Analysis of xx-top95-040-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ...8....9.873...4.6..7.......85..97...........43..75.......3....3...145.4....2..1 initial

Autosolve

position: 3..8..7.9.873...4.6..7.......85..97......8....43..75.....4.3....3...145.4....2..1 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B4: 1,2 => CTR => B4: 6
* PRF # A2: 1,2 => SOL
* DIS # A7: 1,2 => CTR => A7: 5,7,8,9
* DIS # A5: 2,9 => CTR => A5: 5,7
* DIS # C5: 2,9 => CTR => C5: 5,6
* DIS # A7: 2,9 => CTR => A7: 1,5,7,8
* DIS # A8: 2,9 => CTR => A8: 7,8
* DIS # E4: 4,6 => CTR => E4: 3
* DIS # E5: 4,6 => CTR => E5: 3,9
* DIS # I4: 4,6 => CTR => I4: 2,3
* PRF # H6: 1,2 => SOL
* DIS # E5: 3,4 => CTR => E5: 6,9
* DIS # I8: 7,8 => CTR => I8: 2,6
* DIS # H9: 6,9 => CTR => H9: 3,8
* CNT  14 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 # B4: 1,2 => CTR => B4: 6
* DIS B4: 6 # B5: 7 => CTR => B5: 2,9
* DIS B4: 6 + B5: 2,9 # E1: 2 => CTR => E1: 1,4
* DIS B4: 6 + B5: 2,9 + E1: 1,4 # E3: 1,4 => CTR => E3: 2
* PRF B4: 6 + B5: 2,9 + E1: 1,4 + E3: 2 => SOL
* STA B4: 6 + B5: 2,9 + E1: 1,4 + E3: 2
* CNT   5 HDP CHAINS /   6 HYP OPENED

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

Details

Positions

...8....9.873...4.6..7.......85..97...........43..75.......3....3...145.4....2..1 initial
3..8..7.9.873...4.6..7.......85..97......8....43..75.....4.3....3...145.4....2..1 autosolve
351846729287319645694725183168534972725198364943267518516483297832971456479652831 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
A4: 1,2
A6: 2,9
F4: 4,6
D5: 1,2
D6: 1,2
E6: 6,9
D8: 6,9
E8: 7,8
D9: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A4,B4: 1.. / A4 = 1  =>  9 pairs (_) / B4 = 1  =>  0 pairs (X)
D5,D6: 1.. / D5 = 1  =>  0 pairs (*) / D6 = 1  =>  0 pairs (X)
D6,H6: 1.. / D6 = 1  =>  7 pairs (_) / H6 = 1  =>  0 pairs (*)
D5,D6: 2.. / D5 = 2  =>  7 pairs (_) / D6 = 2  =>  0 pairs (*)
E4,E5: 3.. / E4 = 3  =>  9 pairs (_) / E5 = 3  =>  0 pairs (X)
G9,H9: 3.. / G9 = 3  =>  9 pairs (_) / H9 = 3  => 10 pairs (_)
E4,I4: 3.. / E4 = 3  =>  9 pairs (_) / I4 = 3  =>  0 pairs (X)
C1,C3: 4.. / C1 = 4  => 10 pairs (_) / C3 = 4  => 11 pairs (_)
I4,I5: 4.. / I4 = 4  =>  0 pairs (X) / I5 = 4  =>  9 pairs (_)
E5,I5: 4.. / E5 = 4  =>  0 pairs (X) / I5 = 4  =>  9 pairs (_)
I2,I3: 5.. / I2 = 5  => 19 pairs (_) / I3 = 5  =>  0 pairs (X)
E7,E9: 5.. / E7 = 5  => 10 pairs (_) / E9 = 5  => 14 pairs (_)
D8,D9: 6.. / D8 = 6  =>  9 pairs (_) / D9 = 6  => 10 pairs (_)
A5,B5: 7.. / A5 = 7  =>  9 pairs (_) / B5 = 7  => 12 pairs (_)
I7,I8: 7.. / I7 = 7  => 10 pairs (_) / I8 = 7  =>  0 pairs (X)
B9,E9: 7.. / B9 = 7  => 10 pairs (_) / E9 = 7  => 11 pairs (_)
H6,I6: 8.. / H6 = 8  =>  9 pairs (_) / I6 = 8  =>  9 pairs (_)
A7,A8: 8.. / A7 = 8  => 11 pairs (_) / A8 = 8  => 11 pairs (_)
F2,F3: 9.. / F2 = 9  => 10 pairs (_) / F3 = 9  =>  0 pairs (X)
E5,E6: 9.. / E5 = 9  =>  0 pairs (*) / E6 = 9  =>  0 pairs (X)
D8,D9: 9.. / D8 = 9  => 10 pairs (_) / D9 = 9  =>  9 pairs (_)
H7,H9: 9.. / H7 = 9  =>  9 pairs (_) / H9 = 9  =>  0 pairs (X)
A2,F2: 9.. / A2 = 9  =>  0 pairs (X) / F2 = 9  => 10 pairs (_)
A6,E6: 9.. / A6 = 9  =>  0 pairs (*) / E6 = 9  =>  0 pairs (X)
* DURATION: 0:00:37.610941  START: 23:36:33.841497  END: 23:37:11.452438 2017-05-03
* CP COUNT: (24)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,D5,D6,D8,D9,E6,E8,F4)
* 3..8..7.9.873...4.6..7.......85..97......8....43..75.....4.3....3...145.4....2..1
* PAIR A4: 1,2 BLK 4
B4: 1,2,6                                # reduction candidate for 1,2
B4: 1,2 => CTR
* 35.8.67.9.873.964569.7.5..3..8534976....98.34943.675.....4.3.9..396.1452475982361
B4: 6                                    # 28 pairs
* PAIR A4: 1,2 COL A
A2: 1,2,5,9                              # reduction candidate for 1,2
A2: 1,2 => SOLVED
* 351846729287319645694725183168534972725198364943267518516483297832971456479652831
A2: 5,9                                  # 10 pairs
A7: 1,2,5,7,8,9                          # reduction candidate for 1,2
A7: 1,2 => CTR
* 3..8..7.95873.9.4.6..7....5..85..97.7....8...943.675.8...4.3..783..7145.47...2..1
A7: 5,7,8,9                              #  9 pairs
* PAIR A6: 2,9 BLK 4
A5: 2,9,5,7                              # reduction candidate for 2,9
A5: 2,9 => CTR
* 3..8.57.95873...4.6..7......685.497..75..8..4.43..75.....453....3..8145.45..72..1
A5: 5,7                                  # 10 pairs
B5: 2,9,5,6,7                            # reduction candidate for 2,9
B5: 2,9                                  # 20 pairs
C5: 2,9,5,6                              # reduction candidate for 2,9
C5: 2,9 => CTR
* 3..8..7.99873.6.456..7.9..3168534972..9268..42431975.....4.3....329.14564..6.2..1
C5: 5,6                                  # 10 pairs
* PAIR A6: 2,9 COL A
A2: 2,9,1,5                              # reduction candidate for 2,9
A2: 2,9                                  # 19 pairs
A7: 2,9,1,5,7,8                          # reduction candidate for 2,9
A7: 2,9 => CTR
* 3..8.57.95873.9.4.6..7.4..51.85.697.7....8....43.975689..4.3..783.97145.47.6.2.91
A7: 1,5,7,8                              #  9 pairs
A8: 2,9,7,8                              # reduction candidate for 2,9
A8: 2,9 => CTR
* 3..8.57.95873.9.4.6..7.4..51.85.697.7....8....43.975..8..4.3...93.6.145.4..9.2..1
A8: 7,8                                  # 12 pairs
* PAIR F4: 4,6 BLK 5
E4: 4,6,3                                # reduction candidate for 4,6
E4: 4,6 => CTR
* 3..8..7.9.873...4.6..7.......85..973....38..42431975.....4.3....3...145.4....2..1
E4: 3                                    #  9 pairs
E5: 4,6,3,9                              # reduction candidate for 4,6
E5: 4,6 => CTR
* 3..8..7.99873.6.456..7.9..3168534972...268..42431975.....4.3....329.14564..6.2..1
E5: 3,9                                  # 10 pairs
* PAIR F4: 4,6 ROW 4
I4: 4,6,2,3                              # reduction candidate for 4,6
I4: 4,6 => CTR
* 35.8.67.9.873.964569.7.5..3..8534976....98.34943.675.....4.3.9..396.1452475982361
I4: 2,3                                  # 10 pairs
* PAIR F4: 4,6 COL F
F1: 4,6,5                                # reduction candidate for 4,6
F1: 4,6                                  # 21 pairs
F1: 5                                    # 12 pairs
* PAIR D5: 1,2 ROW 5
G5: 1,2,3,6                              # reduction candidate for 1,2
G5: 1,2                                  # 11 pairs
H5: 1,2,3,6                              # reduction candidate for 1,2
H5: 1,2                                  # 12 pairs
* PAIR D6: 1,2 ROW 6
H6: 1,2,6,8                              # reduction candidate for 1,2
H6: 1,2 => SOLVED
* 351846729287319645694725183168534972725198364943267518516483297832971456479652831
H6: 6,8                                  #  9 pairs
* PAIR E6: 6,9 BLK 5
E5: 6,9,3,4                              # reduction candidate for 6,9
E5: 3,4 => CTR
* 3..8..7.9.873...4.6..7.....1685.4972...238...2431975.....4.3....3...145.4....2..1
E5: 6,9                                  # 23 pairs
* PAIR D8: 6,9 ROW 8
C8: 6,9,2                                # reduction candidate for 6,9
C8: 6,9                                  # 10 pairs
C8: 2                                    #  9 pairs
* PAIR E8: 7,8 BLK 8
E7: 7,8,5                                # reduction candidate for 7,8
E7: 7,8                                  # 14 pairs
E9: 7,8,5                                # reduction candidate for 7,8
E9: 7,8                                  # 10 pairs
* PAIR E8: 7,8 ROW 8
A8: 7,8,2,9                              # reduction candidate for 7,8
A8: 7,8                                  # 12 pairs
I8: 7,8,2,6                              # reduction candidate for 7,8
I8: 7,8 => CTR
* 3..8.57.95873.9.4.6..7.4..51.85.697.7....8....43.975..8..4.3...9326.145.4..9.2..1
I8: 2,6                                  # 12 pairs
* PAIR D9: 6,9 ROW 9
B9: 6,9,5,7                              # reduction candidate for 6,9
B9: 6,9                                  # 14 pairs
C9: 6,9,5                                # reduction candidate for 6,9
C9: 6,9                                  # 15 pairs
H9: 6,9,3,8                              # reduction candidate for 6,9
H9: 6,9 => CTR
* 3..8.57.95873.9.4.6..7.4..5..85.697.756.98....43..75.....453..7.3..7145.475.823.1
H9: 3,8                                  # 10 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top95-040-base-pr-000.dot
* REASONING
* DIS # B4: 1,2 => CTR => B4: 6
* PRF # A2: 1,2 => SOL
* DIS # A7: 1,2 => CTR => A7: 5,7,8,9
* DIS # A5: 2,9 => CTR => A5: 5,7
* DIS # C5: 2,9 => CTR => C5: 5,6
* DIS # A7: 2,9 => CTR => A7: 1,5,7,8
* DIS # A8: 2,9 => CTR => A8: 7,8
* DIS # E4: 4,6 => CTR => E4: 3
* DIS # E5: 4,6 => CTR => E5: 3,9
* DIS # I4: 4,6 => CTR => I4: 2,3
* PRF # H6: 1,2 => SOL
* DIS # E5: 3,4 => CTR => E5: 6,9
* DIS # I8: 7,8 => CTR => I8: 2,6
* DIS # H9: 6,9 => CTR => H9: 3,8
* CNT  14 HDP CHAINS /  41 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,D5,D6,D8,D9,E6,E8,F4)
* 3..8..7.9.873...4.6..7.......85..97......8....43..75.....4.3....3...145.4....2..1
* PAIR A4: 1,2 BLK 4
B4: 1,2,6                                # reduction candidate for 1,2
B4: 1,2 => CTR
* 35.8.67.9.873.964569.7.5..3..8534976....98.34943.675.....4.3.9..396.1452475982361
* PAIR A6: 2,9 BLK 4
B5: 2,9,7                                # reduction candidate for 2,9
B5: 7 => CTR
* 32.8.576998732..456..7....3168534972.....8..4.43..75.8.164.3297.329.14564..6.2..1

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A2,A6,B1,B3,B5,C1,C3,D5,D6,E2,E5,E6,F1,F2,F3,G2,G3,G9,H6,H9)
* 3..8..7.9.873...456..7....31685349727.5..8..4.43..75.8516483297832971456479652..1
* PAIR C1: 1,4 ROW 1
E1: 1,4,2                                # reduction candidate for 1,4
E1: 2 => CTR
* 3.482.7192873196456917458231685349727251.8..4.43..75.8516483297832971456479652..1
* PAIR RESTART
* PAIR C3: 1,4 ROW 3
E3: 1,4,2                                # reduction candidate for 1,4
E3: 1,4 => CTR
* 3..8..7.9.8732.1456..7..8231685349727.5..86342431.75.8516483297832971456479652..1
E3: 2 => SOLVED
* 351846729287319645694725183168534972725198364943267518516483297832971456479652831
* DURATION: 0:00:12.946065  START: 23:37:48.816409  END: 23:38:01.762474 2017-05-03
* SOLUTION FOUND
* SAVE PR GRAPH xx-top95-040-base-pr-001.dot
* REASONING
* DIS # B4: 1,2 => CTR => B4: 6
* DIS B4: 6 # B5: 7 => CTR => B5: 2,9
* DIS B4: 6 + B5: 2,9 # E1: 2 => CTR => E1: 1,4
* DIS B4: 6 + B5: 2,9 + E1: 1,4 # E3: 1,4 => CTR => E3: 2
* PRF B4: 6 + B5: 2,9 + E1: 1,4 + E3: 2 => SOL
* STA B4: 6 + B5: 2,9 + E1: 1,4 + E3: 2
* CNT   5 HDP CHAINS /   6 HYP OPENED

Header Info

Top 95 Sudokus 040
[sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt

Solution

position: 351846729287319645694725183168534972725198364943267518516483297832971456479652831 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: 1,2 => CTR => B4: 6
* INC # B4: 6 => UNS
* PRF # A2: 1,2 => SOL
* INC # A2: 5,9 => UNS
* DIS # A7: 1,2 => CTR => A7: 5,7,8,9
* INC # A7: 5,7,8,9 => UNS
* DIS # A5: 2,9 => CTR => A5: 5,7
* INC # A5: 5,7 => UNS
* INC # B5: 2,9 => UNS
* DIS # C5: 2,9 => CTR => C5: 5,6
* INC # C5: 5,6 => UNS
* INC # A2: 2,9 => UNS
* DIS # A7: 2,9 => CTR => A7: 1,5,7,8
* INC # A7: 1,5,7,8 => UNS
* DIS # A8: 2,9 => CTR => A8: 7,8
* INC # A8: 7,8 => UNS
* DIS # E4: 4,6 => CTR => E4: 3
* INC # E4: 3 => UNS
* DIS # E5: 4,6 => CTR => E5: 3,9
* INC # E5: 3,9 => UNS
* DIS # I4: 4,6 => CTR => I4: 2,3
* INC # I4: 2,3 => UNS
* INC # F1: 4,6 => UNS
* INC # F1: 5 => UNS
* INC # G5: 1,2 => UNS
* INC # H5: 1,2 => UNS
* PRF # H6: 1,2 => SOL
* INC # H6: 6,8 => UNS
* INC # E5: 6,9 => UNS
* DIS # E5: 3,4 => CTR => E5: 6,9
* INC # C8: 6,9 => UNS
* INC # C8: 2 => UNS
* INC # E7: 7,8 => UNS
* INC # E9: 7,8 => UNS
* INC # A8: 7,8 => UNS
* DIS # I8: 7,8 => CTR => I8: 2,6
* INC # I8: 2,6 => UNS
* INC # B9: 6,9 => UNS
* INC # C9: 6,9 => UNS
* DIS # H9: 6,9 => CTR => H9: 3,8
* INC # H9: 3,8 => UNS
* CNT  41 HDP CHAINS /  41 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B4: 1,2 => CTR => B4: 6
* INC B4: 6 # B5: 2,9 => UNS
* DIS B4: 6 # B5: 7 => CTR => B5: 2,9
* INC B4: 6 + B5: 2,9 # E1: 1,4 => UNS
* DIS B4: 6 + B5: 2,9 # E1: 2 => CTR => E1: 1,4
* DIS B4: 6 + B5: 2,9 + E1: 1,4 # E3: 1,4 => CTR => E3: 2
* PRF B4: 6 + B5: 2,9 + E1: 1,4 + E3: 2 => SOL
* STA B4: 6 + B5: 2,9 + E1: 1,4 + E3: 2
* CNT   7 HDP CHAINS /   6 HYP OPENED