Analysis of zz-www.sudokuwiki.org-0031-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=31
level: medium
position: ....6..4......17.89....82.........3.35..9...4.8.........23....5..12......7..4..6. initial
Autosolve
position: ....6..4......17.89....82.6.....4.3.35..9...4.8...3.....23....5..12......7..4..62 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 1,2 => CTR => A1: 5,7,8 * PRF # H6: 5,9 => SOL * PRF # G1: 1,5 => SOL * PRF # H6: 1,5 => SOL * PRF # C6: 6,7 => SOL * DIS # D5: 6,7 => CTR => D5: 1,8 * DIS # E4: 2,7 => CTR => E4: 1,5,8 * DIS # C9: 5,8 => CTR => C9: 3,9 * DIS # A1: 5,8 => CTR => A1: 1,2,7 * DIS # C9: 5,9 => CTR => C9: 3,8 * CNT 10 HDP CHAINS / 41 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 1,2 => CTR => A1: 5,7,8 * PRF A1: 5,7,8 # G1: 5,9 => SOL * STA A1: 5,7,8 + G1: 5,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....6..4......17.89....82.........3.35..9...4.8.........23....5..12......7..4..6. | initial |
| ....6..4......17.89....82.6.....4.3.35..9...4.8...3.....23....5..12......7..4..62 | autosolve |
| 718962543265431798934758216129584637356197824487623951892316475641275389573849162 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) B1: 1,2 H2: 5,9 H3: 1,5 C5: 6,7 F5: 2,7 A9: 5,8 F9: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E7,D9: 1.. / E7 = 1 => 9 pairs (_) / D9 = 1 => 0 pairs (X) B3,H3: 1.. / B3 = 1 => 0 pairs (X) / H3 = 1 => 10 pairs (_) D9,G9: 1.. / D9 = 1 => 0 pairs (X) / G9 = 1 => 9 pairs (_) F1,E2: 2.. / F1 = 2 => 0 pairs (*) / E2 = 2 => 0 pairs (X) H5,H6: 2.. / H5 = 2 => 0 pairs (*) / H6 = 2 => 0 pairs (X) F5,H5: 2.. / F5 = 2 => 12 pairs (_) / H5 = 2 => 0 pairs (*) F1,F5: 2.. / F1 = 2 => 0 pairs (*) / F5 = 2 => 0 pairs (X) E2,E3: 3.. / E2 = 3 => 0 pairs (*) / E3 = 3 => 0 pairs (X) G1,I1: 3.. / G1 = 3 => 12 pairs (_) / I1 = 3 => 20 pairs (_) B8,C9: 3.. / B8 = 3 => 0 pairs (X) / C9 = 3 => 7 pairs (_) C9,G9: 3.. / C9 = 3 => 7 pairs (_) / G9 = 3 => 0 pairs (X) I1,I8: 3.. / I1 = 3 => 20 pairs (_) / I8 = 3 => 12 pairs (_) D2,D3: 4.. / D2 = 4 => 9 pairs (_) / D3 = 4 => 11 pairs (_) A6,C6: 4.. / A6 = 4 => 0 pairs (*) / C6 = 4 => 0 pairs (X) G7,G8: 4.. / G7 = 4 => 9 pairs (_) / G8 = 4 => 7 pairs (_) F7,F8: 6.. / F7 = 6 => 9 pairs (_) / F8 = 6 => 8 pairs (_) A1,C1: 8.. / A1 = 8 => 0 pairs (X) / C1 = 8 => 7 pairs (_) C1,C9: 8.. / C1 = 8 => 7 pairs (_) / C9 = 8 => 0 pairs (X) D2,H2: 9.. / D2 = 9 => 0 pairs (X) / H2 = 9 => 9 pairs (_) * DURATION: 0:00:24.322409 START: 04:00:00.549043 END: 04:00:24.871452 2017-05-01 * CP COUNT: (19) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B1,C5,F5,F9,H2,H3) * ....6..4......17.89....82.6.....4.3.35..9...4.8...3.....23....5..12......7..4..62 * PAIR B1: 1,2 BLK 1 A1: 1,2,5,7,8 # reduction candidate for 1,2 A1: 1,2 => CTR * ..8.6.543...421798947538216..9.54.3.356.92..4284..3.5...23....5..12......7..4..62 A1: 5,7,8 # 7 pairs * PAIR B1: 1,2 COL B B4: 1,2,6,9 # reduction candidate for 1,2 B4: 6,9 # 13 pairs B4: 1,2 # 11 pairs * PAIR H2: 5,9 BLK 3 G1: 5,9,1,3 # reduction candidate for 5,9 G1: 5,9 # 20 pairs G1: 1,3 # 8 pairs * PAIR H2: 5,9 ROW 2 D2: 5,9,4 # reduction candidate for 5,9 D2: 5,9 # 11 pairs D2: 4 # 9 pairs * PAIR H2: 5,9 COL H H6: 5,9,1,2,7 # reduction candidate for 5,9 H6: 5,9 => SOLVED * 718962543265431798934758216129584637356197824487623951892316475641275389573849162 H6: 1,2,7 # 7 pairs * PAIR H3: 1,5 BLK 3 G1: 1,5,3,9 # reduction candidate for 1,5 G1: 1,5 => SOLVED * 718962543265431798934758216129584637356197824487623951892316475641275389573849162 G1: 3,9 # 8 pairs * PAIR H3: 1,5 COL H H6: 1,5,2,7,9 # reduction candidate for 1,5 H6: 1,5 => SOLVED * 718962543265431798934758216129584637356197824487623951892316475641275389573849162 H6: 2,7,9 # 7 pairs * PAIR C5: 6,7 BLK 4 A4: 6,7,1,2 # reduction candidate for 6,7 A4: 6,7 # 17 pairs C4: 6,7,9 # reduction candidate for 6,7 C4: 6,7 # 12 pairs A6: 6,7,1,2,4 # reduction candidate for 6,7 A6: 6,7 # 19 pairs C6: 6,7,4,9 # reduction candidate for 6,7 C6: 6,7 => SOLVED * 718962543265431798934758216129584637356197824487623951892316475641275389573849162 C6: 4,9 # 8 pairs * PAIR C5: 6,7 ROW 5 D5: 6,7,1,8 # reduction candidate for 6,7 D5: 6,7 => CTR * .28.6.341.35.2179891..382562....4.3.35..92..4184..3.2...23....5..12....3.73.4..62 D5: 1,8 # 8 pairs * PAIR F5: 2,7 BLK 5 E4: 2,7,1,5,8 # reduction candidate for 2,7 E4: 2,7 => CTR * 728.6..4.....217.891.7382562...74.31357192684184..3.27..23....5..12......7..4..62 E4: 1,5,8 # 7 pairs E6: 2,7,1,5 # reduction candidate for 2,7 E6: 2,7 # 9 pairs * PAIR F5: 2,7 ROW 5 H5: 2,7,1,8 # reduction candidate for 2,7 H5: 1,8 # 14 pairs H5: 2,7 # 11 pairs * PAIR F5: 2,7 COL F F1: 2,7,5,9 # reduction candidate for 2,7 F1: 5,9 # 18 pairs F1: 2,7 # 12 pairs * PAIR A9: 5,8 BLK 7 A8: 5,8,4,6 # reduction candidate for 5,8 A8: 5,8 # 10 pairs C9: 5,8,3,9 # reduction candidate for 5,8 C9: 5,8 => CTR * ....6..43.....17.89....82.6.....4.3.35..9...4.8...3....923....5.312......7.149362 C9: 3,9 # 8 pairs * PAIR A9: 5,8 ROW 9 D9: 5,8,1,9 # reduction candidate for 5,8 D9: 5,8 # 9 pairs D9: 1,9 # 8 pairs * PAIR A9: 5,8 COL A A1: 5,8,1,2,7 # reduction candidate for 5,8 A1: 5,8 => CTR * .1.96254326.4.179894.7.8216.29..4.3.356.97.24.84.2395.4923.61.56312..4.9578149362 A1: 1,2,7 # 7 pairs * PAIR F9: 5,9 BLK 8 F8: 5,9,6,7 # reduction candidate for 5,9 F8: 5,9 # 14 pairs D9: 5,9,1,8 # reduction candidate for 5,9 D9: 5,9 # 24 pairs * PAIR F9: 5,9 ROW 9 C9: 5,9,3,8 # reduction candidate for 5,9 C9: 5,9 => CTR * ..8.6..43.....17.89....82.6.....4.3.35..9...4.8...3.....23....5.312.....87.14.362 C9: 3,8 # 8 pairs * PAIR F9: 5,9 COL F F1: 5,9,2,7 # reduction candidate for 5,9 F1: 5,9 # 18 pairs F1: 2,7 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0031-base-pr-000.dot * REASONING * DIS # A1: 1,2 => CTR => A1: 5,7,8 * PRF # H6: 5,9 => SOL * PRF # G1: 1,5 => SOL * PRF # H6: 1,5 => SOL * PRF # C6: 6,7 => SOL * DIS # D5: 6,7 => CTR => D5: 1,8 * DIS # E4: 2,7 => CTR => E4: 1,5,8 * DIS # C9: 5,8 => CTR => C9: 3,9 * DIS # A1: 5,8 => CTR => A1: 1,2,7 * DIS # C9: 5,9 => CTR => C9: 3,8 * CNT 10 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B1,C5,F5,F9,H2,H3) * ....6..4......17.89....82.6.....4.3.35..9...4.8...3.....23....5..12......7..4..62 * PAIR B1: 1,2 BLK 1 A1: 1,2,5,7,8 # reduction candidate for 1,2 A1: 1,2 => CTR * ..8.6.543...421798947538216..9.54.3.356.92..4284..3.5...23....5..12......7..4..62 * PAIR H2: 5,9 BLK 3 G1: 5,9,1,3 # reduction candidate for 5,9 G1: 5,9 => SOLVED * 718962543265431798934758216129584637356197824487623951892316475641275389573849162 * DURATION: 0:00:04.132985 START: 04:00:55.619281 END: 04:00:59.752266 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0031-base-pr-001.dot * REASONING * DIS # A1: 1,2 => CTR => A1: 5,7,8 * PRF A1: 5,7,8 # G1: 5,9 => SOL * STA A1: 5,7,8 + G1: 5,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=31
Solution
position: 718962543265431798934758216129584637356197824487623951892316475641275389573849162 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 # A1: 1,2 => CTR => A1: 5,7,8 * INC # A1: 5,7,8 => UNS * INC # B4: 1,2 => UNS * INC # B4: 6,9 => UNS * INC # G1: 5,9 => UNS * INC # G1: 1,3 => UNS * INC # D2: 5,9 => UNS * INC # D2: 4 => UNS * PRF # H6: 5,9 => SOL * INC # H6: 1,2,7 => UNS * PRF # G1: 1,5 => SOL * INC # G1: 3,9 => UNS * PRF # H6: 1,5 => SOL * INC # H6: 2,7,9 => UNS * INC # A4: 6,7 => UNS * INC # C4: 6,7 => UNS * INC # A6: 6,7 => UNS * PRF # C6: 6,7 => SOL * INC # C6: 4,9 => UNS * DIS # D5: 6,7 => CTR => D5: 1,8 * INC # D5: 1,8 => UNS * DIS # E4: 2,7 => CTR => E4: 1,5,8 * INC # E4: 1,5,8 => UNS * INC # E6: 2,7 => UNS * INC # H5: 2,7 => UNS * INC # H5: 1,8 => UNS * INC # F1: 2,7 => UNS * INC # F1: 5,9 => UNS * INC # A8: 5,8 => UNS * DIS # C9: 5,8 => CTR => C9: 3,9 * INC # C9: 3,9 => UNS * INC # D9: 5,8 => UNS * INC # D9: 1,9 => UNS * DIS # A1: 5,8 => CTR => A1: 1,2,7 * INC # A1: 1,2,7 => UNS * INC # F8: 5,9 => UNS * INC # D9: 5,9 => UNS * DIS # C9: 5,9 => CTR => C9: 3,8 * INC # C9: 3,8 => UNS * INC # F1: 5,9 => UNS * INC # F1: 2,7 => UNS * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 1,2 => CTR => A1: 5,7,8 * PRF A1: 5,7,8 # G1: 5,9 => SOL * STA A1: 5,7,8 + G1: 5,9 * CNT 2 HDP CHAINS / 2 HYP OPENED