Analysis of xx-top500-270-base.sdk
Contents
Original Sudoku
level: medium
position: 2...74....6....3............3.1.......8.....4.....2.7.7.4....5....63..........1.. initial
Autosolve
position: 2.3.74.1646....3.7.71.634...3714.26.1287.6.3464.3.2.717.4...653..263.74.3.64.71.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 5,9 => CTR => A3: 8 * PRF # F4: 5,9 => SOL * DIS # F4: 8 => CTR => F4: 5,9 * DIS # I4: 5,9 => CTR => I4: 8 * PRF # I4: 8 => SOL * DIS # A3: 5,9 => CTR => A3: 8 * DIS # E6: 5,9 => CTR => E6: 8 * PRF # E6: 8 => SOL * PRF # G6: 5,9 => SOL * DIS # G6: 8 => CTR => G6: 5,9 * PRF # F4: 5,9 => SOL * DIS # F4: 8 => CTR => F4: 5,9 * DIS # E6: 5,9 => CTR => E6: 8 * PRF # E6: 8 => SOL * PRF # E9: 5,9 => SOL * DIS # E9: 8 => CTR => E9: 5,9 * DIS # I4: 5,9 => CTR => I4: 8 * PRF # I4: 8 => SOL * PRF # G6: 5,9 => SOL * DIS # G6: 8 => CTR => G6: 5,9 * DIS # G1: 5,9 => CTR => G1: 8 * PRF # G1: 8 => SOL * DIS # I9: 8,9 => CTR => I9: 2 * PRF # B8: 8,9 => SOL * DIS # F8: 8,9 => CTR => F8: 1,5 * DIS # I3: 8,9 => CTR => I3: 2,5 * CNT 26 HDP CHAINS / 39 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 5,9 => CTR => A3: 8 * DIS A3: 8 # D2: 2,8 => CTR => D2: 5,9 * PRF A3: 8 + D2: 5,9 # F4: 5,9 => SOL * STA A3: 8 + D2: 5,9 + F4: 5,9 * CNT 3 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2...74....6....3............3.1.......8.....4.....2.7.7.4....5....63..........1.. | initial |
| 2.3.74.1646....3.7.71.634...3714.26.1287.6.3464.3.2.717.4...653..263.74.3.64.71.. | autosolve |
| 253974816469518327871263495937145268128796534645382971714829653582631749396457182 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) C2: 5,9 E2: 1,2 A4: 5,9 C6: 5,9 E5: 5,9 G5: 5,9 E7: 1,2 I8: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,F2: 1.. / E2 = 1 => 8 pairs (_) / F2 = 1 => 9 pairs (_) B7,B8: 1.. / B7 = 1 => 0 pairs (*) / B8 = 1 => 0 pairs (X) B8,F8: 1.. / B8 = 1 => 9 pairs (_) / F8 = 1 => 0 pairs (*) E2,E7: 1.. / E2 = 1 => 8 pairs (_) / E7 = 1 => 9 pairs (_) D7,E7: 2.. / D7 = 2 => 9 pairs (_) / E7 = 2 => 8 pairs (_) H9,I9: 2.. / H9 = 2 => 0 pairs (X) / I9 = 2 => 9 pairs (_) E2,E7: 2.. / E2 = 2 => 9 pairs (_) / E7 = 2 => 8 pairs (_) I3,I9: 2.. / I3 = 2 => 0 pairs (X) / I9 = 2 => 9 pairs (_) G1,I3: 5.. / G1 = 5 => 0 pairs (X) / I3 = 5 => 12 pairs (_) A4,C6: 5.. / A4 = 5 => 16 pairs (_) / C6 = 5 => 18 pairs (_) F8,E9: 5.. / F8 = 5 => 13 pairs (_) / E9 = 5 => 0 pairs (*) C2,D2: 5.. / C2 = 5 => 16 pairs (_) / D2 = 5 => 18 pairs (_) E5,G5: 5.. / E5 = 5 => 15 pairs (_) / G5 = 5 => 14 pairs (_) B9,E9: 5.. / B9 = 5 => 13 pairs (_) / E9 = 5 => 0 pairs (*) C2,C6: 5.. / C2 = 5 => 16 pairs (_) / C6 = 5 => 18 pairs (_) F4,F8: 5.. / F4 = 5 => 0 pairs (*) / F8 = 5 => 0 pairs (X) I3,I4: 5.. / I3 = 5 => 12 pairs (_) / I4 = 5 => 0 pairs (X) B1,A3: 8.. / B1 = 8 => 0 pairs (X) / A3 = 8 => 11 pairs (_) F4,E6: 8.. / F4 = 8 => 0 pairs (X) / E6 = 8 => 0 pairs (_) I4,G6: 8.. / I4 = 8 => 0 pairs (*) / G6 = 8 => 0 pairs (X) F4,I4: 8.. / F4 = 8 => 0 pairs (X) / I4 = 8 => 0 pairs (_) E6,G6: 8.. / E6 = 8 => 0 pairs (*) / G6 = 8 => 0 pairs (X) A3,A8: 8.. / A3 = 8 => 11 pairs (_) / A8 = 8 => 0 pairs (X) E6,E9: 8.. / E6 = 8 => 0 pairs (*) / E9 = 8 => 0 pairs (X) G1,G6: 8.. / G1 = 8 => 0 pairs (*) / G6 = 8 => 0 pairs (X) A4,C6: 9.. / A4 = 9 => 18 pairs (_) / C6 = 9 => 16 pairs (_) E5,G5: 9.. / E5 = 9 => 14 pairs (_) / G5 = 9 => 15 pairs (_) C2,C6: 9.. / C2 = 9 => 18 pairs (_) / C6 = 9 => 16 pairs (_) * DURATION: 0:00:48.595392 START: 12:08:29.727311 END: 12:09:18.322703 2017-05-04 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,C2,C6,E2,E5,E7,G5,I8) * 2.3.74.1646....3.7.71.634...3714.26.1287.6.3464.3.2.717.4...653..263.74.3.64.71.. * PAIR C2: 5,9 BLK 1 B1: 5,9,8 # reduction candidate for 5,9 B1: 5,9 # 11 pairs A3: 5,9,8 # reduction candidate for 5,9 A3: 5,9 => CTR * 283.74.1646....3.7.71.634...3714.26.1287.6.3464.3.28717.4...6538.263.7493.648712. A3: 8 # 11 pairs * PAIR C2: 5,9 ROW 2 D2: 5,9,2,8 # reduction candidate for 5,9 D2: 2,8 # 17 pairs D2: 5,9 # 12 pairs * PAIR A4: 5,9 ROW 4 F4: 5,9,8 # reduction candidate for 5,9 F4: 5,9 => SOLVED * 253974816469518327871263495937145268128796534645382971714829653582631749396457182 F4: 8 => CTR * 293874516465...3878715634..53714826.1287.6.3464.3.2871784...6539126357483564871.. I4: 5,9,8 # reduction candidate for 5,9 I4: 5,9 => CTR * 293874516465...3878715634..53714826.1287.6.3464.3.2871784...6539126357483564871.. I4: 8 => SOLVED * 253974816469518327871263495937145268128796534645382971714829653582631749396457182 * PAIR A4: 5,9 COL A A3: 5,9,8 # reduction candidate for 5,9 A3: 5,9 => CTR * 283.74.1646....3.7.71.634...3714.26.1287.6.3464.3.28717.4...6538.263.7493.648712. A3: 8 # 11 pairs A8: 5,9,8 # reduction candidate for 5,9 A8: 5,9 # 11 pairs * PAIR C6: 5,9 ROW 6 E6: 5,9,8 # reduction candidate for 5,9 E6: 5,9 => CTR * 293874516465...3878715634..53714826.1287.6.3464.3.2871784...6539126357483564871.. E6: 8 => SOLVED * 253974816469518327871263495937145268128796534645382971714829653582631749396457182 G6: 5,9,8 # reduction candidate for 5,9 G6: 5,9 => SOLVED * 253974816469518327871263495937145268128796534645382971714829653582631749396457182 G6: 8 => CTR * 293874516465...3878715634..5371482691287.6.3464.3.2871784...653.126357483564871.. * PAIR E5: 5,9 BLK 5 F4: 5,9,8 # reduction candidate for 5,9 F4: 5,9 => SOLVED * 253974816469518327871263495937145268128796534645382971714829653582631749396457182 F4: 8 => CTR * 293874516465...3878715634..53714826.1287.6.3464.3.2871784...6539126357483564871.. E6: 5,9,8 # reduction candidate for 5,9 E6: 5,9 => CTR * 293874516465...3878715634..53714826.1287.6.3464.3.2871784...6539126357483564871.. E6: 8 => SOLVED * 253974816469518327871263495937145268128796534645382971714829653582631749396457182 * PAIR E5: 5,9 COL E E9: 5,9,8 # reduction candidate for 5,9 E9: 5,9 => SOLVED * 253974816469518327871263495937145268128796534645382971714829653582631749396457182 E9: 8 => CTR * 293874516465...3878715634..53714826.1287.6.3464.3.2871784...6539126357483564871.. * PAIR G5: 5,9 BLK 6 I4: 5,9,8 # reduction candidate for 5,9 I4: 5,9 => CTR * 293874516465...3878715634..53714826.1287.6.3464.3.2871784...6539126357483564871.. I4: 8 => SOLVED * 253974816469518327871263495937145268128796534645382971714829653582631749396457182 G6: 5,9,8 # reduction candidate for 5,9 G6: 5,9 => SOLVED * 253974816469518327871263495937145268128796534645382971714829653582631749396457182 G6: 8 => CTR * 293874516465...3878715634..5371482691287.6.3464.3.2871784...653.126357483564871.. * PAIR G5: 5,9 COL G G1: 5,9,8 # reduction candidate for 5,9 G1: 5,9 => CTR * 293874516465...3878715634..5371482691287.6.3464.3.2871784...653.126357483564871.. G1: 8 => SOLVED * 253974816469518327871263495937145268128796534645382971714829653582631749396457182 * PAIR I8: 8,9 BLK 9 H9: 8,9,2 # reduction candidate for 8,9 H9: 8,9 # 9 pairs I9: 8,9,2 # reduction candidate for 8,9 I9: 8,9 => CTR * 2.3.74516469521387571863492937148265128756934645392871784...653..263574.356487129 I9: 2 # 9 pairs * PAIR I8: 8,9 ROW 8 A8: 8,9,5 # reduction candidate for 8,9 A8: 8,9 # 12 pairs B8: 8,9,1,5 # reduction candidate for 8,9 B8: 8,9 => SOLVED * 253974816469518327871263495937145268128796534645382971714829653582631749396457182 B8: 1,5 # 9 pairs F8: 8,9,1,5 # reduction candidate for 8,9 F8: 8,9 => CTR * 2539748164695.83.7.71.634...371452681287965346453829717.4...653.1263.749396457182 F8: 1,5 # 9 pairs * PAIR I8: 8,9 COL I I3: 8,9,2,5 # reduction candidate for 8,9 I3: 8,9 => CTR * 2.3.745164695..3.7571.634..937148265128756934645392871784...653..263574.3564871.2 I3: 2,5 # 9 pairs I4: 8,9,5 # reduction candidate for 8,9 I4: 8,9 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-270-base-pr-000.dot * REASONING * DIS # A3: 5,9 => CTR => A3: 8 * PRF # F4: 5,9 => SOL * DIS # F4: 8 => CTR => F4: 5,9 * DIS # I4: 5,9 => CTR => I4: 8 * PRF # I4: 8 => SOL * DIS # A3: 5,9 => CTR => A3: 8 * DIS # E6: 5,9 => CTR => E6: 8 * PRF # E6: 8 => SOL * PRF # G6: 5,9 => SOL * DIS # G6: 8 => CTR => G6: 5,9 * PRF # F4: 5,9 => SOL * DIS # F4: 8 => CTR => F4: 5,9 * DIS # E6: 5,9 => CTR => E6: 8 * PRF # E6: 8 => SOL * PRF # E9: 5,9 => SOL * DIS # E9: 8 => CTR => E9: 5,9 * DIS # I4: 5,9 => CTR => I4: 8 * PRF # I4: 8 => SOL * PRF # G6: 5,9 => SOL * DIS # G6: 8 => CTR => G6: 5,9 * DIS # G1: 5,9 => CTR => G1: 8 * PRF # G1: 8 => SOL * DIS # I9: 8,9 => CTR => I9: 2 * PRF # B8: 8,9 => SOL * DIS # F8: 8,9 => CTR => F8: 1,5 * DIS # I3: 8,9 => CTR => I3: 2,5 * CNT 26 HDP CHAINS / 39 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,C2,C6,E2,E5,E7,G5,I8) * 2.3.74.1646....3.7.71.634...3714.26.1287.6.3464.3.2.717.4...653..263.74.3.64.71.. * PAIR C2: 5,9 BLK 1 B1: 5,9,8 # reduction candidate for 5,9 B1: 5,9 # 11 pairs A3: 5,9,8 # reduction candidate for 5,9 A3: 5,9 => CTR * 283.74.1646....3.7.71.634...3714.26.1287.6.3464.3.28717.4...6538.263.7493.648712. * RESTART * PAIR C2: 5,9 ROW 2 D2: 5,9,2,8 # reduction candidate for 5,9 D2: 2,8 => CTR * 293.74.16465...387871.634.553714.26.1287.6.346493.2.717.4...6539.26357483564871.. * PAIR RESTART * PAIR A4: 5,9 ROW 4 F4: 5,9,8 # reduction candidate for 5,9 F4: 5,9 => SOLVED * 253974816469518327871263495937145268128796534645382971714829653582631749396457182 * DURATION: 0:00:06.194283 START: 12:10:00.136308 END: 12:10:06.330591 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-270-base-pr-001.dot * REASONING * DIS # A3: 5,9 => CTR => A3: 8 * DIS A3: 8 # D2: 2,8 => CTR => D2: 5,9 * PRF A3: 8 + D2: 5,9 # F4: 5,9 => SOL * STA A3: 8 + D2: 5,9 + F4: 5,9 * CNT 3 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 270 solution: 253974816469518327871263495937145268128796534645382971714829653582631749396457182 info: 2149 FNBTHWX S8.f 27479 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 253974816469518327871263495937145268128796534645382971714829653582631749396457182 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 # B1: 5,9 => UNS * DIS # A3: 5,9 => CTR => A3: 8 * INC # A3: 8 => UNS * INC # D2: 5,9 => UNS * INC # D2: 2,8 => UNS * PRF # F4: 5,9 => SOL * DIS # F4: 8 => CTR => F4: 5,9 * DIS # I4: 5,9 => CTR => I4: 8 * PRF # I4: 8 => SOL * DIS # A3: 5,9 => CTR => A3: 8 * INC # A3: 8 => UNS * INC # A8: 5,9 => UNS * DIS # E6: 5,9 => CTR => E6: 8 * PRF # E6: 8 => SOL * PRF # G6: 5,9 => SOL * DIS # G6: 8 => CTR => G6: 5,9 * PRF # F4: 5,9 => SOL * DIS # F4: 8 => CTR => F4: 5,9 * DIS # E6: 5,9 => CTR => E6: 8 * PRF # E6: 8 => SOL * PRF # E9: 5,9 => SOL * DIS # E9: 8 => CTR => E9: 5,9 * DIS # I4: 5,9 => CTR => I4: 8 * PRF # I4: 8 => SOL * PRF # G6: 5,9 => SOL * DIS # G6: 8 => CTR => G6: 5,9 * DIS # G1: 5,9 => CTR => G1: 8 * PRF # G1: 8 => SOL * INC # H9: 8,9 => UNS * DIS # I9: 8,9 => CTR => I9: 2 * INC # I9: 2 => UNS * INC # A8: 8,9 => UNS * PRF # B8: 8,9 => SOL * INC # B8: 1,5 => UNS * DIS # F8: 8,9 => CTR => F8: 1,5 * INC # F8: 1,5 => UNS * DIS # I3: 8,9 => CTR => I3: 2,5 * INC # I3: 2,5 => UNS * INC # I4: 8,9 => UNS * CNT 39 HDP CHAINS / 39 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 5,9 => UNS * DIS # A3: 5,9 => CTR => A3: 8 * INC A3: 8 # D2: 5,9 => UNS * DIS A3: 8 # D2: 2,8 => CTR => D2: 5,9 * PRF A3: 8 + D2: 5,9 # F4: 5,9 => SOL * STA A3: 8 + D2: 5,9 + F4: 5,9 * CNT 5 HDP CHAINS / 5 HYP OPENED