * 135867942694521783872934516458276391729153864361498257286719435917345628543682179 G1: 2 => CTR * 1358672496..5217838..934516458.763.17...5386436.4.8.572867..435...3.56..5.36.2... * PAIR I9: 8,9 BLK 9 I8: 8,9,2 # reduction candidate for 8,9 I8: 8,9 => SOLVED * 135867942694521783872934516458276391729153864361498257286719435917345628543682179 I8: 2 => CTR * .358672496..52.7838..934516458.763.17...5386436.4.8.572867..435...3856.25.3642..8 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-015-base-pr-000.dot * REASONING * PRF # G1: 1,9 => SOL * DIS # G1: 2 => CTR => G1: 1,9 * PRF # D5: 1,9 => SOL * DIS # D5: 2 => CTR => D5: 1,9 * PRF # G1: 2,9 => SOL * DIS # G1: 1 => CTR => G1: 2,9 * PRF # I8: 8 => SOL * PRF # G1: 1,9 => SOL * DIS # G1: 2 => CTR => G1: 1,9 * DIS # H8: 1,9 => CTR => H8: 2,7 * DIS # H9: 1,9 => CTR => H9: 7 * DIS # D5: 2,9 => CTR => D5: 1 * PRF # D5: 1 => SOL * PRF # D5: 1,9 => SOL * DIS # D5: 2 => CTR => D5: 1,9 * PRF # C6: 1,9 => SOL * DIS # C6: 2 => CTR => C6: 1,9 * PRF # H8: 2,9 => SOL * DIS # H8: 1,7 => CTR => H8: 2,9 * DIS # C6: 2,9 => CTR => C6: 1 * PRF # C6: 1 => SOL * PRF # G1: 2,9 => SOL * DIS # G1: 1 => CTR => G1: 2,9 * DIS # H8: 1,9 => CTR => H8: 2,7 * DIS # H8: 1,9 => CTR => H8: 2,7 * DIS # H9: 1,9 => CTR => H9: 7 * PRF # G1: 1,9 => SOL * DIS # G1: 2 => CTR => G1: 1,9 * PRF # I8: 8,9 => SOL * DIS # I8: 2 => CTR => I8: 8,9 * CNT 30 HDP CHAINS / 45 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A8,B3,C3,D3,D4,E6,E7,E8,E9,F2,F7,G6,G9,H3,H4,I1,I9) * .35867.4.6..52.7838...345.6458.763.17...5386436.4.8.572867..435...3.56..5.36.2... * PAIR A1: 1,9 BLK 1 B2: 1,9,4 # reduction candidate for 1,9 B2: 1,9 # 19 pairs C2: 1,9,4 # reduction candidate for 1,9 C2: 1,9 # 16 pairs * PAIR A1: 1,9 ROW 1 G1: 1,9,2 # reduction candidate for 1,9 G1: 1,9 => SOLVED * 135867942694521783872934516458276391729153864361498257286719435917345628543682179 * DURATION: 0:00:04.040147 START: 03:08:04.128757 END: 03:08:08.168904 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-015-base-pr-001.dot * REASONING * PRF # G1: 1,9 => SOL * STA G1: 1,9 * CNT 1 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 015 solution: 135867942694521783872934516458276391729153864361498257286719435917345628543682179 info: 1310 FNBTWXY S8.f 18378 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 135867942694521783872934516458276391729153864361498257286719435917345628543682179 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 # B2: 1,9 => UNS * INC # C2: 1,9 => UNS * PRF # G1: 1,9 => SOL * DIS # G1: 2 => CTR => G1: 1,9 * INC # B2: 1,9 => UNS * INC # C2: 1,9 => UNS * PRF # D5: 1,9 => SOL * DIS # D5: 2 => CTR => D5: 1,9 * PRF # G1: 2,9 => SOL * DIS # G1: 1 => CTR => G1: 2,9 * INC # I8: 2,9 => UNS * PRF # I8: 8 => SOL * PRF # G1: 1,9 => SOL * DIS # G1: 2 => CTR => G1: 1,9 * DIS # H8: 1,9 => CTR => H8: 2,7 * INC # H8: 2,7 => UNS * DIS # H9: 1,9 => CTR => H9: 7 * INC # H9: 7 => UNS * DIS # D5: 2,9 => CTR => D5: 1 * PRF # D5: 1 => SOL * PRF # D5: 1,9 => SOL * DIS # D5: 2 => CTR => D5: 1,9 * PRF # C6: 1,9 => SOL * DIS # C6: 2 => CTR => C6: 1,9 * PRF # H8: 2,9 => SOL * DIS # H8: 1,7 => CTR => H8: 2,9 * DIS # C6: 2,9 => CTR => C6: 1 * PRF # C6: 1 => SOL * PRF # G1: 2,9 => SOL * DIS # G1: 1 => CTR => G1: 2,9 * INC # B8: 1,9 => UNS * INC # C8: 1,9 => UNS * INC # B9: 1,9 => UNS * DIS # H8: 1,9 => CTR => H8: 2,7 * INC # H8: 2,7 => UNS * DIS # H8: 1,9 => CTR => H8: 2,7 * INC # H8: 2,7 => UNS * DIS # H9: 1,9 => CTR => H9: 7 * INC # H9: 7 => UNS * INC # B9: 1,9 => UNS * INC # B9: 4,7 => UNS * PRF # G1: 1,9 => SOL * DIS # G1: 2 => CTR => G1: 1,9 * PRF # I8: 8,9 => SOL * DIS # I8: 2 => CTR => I8: 8,9 * CNT 45 HDP CHAINS / 45 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 1,9 => UNS * INC # C2: 1,9 => UNS * PRF # G1: 1,9 => SOL * STA G1: 1,9 * CNT 3 HDP CHAINS / 3 HYP OPENED