Analysis of xx-top500-157-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 1...52.4.....6..........3.....3..7.65..7...........8....2....5..3.8.............1 initial

Autosolve

position: 1739526482..1635796594..312..13.572652.7..1343.721.8958126...53.35821.677..53.281 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B4: 4,8 => CTR => B4: 9
* PRF # B4: 9 => SOL
* PRF # B4: 4,9 => SOL
* DIS # B4: 8 => CTR => B4: 4,9
* DIS # F5: 9 => CTR => F5: 6,8
* PRF # B9: 4,6 => SOL
* DIS # B9: 9 => CTR => B9: 4,6
* DIS # B4: 4,8 => CTR => B4: 9
* PRF # B4: 9 => SOL
* DIS # F5: 8,9 => CTR => F5: 6
* PRF # F5: 6 => SOL
* PRF # B9: 4,9 => SOL
* DIS # B9: 6 => CTR => B9: 4,9
* PRF # B9: 4,6 => SOL
* DIS # B9: 9 => CTR => B9: 4,6
* DIS # F7: 4,9 => CTR => F7: 7
* PRF # B9: 4,9 => SOL
* DIS # B9: 6 => CTR => B9: 4,9
* DIS # F7: 4,9 => CTR => F7: 7
* CNT  19 HDP CHAINS /  24 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # B4: 4,8 => CTR => B4: 9
* PRF B4: 9 => SOL
* STA B4: 9
* CNT   2 HDP CHAINS /   1 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Details

Positions

1...52.4.....6..........3.....3..7.65..7...........8....2....5..3.8.............1 initial
1739526482..1635796594..312..13.572652.7..1343.721.8958126...53.35821.677..53.281 autosolve
173952648284163579659478312491385726528796134367214895812647953935821467746539281 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (15)
B2: 4,8
C2: 4,8
E3: 7,8
F3: 7,8
A4: 4,9
C5: 6,8
B6: 4,6
E4: 4,8
E5: 8,9
F6: 4,6
A8: 4,9
C9: 4,6
F9: 4,9
G7: 4,9
G8: 4,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B2,C2: 4.. / B2 = 4  =>  0 pairs (X) / C2 = 4  =>  0 pairs (_)
E4,F6: 4.. / E4 = 4  =>  0 pairs (X) / F6 = 4  =>  0 pairs (_)
G7,G8: 4.. / G7 = 4  =>  0 pairs (X) / G8 = 4  =>  0 pairs (_)
B6,F6: 4.. / B6 = 4  =>  0 pairs (X) / F6 = 4  =>  0 pairs (_)
A8,G8: 4.. / A8 = 4  =>  0 pairs (X) / G8 = 4  =>  0 pairs (_)
A4,A8: 4.. / A4 = 4  =>  0 pairs (*) / A8 = 4  =>  0 pairs (X)
C2,C9: 4.. / C2 = 4  =>  0 pairs (*) / C9 = 4  =>  0 pairs (X)
E4,E7: 4.. / E4 = 4  =>  0 pairs (X) / E7 = 4  =>  0 pairs (_)
C5,B6: 6.. / C5 = 6  =>  0 pairs (X) / B6 = 6  =>  0 pairs (_)
F5,F6: 6.. / F5 = 6  =>  0 pairs (*) / F6 = 6  =>  0 pairs (X)
B9,C9: 6.. / B9 = 6  =>  0 pairs (X) / C9 = 6  =>  0 pairs (_)
C5,F5: 6.. / C5 = 6  =>  0 pairs (X) / F5 = 6  =>  0 pairs (_)
B6,F6: 6.. / B6 = 6  =>  0 pairs (*) / F6 = 6  =>  0 pairs (X)
B6,B9: 6.. / B6 = 6  =>  0 pairs (*) / B9 = 6  =>  0 pairs (X)
C5,C9: 6.. / C5 = 6  =>  0 pairs (X) / C9 = 6  =>  0 pairs (_)
E3,F3: 7.. / E3 = 7  => 15 pairs (_) / F3 = 7  =>  0 pairs (X)
E7,F7: 7.. / E7 = 7  =>  0 pairs (X) / F7 = 7  => 15 pairs (_)
E3,E7: 7.. / E3 = 7  => 15 pairs (_) / E7 = 7  =>  0 pairs (X)
F3,F7: 7.. / F3 = 7  =>  0 pairs (X) / F7 = 7  => 15 pairs (_)
B2,C2: 8.. / B2 = 8  =>  0 pairs (*) / C2 = 8  =>  0 pairs (X)
E3,F3: 8.. / E3 = 8  =>  0 pairs (X) / F3 = 8  => 15 pairs (_)
B4,C5: 8.. / B4 = 8  =>  0 pairs (X) / C5 = 8  =>  0 pairs (_)
B4,E4: 8.. / B4 = 8  =>  0 pairs (X) / E4 = 8  =>  0 pairs (_)
B2,B4: 8.. / B2 = 8  =>  0 pairs (*) / B4 = 8  =>  0 pairs (X)
C2,C5: 8.. / C2 = 8  =>  0 pairs (X) / C5 = 8  =>  0 pairs (_)
F3,F5: 8.. / F3 = 8  => 15 pairs (_) / F5 = 8  =>  0 pairs (X)
A4,B4: 9.. / A4 = 9  =>  0 pairs (X) / B4 = 9  =>  0 pairs (_)
E5,F5: 9.. / E5 = 9  => 16 pairs (_) / F5 = 9  =>  0 pairs (X)
A8,B9: 9.. / A8 = 9  =>  0 pairs (*) / B9 = 9  =>  0 pairs (X)
G7,G8: 9.. / G7 = 9  =>  0 pairs (*) / G8 = 9  =>  0 pairs (X)
A8,G8: 9.. / A8 = 9  =>  0 pairs (*) / G8 = 9  =>  0 pairs (X)
B9,F9: 9.. / B9 = 9  =>  0 pairs (X) / F9 = 9  =>  0 pairs (_)
A4,A8: 9.. / A4 = 9  =>  0 pairs (X) / A8 = 9  =>  0 pairs (_)
B4,B9: 9.. / B4 = 9  =>  0 pairs (*) / B9 = 9  =>  0 pairs (X)
E5,E7: 9.. / E5 = 9  => 16 pairs (_) / E7 = 9  =>  0 pairs (X)
* DURATION: 0:01:01.797063  START: 08:06:58.638262  END: 08:08:00.435325 2017-05-04
* CP COUNT: (35)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A8,B2,B6,C2,C5,C9,E3,E4,E5,F3,F6,F9,G7,G8)
* 1739526482..1635796594..312..13.572652.7..1343.721.8958126...53.35821.677..53.281
* PAIR B2: 4,8 COL B
B4: 4,8,9                                # reduction candidate for 4,8
B4: 4,8 => CTR
* 1739526482..1635796594..3129.13.572652.7..1343.721.8958126...53435821967796534281
B4: 9 => SOLVED
* 173952648284163579659478312491385726528796134367214895812647953935821467746539281
* PAIR A4: 4,9 BLK 4
B4: 4,9,8                                # reduction candidate for 4,9
B4: 4,9 => SOLVED
* 173952648284163579659478312491385726528796134367214895812647953935821467746539281
B4: 8 => CTR
* 1739526482..1635796594..3129813457265267..13434721.8958126...53.35821.677..53.281
* PAIR C5: 6,8 ROW 5
F5: 6,8,9                                # reduction candidate for 6,8
F5: 9 => CTR
* 1739526482..1635796594.8312..13.572652678913434721.8958126...53.35821.677..53.281
F5: 6,8                                  # 16 pairs
* PAIR B6: 4,6 COL B
B9: 4,6,9                                # reduction candidate for 4,6
B9: 4,6 => SOLVED
* 173952648284163579659478312491385726528796134367214895812647953935821467746539281
B9: 9 => CTR
* 1739526482..1635796594..312..13.572652.7..134367214895812647953935821.677..53.281
* PAIR E4: 4,8 ROW 4
B4: 4,8,9                                # reduction candidate for 4,8
B4: 4,8 => CTR
* 1739526482..1635796594..3129.13.572652.7..1343.721.8958126...53435821967796534281
B4: 9 => SOLVED
* 173952648284163579659478312491385726528796134367214895812647953935821467746539281
* PAIR E5: 8,9 BLK 5
F5: 8,9,6                                # reduction candidate for 8,9
F5: 8,9 => CTR
* 1739526482..1635796594..312..13.57265267..1343472168958126...53435821.677..53.281
F5: 6 => SOLVED
* 173952648284163579659478312491385726528796134367214895812647953935821467746539281
* PAIR A8: 4,9 BLK 7
B9: 4,9,6                                # reduction candidate for 4,9
B9: 4,9 => SOLVED
* 173952648284163579659478312491385726528796134367214895812647953935821467746539281
B9: 6 => CTR
* 1739526482..1635796594..312.9138572652879613436721.8958126...53.35821.677..53.281
* PAIR C9: 4,6 BLK 7
B9: 4,6,9                                # reduction candidate for 4,6
B9: 4,6 => SOLVED
* 173952648284163579659478312491385726528796134367214895812647953935821467746539281
B9: 9 => CTR
* 1739526482..1635796594..312..13.572652.7..134367214895812647953935821.677..53.281
* PAIR F9: 4,9 BLK 8
E7: 4,9,7                                # reduction candidate for 4,9
E7: 4,9                                  # 15 pairs
F7: 4,9,7                                # reduction candidate for 4,9
F7: 4,9 => CTR
* 1739526482..1635796594.7312..13.572652.7.81343.721689581267..53.35821.67764539281
F7: 7                                    # 15 pairs
* PAIR F9: 4,9 ROW 9
B9: 4,9,6                                # reduction candidate for 4,9
B9: 4,9 => SOLVED
* 173952648284163579659478312491385726528796134367214895812647953935821467746539281
B9: 6 => CTR
* 1739526482..1635796594..312.9138572652879613436721.8958126...53.35821.677..53.281
* PAIR G7: 4,9 ROW 7
E7: 4,9,7                                # reduction candidate for 4,9
E7: 4,9                                  # 15 pairs
F7: 4,9,7                                # reduction candidate for 4,9
F7: 4,9 => CTR
* 1739526482..1635796594.7312..13.572652.7.81343.721689581267..53.35821.67764539281
F7: 7                                    # 15 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-157-base-pr-000.dot
* REASONING
* DIS # B4: 4,8 => CTR => B4: 9
* PRF # B4: 9 => SOL
* PRF # B4: 4,9 => SOL
* DIS # B4: 8 => CTR => B4: 4,9
* DIS # F5: 9 => CTR => F5: 6,8
* PRF # B9: 4,6 => SOL
* DIS # B9: 9 => CTR => B9: 4,6
* DIS # B4: 4,8 => CTR => B4: 9
* PRF # B4: 9 => SOL
* DIS # F5: 8,9 => CTR => F5: 6
* PRF # F5: 6 => SOL
* PRF # B9: 4,9 => SOL
* DIS # B9: 6 => CTR => B9: 4,9
* PRF # B9: 4,6 => SOL
* DIS # B9: 9 => CTR => B9: 4,6
* DIS # F7: 4,9 => CTR => F7: 7
* PRF # B9: 4,9 => SOL
* DIS # B9: 6 => CTR => B9: 4,9
* DIS # F7: 4,9 => CTR => F7: 7
* CNT  19 HDP CHAINS /  24 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A8,B2,B6,C2,C5,C9,E3,E4,E5,F3,F6,F9,G7,G8)
* 1739526482..1635796594..312..13.572652.7..1343.721.8958126...53.35821.677..53.281
* PAIR B2: 4,8 COL B
B4: 4,8,9                                # reduction candidate for 4,8
B4: 4,8 => CTR
* 1739526482..1635796594..3129.13.572652.7..1343.721.8958126...53435821967796534281
B4: 9 => SOLVED
* 173952648284163579659478312491385726528796134367214895812647953935821467746539281
* DURATION: 0:00:02.755548  START: 08:08:26.475514  END: 08:08:29.231062 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-157-base-pr-001.dot
* REASONING
* DIS # B4: 4,8 => CTR => B4: 9
* PRF B4: 9 => SOL
* STA B4: 9
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 157

solution: 173952648284163579659478312491385726528796134367214895812647953935821467746539281
info: 1819     FNBWY    S8.f     25339

http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/

Solution

position: 173952648284163579659478312491385726528796134367214895812647953935821467746539281 solved
Solution

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 # B4: 4,8 => CTR => B4: 9
* PRF # B4: 9 => SOL
* PRF # B4: 4,9 => SOL
* DIS # B4: 8 => CTR => B4: 4,9
* INC # F5: 6,8 => UNS
* DIS # F5: 9 => CTR => F5: 6,8
* PRF # B9: 4,6 => SOL
* DIS # B9: 9 => CTR => B9: 4,6
* DIS # B4: 4,8 => CTR => B4: 9
* PRF # B4: 9 => SOL
* DIS # F5: 8,9 => CTR => F5: 6
* PRF # F5: 6 => SOL
* PRF # B9: 4,9 => SOL
* DIS # B9: 6 => CTR => B9: 4,9
* PRF # B9: 4,6 => SOL
* DIS # B9: 9 => CTR => B9: 4,6
* INC # E7: 4,9 => UNS
* DIS # F7: 4,9 => CTR => F7: 7
* INC # F7: 7 => UNS
* PRF # B9: 4,9 => SOL
* DIS # B9: 6 => CTR => B9: 4,9
* INC # E7: 4,9 => UNS
* DIS # F7: 4,9 => CTR => F7: 7
* INC # F7: 7 => UNS
* CNT  24 HDP CHAINS /  24 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B4: 4,8 => CTR => B4: 9
* PRF B4: 9 => SOL
* STA B4: 9
* CNT   2 HDP CHAINS /   1 HYP OPENED