Analysis of xx-top500-359-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 7.....4.98..2...........6......48.5.9............1.......3.7....4.....2..6.9..... initial

Autosolve

position: 726...4.98.4296.7..9.47.6826.274895.9..632.4.4..51926.2..367.94349...726.67924... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # C3: 1,3 => SOL
* DIS # C3: 5 => CTR => C3: 1,3
* DIS # G2: 5 => CTR => G2: 1,3
* DIS # C3: 1,5 => CTR => C3: 3
* PRF # C3: 3 => SOL
* DIS # F1: 5 => CTR => F1: 1,3
* PRF # C3: 1,3 => SOL
* DIS # C3: 5 => CTR => C3: 1,3
* DIS # G2: 5 => CTR => G2: 1,3
* DIS # F1: 5 => CTR => F1: 1,3
* DIS # G2: 1,5 => CTR => G2: 3
* PRF # G2: 3 => SOL
* DIS # I9: 1,5 => CTR => I9: 8
* DIS # B5: 7,8 => CTR => B5: 5
* DIS # I6: 7,8 => CTR => I6: 3
* PRF # I6: 3 => SOL
* DIS # I6: 7 => CTR => I6: 3,8
* DIS # I5: 1,8 => CTR => I5: 7
* DIS # C5: 5 => CTR => C5: 1,8
* DIS # G9: 1,8 => CTR => G9: 3,5
* PRF # C7: 5,8 => SOL
* DIS # C7: 1 => CTR => C7: 5,8
* DIS # B5: 7 => CTR => B5: 5,8
* DIS # C7: 8 => CTR => C7: 1,5
* PRF # G9: 1,5 => SOL
* DIS # I9: 1,5 => CTR => I9: 8
* DIS # F1: 1,5 => CTR => F1: 3
* PRF # F1: 3 => SOL
* PRF # G9: 1,5 => SOL
* DIS # I9: 1,5 => CTR => I9: 8
* DIS # C7: 8 => CTR => C7: 1,5
* DIS # G2: 1,5 => CTR => G2: 3
* PRF # G2: 3 => SOL
* DIS # G9: 1,3 => CTR => G9: 5,8
* PRF # G9: 5,8 => SOL
* CNT  35 HDP CHAINS /  52 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* PRF # C3: 1,3 => SOL
* STA C3: 1,3
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

7.....4.98..2...........6......48.5.9............1.......3.7....4.....2..6.9..... initial
726...4.98.4296.7..9.47.6826.274895.9..632.4.4..51926.2..367.94349...726.67924... autosolve
726853419814296375593471682632748951951632847478519263285367194349185726167924538 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (19)
B2: 1,3
A3: 1,5
D1: 1,8
E1: 5,8
F3: 1,3
H1: 1,3
I2: 1,5
B4: 1,3
B6: 7,8
C6: 3,8
I4: 1,3
G5: 1,8
B7: 5,8
A9: 1,5
D8: 1,8
E8: 5,8
F8: 1,5
G7: 1,5
H9: 1,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B4,C5: 1.. / B4 = 1  =>  0 pairs (X) / C5 = 1  =>  0 pairs (_)
C7,A9: 1.. / C7 = 1  =>  0 pairs (X) / A9 = 1  =>  0 pairs (_)
D8,F8: 1.. / D8 = 1  => 15 pairs (_) / F8 = 1  =>  0 pairs (X)
B4,I4: 1.. / B4 = 1  =>  0 pairs (X) / I4 = 1  =>  0 pairs (_)
C7,G7: 1.. / C7 = 1  =>  0 pairs (X) / G7 = 1  =>  0 pairs (_)
A3,A9: 1.. / A3 = 1  =>  0 pairs (X) / A9 = 1  =>  0 pairs (_)
B2,B4: 1.. / B2 = 1  =>  0 pairs (*) / B4 = 1  =>  0 pairs (X)
D1,D8: 1.. / D1 = 1  =>  0 pairs (X) / D8 = 1  => 15 pairs (_)
H1,H9: 1.. / H1 = 1  =>  0 pairs (*) / H9 = 1  =>  0 pairs (X)
B2,C3: 3.. / B2 = 3  =>  0 pairs (X) / C3 = 3  =>  0 pairs (_)
F1,F3: 3.. / F1 = 3  =>  0 pairs (*) / F3 = 3  =>  0 pairs (X)
H1,G2: 3.. / H1 = 3  =>  0 pairs (X) / G2 = 3  =>  0 pairs (_)
B4,C6: 3.. / B4 = 3  =>  0 pairs (*) / C6 = 3  =>  0 pairs (X)
I4,I6: 3.. / I4 = 3  =>  0 pairs (X) / I6 = 3  =>  0 pairs (_)
G9,H9: 3.. / G9 = 3  =>  0 pairs (X) / H9 = 3  =>  0 pairs (_)
F1,H1: 3.. / F1 = 3  =>  0 pairs (*) / H1 = 3  =>  0 pairs (X)
B2,G2: 3.. / B2 = 3  =>  0 pairs (X) / G2 = 3  =>  0 pairs (_)
C3,F3: 3.. / C3 = 3  =>  0 pairs (*) / F3 = 3  =>  0 pairs (X)
B4,I4: 3.. / B4 = 3  =>  0 pairs (*) / I4 = 3  =>  0 pairs (X)
C6,I6: 3.. / C6 = 3  =>  0 pairs (X) / I6 = 3  =>  0 pairs (_)
B2,B4: 3.. / B2 = 3  =>  0 pairs (X) / B4 = 3  =>  0 pairs (_)
C3,C6: 3.. / C3 = 3  =>  0 pairs (*) / C6 = 3  =>  0 pairs (X)
G2,G9: 3.. / G2 = 3  =>  0 pairs (*) / G9 = 3  =>  0 pairs (X)
H1,H9: 3.. / H1 = 3  =>  0 pairs (X) / H9 = 3  =>  0 pairs (_)
A3,C3: 5.. / A3 = 5  =>  0 pairs (*) / C3 = 5  =>  0 pairs (X)
E1,F1: 5.. / E1 = 5  => 15 pairs (_) / F1 = 5  =>  0 pairs (X)
G2,I2: 5.. / G2 = 5  =>  0 pairs (X) / I2 = 5  => 20 pairs (_)
B5,C5: 5.. / B5 = 5  => 20 pairs (_) / C5 = 5  =>  0 pairs (X)
E8,F8: 5.. / E8 = 5  =>  0 pairs (X) / F8 = 5  => 15 pairs (_)
A3,A9: 5.. / A3 = 5  =>  0 pairs (*) / A9 = 5  =>  0 pairs (X)
B5,B7: 5.. / B5 = 5  => 20 pairs (_) / B7 = 5  =>  0 pairs (X)
E1,E8: 5.. / E1 = 5  => 15 pairs (_) / E8 = 5  =>  0 pairs (X)
F1,F8: 5.. / F1 = 5  =>  0 pairs (X) / F8 = 5  => 15 pairs (_)
I2,I9: 5.. / I2 = 5  => 20 pairs (_) / I9 = 5  =>  0 pairs (X)
B5,B6: 7.. / B5 = 7  =>  0 pairs (X) / B6 = 7  => 20 pairs (_)
I5,I6: 7.. / I5 = 7  => 20 pairs (_) / I6 = 7  =>  0 pairs (X)
B5,I5: 7.. / B5 = 7  =>  0 pairs (X) / I5 = 7  => 20 pairs (_)
B6,I6: 7.. / B6 = 7  => 20 pairs (_) / I6 = 7  =>  0 pairs (X)
D1,E1: 8.. / D1 = 8  => 15 pairs (_) / E1 = 8  =>  0 pairs (X)
B7,C7: 8.. / B7 = 8  => 20 pairs (_) / C7 = 8  =>  0 pairs (X)
D8,E8: 8.. / D8 = 8  =>  0 pairs (X) / E8 = 8  => 15 pairs (_)
G9,I9: 8.. / G9 = 8  =>  0 pairs (X) / I9 = 8  => 22 pairs (_)
D1,D8: 8.. / D1 = 8  => 15 pairs (_) / D8 = 8  =>  0 pairs (X)
E1,E8: 8.. / E1 = 8  =>  0 pairs (X) / E8 = 8  => 15 pairs (_)
G5,G9: 8.. / G5 = 8  => 22 pairs (_) / G9 = 8  =>  0 pairs (X)
* DURATION: 0:01:26.176567  START: 15:01:56.197850  END: 15:03:22.374417 2017-05-04
* CP COUNT: (45)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A9,B2,B4,B6,B7,C6,D1,D8,E1,E8,F3,F8,G5,G7,H1,H9,I2,I4)
* 726...4.98.4296.7..9.47.6826.274895.9..632.4.4..51926.2..367.94349...726.67924...
* PAIR B2: 1,3 BLK 1
C3: 1,3,5                                # reduction candidate for 1,3
C3: 1,3 => SOLVED
* 726853419814296375593471682632748951951632847478519263285367194349185726167924538
C3: 5 => CTR
* 726...4.9834296.7.19547368261274895395863214.4..51926.2..367.94349...726.67924...
* PAIR B2: 1,3 ROW 2
G2: 1,3,5                                # reduction candidate for 1,3
G2: 5 => CTR
* 726...439834296571.9.4736826127489539..63214.4..51926.2..367.94349...726.67924...
G2: 1,3                                  # 20 pairs
* PAIR A3: 1,5 BLK 1
C3: 1,5,3                                # reduction candidate for 1,5
C3: 1,5 => CTR
* 726...439834296.75195473682612748953958632.4.4.351926.2..367.94349...726.67924318
C3: 3 => SOLVED
* 726853419814296375593471682632748951951632847478519263285367194349185726167924538
* PAIR F3: 1,3 BLK 2
F1: 1,3,5                                # reduction candidate for 1,3
F1: 5 => CTR
* 726185439834296.75195473682612748953958632.4.4.351926.2..367.94349.51726.67924318
F1: 1,3                                  # 15 pairs
* PAIR F3: 1,3 ROW 3
C3: 1,3,5                                # reduction candidate for 1,3
C3: 1,3 => SOLVED
* 726853419814296375593471682632748951951632847478519263285367194349185726167924538
C3: 5 => CTR
* 726...4.9834296.7.19547368261274895395863214.4..51926.2..367.94349...726.67924...
* PAIR H1: 1,3 BLK 3
G2: 1,3,5                                # reduction candidate for 1,3
G2: 5 => CTR
* 726...439834296571.9.4736826127489539..63214.4..51926.2..367.94349...726.67924...
G2: 1,3                                  # 20 pairs
* PAIR H1: 1,3 ROW 1
F1: 1,3,5                                # reduction candidate for 1,3
F1: 5 => CTR
* 726185439834296.75195473682612748953958632.4.4.351926.2..367.94349.51726.67924318
F1: 1,3                                  # 15 pairs
* PAIR I2: 1,5 BLK 3
G2: 1,5,3                                # reduction candidate for 1,5
G2: 1,5 => CTR
* 726...439834296.75195473682612748953958632.4.4.351926.2..367.94349...726.67924318
G2: 3 => SOLVED
* 726853419814296375593471682632748951951632847478519263285367194349185726167924538
* PAIR I2: 1,5 COL I
I9: 1,5,8                                # reduction candidate for 1,5
I9: 1,5 => CTR
* 726..341981429637559.47.6826.274895.9..632.4.4..51926.2..367.94349...726.6792483.
I9: 8                                    # 22 pairs
* PAIR B6: 7,8 BLK 4
B5: 7,8,5                                # reduction candidate for 7,8
B5: 7,8 => CTR
* 726..3419814296.7..9.47.6826.274895.9.5632.4.4..51926.258367194349...726167924.3.
B5: 5                                    # 20 pairs
* PAIR B6: 7,8 ROW 6
I6: 7,8,3                                # reduction candidate for 7,8
I6: 7,8 => CTR
* 726...439834296.75195473682612748953958632.4.4.351926.2..367.94349...726.67924318
I6: 3 => SOLVED
* 726853419814296375593471682632748951951632847478519263285367194349185726167924538
* PAIR C6: 3,8 ROW 6
I6: 3,8,7                                # reduction candidate for 3,8
I6: 7 => CTR
* 726...4.9834296.7..9.473682612748953975632.4.483519267258367194349...7261679243..
I6: 3,8                                  # 20 pairs
* PAIR G5: 1,8 BLK 6
I5: 1,8,7                                # reduction candidate for 1,8
I5: 1,8 => CTR
* 726..34198.4296.7..9.47.6826.274895.975632.4.483519267258367194349...726167924.3.
I5: 7                                    # 20 pairs
* PAIR G5: 1,8 ROW 5
C5: 1,8,5                                # reduction candidate for 1,8
C5: 5 => CTR
* 726..341983429657..9.47.6826127489539.5632.4.4.351926.258367194349...726167924.3.
C5: 1,8                                  # 20 pairs
* PAIR G5: 1,8 COL G
G9: 1,8,3,5                              # reduction candidate for 1,8
G9: 1,8 => CTR
* 726...4.98.4296375.934716826327489519.163284.4..51926.2..367.94349...726.67924...
G9: 3,5                                  # 23 pairs
* PAIR B7: 5,8 BLK 7
C7: 5,8,1                                # reduction candidate for 5,8
C7: 5,8 => SOLVED
* 726853419814296375593471682632748951951632847478519263285367194349185726167924538
C7: 1 => CTR
* 726...4.98.4296.75195473682612748953958632147473519268281367594349...72656792483.
* PAIR B7: 5,8 COL B
B5: 5,8,7                                # reduction candidate for 5,8
B5: 7 => CTR
* 726..34198.4296.7..9.47.6826.274895.975632.4.483519267258367194349...726167924.3.
B5: 5,8                                  # 20 pairs
* PAIR A9: 1,5 BLK 7
C7: 1,5,8                                # reduction candidate for 1,5
C7: 8 => CTR
* 726..341981429637559347.6826.274895.9..632.4.4..51926.2.8367194349...726167924.3.
C7: 1,5                                  # 20 pairs
* PAIR A9: 1,5 ROW 9
G9: 1,5,3,8                              # reduction candidate for 1,5
G9: 1,5 => SOLVED
* 726853419814296375593471682632748951951632847478519263285367194349185726167924538
G9: 3,8                                  # 20 pairs
I9: 1,5,8                                # reduction candidate for 1,5
I9: 1,5 => CTR
* 726..341981429637559.47.6826.274895.9..632.4.4..51926.2..367.94349...726.6792483.
I9: 8                                    # 22 pairs
* PAIR F8: 1,5 COL F
F1: 1,5,3                                # reduction candidate for 1,5
F1: 1,5 => CTR
* 726...439834296.75195473682612748953958632.4.4.351926.2..367.94349...726.67924318
F1: 3 => SOLVED
* 726853419814296375593471682632748951951632847478519263285367194349185726167924538
* PAIR G7: 1,5 BLK 9
G9: 1,5,3,8                              # reduction candidate for 1,5
G9: 1,5 => SOLVED
* 726853419814296375593471682632748951951632847478519263285367194349185726167924538
G9: 3,8                                  # 20 pairs
I9: 1,5,8                                # reduction candidate for 1,5
I9: 1,5 => CTR
* 726..341981429637559.47.6826.274895.9..632.4.4..51926.2..367.94349...726.6792483.
I9: 8                                    # 22 pairs
* PAIR G7: 1,5 ROW 7
C7: 1,5,8                                # reduction candidate for 1,5
C7: 8 => CTR
* 726..341981429637559347.6826.274895.9..632.4.4..51926.2.8367194349...726167924.3.
C7: 1,5                                  # 20 pairs
* PAIR G7: 1,5 COL G
G2: 1,5,3                                # reduction candidate for 1,5
G2: 1,5 => CTR
* 726...439834296.75195473682612748953958632.4.4.351926.2..367.94349...726.67924318
G2: 3 => SOLVED
* 726853419814296375593471682632748951951632847478519263285367194349185726167924538
* PAIR H9: 1,3 BLK 9
G9: 1,3,5,8                              # reduction candidate for 1,3
G9: 1,3 => CTR
* 726...4.98.4296.7519547368261274895.9..63284.4..51926.2..367594349...726567924..8
G9: 5,8 => SOLVED
* 726853419814296375593471682632748951951632847478519263285367194349185726167924538
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-359-base-pr-000.dot
* REASONING
* PRF # C3: 1,3 => SOL
* DIS # C3: 5 => CTR => C3: 1,3
* DIS # G2: 5 => CTR => G2: 1,3
* DIS # C3: 1,5 => CTR => C3: 3
* PRF # C3: 3 => SOL
* DIS # F1: 5 => CTR => F1: 1,3
* PRF # C3: 1,3 => SOL
* DIS # C3: 5 => CTR => C3: 1,3
* DIS # G2: 5 => CTR => G2: 1,3
* DIS # F1: 5 => CTR => F1: 1,3
* DIS # G2: 1,5 => CTR => G2: 3
* PRF # G2: 3 => SOL
* DIS # I9: 1,5 => CTR => I9: 8
* DIS # B5: 7,8 => CTR => B5: 5
* DIS # I6: 7,8 => CTR => I6: 3
* PRF # I6: 3 => SOL
* DIS # I6: 7 => CTR => I6: 3,8
* DIS # I5: 1,8 => CTR => I5: 7
* DIS # C5: 5 => CTR => C5: 1,8
* DIS # G9: 1,8 => CTR => G9: 3,5
* PRF # C7: 5,8 => SOL
* DIS # C7: 1 => CTR => C7: 5,8
* DIS # B5: 7 => CTR => B5: 5,8
* DIS # C7: 8 => CTR => C7: 1,5
* PRF # G9: 1,5 => SOL
* DIS # I9: 1,5 => CTR => I9: 8
* DIS # F1: 1,5 => CTR => F1: 3
* PRF # F1: 3 => SOL
* PRF # G9: 1,5 => SOL
* DIS # I9: 1,5 => CTR => I9: 8
* DIS # C7: 8 => CTR => C7: 1,5
* DIS # G2: 1,5 => CTR => G2: 3
* PRF # G2: 3 => SOL
* DIS # G9: 1,3 => CTR => G9: 5,8
* PRF # G9: 5,8 => SOL
* CNT  35 HDP CHAINS /  52 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A9,B2,B4,B6,B7,C6,D1,D8,E1,E8,F3,F8,G5,G7,H1,H9,I2,I4)
* 726...4.98.4296.7..9.47.6826.274895.9..632.4.4..51926.2..367.94349...726.67924...
* PAIR B2: 1,3 BLK 1
C3: 1,3,5                                # reduction candidate for 1,3
C3: 1,3 => SOLVED
* 726853419814296375593471682632748951951632847478519263285367194349185726167924538
* DURATION: 0:00:02.130154  START: 15:04:19.581050  END: 15:04:21.711204 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-359-base-pr-001.dot
* REASONING
* PRF # C3: 1,3 => SOL
* STA C3: 1,3
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 359

solution: 726853419814296375593471682632748951951632847478519263285367194349185726167924538
info: 4898     FNBTWY   S8.f     43240

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

Solution

position: 726853419814296375593471682632748951951632847478519263285367194349185726167924538 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:

* PRF # C3: 1,3 => SOL
* DIS # C3: 5 => CTR => C3: 1,3
* INC # G2: 1,3 => UNS
* DIS # G2: 5 => CTR => G2: 1,3
* DIS # C3: 1,5 => CTR => C3: 3
* PRF # C3: 3 => SOL
* INC # F1: 1,3 => UNS
* DIS # F1: 5 => CTR => F1: 1,3
* PRF # C3: 1,3 => SOL
* DIS # C3: 5 => CTR => C3: 1,3
* INC # G2: 1,3 => UNS
* DIS # G2: 5 => CTR => G2: 1,3
* INC # F1: 1,3 => UNS
* DIS # F1: 5 => CTR => F1: 1,3
* DIS # G2: 1,5 => CTR => G2: 3
* PRF # G2: 3 => SOL
* DIS # I9: 1,5 => CTR => I9: 8
* INC # I9: 8 => UNS
* DIS # B5: 7,8 => CTR => B5: 5
* INC # B5: 5 => UNS
* DIS # I6: 7,8 => CTR => I6: 3
* PRF # I6: 3 => SOL
* INC # I6: 3,8 => UNS
* DIS # I6: 7 => CTR => I6: 3,8
* DIS # I5: 1,8 => CTR => I5: 7
* INC # I5: 7 => UNS
* INC # C5: 1,8 => UNS
* DIS # C5: 5 => CTR => C5: 1,8
* DIS # G9: 1,8 => CTR => G9: 3,5
* INC # G9: 3,5 => UNS
* PRF # C7: 5,8 => SOL
* DIS # C7: 1 => CTR => C7: 5,8
* INC # B5: 5,8 => UNS
* DIS # B5: 7 => CTR => B5: 5,8
* INC # C7: 1,5 => UNS
* DIS # C7: 8 => CTR => C7: 1,5
* PRF # G9: 1,5 => SOL
* INC # G9: 3,8 => UNS
* DIS # I9: 1,5 => CTR => I9: 8
* INC # I9: 8 => UNS
* DIS # F1: 1,5 => CTR => F1: 3
* PRF # F1: 3 => SOL
* PRF # G9: 1,5 => SOL
* INC # G9: 3,8 => UNS
* DIS # I9: 1,5 => CTR => I9: 8
* INC # I9: 8 => UNS
* INC # C7: 1,5 => UNS
* DIS # C7: 8 => CTR => C7: 1,5
* DIS # G2: 1,5 => CTR => G2: 3
* PRF # G2: 3 => SOL
* DIS # G9: 1,3 => CTR => G9: 5,8
* PRF # G9: 5,8 => SOL
* CNT  52 HDP CHAINS /  52 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # C3: 1,3 => SOL
* STA C3: 1,3
* CNT   1 HDP CHAINS /   1 HYP OPENED