Analysis of xx-top95-068-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .4..5..67...1...4....2.....1..8..3........2...6...........4..5.3.....8..2........ initial

Autosolve

position: .42.5.167...1...42...2.4.3812.8..394......2.6.6..2.7.5....4265.3.46..82.2.6...47. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A2: 8,9 => CTR => A2: 5,6,7
* DIS # B2: 8,9 => CTR => B2: 3,7
* DIS # F1: 3 => CTR => F1: 8,9
* DIS # A5: 8,9 => CTR => A5: 4,5,7
* DIS # A7: 8,9 => CTR => A7: 7
* PRF # F1: 3,9 => SOL
* DIS # F1: 8 => CTR => F1: 3,9
* DIS # D5: 3,9 => CTR => D5: 4,5,7
* DIS # D6: 3,9 => CTR => D6: 4
* DIS # D9: 3,9 => CTR => D9: 5
* DIS # A3: 5,9 => CTR => A3: 6,7
* DIS # A5: 5,7 => CTR => A5: 4,8,9
* DIS # F4: 6 => CTR => F4: 5,7
* DIS # F4: 6,7 => CTR => F4: 5
* DIS # E2: 6,7 => CTR => E2: 8,9
* DIS # I7: 1,9 => CTR => I7: 3
* DIS # B8: 1,9 => CTR => B8: 5,7
* DIS # F8: 1,9 => CTR => F8: 5,7
* CNT  18 HDP CHAINS /  46 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 # A2: 8,9 => CTR => A2: 5,6,7
* DIS A2: 5,6,7 # B2: 8,9 => CTR => B2: 3,7
* PRF A2: 5,6,7 + B2: 3,7 # C2: 3,5,7 => SOL
* STA A2: 5,6,7 + B2: 3,7 + C2: 3,5,7
* CNT   3 HDP CHAINS /   5 HYP OPENED

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

Details

Positions

.4..5..67...1...4....2.....1..8..3........2...6...........4..5.3.....8..2........ initial
.42.5.167...1...42...2.4.3812.8..394......2.6.6..2.7.5....4265.3.46..82.2.6...47. autosolve
842359167573186942619274538127865394435791286968423715781942653354617829296538471 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
A1: 8,9
D1: 3,9
G2: 5,9
G3: 5,9
C4: 5,7
E4: 6,7
H5: 1,8
H6: 1,8
I8: 1,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B3,C3: 1.. / B3 = 1  => 11 pairs (_) / C3 = 1  => 10 pairs (_)
H5,H6: 1.. / H5 = 1  =>  9 pairs (_) / H6 = 1  =>  8 pairs (_)
F6,H6: 1.. / F6 = 1  =>  9 pairs (_) / H6 = 1  =>  8 pairs (_)
C3,C7: 1.. / C3 = 1  => 10 pairs (_) / C7 = 1  => 11 pairs (_)
B2,C2: 3.. / B2 = 3  =>  9 pairs (_) / C2 = 3  =>  0 pairs (*)
D1,F1: 3.. / D1 = 3  => 17 pairs (_) / F1 = 3  =>  0 pairs (X)
I7,I9: 3.. / I7 = 3  => 12 pairs (_) / I9 = 3  =>  0 pairs (X)
D7,I7: 3.. / D7 = 3  =>  0 pairs (X) / I7 = 3  => 12 pairs (_)
B2,B5: 3.. / B2 = 3  =>  9 pairs (_) / B5 = 3  =>  0 pairs (*)
E5,E9: 3.. / E5 = 3  => 11 pairs (_) / E9 = 3  =>  0 pairs (*)
A5,A6: 4.. / A5 = 4  => 13 pairs (_) / A6 = 4  =>  0 pairs (X)
D5,D6: 4.. / D5 = 4  =>  0 pairs (X) / D6 = 4  => 13 pairs (_)
A5,D5: 4.. / A5 = 4  => 13 pairs (_) / D5 = 4  =>  0 pairs (X)
A6,D6: 4.. / A6 = 4  =>  0 pairs (X) / D6 = 4  => 13 pairs (_)
G2,G3: 5.. / G2 = 5  => 14 pairs (_) / G3 = 5  =>  7 pairs (_)
B8,B9: 5.. / B8 = 5  => 13 pairs (_) / B9 = 5  =>  0 pairs (X)
C4,F4: 5.. / C4 = 5  =>  0 pairs (X) / F4 = 5  => 13 pairs (_)
B8,F8: 5.. / B8 = 5  => 13 pairs (_) / F8 = 5  =>  0 pairs (X)
D5,D9: 5.. / D5 = 5  =>  0 pairs (X) / D9 = 5  => 13 pairs (_)
A2,A3: 6.. / A2 = 6  =>  0 pairs (X) / A3 = 6  => 10 pairs (_)
E4,F4: 6.. / E4 = 6  => 13 pairs (_) / F4 = 6  =>  0 pairs (X)
A3,E3: 6.. / A3 = 6  => 10 pairs (_) / E3 = 6  =>  0 pairs (X)
F2,F4: 6.. / F2 = 6  => 13 pairs (_) / F4 = 6  =>  0 pairs (X)
D5,D7: 7.. / D5 = 7  => 13 pairs (_) / D7 = 7  =>  0 pairs (X)
H5,H6: 8.. / H5 = 8  =>  8 pairs (_) / H6 = 8  =>  9 pairs (_)
E9,F9: 8.. / E9 = 8  =>  0 pairs (X) / F9 = 8  =>  0 pairs (_)
A1,F1: 8.. / A1 = 8  =>  0 pairs (*) / F1 = 8  =>  0 pairs (X)
E2,E9: 8.. / E2 = 8  =>  0 pairs (*) / E9 = 8  =>  0 pairs (X)
G2,G3: 9.. / G2 = 9  =>  7 pairs (_) / G3 = 9  => 14 pairs (_)
* DURATION: 0:00:53.422274  START: 00:23:49.218871  END: 00:24:42.641145 2017-05-04
* CP COUNT: (29)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,C4,D1,E4,G2,G3,H5,H6,I8)
* .42.5.167...1...42...2.4.3812.8..394......2.6.6..2.7.5....4265.3.46..82.2.6...47.
* PAIR A1: 8,9 BLK 1
A2: 8,9,5,6,7                            # reduction candidate for 8,9
A2: 8,9 => CTR
* .42.5.167...1...426..2.4.3812.8..3945..4..2.646..2.7.57...4265.3.46..82.2.65..47.
A2: 5,6,7                                #  9 pairs
B2: 8,9,3,7                              # reduction candidate for 8,9
B2: 8,9 => CTR
* 842359167.9318.542.1.2.493812.8..394.3.59.2.6.6942.7.5.81.426533.46..82.256938471
B2: 3,7                                  # 10 pairs
C2: 8,9,3,5,7                            # reduction candidate for 8,9
C2: 8,9                                  # 11 pairs
* PAIR A1: 8,9 ROW 1
F1: 8,9,3                                # reduction candidate for 8,9
F1: 3 => CTR
* 842953167.371869426..274.3812.8..3944...3.2169634217857..34265.3546.782.2.65.8473
F1: 8,9                                  # 17 pairs
* PAIR A1: 8,9 COL A
A5: 8,9,4,5,7                            # reduction candidate for 8,9
A5: 8,9 => CTR
* .42.5.167...1...42...2.4.3812.8..394...4..2.646..2.7.5...7426533746.582.256...47.
A5: 4,5,7                                #  9 pairs
A6: 8,9,4                                # reduction candidate for 8,9
A6: 8,9                                  # 13 pairs
A7: 8,9,7                                # reduction candidate for 8,9
A7: 8,9 => CTR
* .42.5.167...1...42...2.4.3812.8..394...4..2.646..2.7.5...7426533746.582.256...47.
A7: 7                                    # 13 pairs
* PAIR D1: 3,9 BLK 2
F1: 3,9,8                                # reduction candidate for 3,9
F1: 3,9 => SOLVED
* 842359167573186942619274538127865394435791286968423715781942653354617829296538471
F1: 8 => CTR
* 942358167.3.1...42...2.4.3812.8..3944...31286863429715781942653354617829296583471
* PAIR D1: 3,9 COL D
D5: 3,9,4,5,7                            # reduction candidate for 3,9
D5: 3,9 => CTR
* .42.5.167...1...42...2.4.3812.8..3944.....2.6.6.42.7.5...7426533746.582.256...47.
D5: 4,5,7                                #  9 pairs
D6: 3,9,4                                # reduction candidate for 3,9
D6: 3,9 => CTR
* .42.5.167...1...42...2.4.3812.8..394...4..2.646..2.7.5...7426533746.582.256...47.
D6: 4                                    # 13 pairs
D7: 3,9,7                                # reduction candidate for 3,9
D7: 3,9                                  # 13 pairs
D9: 3,9,5                                # reduction candidate for 3,9
D9: 3,9 => CTR
* .42.5.167...1...42...2.4.381258..3944.75..2.6.6.42.7.5...7426533746.582.256...47.
D9: 5                                    # 13 pairs
* PAIR G2: 5,9 ROW 2
A2: 5,9,6,7,8                            # reduction candidate for 5,9
A2: 5,9                                  # 11 pairs
C2: 5,9,3,7,8                            # reduction candidate for 5,9
C2: 5,9                                  # 12 pairs
* PAIR G3: 5,9 ROW 3
A3: 5,9,6,7                              # reduction candidate for 5,9
A3: 5,9 => CTR
* .42.5.1676..1.7.42..7264.381258763947.....2.6.6..2.7.5...7426533746.582.256...47.
A3: 6,7                                  # 10 pairs
C3: 5,9,1,7                              # reduction candidate for 5,9
C3: 5,9                                  # 19 pairs
* PAIR C4: 5,7 BLK 4
A5: 5,7,4,8,9                            # reduction candidate for 5,7
A5: 5,7 => CTR
* .42.5.167...1...42...2.4.3812.8..394...4..2.646..2.7.5...7426533746.582.256...47.
A5: 4,8,9                                # 13 pairs
C5: 5,7,3,8,9                            # reduction candidate for 5,7
C5: 5,7                                  # 13 pairs
* PAIR C4: 5,7 ROW 4
F4: 5,7,6                                # reduction candidate for 5,7
F4: 6 => CTR
* .42.5.167...1.7.427..2645381258763944.75..2.6.6.42.7.5...7426533746.582.256...47.
F4: 5,7                                  # 13 pairs
* PAIR C4: 5,7 COL C
C2: 5,7,3,8,9                            # reduction candidate for 5,7
C2: 5,7                                  # 13 pairs
C3: 5,7,1,9                              # reduction candidate for 5,7
C3: 5,7                                  # 12 pairs
* PAIR E4: 6,7 BLK 5
F4: 6,7,5                                # reduction candidate for 6,7
F4: 6,7 => CTR
* .42.5.167...1...42...2.4.381258..3944.75..2.6.6.42.7.5...7426533746.582.256...47.
F4: 5                                    # 13 pairs
* PAIR E4: 6,7 COL E
E2: 6,7,8,9                              # reduction candidate for 6,7
E2: 6,7 => CTR
* 942358167.3.1..9426..29453812.8..3944...31286863429715781942653354617829296583471
E2: 8,9                                  # 15 pairs
E3: 6,7,9                                # reduction candidate for 6,7
E3: 6,7                                  # 15 pairs
* PAIR I8: 1,9 BLK 9
I7: 1,9,3                                # reduction candidate for 1,9
I7: 1,9 => CTR
* 842953167.391.6542...2.4.381278653944.573.2.69634217857.834265.3546..82.2.65..473
I7: 3                                    # 12 pairs
I9: 1,9,3                                # reduction candidate for 1,9
I9: 1,9                                  # 12 pairs
* PAIR I8: 1,9 ROW 8
B8: 1,9,5,7                              # reduction candidate for 1,9
B8: 1,9 => CTR
* .42.5.167...1...42...2.4.381258..394...5..2.6.6.42.7.5...7426533.46.582.256...47.
B8: 5,7                                  # 10 pairs
E8: 1,9,7                                # reduction candidate for 1,9
E8: 1,9                                  # 12 pairs
F8: 1,9,5,7                              # reduction candidate for 1,9
F8: 1,9 => CTR
* .42.5.167...1.7.42...2.4.3812786.394......2.6.6..2.7.5....4265.35467.82.2.6...47.
F8: 5,7                                  # 10 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top95-068-base-pr-000.dot
* REASONING
* DIS # A2: 8,9 => CTR => A2: 5,6,7
* DIS # B2: 8,9 => CTR => B2: 3,7
* DIS # F1: 3 => CTR => F1: 8,9
* DIS # A5: 8,9 => CTR => A5: 4,5,7
* DIS # A7: 8,9 => CTR => A7: 7
* PRF # F1: 3,9 => SOL
* DIS # F1: 8 => CTR => F1: 3,9
* DIS # D5: 3,9 => CTR => D5: 4,5,7
* DIS # D6: 3,9 => CTR => D6: 4
* DIS # D9: 3,9 => CTR => D9: 5
* DIS # A3: 5,9 => CTR => A3: 6,7
* DIS # A5: 5,7 => CTR => A5: 4,8,9
* DIS # F4: 6 => CTR => F4: 5,7
* DIS # F4: 6,7 => CTR => F4: 5
* DIS # E2: 6,7 => CTR => E2: 8,9
* DIS # I7: 1,9 => CTR => I7: 3
* DIS # B8: 1,9 => CTR => B8: 5,7
* DIS # F8: 1,9 => CTR => F8: 5,7
* CNT  18 HDP CHAINS /  46 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,C4,D1,E4,G2,G3,H5,H6,I8)
* .42.5.167...1...42...2.4.3812.8..394......2.6.6..2.7.5....4265.3.46..82.2.6...47.
* PAIR A1: 8,9 BLK 1
A2: 8,9,5,6,7                            # reduction candidate for 8,9
A2: 8,9 => CTR
* .42.5.167...1...426..2.4.3812.8..3945..4..2.646..2.7.57...4265.3.46..82.2.65..47.
B2: 8,9,3,7                              # reduction candidate for 8,9
B2: 8,9 => CTR
* 842359167.9318.542.1.2.493812.8..394.3.59.2.6.6942.7.5.81.426533.46..82.256938471
C2: 8,9,3,5,7                            # reduction candidate for 8,9
C2: 8,9                                  # 11 pairs
* RESTART
* PAIR A1: 8,9 BLK 1
C2: 8,9,3,5,7                            # reduction candidate for 8,9
C2: 3,5,7 => SOLVED
* 842359167573186942619274538127865394435791286968423715781942653354617829296538471
* DURATION: 0:00:06.645261  START: 00:25:27.234545  END: 00:25:33.879806 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top95-068-base-pr-001.dot
* REASONING
* DIS # A2: 8,9 => CTR => A2: 5,6,7
* DIS A2: 5,6,7 # B2: 8,9 => CTR => B2: 3,7
* PRF A2: 5,6,7 + B2: 3,7 # C2: 3,5,7 => SOL
* STA A2: 5,6,7 + B2: 3,7 + C2: 3,5,7
* CNT   3 HDP CHAINS /   5 HYP OPENED

Header Info

Top 95 Sudokus 068
[sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt

Solution

position: 842359167573186942619274538127865394435791286968423715781942653354617829296538471 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 # A2: 8,9 => CTR => A2: 5,6,7
* INC # A2: 5,6,7 => UNS
* DIS # B2: 8,9 => CTR => B2: 3,7
* INC # B2: 3,7 => UNS
* INC # C2: 8,9 => UNS
* INC # F1: 8,9 => UNS
* DIS # F1: 3 => CTR => F1: 8,9
* DIS # A5: 8,9 => CTR => A5: 4,5,7
* INC # A5: 4,5,7 => UNS
* INC # A6: 8,9 => UNS
* DIS # A7: 8,9 => CTR => A7: 7
* INC # A7: 7 => UNS
* PRF # F1: 3,9 => SOL
* DIS # F1: 8 => CTR => F1: 3,9
* DIS # D5: 3,9 => CTR => D5: 4,5,7
* INC # D5: 4,5,7 => UNS
* DIS # D6: 3,9 => CTR => D6: 4
* INC # D6: 4 => UNS
* INC # D7: 3,9 => UNS
* DIS # D9: 3,9 => CTR => D9: 5
* INC # D9: 5 => UNS
* INC # A2: 5,9 => UNS
* INC # C2: 5,9 => UNS
* DIS # A3: 5,9 => CTR => A3: 6,7
* INC # A3: 6,7 => UNS
* INC # C3: 5,9 => UNS
* DIS # A5: 5,7 => CTR => A5: 4,8,9
* INC # A5: 4,8,9 => UNS
* INC # C5: 5,7 => UNS
* INC # F4: 5,7 => UNS
* DIS # F4: 6 => CTR => F4: 5,7
* INC # C2: 5,7 => UNS
* INC # C3: 5,7 => UNS
* DIS # F4: 6,7 => CTR => F4: 5
* INC # F4: 5 => UNS
* DIS # E2: 6,7 => CTR => E2: 8,9
* INC # E2: 8,9 => UNS
* INC # E3: 6,7 => UNS
* DIS # I7: 1,9 => CTR => I7: 3
* INC # I7: 3 => UNS
* INC # I9: 1,9 => UNS
* DIS # B8: 1,9 => CTR => B8: 5,7
* INC # B8: 5,7 => UNS
* INC # E8: 1,9 => UNS
* DIS # F8: 1,9 => CTR => F8: 5,7
* INC # F8: 5,7 => UNS
* CNT  46 HDP CHAINS /  46 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A2: 8,9 => CTR => A2: 5,6,7
* DIS A2: 5,6,7 # B2: 8,9 => CTR => B2: 3,7
* INC A2: 5,6,7 + B2: 3,7 # C2: 8,9 => UNS
* INC A2: 5,6,7 + B2: 3,7 # C2: 8,9 => UNS
* PRF A2: 5,6,7 + B2: 3,7 # C2: 3,5,7 => SOL
* STA A2: 5,6,7 + B2: 3,7 + C2: 3,5,7
* CNT   5 HDP CHAINS /   5 HYP OPENED