Analysis of zz-google-002-base.sdk
Contents
Original Sudoku
level: medium
position: ..4.2.....9..8.....17..5..24..23.....58.7..2...2.....7.25.9.3..74.............81. initial
Autosolve
position: 584.2.7..29..875...17..5.8247.23.158158.7..23..2518..7825.9.37.7418.32.....7.281. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H2: 3,6 => CTR => H2: 4 * DIS # C9: 9 => CTR => C9: 3,6 * DIS # D3: 3,6 => CTR => D3: 4,9 * PRF # D3: 4,9 => SOL * DIS # A9: 3,6 => CTR => A9: 9 * PRF # D3: 4,6 => SOL * DIS # G3: 4,6 => CTR => G3: 9 * PRF # G3: 9 => SOL * PRF # I1: 1,6 => SOL * DIS # I1: 9 => CTR => I1: 1,6 * DIS # D2: 1,6 => CTR => D2: 3,4 * DIS # A6: 3 => CTR => A6: 6,9 * DIS # C9: 6,9 => CTR => C9: 3 * DIS # A6: 9 => CTR => A6: 3,6 * DIS # F5: 6,9 => CTR => F5: 4 * DIS # G6: 6,9 => CTR => G6: 4 * DIS # F5: 6,9 => CTR => F5: 4 * DIS # G3: 4 => CTR => G3: 6,9 * DIS # A9: 3,6 => CTR => A9: 9 * DIS # I8: 5,6 => CTR => I8: 9 * PRF # I8: 9 => SOL * PRF # I8: 6,9 => SOL * DIS # I8: 5 => CTR => I8: 6,9 * DIS # H1: 6,9 => CTR => H1: 3 * CNT 24 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H2: 3,6 => CTR => H2: 4 * DIS H2: 4 # D2: 1 => CTR => D2: 3,6 * PRF H2: 4 + D2: 3,6 # C9: 3,6 => SOL * STA H2: 4 + D2: 3,6 + C9: 3,6 * CNT 3 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..4.2.....9..8.....17..5..24..23.....58.7..2...2.....7.25.9.3..74.............81. | initial |
| 584.2.7..29..875...17..5.8247.23.158158.7..23..2518..7825.9.37.7418.32.....7.281. | autosolve |
| 584129736296387541317465982479236158158974623632518497825691374741853269963742815 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) C2: 3,6 A3: 3,6 E3: 4,6 I2: 1,6 C4: 6,9 B6: 3,6 F4: 6,9 G5: 6,9 B9: 3,6 E8: 5,6 E9: 4,5 I7: 4,6 H8: 6,9 I9: 4,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I1,I2: 1.. / I1 = 1 => 0 pairs (X) / I2 = 1 => 14 pairs (_) D7,F7: 1.. / D7 = 1 => 16 pairs (_) / F7 = 1 => 17 pairs (_) D2,I2: 1.. / D2 = 1 => 0 pairs (X) / I2 = 1 => 14 pairs (_) F1,F7: 1.. / F1 = 1 => 16 pairs (_) / F7 = 1 => 17 pairs (_) C2,A3: 3.. / C2 = 3 => 0 pairs (X) / A3 = 3 => 16 pairs (_) H1,H2: 3.. / H1 = 3 => 15 pairs (_) / H2 = 3 => 0 pairs (X) A6,B6: 3.. / A6 = 3 => 0 pairs (X) / B6 = 3 => 15 pairs (_) D1,H1: 3.. / D1 = 3 => 0 pairs (X) / H1 = 3 => 15 pairs (_) A3,D3: 3.. / A3 = 3 => 16 pairs (_) / D3 = 3 => 0 pairs (X) B6,B9: 3.. / B6 = 3 => 15 pairs (_) / B9 = 3 => 0 pairs (X) C2,C9: 3.. / C2 = 3 => 0 pairs (X) / C9 = 3 => 16 pairs (_) H2,G3: 4.. / H2 = 4 => 16 pairs (_) / G3 = 4 => 0 pairs (X) D5,F5: 4.. / D5 = 4 => 0 pairs (X) / F5 = 4 => 16 pairs (_) G6,H6: 4.. / G6 = 4 => 16 pairs (_) / H6 = 4 => 0 pairs (X) I7,I9: 4.. / I7 = 4 => 0 pairs (*) / I9 = 4 => 0 pairs (X) D2,H2: 4.. / D2 = 4 => 0 pairs (X) / H2 = 4 => 16 pairs (_) E9,I9: 4.. / E9 = 4 => 0 pairs (*) / I9 = 4 => 0 pairs (X) E3,E9: 4.. / E3 = 4 => 0 pairs (X) / E9 = 4 => 0 pairs (_) F5,F7: 4.. / F5 = 4 => 16 pairs (_) / F7 = 4 => 0 pairs (X) G3,G6: 4.. / G3 = 4 => 0 pairs (X) / G6 = 4 => 16 pairs (_) H2,H6: 4.. / H2 = 4 => 16 pairs (_) / H6 = 4 => 0 pairs (X) E8,E9: 5.. / E8 = 5 => 0 pairs (*) / E9 = 5 => 0 pairs (X) I8,I9: 5.. / I8 = 5 => 0 pairs (X) / I9 = 5 => 0 pairs (_) E8,I8: 5.. / E8 = 5 => 0 pairs (*) / I8 = 5 => 0 pairs (X) E9,I9: 5.. / E9 = 5 => 0 pairs (X) / I9 = 5 => 0 pairs (_) C2,A3: 6.. / C2 = 6 => 16 pairs (_) / A3 = 6 => 0 pairs (X) C4,F4: 6.. / C4 = 6 => 0 pairs (X) / F4 = 6 => 20 pairs (_) B6,B9: 6.. / B6 = 6 => 0 pairs (X) / B9 = 6 => 15 pairs (_) E3,E8: 6.. / E3 = 6 => 0 pairs (*) / E8 = 6 => 0 pairs (X) C4,A6: 9.. / C4 = 9 => 20 pairs (_) / A6 = 9 => 0 pairs (X) A9,C9: 9.. / A9 = 9 => 20 pairs (_) / C9 = 9 => 0 pairs (X) H8,I8: 9.. / H8 = 9 => 0 pairs (X) / I8 = 9 => 0 pairs (_) D3,G3: 9.. / D3 = 9 => 0 pairs (X) / G3 = 9 => 0 pairs (_) C4,F4: 9.. / C4 = 9 => 20 pairs (_) / F4 = 9 => 0 pairs (X) A6,A9: 9.. / A6 = 9 => 0 pairs (X) / A9 = 9 => 20 pairs (_) C4,C9: 9.. / C4 = 9 => 20 pairs (_) / C9 = 9 => 0 pairs (X) I1,I8: 9.. / I1 = 9 => 0 pairs (X) / I8 = 9 => 0 pairs (_) * DURATION: 0:01:03.763899 START: 06:22:59.087105 END: 06:24:02.851004 2017-05-01 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B6,B9,C2,C4,E3,E8,E9,F4,G5,H8,I2,I7,I9) * 584.2.7..29..875...17..5.8247.23.158158.7..23..2518..7825.9.37.7418.32.....7.281. * PAIR C2: 3,6 ROW 2 D2: 3,6,1,4 # reduction candidate for 3,6 D2: 3,6 # 17 pairs H2: 3,6,4 # reduction candidate for 3,6 H2: 3,6 => CTR * 584.2.7..29648753131796548247923.158158.74.23..2518.47825.9.3747418532.....742815 H2: 4 # 16 pairs * PAIR C2: 3,6 COL C C9: 3,6,9 # reduction candidate for 3,6 C9: 9 => CTR * 584.2.7..293.875..617345982476239158158.7.6239325184.7825.9.37.7418.32.....7.281. C9: 3,6 # 20 pairs * PAIR A3: 3,6 ROW 3 D3: 3,6,4,9 # reduction candidate for 3,6 D3: 3,6 => CTR * 584.2.7..29..875...17..598247.23.158158.7.623..2518497825.9.37.7418.32699..7.2815 D3: 4,9 => SOLVED * 584129736296387541317465982479236158158974623632518497825691374741853269963742815 * PAIR A3: 3,6 COL A A6: 3,6,9 # reduction candidate for 3,6 A6: 3,6 # 20 pairs A9: 3,6,9 # reduction candidate for 3,6 A9: 3,6 => CTR * 584.2.7..293.875..617345982476239158158.7.6239325184.7825.9.37.7418.32...697.281. A9: 9 # 20 pairs * PAIR E3: 4,6 BLK 2 D2: 4,6,1,3 # reduction candidate for 4,6 D2: 4,6 # 20 pairs D3: 4,6,3,9 # reduction candidate for 4,6 D3: 4,6 => SOLVED * 584129736296387541317465982479236158158974623632518497825691374741853269963742815 D3: 3,9 # 15 pairs * PAIR E3: 4,6 ROW 3 G3: 4,6,9 # reduction candidate for 4,6 G3: 4,6 => CTR * 584.2.7..296.875.13179.5.82479236158158479623632518947825.943767418632...637.281. G3: 9 => SOLVED * 584129736296387541317465982479236158158974623632518497825691374741853269963742815 * PAIR I2: 1,6 BLK 3 I1: 1,6,9 # reduction candidate for 1,6 I1: 1,6 => SOLVED * 584129736296387541317465982479236158158974623632518497825691374741853269963742815 I1: 9 => CTR * 584.2.7.9296.875.13179.5.82479236158158479623632518947825.9437674186329..637.281. * PAIR I2: 1,6 ROW 2 D2: 1,6,3,4 # reduction candidate for 1,6 D2: 1,6 => CTR * 584.2.73.293.8754.61734598247.23.158158.7.623.62518497825.9.37.7418632.....7.281. D2: 3,4 # 15 pairs * PAIR C4: 6,9 BLK 4 A6: 6,9,3 # reduction candidate for 6,9 A6: 3 => CTR * 584.2.7..293.875..617345982479236158158.7.623362518497825.9.37.7418632..9367.281. A6: 6,9 # 15 pairs * PAIR C4: 6,9 COL C C9: 6,9,3 # reduction candidate for 6,9 C9: 6,9 => CTR * 584.2.7..293.875..61734598247.23.158158.7.623.62518497825.9.37.7418632.....7.281. C9: 3 # 16 pairs * PAIR B6: 3,6 BLK 4 A6: 3,6,9 # reduction candidate for 3,6 A6: 9 => CTR * 584.2.7..293.875..617345982476239158158.7.6239325184.7825.9.37.7418.32...697.281. A6: 3,6 # 20 pairs * PAIR F4: 6,9 BLK 5 D5: 6,9,4 # reduction candidate for 6,9 D5: 6,9 # 16 pairs F5: 6,9,4 # reduction candidate for 6,9 F5: 6,9 => CTR * 584.217.929..87541.1794568247.23.1581584769239325184678251943767418632956..752814 F5: 4 # 16 pairs * PAIR F4: 6,9 COL F F1: 6,9,1 # reduction candidate for 6,9 F1: 6,9 # 17 pairs F1: 1 # 16 pairs * PAIR G5: 6,9 BLK 6 G6: 6,9,4 # reduction candidate for 6,9 G6: 6,9 => CTR * 584.2.7..29.4875.1.1796548247.23.1581586749239325186478251963747418532..6..742815 G6: 4 # 16 pairs H6: 6,9,4 # reduction candidate for 6,9 H6: 6,9 # 16 pairs * PAIR G5: 6,9 ROW 5 D5: 6,9,4 # reduction candidate for 6,9 D5: 6,9 # 16 pairs F5: 6,9,4 # reduction candidate for 6,9 F5: 6,9 => CTR * 584.217.929..87541.1794568247.23.1581584769239325184678251943767418632956..752814 F5: 4 # 16 pairs * PAIR G5: 6,9 COL G G3: 6,9,4 # reduction candidate for 6,9 G3: 4 => CTR * 584.2.7..29.4875.131796548247.23.1581586749239325186478251963747418532..6..742815 G3: 6,9 # 16 pairs * PAIR B9: 3,6 BLK 7 A9: 3,6,9 # reduction candidate for 3,6 A9: 3,6 => CTR * 584.2.7..293.875..617345982476239158158.7.6239325184.7825.9.37.7418.32...697.281. A9: 9 # 20 pairs C9: 3,6,9 # reduction candidate for 3,6 C9: 3,6 # 20 pairs * PAIR E8: 5,6 ROW 8 I8: 5,6,9 # reduction candidate for 5,6 I8: 5,6 => CTR * 584.2.7.9296.875.13179.5.82479236158158479623632518947825.9437674186329..637.281. I8: 9 => SOLVED * 584129736296387541317465982479236158158974623632518497825691374741853269963742815 * PAIR I7: 4,6 ROW 7 D7: 4,6,1 # reduction candidate for 4,6 D7: 4,6 # 17 pairs F7: 4,6,1 # reduction candidate for 4,6 F7: 4,6 # 16 pairs * PAIR H8: 6,9 BLK 9 I8: 6,9,5 # reduction candidate for 6,9 I8: 6,9 => SOLVED * 584129736296387541317465982479236158158974623632518497825691374741853269963742815 I8: 5 => CTR * 584.2.7.929..875.131794568247.23.158158.7.923932518467825.9.3767418632956..752814 * PAIR H8: 6,9 COL H H1: 6,9,3 # reduction candidate for 6,9 H1: 6,9 => CTR * 58432.7..296487531317965482479236158158.7..23.32518.47825.9.37.7418.32...63742815 H1: 3 # 15 pairs H6: 6,9,4 # reduction candidate for 6,9 H6: 6,9 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-google-002-base-pr-000.dot * REASONING * DIS # H2: 3,6 => CTR => H2: 4 * DIS # C9: 9 => CTR => C9: 3,6 * DIS # D3: 3,6 => CTR => D3: 4,9 * PRF # D3: 4,9 => SOL * DIS # A9: 3,6 => CTR => A9: 9 * PRF # D3: 4,6 => SOL * DIS # G3: 4,6 => CTR => G3: 9 * PRF # G3: 9 => SOL * PRF # I1: 1,6 => SOL * DIS # I1: 9 => CTR => I1: 1,6 * DIS # D2: 1,6 => CTR => D2: 3,4 * DIS # A6: 3 => CTR => A6: 6,9 * DIS # C9: 6,9 => CTR => C9: 3 * DIS # A6: 9 => CTR => A6: 3,6 * DIS # F5: 6,9 => CTR => F5: 4 * DIS # G6: 6,9 => CTR => G6: 4 * DIS # F5: 6,9 => CTR => F5: 4 * DIS # G3: 4 => CTR => G3: 6,9 * DIS # A9: 3,6 => CTR => A9: 9 * DIS # I8: 5,6 => CTR => I8: 9 * PRF # I8: 9 => SOL * PRF # I8: 6,9 => SOL * DIS # I8: 5 => CTR => I8: 6,9 * DIS # H1: 6,9 => CTR => H1: 3 * CNT 24 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B6,B9,C2,C4,E3,E8,E9,F4,G5,H8,I2,I7,I9) * 584.2.7..29..875...17..5.8247.23.158158.7..23..2518..7825.9.37.7418.32.....7.281. * PAIR C2: 3,6 ROW 2 D2: 3,6,1,4 # reduction candidate for 3,6 D2: 3,6 # 17 pairs H2: 3,6,4 # reduction candidate for 3,6 H2: 3,6 => CTR * 584.2.7..29648753131796548247923.158158.74.23..2518.47825.9.3747418532.....742815 * RESTART * PAIR C2: 3,6 ROW 2 D2: 3,6,1 # reduction candidate for 3,6 D2: 1 => CTR * 584.2.73.29318754661734598247.23.158158.7.623.62518497825.913747418.32.....7.281. * PAIR C2: 3,6 COL C C9: 3,6,9 # reduction candidate for 3,6 C9: 3,6 => SOLVED * 584129736296387541317465982479236158158974623632518497825691374741853269963742815 * DURATION: 0:00:06.058386 START: 06:24:51.422267 END: 06:24:57.480653 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-google-002-base-pr-001.dot * REASONING * DIS # H2: 3,6 => CTR => H2: 4 * DIS H2: 4 # D2: 1 => CTR => D2: 3,6 * PRF H2: 4 + D2: 3,6 # C9: 3,6 => SOL * STA H2: 4 + D2: 3,6 + C9: 3,6 * CNT 3 HDP CHAINS / 5 HYP OPENED
Header Info
* PAIR REDUCTION .. * ROUND 1: 584.2.7..29..875...17..5.8247.23.158158.7..23..2518..7825.9.37.7418.32.....7.281. C2: 3,6 D2: 1,3,4,6 # reduction candidate for 3,6 H2: 3,4,6 # reduction candidate for 3,6 H2: 3,6 => CTR * 584.2.7..29648753131796548247923.158158.74.23..2518.47825.9.3747418532.....742815 C9: 3,6,9 # reduction candidate for 3,6 C9: 3,6 => SOLVED * 584129736296387541317465982479236158158974623632518497825691374741853269963742815 * SOLVED! -------------------------------------------------- -------------------------------------------------- quadruple: D3: 3,4,6,9 G3: 4,6,9 D5: 4,6,9 G5: 6,9 => D3 = 3 |:step:| 00 -------------------------------------------------- |:info:| alternate But even without any single row/column constraints: E9 := !4 => CTR E9 := 4 => SOL With single row/column constraints:: I1 := !9 => SOL I1 := 9 => CTR
Solution
position: 584129736296387541317465982479236158158974623632518497825691374741853269963742815 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 # D2: 3,6 => UNS * DIS # H2: 3,6 => CTR => H2: 4 * INC # H2: 4 => UNS * INC # C9: 3,6 => UNS * DIS # C9: 9 => CTR => C9: 3,6 * DIS # D3: 3,6 => CTR => D3: 4,9 * PRF # D3: 4,9 => SOL * INC # A6: 3,6 => UNS * DIS # A9: 3,6 => CTR => A9: 9 * INC # A9: 9 => UNS * INC # D2: 4,6 => UNS * PRF # D3: 4,6 => SOL * INC # D3: 3,9 => UNS * DIS # G3: 4,6 => CTR => G3: 9 * PRF # G3: 9 => SOL * PRF # I1: 1,6 => SOL * DIS # I1: 9 => CTR => I1: 1,6 * DIS # D2: 1,6 => CTR => D2: 3,4 * INC # D2: 3,4 => UNS * INC # A6: 6,9 => UNS * DIS # A6: 3 => CTR => A6: 6,9 * DIS # C9: 6,9 => CTR => C9: 3 * INC # C9: 3 => UNS * INC # A6: 3,6 => UNS * DIS # A6: 9 => CTR => A6: 3,6 * INC # D5: 6,9 => UNS * DIS # F5: 6,9 => CTR => F5: 4 * INC # F5: 4 => UNS * INC # F1: 6,9 => UNS * INC # F1: 1 => UNS * DIS # G6: 6,9 => CTR => G6: 4 * INC # G6: 4 => UNS * INC # H6: 6,9 => UNS * INC # D5: 6,9 => UNS * DIS # F5: 6,9 => CTR => F5: 4 * INC # F5: 4 => UNS * INC # G3: 6,9 => UNS * DIS # G3: 4 => CTR => G3: 6,9 * DIS # A9: 3,6 => CTR => A9: 9 * INC # A9: 9 => UNS * INC # C9: 3,6 => UNS * DIS # I8: 5,6 => CTR => I8: 9 * PRF # I8: 9 => SOL * INC # D7: 4,6 => UNS * INC # F7: 4,6 => UNS * PRF # I8: 6,9 => SOL * DIS # I8: 5 => CTR => I8: 6,9 * DIS # H1: 6,9 => CTR => H1: 3 * INC # H1: 3 => UNS * INC # H6: 6,9 => UNS * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D2: 3,6 => UNS * DIS # H2: 3,6 => CTR => H2: 4 * INC H2: 4 # D2: 3,6 => UNS * DIS H2: 4 # D2: 1 => CTR => D2: 3,6 * PRF H2: 4 + D2: 3,6 # C9: 3,6 => SOL * STA H2: 4 + D2: 3,6 + C9: 3,6 * CNT 5 HDP CHAINS / 5 HYP OPENED