Analysis of xx-top500-041-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 5......79...6.1...4............9.3..7...5.....8....6...623............5..1....... initial

Autosolve

position: 536..41792986715..471539...654.9.3.7723.56...1897.36.5.623.57..347....5..15..7... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D8: 2,8 => CTR => D8: 9
* DIS # D9: 2,8 => CTR => D9: 4,9
* PRF # E9: 2,8 => SOL
* DIS # H9: 6,8,9 => CTR => H9: 3,4
* DIS # I9: 3,4 => CTR => I9: 2,6,8
* DIS # I3: 6 => CTR => I3: 2,8
* DIS # G9: 2,8 => CTR => G9: 4,9
* DIS # I3: 6,8 => CTR => I3: 2
* DIS # H9: 6,8 => CTR => H9: 3,4,9
* PRF # E9: 2,4 => SOL
* DIS # D9: 8,9 => CTR => D9: 2,4
* DIS # H9: 8,9 => CTR => H9: 3,4,6
* DIS # D8: 2,8 => CTR => D8: 9
* DIS # D9: 2,8 => CTR => D9: 4,9
* PRF # E9: 2,8 => SOL
* DIS # G8: 9 => CTR => G8: 2,8
* CNT  16 HDP CHAINS /  41 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 # D8: 2,8 => CTR => D8: 9
* DIS D8: 9 # D9: 2,8 => CTR => D9: 4
* DIS D8: 9 + D9: 4 # D4: 1 => CTR => D4: 2,8
* PRF D8: 9 + D9: 4 + D4: 2,8 # I9: 2,6 => SOL
* STA D8: 9 + D9: 4 + D4: 2,8 + I9: 2,6
* CNT   4 HDP CHAINS /   6 HYP OPENED

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

Details

Positions

5......79...6.1...4............9.3..7...5.....8....6...623............5..1....... initial
536..41792986715..471539...654.9.3.7723.56...1897.36.5.623.57..347....5..15..7... autosolve
536284179298671543471539862654892317723156498189743625962315784347968251815427936 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
D1: 2,8
E1: 2,8
H2: 3,4
I2: 3,4
G3: 2,8
H3: 6,8
F4: 2,8
E6: 2,4
H6: 2,4
A7: 8,9
A9: 8,9
E8: 1,6
F8: 2,8
I8: 1,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D4,D5: 1.. / D4 = 1  => 16 pairs (_) / D5 = 1  => 18 pairs (_)
E7,E8: 1.. / E7 = 1  =>  0 pairs (*) / E8 = 1  =>  0 pairs (X)
D4,H4: 1.. / D4 = 1  => 16 pairs (_) / H4 = 1  => 18 pairs (_)
E8,I8: 1.. / E8 = 1  => 13 pairs (_) / I8 = 1  =>  0 pairs (*)
D1,E1: 2.. / D1 = 2  => 15 pairs (_) / E1 = 2  =>  0 pairs (X)
G3,I3: 2.. / G3 = 2  =>  0 pairs (X) / I3 = 2  => 16 pairs (_)
H4,H6: 2.. / H4 = 2  =>  0 pairs (X) / H6 = 2  => 17 pairs (_)
E6,H6: 2.. / E6 = 2  =>  0 pairs (X) / H6 = 2  => 17 pairs (_)
F4,F8: 2.. / F4 = 2  =>  0 pairs (*) / F8 = 2  =>  0 pairs (X)
I3,I9: 2.. / I3 = 2  => 16 pairs (_) / I9 = 2  =>  0 pairs (X)
H2,I2: 3.. / H2 = 3  =>  0 pairs (X) / I2 = 3  => 16 pairs (_)
H9,I9: 3.. / H9 = 3  => 16 pairs (_) / I9 = 3  =>  0 pairs (X)
H2,H9: 3.. / H2 = 3  =>  0 pairs (X) / H9 = 3  => 16 pairs (_)
I2,I9: 3.. / I2 = 3  => 16 pairs (_) / I9 = 3  =>  0 pairs (X)
H2,I2: 4.. / H2 = 4  => 16 pairs (_) / I2 = 4  =>  0 pairs (X)
D5,E6: 4.. / D5 = 4  =>  0 pairs (X) / E6 = 4  => 17 pairs (_)
E6,H6: 4.. / E6 = 4  => 17 pairs (_) / H6 = 4  =>  0 pairs (X)
D5,D9: 4.. / D5 = 4  =>  0 pairs (X) / D9 = 4  => 17 pairs (_)
G5,G9: 4.. / G5 = 4  => 17 pairs (_) / G9 = 4  =>  0 pairs (X)
H3,I3: 6.. / H3 = 6  => 14 pairs (_) / I3 = 6  =>  0 pairs (X)
E8,E9: 6.. / E8 = 6  =>  0 pairs (*) / E9 = 6  =>  0 pairs (X)
E8,I8: 6.. / E8 = 6  =>  0 pairs (*) / I8 = 6  =>  0 pairs (X)
H3,H9: 6.. / H3 = 6  => 14 pairs (_) / H9 = 6  =>  0 pairs (X)
D1,E1: 8.. / D1 = 8  =>  0 pairs (X) / E1 = 8  => 15 pairs (_)
A7,A9: 8.. / A7 = 8  =>  0 pairs (X) / A9 = 8  => 12 pairs (_)
F4,F8: 8.. / F4 = 8  => 17 pairs (_) / F8 = 8  =>  0 pairs (*)
G5,H5: 9.. / G5 = 9  =>  0 pairs (X) / H5 = 9  => 13 pairs (_)
A7,A9: 9.. / A7 = 9  => 12 pairs (_) / A9 = 9  =>  0 pairs (X)
D8,D9: 9.. / D8 = 9  => 17 pairs (_) / D9 = 9  =>  0 pairs (X)
A7,H7: 9.. / A7 = 9  => 12 pairs (_) / H7 = 9  =>  0 pairs (X)
D8,G8: 9.. / D8 = 9  => 17 pairs (_) / G8 = 9  =>  0 pairs (X)
* DURATION: 0:00:57.597408  START: 04:04:12.444390  END: 04:05:10.041798 2017-05-04
* CP COUNT: (31)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,D1,E1,E6,E8,F4,F8,G3,H2,H3,H6,I2,I8)
* 536..41792986715..471539...654.9.3.7723.56...1897.36.5.623.57..347....5..15..7...
* PAIR D1: 2,8 COL D
D4: 2,8,1                                # reduction candidate for 2,8
D4: 2,8                                  # 18 pairs
D8: 2,8,9                                # reduction candidate for 2,8
D8: 2,8 => CTR
* 536..41792986715..471539...654.9.3.77234568911897236459623.571.347.1295681596743.
D8: 9                                    # 17 pairs
D9: 2,8,4,9                              # reduction candidate for 2,8
D9: 2,8 => CTR
* 536..41792986715..471539...654.9.3.7723456...189723645.623.57..3479.285..158.74.2
D9: 4,9                                  # 15 pairs
* PAIR E1: 2,8 COL E
E9: 2,8,4,6                              # reduction candidate for 2,8
E9: 2,8 => SOLVED
* 536284179298671543471539862654892317723156498189743625962315784347968251815427936
E9: 4,6                                  # 15 pairs
* PAIR H2: 3,4 COL H
H9: 3,4,6,8,9                            # reduction candidate for 3,4
H9: 6,8,9 => CTR
* 536284179298671534471539862654.9.3.7723.56...189723645.623457..347.12956.15.67..3
H9: 3,4                                  # 16 pairs
* PAIR I2: 3,4 COL I
I9: 3,4,2,6,8                            # reduction candidate for 3,4
I9: 3,4 => CTR
* 5362841792986715..471539862654.9.3.7723.56...189723645.623457..347.12956.15.67...
I9: 2,6,8                                # 16 pairs
* PAIR G3: 2,8 BLK 3
I3: 2,8,6                                # reduction candidate for 2,8
I3: 6 => CTR
* 536..41792986715..471539286654.9.3.7723.56...1897.36.5.623.57..347.6..51.15..7.6.
I3: 2,8                                  # 14 pairs
* PAIR G3: 2,8 COL G
G8: 2,8,9                                # reduction candidate for 2,8
G8: 2,8                                  # 17 pairs
G9: 2,8,4,9                              # reduction candidate for 2,8
G9: 2,8 => CTR
* 536..41792986715..471539...654.9.3.7723.5649.1897436259623.57..347...95.815..7...
G9: 4,9                                  # 15 pairs
* PAIR H3: 6,8 BLK 3
I3: 6,8,2                                # reduction candidate for 6,8
I3: 6,8 => CTR
* 536.24179298671543471539268654.9.3.7723.56491189743625962385714347912856815467932
I3: 2                                    # 16 pairs
* PAIR H3: 6,8 COL H
H9: 6,8,3,4,9                            # reduction candidate for 6,8
H9: 6,8 => CTR
* 536..4179298671534471539862654.9.3.7723.56..81897.36.58623.5791347918256915267483
H9: 3,4,9                                # 14 pairs
* PAIR F4: 2,8 BLK 5
D4: 2,8,1                                # reduction candidate for 2,8
D4: 2,8                                  # 18 pairs
D4: 1                                    # 16 pairs
* PAIR F4: 2,8 ROW 4
H4: 2,8,1                                # reduction candidate for 2,8
H4: 1                                    # 18 pairs
H4: 2,8                                  # 16 pairs
* PAIR E6: 2,4 COL E
E9: 2,4,6,8                              # reduction candidate for 2,4
E9: 2,4 => SOLVED
* 536284179298671543471539862654892317723156498189743625962315784347968251815427936
E9: 6,8                                  # 15 pairs
* PAIR A7: 8,9 ROW 7
H7: 8,9,1,4                              # reduction candidate for 8,9
H7: 8,9                                  # 18 pairs
H7: 1,4                                  # 13 pairs
* PAIR A9: 8,9 ROW 9
D9: 8,9,2,4                              # reduction candidate for 8,9
D9: 8,9 => CTR
* 536..41792986715..471539...654.9.3.7723456...189723645.623.57..347..2.5..15..74.2
D9: 2,4                                  # 18 pairs
G9: 8,9,2,4                              # reduction candidate for 8,9
G9: 8,9                                  # 17 pairs
H9: 8,9,3,4,6                            # reduction candidate for 8,9
H9: 8,9 => CTR
* 536284179298671534471539862654.9.3.7723.56...189723645.623457..347.12956.15.67..3
H9: 3,4,6                                # 14 pairs
* PAIR F8: 2,8 BLK 8
D8: 2,8,9                                # reduction candidate for 2,8
D8: 2,8 => CTR
* 536..41792986715..471539...654.9.3.77234568911897236459623.571.347.1295681596743.
D8: 9                                    # 17 pairs
D9: 2,8,4,9                              # reduction candidate for 2,8
D9: 2,8 => CTR
* 536..41792986715..471539...654.9.3.7723456...189723645.623.57..3479.285..158.74.2
D9: 4,9                                  # 15 pairs
E9: 2,8,4,6                              # reduction candidate for 2,8
E9: 2,8 => SOLVED
* 536284179298671543471539862654892317723156498189743625962315784347968251815427936
E9: 4,6                                  # 15 pairs
* PAIR F8: 2,8 ROW 8
G8: 2,8,9                                # reduction candidate for 2,8
G8: 9 => CTR
* 536..41792986715..471539...654.9.3.77234568911897236459623.571.347.1295681596743.
G8: 2,8                                  # 17 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-041-base-pr-000.dot
* REASONING
* DIS # D8: 2,8 => CTR => D8: 9
* DIS # D9: 2,8 => CTR => D9: 4,9
* PRF # E9: 2,8 => SOL
* DIS # H9: 6,8,9 => CTR => H9: 3,4
* DIS # I9: 3,4 => CTR => I9: 2,6,8
* DIS # I3: 6 => CTR => I3: 2,8
* DIS # G9: 2,8 => CTR => G9: 4,9
* DIS # I3: 6,8 => CTR => I3: 2
* DIS # H9: 6,8 => CTR => H9: 3,4,9
* PRF # E9: 2,4 => SOL
* DIS # D9: 8,9 => CTR => D9: 2,4
* DIS # H9: 8,9 => CTR => H9: 3,4,6
* DIS # D8: 2,8 => CTR => D8: 9
* DIS # D9: 2,8 => CTR => D9: 4,9
* PRF # E9: 2,8 => SOL
* DIS # G8: 9 => CTR => G8: 2,8
* CNT  16 HDP CHAINS /  41 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,D1,E1,E6,E8,F4,F8,G3,H2,H3,H6,I2,I8)
* 536..41792986715..471539...654.9.3.7723.56...1897.36.5.623.57..347....5..15..7...
* PAIR D1: 2,8 COL D
D4: 2,8,1                                # reduction candidate for 2,8
D4: 2,8                                  # 18 pairs
D8: 2,8,9                                # reduction candidate for 2,8
D8: 2,8 => CTR
* 536..41792986715..471539...654.9.3.77234568911897236459623.571.347.1295681596743.
D9: 2,8,4                                # reduction candidate for 2,8
D9: 2,8 => CTR
* 536..41792986715..471539...654.9.3.77234569..189723645.623.57..3479.285..158.74.2
* RESTART
* PAIR D1: 2,8 COL D
D4: 2,8,1                                # reduction candidate for 2,8
D4: 1 => CTR
* 5362841792986715..471539...65419238772385649118974362596231574834796..5.8154.79..
* PAIR RESTART

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (D1,D4,E1,E7,E8,E9,F4,F8,G3,G8,H2,H3,H7,H9,I2,I3,I7,I8)
* 536..41792986715..471539...654.9.3177231564981897436259623.57..3479...5.8154.79..
* PAIR I3: 2,6 COL I
I9: 2,6,3                                # reduction candidate for 2,6
I9: 2,6 => SOLVED
* 536284179298671543471539862654892317723156498189743625962315784347968251815427936
* DURATION: 0:00:08.556199  START: 04:05:51.837363  END: 04:06:00.393562 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-041-base-pr-001.dot
* REASONING
* DIS # D8: 2,8 => CTR => D8: 9
* DIS D8: 9 # D9: 2,8 => CTR => D9: 4
* DIS D8: 9 + D9: 4 # D4: 1 => CTR => D4: 2,8
* PRF D8: 9 + D9: 4 + D4: 2,8 # I9: 2,6 => SOL
* STA D8: 9 + D9: 4 + D4: 2,8 + I9: 2,6
* CNT   4 HDP CHAINS /   6 HYP OPENED

Header Info

Top 500 Minimum 17 041

solution: 536284179298671543471539862654892317723156498189743625962315784347968251815427936
info: 1372     FNBHWY   S8.f     31992

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

Solution

position: 536284179298671543471539862654892317723156498189743625962315784347968251815427936 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:

* INC # D4: 2,8 => UNS
* DIS # D8: 2,8 => CTR => D8: 9
* INC # D8: 9 => UNS
* DIS # D9: 2,8 => CTR => D9: 4,9
* INC # D9: 4,9 => UNS
* PRF # E9: 2,8 => SOL
* INC # E9: 4,6 => UNS
* INC # H9: 3,4 => UNS
* DIS # H9: 6,8,9 => CTR => H9: 3,4
* DIS # I9: 3,4 => CTR => I9: 2,6,8
* INC # I9: 2,6,8 => UNS
* INC # I3: 2,8 => UNS
* DIS # I3: 6 => CTR => I3: 2,8
* INC # G8: 2,8 => UNS
* DIS # G9: 2,8 => CTR => G9: 4,9
* INC # G9: 4,9 => UNS
* DIS # I3: 6,8 => CTR => I3: 2
* INC # I3: 2 => UNS
* DIS # H9: 6,8 => CTR => H9: 3,4,9
* INC # H9: 3,4,9 => UNS
* INC # D4: 2,8 => UNS
* INC # D4: 1 => UNS
* INC # H4: 2,8 => UNS
* INC # H4: 1 => UNS
* PRF # E9: 2,4 => SOL
* INC # E9: 6,8 => UNS
* INC # H7: 8,9 => UNS
* INC # H7: 1,4 => UNS
* DIS # D9: 8,9 => CTR => D9: 2,4
* INC # D9: 2,4 => UNS
* INC # G9: 8,9 => UNS
* DIS # H9: 8,9 => CTR => H9: 3,4,6
* INC # H9: 3,4,6 => UNS
* DIS # D8: 2,8 => CTR => D8: 9
* INC # D8: 9 => UNS
* DIS # D9: 2,8 => CTR => D9: 4,9
* INC # D9: 4,9 => UNS
* PRF # E9: 2,8 => SOL
* INC # E9: 4,6 => UNS
* INC # G8: 2,8 => UNS
* DIS # G8: 9 => CTR => G8: 2,8
* CNT  41 HDP CHAINS /  41 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # D4: 2,8 => UNS
* DIS # D8: 2,8 => CTR => D8: 9
* DIS D8: 9 # D9: 2,8 => CTR => D9: 4
* INC D8: 9 + D9: 4 # D4: 2,8 => UNS
* DIS D8: 9 + D9: 4 # D4: 1 => CTR => D4: 2,8
* PRF D8: 9 + D9: 4 + D4: 2,8 # I9: 2,6 => SOL
* STA D8: 9 + D9: 4 + D4: 2,8 + I9: 2,6
* CNT   6 HDP CHAINS /   6 HYP OPENED