Analysis of xx-top500-104-base.sdk
Contents
Original Sudoku
level: medium
position: 5..17.....3....2.....6.........248..1.............3....28........4.....6...7...5. initial
Autosolve
position: 5..17....83.4592.....63........248..1...67.......13...628345...754291386...786452 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H1: 6,9 => CTR => H1: 3,4 * PRF # B1: 6,9 => SOL * DIS # G6: 6,9 => CTR => G6: 5,7 * DIS # G3: 1,7 => CTR => G3: 5,9 * DIS # H3: 1,7 => CTR => H3: 4,9 * DIS # I3: 1,7 => CTR => I3: 4,5,8,9 * DIS # C2: 1,7 => CTR => C2: 6 * DIS # I7: 1,7 => CTR => I7: 9 * PRF # I5: 5,9 => SOL * DIS # G6: 5,9 => CTR => G6: 6,7 * DIS # C5: 5,9 => CTR => C5: 2,3 * DIS # G3: 1,7 => CTR => G3: 5,9 * CNT 12 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H1: 6,9 => CTR => H1: 3,4 * PRF H1: 3,4 # B1: 6,9 => SOL * STA H1: 3,4 + B1: 6,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 5..17.....3....2.....6.........248..1.............3....28........4.....6...7...5. | initial |
| 5..17....83.4592.....63........248..1...67.......13...628345...754291386...786452 | autosolve |
| 592178643836459217471632598967524831143867925285913764628345179754291386319786452 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) A3: 2,4 F1: 2,8 F3: 2,8 G1: 6,9 I2: 1,7 A4: 3,9 A6: 2,4 D4: 5,9 G5: 5,9 A9: 3,9 B9: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H4,I4: 1.. / H4 = 1 => 13 pairs (_) / I4 = 1 => 15 pairs (_) B9,C9: 1.. / B9 = 1 => 11 pairs (_) / C9 = 1 => 16 pairs (_) B3,B9: 1.. / B3 = 1 => 16 pairs (_) / B9 = 1 => 11 pairs (_) G3,G7: 1.. / G3 = 1 => 0 pairs (X) / G7 = 1 => 13 pairs (_) F1,F3: 2.. / F1 = 2 => 12 pairs (_) / F3 = 2 => 0 pairs (*) H5,H6: 2.. / H5 = 2 => 11 pairs (_) / H6 = 2 => 0 pairs (X) C1,F1: 2.. / C1 = 2 => 0 pairs (*) / F1 = 2 => 0 pairs (X) C5,H5: 2.. / C5 = 2 => 0 pairs (X) / H5 = 2 => 11 pairs (_) A3,A6: 2.. / A3 = 2 => 12 pairs (_) / A6 = 2 => 0 pairs (*) H1,I1: 3.. / H1 = 3 => 11 pairs (_) / I1 = 3 => 0 pairs (*) A9,C9: 3.. / A9 = 3 => 13 pairs (_) / C9 = 3 => 8 pairs (_) A4,A9: 3.. / A4 = 3 => 8 pairs (_) / A9 = 3 => 13 pairs (_) A3,A6: 4.. / A3 = 4 => 0 pairs (*) / A6 = 4 => 0 pairs (X) G3,I3: 5.. / G3 = 5 => 21 pairs (_) / I3 = 5 => 0 pairs (X) C2,H2: 6.. / C2 = 6 => 20 pairs (_) / H2 = 6 => 0 pairs (X) G1,G6: 6.. / G1 = 6 => 20 pairs (_) / G6 = 6 => 0 pairs (X) F1,F3: 8.. / F1 = 8 => 0 pairs (*) / F3 = 8 => 0 pairs (X) I1,I3: 8.. / I1 = 8 => 12 pairs (_) / I3 = 8 => 0 pairs (*) B5,B6: 8.. / B5 = 8 => 14 pairs (_) / B6 = 8 => 13 pairs (_) D5,D6: 8.. / D5 = 8 => 13 pairs (_) / D6 = 8 => 14 pairs (_) F1,I1: 8.. / F1 = 8 => 0 pairs (*) / I1 = 8 => 0 pairs (X) F3,I3: 8.. / F3 = 8 => 12 pairs (_) / I3 = 8 => 0 pairs (*) B5,D5: 8.. / B5 = 8 => 14 pairs (_) / D5 = 8 => 13 pairs (_) B6,D6: 8.. / B6 = 8 => 13 pairs (_) / D6 = 8 => 14 pairs (_) A4,A9: 9.. / A4 = 9 => 13 pairs (_) / A9 = 9 => 8 pairs (_) * DURATION: 0:00:42.917319 START: 06:19:34.531436 END: 06:20:17.448755 2017-05-04 * CP COUNT: (25) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A6,A9,B9,D4,F1,F3,G1,G5,I2) * 5..17....83.4592.....63........248..1...67.......13...628345...754291386...786452 * PAIR G1: 6,9 BLK 3 H1: 6,9,3,4 # reduction candidate for 6,9 H1: 6,9 => CTR * 54.178..383.4592..2..63...8....248..1...67.......13...628345...754291386...786452 H1: 3,4 # 12 pairs * PAIR G1: 6,9 ROW 1 B1: 6,9,4 # reduction candidate for 6,9 B1: 6,9 => SOLVED * 592178643836459217471632598967524831143867925285913764628345179754291386319786452 B1: 4 # 12 pairs C1: 6,9,2 # reduction candidate for 6,9 C1: 6,9 # 12 pairs * PAIR G1: 6,9 COL G G6: 6,9,5,7 # reduction candidate for 6,9 G6: 6,9 => CTR * 54617293883.45926.2..638.45.6..248.31.3.675244.25136..628345...7542913863..786452 G6: 5,7 # 20 pairs * PAIR I2: 1,7 BLK 3 H2: 1,7,6 # reduction candidate for 1,7 H2: 1,7 # 20 pairs G3: 1,7,5,9 # reduction candidate for 1,7 G3: 1,7 => CTR * 54617293883.45926.2..638.45.6..248.31.3.675244.25136..628345...7542913863..786452 G3: 5,9 # 20 pairs H3: 1,7,4,9 # reduction candidate for 1,7 H3: 1,7 => CTR * 5..17.9..83.45926....63.5......248..1...67.......13...628345...754291386...786452 H3: 4,9 # 12 pairs I3: 1,7,4,5,8,9 # reduction candidate for 1,7 I3: 1,7 => CTR * 5..1726388364592.....6385......248..1...679......13...6283451.9754291386...786452 I3: 4,5,8,9 # 11 pairs * PAIR I2: 1,7 ROW 2 C2: 1,7,6 # reduction candidate for 1,7 C2: 1,7 => CTR * 54617293883.45926.2..638.45.6..248.31.3.675244.25136..628345...7542913863..786452 C2: 6 # 20 pairs * PAIR I2: 1,7 COL I I4: 1,7,3,5,9 # reduction candidate for 1,7 I4: 1,7 # 15 pairs I7: 1,7,9 # reduction candidate for 1,7 I7: 1,7 => CTR * 54.172.3883.4592..2..638.4..67.2481.1.5.6792.4.2.13...628345.9.754291386...786452 I7: 9 # 13 pairs * PAIR A4: 3,9 BLK 4 C4: 3,9,5,6,7 # reduction candidate for 3,9 C4: 3,9 # 22 pairs C5: 3,9,2,5 # reduction candidate for 3,9 C5: 3,9 # 14 pairs * PAIR A4: 3,9 ROW 4 H4: 3,9,1,6,7 # reduction candidate for 3,9 H4: 3,9 # 23 pairs I4: 3,9,1,5,7 # reduction candidate for 3,9 I4: 3,9 # 17 pairs * PAIR A6: 2,4 ROW 6 H6: 2,4,6,7,9 # reduction candidate for 2,4 H6: 2,4 # 12 pairs H6: 6,7,9 # 11 pairs * PAIR D4: 5,9 BLK 5 D5: 5,9,8 # reduction candidate for 5,9 D5: 5,9 # 14 pairs D6: 5,9,8 # reduction candidate for 5,9 D6: 5,9 # 13 pairs * PAIR D4: 5,9 ROW 4 C4: 5,9,3,6,7 # reduction candidate for 5,9 C4: 5,9 # 16 pairs I4: 5,9,1,3,7 # reduction candidate for 5,9 I4: 5,9 # 18 pairs * PAIR G5: 5,9 BLK 6 I4: 5,9,1,3,7 # reduction candidate for 5,9 I4: 5,9 # 18 pairs I5: 5,9,3,4 # reduction candidate for 5,9 I5: 5,9 => SOLVED * 592178643836459217471632598967524831143867925285913764628345179754291386319786452 I5: 3,4 # 12 pairs G6: 5,9,6,7 # reduction candidate for 5,9 G6: 5,9 => CTR * 5..17.6..8364592.....63........248..1...67.......13...628345...754291386...786452 G6: 6,7 # 12 pairs I6: 5,9,4,7 # reduction candidate for 5,9 I6: 5,9 # 14 pairs * PAIR G5: 5,9 ROW 5 C5: 5,9,2,3 # reduction candidate for 5,9 C5: 5,9 => CTR * 5.21786348364592..4..632598.6..248..14586792328..13745628345179754291386...786452 C5: 2,3 # 12 pairs D5: 5,9,8 # reduction candidate for 5,9 D5: 5,9 # 14 pairs * PAIR G5: 5,9 COL G G3: 5,9,1,7 # reduction candidate for 5,9 G3: 1,7 => CTR * 54617293883.45926.2..638.45.6..248.31.3.675244.25136..628345...7542913863..786452 G3: 5,9 # 20 pairs * PAIR A9: 3,9 BLK 7 C9: 3,9,1 # reduction candidate for 3,9 C9: 1 # 16 pairs C9: 3,9 # 11 pairs * PAIR B9: 1,9 BLK 7 C9: 1,9,3 # reduction candidate for 1,9 C9: 1,9 # 13 pairs C9: 3 # 8 pairs * PAIR B9: 1,9 COL B B3: 1,9,4,7 # reduction candidate for 1,9 B3: 1,9 # 15 pairs B3: 4,7 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-104-base-pr-000.dot * REASONING * DIS # H1: 6,9 => CTR => H1: 3,4 * PRF # B1: 6,9 => SOL * DIS # G6: 6,9 => CTR => G6: 5,7 * DIS # G3: 1,7 => CTR => G3: 5,9 * DIS # H3: 1,7 => CTR => H3: 4,9 * DIS # I3: 1,7 => CTR => I3: 4,5,8,9 * DIS # C2: 1,7 => CTR => C2: 6 * DIS # I7: 1,7 => CTR => I7: 9 * PRF # I5: 5,9 => SOL * DIS # G6: 5,9 => CTR => G6: 6,7 * DIS # C5: 5,9 => CTR => C5: 2,3 * DIS # G3: 1,7 => CTR => G3: 5,9 * CNT 12 HDP CHAINS / 46 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A6,A9,B9,D4,F1,F3,G1,G5,I2) * 5..17....83.4592.....63........248..1...67.......13...628345...754291386...786452 * PAIR G1: 6,9 BLK 3 H1: 6,9,3,4 # reduction candidate for 6,9 H1: 6,9 => CTR * 54.178..383.4592..2..63...8....248..1...67.......13...628345...754291386...786452 * PAIR G1: 6,9 ROW 1 B1: 6,9,4 # reduction candidate for 6,9 B1: 6,9 => SOLVED * 592178643836459217471632598967524831143867925285913764628345179754291386319786452 * DURATION: 0:00:04.122722 START: 06:20:59.562580 END: 06:21:03.685302 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-104-base-pr-001.dot * REASONING * DIS # H1: 6,9 => CTR => H1: 3,4 * PRF H1: 3,4 # B1: 6,9 => SOL * STA H1: 3,4 + B1: 6,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 104 solution: 592178643836459217471632598967524831143867925285913764628345179754291386319786452 info: 1620 FNBHXY S8.f 32733 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 592178643836459217471632598967524831143867925285913764628345179754291386319786452 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 # H1: 6,9 => CTR => H1: 3,4 * INC # H1: 3,4 => UNS * PRF # B1: 6,9 => SOL * INC # B1: 4 => UNS * INC # C1: 6,9 => UNS * DIS # G6: 6,9 => CTR => G6: 5,7 * INC # G6: 5,7 => UNS * INC # H2: 1,7 => UNS * DIS # G3: 1,7 => CTR => G3: 5,9 * INC # G3: 5,9 => UNS * DIS # H3: 1,7 => CTR => H3: 4,9 * INC # H3: 4,9 => UNS * DIS # I3: 1,7 => CTR => I3: 4,5,8,9 * INC # I3: 4,5,8,9 => UNS * DIS # C2: 1,7 => CTR => C2: 6 * INC # C2: 6 => UNS * INC # I4: 1,7 => UNS * DIS # I7: 1,7 => CTR => I7: 9 * INC # I7: 9 => UNS * INC # C4: 3,9 => UNS * INC # C5: 3,9 => UNS * INC # H4: 3,9 => UNS * INC # I4: 3,9 => UNS * INC # H6: 2,4 => UNS * INC # H6: 6,7,9 => UNS * INC # D5: 5,9 => UNS * INC # D6: 5,9 => UNS * INC # C4: 5,9 => UNS * INC # I4: 5,9 => UNS * INC # I4: 5,9 => UNS * PRF # I5: 5,9 => SOL * INC # I5: 3,4 => UNS * DIS # G6: 5,9 => CTR => G6: 6,7 * INC # G6: 6,7 => UNS * INC # I6: 5,9 => UNS * DIS # C5: 5,9 => CTR => C5: 2,3 * INC # C5: 2,3 => UNS * INC # D5: 5,9 => UNS * INC # G3: 5,9 => UNS * DIS # G3: 1,7 => CTR => G3: 5,9 * INC # C9: 3,9 => UNS * INC # C9: 1 => UNS * INC # C9: 1,9 => UNS * INC # C9: 3 => UNS * INC # B3: 1,9 => UNS * INC # B3: 4,7 => UNS * CNT 46 HDP CHAINS / 46 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # H1: 6,9 => CTR => H1: 3,4 * PRF H1: 3,4 # B1: 6,9 => SOL * STA H1: 3,4 + B1: 6,9 * CNT 2 HDP CHAINS / 2 HYP OPENED