Analysis of xx-top500-208-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .429.........6..3..8..........4..2..1......5.............8..4.13...1.9..5........ initial

Autosolve

position: .429..51..51.6483..831...4.8.54.12.312.3...5443.5..1.82..8..4.13.4.1.985518.4932. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A3: 6,7 => CTR => A3: 9
* PRF # A3: 9 => SOL
* PRF # A3: 7,9 => SOL
* DIS # A3: 6 => CTR => A3: 7,9
* DIS # D8: 2,7 => CTR => D8: 6
* PRF # D8: 6 => SOL
* DIS # A3: 6,7 => CTR => A3: 9
* PRF # A3: 9 => SOL
* DIS # E6: 7,9 => CTR => E6: 2
* PRF # B4: 7,9 => SOL
* DIS # B4: 6 => CTR => B4: 7,9
* DIS # H4: 7,9 => CTR => H4: 6
* PRF # H4: 6 => SOL
* DIS # H6: 6,7 => CTR => H6: 9
* PRF # B7: 6,7 => SOL
* PRF # D8: 6,7 => SOL
* DIS # D8: 2 => CTR => D8: 6,7
* PRF # B4: 9 => SOL
* DIS # D8: 2,7 => CTR => D8: 6
* PRF # D8: 6 => SOL
* DIS # F6: 2,7 => CTR => F6: 6
* PRF # D8: 6,7 => SOL
* DIS # D8: 2 => CTR => D8: 6,7
* PRF # B7: 6,7 => SOL
* DIS # H6: 6,7 => CTR => H6: 9
* CNT  25 HDP CHAINS /  42 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 # A3: 6,7 => CTR => A3: 9
* PRF A3: 9 => SOL
* STA A3: 9
* CNT   2 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

.429.........6..3..8..........4..2..1......5.............8..4.13...1.9..5........ initial
.429..51..51.6483..831...4.8.54.12.312.3...5443.5..1.82..8..4.13.4.1.985518.4932. autosolve
642983517751264839983157642895471263126398754437526198269835471374612985518749326 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (18)
A1: 6,7
A2: 7,9
E1: 3,8
F1: 3,8
D2: 2,7
I1: 6,7
I2: 2,9
G3: 6,7
I3: 2,9
E4: 7,9
G5: 6,7
B8: 6,7
E7: 3,5
F7: 3,5
F8: 2,7
D9: 6,7
H7: 6,7
I9: 6,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
I2,I3: 2.. / I2 = 2  =>  0 pairs (X) / I3 = 2  =>  0 pairs (_)
E6,F6: 2.. / E6 = 2  => 20 pairs (_) / F6 = 2  =>  0 pairs (X)
D8,F8: 2.. / D8 = 2  =>  0 pairs (X) / F8 = 2  =>  0 pairs (_)
D2,I2: 2.. / D2 = 2  =>  0 pairs (*) / I2 = 2  =>  0 pairs (X)
D2,D8: 2.. / D2 = 2  =>  0 pairs (*) / D8 = 2  =>  0 pairs (X)
E3,E6: 2.. / E3 = 2  =>  0 pairs (X) / E6 = 2  => 20 pairs (_)
E1,F1: 3.. / E1 = 3  => 19 pairs (_) / F1 = 3  => 18 pairs (_)
E7,F7: 3.. / E7 = 3  => 18 pairs (_) / F7 = 3  => 19 pairs (_)
E1,E7: 3.. / E1 = 3  => 19 pairs (_) / E7 = 3  => 18 pairs (_)
F1,F7: 3.. / F1 = 3  => 18 pairs (_) / F7 = 3  => 19 pairs (_)
E3,F3: 5.. / E3 = 5  => 18 pairs (_) / F3 = 5  => 19 pairs (_)
E7,F7: 5.. / E7 = 5  => 19 pairs (_) / F7 = 5  => 18 pairs (_)
E3,E7: 5.. / E3 = 5  => 18 pairs (_) / E7 = 5  => 19 pairs (_)
F3,F7: 5.. / F3 = 5  => 19 pairs (_) / F7 = 5  => 18 pairs (_)
A1,A3: 6.. / A1 = 6  =>  0 pairs (*) / A3 = 6  =>  0 pairs (X)
I1,G3: 6.. / I1 = 6  =>  0 pairs (X) / G3 = 6  =>  0 pairs (_)
F5,F6: 6.. / F5 = 6  =>  0 pairs (X) / F6 = 6  => 22 pairs (_)
D8,D9: 6.. / D8 = 6  =>  0 pairs (*) / D9 = 6  =>  0 pairs (X)
H7,I9: 6.. / H7 = 6  =>  0 pairs (X) / I9 = 6  =>  0 pairs (_)
A1,I1: 6.. / A1 = 6  =>  0 pairs (*) / I1 = 6  =>  0 pairs (X)
A3,G3: 6.. / A3 = 6  =>  0 pairs (X) / G3 = 6  =>  0 pairs (_)
B4,H4: 6.. / B4 = 6  =>  0 pairs (X) / H4 = 6  =>  0 pairs (_)
B8,D8: 6.. / B8 = 6  =>  0 pairs (X) / D8 = 6  =>  0 pairs (_)
D9,I9: 6.. / D9 = 6  =>  0 pairs (X) / I9 = 6  =>  0 pairs (_)
G3,G5: 6.. / G3 = 6  =>  0 pairs (*) / G5 = 6  =>  0 pairs (X)
I1,I9: 6.. / I1 = 6  =>  0 pairs (X) / I9 = 6  =>  0 pairs (_)
I1,G3: 7.. / I1 = 7  =>  0 pairs (*) / G3 = 7  =>  0 pairs (X)
H7,I9: 7.. / H7 = 7  =>  0 pairs (*) / I9 = 7  =>  0 pairs (X)
A1,I1: 7.. / A1 = 7  =>  0 pairs (X) / I1 = 7  =>  0 pairs (_)
A2,D2: 7.. / A2 = 7  =>  0 pairs (*) / D2 = 7  =>  0 pairs (X)
D9,I9: 7.. / D9 = 7  =>  0 pairs (*) / I9 = 7  =>  0 pairs (X)
G3,G5: 7.. / G3 = 7  =>  0 pairs (X) / G5 = 7  =>  0 pairs (_)
I1,I9: 7.. / I1 = 7  =>  0 pairs (*) / I9 = 7  =>  0 pairs (X)
E1,F1: 8.. / E1 = 8  => 18 pairs (_) / F1 = 8  => 19 pairs (_)
E5,F5: 8.. / E5 = 8  => 19 pairs (_) / F5 = 8  => 18 pairs (_)
E1,E5: 8.. / E1 = 8  => 18 pairs (_) / E5 = 8  => 19 pairs (_)
F1,F5: 8.. / F1 = 8  => 19 pairs (_) / F5 = 8  => 18 pairs (_)
A2,A3: 9.. / A2 = 9  =>  0 pairs (X) / A3 = 9  =>  0 pairs (_)
I2,I3: 9.. / I2 = 9  =>  0 pairs (*) / I3 = 9  =>  0 pairs (X)
H4,H6: 9.. / H4 = 9  =>  0 pairs (X) / H6 = 9  => 21 pairs (_)
B7,C7: 9.. / B7 = 9  => 20 pairs (_) / C7 = 9  =>  0 pairs (*)
A2,I2: 9.. / A2 = 9  =>  0 pairs (X) / I2 = 9  =>  0 pairs (_)
A3,I3: 9.. / A3 = 9  =>  0 pairs (*) / I3 = 9  =>  0 pairs (X)
C5,E5: 9.. / C5 = 9  => 22 pairs (_) / E5 = 9  => 20 pairs (_)
B4,B7: 9.. / B4 = 9  =>  0 pairs (*) / B7 = 9  =>  0 pairs (X)
* DURATION: 0:01:42.421195  START: 09:55:36.589786  END: 09:57:19.010981 2017-05-04
* CP COUNT: (45)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,B8,D2,D9,E1,E4,E7,F1,F7,F8,G3,G5,H7,I1,I2,I3,I9)
* .429..51..51.6483..831...4.8.54.12.312.3...5443.5..1.82..8..4.13.4.1.985518.4932.
* PAIR A1: 6,7 BLK 1
A3: 6,7,9                                # reduction candidate for 6,7
A3: 6,7 => CTR
* 7429..5169517648326831..7498.54.12.312.3..65443.5.61.82.68..4.13.4217985518649327
A3: 9 => SOLVED
* 642983517751264839983157642895471263126398754437526198269835471374612985518749326
* PAIR A2: 7,9 BLK 1
A3: 7,9,6                                # reduction candidate for 7,9
A3: 7,9 => SOLVED
* 642983517751264839983157642895471263126398754437526198269835471374612985518749326
A3: 6 => CTR
* .429..51.9517648326831..7498.54.12.312.3..65443.5.61.82.68..4713.4.1.985518.4932.
* PAIR D2: 2,7 BLK 2
E3: 2,7,5                                # reduction candidate for 2,7
E3: 2,7                                  # 19 pairs
F3: 2,7,5                                # reduction candidate for 2,7
F3: 2,7                                  # 18 pairs
* PAIR D2: 2,7 COL D
D8: 2,7,6                                # reduction candidate for 2,7
D8: 2,7 => CTR
* 7429..5169517648326831..7498.54.126312.3...5443.5..1.82..8..4.1364.1.985518649327
D8: 6 => SOLVED
* 642983517751264839983157642895471263126398754437526198269835471374612985518749326
* PAIR G3: 6,7 ROW 3
A3: 6,7,9                                # reduction candidate for 6,7
A3: 6,7 => CTR
* 7429..5169517648326831..7498.54.12.312.3..65443.5.61.82.68..4.13.4217985518649327
A3: 9 => SOLVED
* 642983517751264839983157642895471263126398754437526198269835471374612985518749326
* PAIR E4: 7,9 BLK 5
E5: 7,9,8                                # reduction candidate for 7,9
E5: 7,9                                  # 18 pairs
E6: 7,9,2                                # reduction candidate for 7,9
E6: 7,9 => CTR
* 7429385169517648326831257498.54.12.312.386.5443.5.21.82..8534.13.4217985518649327
E6: 2                                    # 20 pairs
* PAIR E4: 7,9 ROW 4
B4: 7,9,6                                # reduction candidate for 7,9
B4: 7,9 => SOLVED
* 642983517751264839983157642895471263126398754437526198269835471374612985518749326
B4: 6 => CTR
* 6429..5177512648399831..64286547129312.3.6.5443.5..1.82968..471374612985518749326
H4: 7,9,6                                # reduction candidate for 7,9
H4: 7,9 => CTR
* 6429..5177512648399831..64286547129312.3.6.5443.5..1.82968..471374612985518749326
H4: 6 => SOLVED
* 642983517751264839983157642895471263126398754437526198269835471374612985518749326
* PAIR G5: 6,7 BLK 6
H4: 6,7,9                                # reduction candidate for 6,7
H4: 6,7                                  # 21 pairs
H6: 6,7,9                                # reduction candidate for 6,7
H6: 6,7 => CTR
* .429..51..51.6483..831...4.86547129312.3...5443.5..1.82968..471374612985518749326
H6: 9                                    # 21 pairs
* PAIR G5: 6,7 ROW 5
C5: 6,7,9                                # reduction candidate for 6,7
C5: 6,7                                  # 20 pairs
F5: 6,7,8                                # reduction candidate for 6,7
F5: 6,7                                  # 19 pairs
* PAIR B8: 6,7 BLK 7
B7: 6,7,9                                # reduction candidate for 6,7
B7: 6,7 => SOLVED
* 642983517751264839983157642895471263126398754437526198269835471374612985518749326
B7: 9                                    # 20 pairs
C7: 6,7,9                                # reduction candidate for 6,7
C7: 6,7                                  # 20 pairs
* PAIR B8: 6,7 ROW 8
D8: 6,7,2                                # reduction candidate for 6,7
D8: 6,7 => SOLVED
* 642983517751264839983157642895471263126398754437526198269835471374612985518749326
D8: 2 => CTR
* 7429..5169517648326831..7498.54.126312.3...5443.5..1.82..8..4.1364217985518649327
* PAIR B8: 6,7 COL B
B4: 6,7,9                                # reduction candidate for 6,7
B4: 9 => SOLVED
* 642983517751264839983157642895471263126398754437526198269835471374612985518749326
B4: 6,7                                  # 20 pairs
* PAIR F8: 2,7 BLK 8
D8: 2,7,6                                # reduction candidate for 2,7
D8: 2,7 => CTR
* 7429..5169517648326831..7498.54.126312.3...5443.5..1.82..8..4.1364.1.985518649327
D8: 6 => SOLVED
* 642983517751264839983157642895471263126398754437526198269835471374612985518749326
* PAIR F8: 2,7 COL F
F3: 2,7,5                                # reduction candidate for 2,7
F3: 2,7                                  # 18 pairs
F6: 2,7,6                                # reduction candidate for 2,7
F6: 2,7 => CTR
* 6429.85177512648399831..6428.54712.312.3.675443.5..1.82..8..471374612985518749326
F6: 6                                    # 22 pairs
* PAIR D9: 6,7 BLK 8
D8: 6,7,2                                # reduction candidate for 6,7
D8: 6,7 => SOLVED
* 642983517751264839983157642895471263126398754437526198269835471374612985518749326
D8: 2 => CTR
* 7429..5169517648326831..7498.54.126312.3...5443.5..1.82..8..4.1364217985518649327
* PAIR H7: 6,7 ROW 7
B7: 6,7,9                                # reduction candidate for 6,7
B7: 6,7 => SOLVED
* 642983517751264839983157642895471263126398754437526198269835471374612985518749326
B7: 9                                    # 20 pairs
C7: 6,7,9                                # reduction candidate for 6,7
C7: 6,7                                  # 20 pairs
* PAIR H7: 6,7 COL H
H4: 6,7,9                                # reduction candidate for 6,7
H4: 6,7                                  # 21 pairs
H6: 6,7,9                                # reduction candidate for 6,7
H6: 6,7 => CTR
* .429..51..51.6483..831...4.86547129312.3...5443.5..1.82968..471374612985518749326
H6: 9                                    # 21 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-208-base-pr-000.dot
* REASONING
* DIS # A3: 6,7 => CTR => A3: 9
* PRF # A3: 9 => SOL
* PRF # A3: 7,9 => SOL
* DIS # A3: 6 => CTR => A3: 7,9
* DIS # D8: 2,7 => CTR => D8: 6
* PRF # D8: 6 => SOL
* DIS # A3: 6,7 => CTR => A3: 9
* PRF # A3: 9 => SOL
* DIS # E6: 7,9 => CTR => E6: 2
* PRF # B4: 7,9 => SOL
* DIS # B4: 6 => CTR => B4: 7,9
* DIS # H4: 7,9 => CTR => H4: 6
* PRF # H4: 6 => SOL
* DIS # H6: 6,7 => CTR => H6: 9
* PRF # B7: 6,7 => SOL
* PRF # D8: 6,7 => SOL
* DIS # D8: 2 => CTR => D8: 6,7
* PRF # B4: 9 => SOL
* DIS # D8: 2,7 => CTR => D8: 6
* PRF # D8: 6 => SOL
* DIS # F6: 2,7 => CTR => F6: 6
* PRF # D8: 6,7 => SOL
* DIS # D8: 2 => CTR => D8: 6,7
* PRF # B7: 6,7 => SOL
* DIS # H6: 6,7 => CTR => H6: 9
* CNT  25 HDP CHAINS /  42 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,B8,D2,D9,E1,E4,E7,F1,F7,F8,G3,G5,H7,I1,I2,I3,I9)
* .429..51..51.6483..831...4.8.54.12.312.3...5443.5..1.82..8..4.13.4.1.985518.4932.
* PAIR A1: 6,7 BLK 1
A3: 6,7,9                                # reduction candidate for 6,7
A3: 6,7 => CTR
* 7429..5169517648326831..7498.54.12.312.3..65443.5.61.82.68..4.13.4217985518649327
A3: 9 => SOLVED
* 642983517751264839983157642895471263126398754437526198269835471374612985518749326
* DURATION: 0:00:03.714368  START: 09:58:16.792333  END: 09:58:20.506701 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-208-base-pr-001.dot
* REASONING
* DIS # A3: 6,7 => CTR => A3: 9
* PRF A3: 9 => SOL
* STA A3: 9
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 208

solution: 642983517751264839983157642895471263126398754437526198269835471374612985518749326
info: 1915     FNBTHWX  S8.f     39526

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

Solution

position: 642983517751264839983157642895471263126398754437526198269835471374612985518749326 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 # A3: 6,7 => CTR => A3: 9
* PRF # A3: 9 => SOL
* PRF # A3: 7,9 => SOL
* DIS # A3: 6 => CTR => A3: 7,9
* INC # E3: 2,7 => UNS
* INC # F3: 2,7 => UNS
* DIS # D8: 2,7 => CTR => D8: 6
* PRF # D8: 6 => SOL
* DIS # A3: 6,7 => CTR => A3: 9
* PRF # A3: 9 => SOL
* INC # E5: 7,9 => UNS
* DIS # E6: 7,9 => CTR => E6: 2
* INC # E6: 2 => UNS
* PRF # B4: 7,9 => SOL
* DIS # B4: 6 => CTR => B4: 7,9
* DIS # H4: 7,9 => CTR => H4: 6
* PRF # H4: 6 => SOL
* INC # H4: 6,7 => UNS
* DIS # H6: 6,7 => CTR => H6: 9
* INC # H6: 9 => UNS
* INC # C5: 6,7 => UNS
* INC # F5: 6,7 => UNS
* PRF # B7: 6,7 => SOL
* INC # B7: 9 => UNS
* INC # C7: 6,7 => UNS
* PRF # D8: 6,7 => SOL
* DIS # D8: 2 => CTR => D8: 6,7
* INC # B4: 6,7 => UNS
* PRF # B4: 9 => SOL
* DIS # D8: 2,7 => CTR => D8: 6
* PRF # D8: 6 => SOL
* INC # F3: 2,7 => UNS
* DIS # F6: 2,7 => CTR => F6: 6
* INC # F6: 6 => UNS
* PRF # D8: 6,7 => SOL
* DIS # D8: 2 => CTR => D8: 6,7
* PRF # B7: 6,7 => SOL
* INC # B7: 9 => UNS
* INC # C7: 6,7 => UNS
* INC # H4: 6,7 => UNS
* DIS # H6: 6,7 => CTR => H6: 9
* INC # H6: 9 => UNS
* CNT  42 HDP CHAINS /  42 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A3: 6,7 => CTR => A3: 9
* PRF A3: 9 => SOL
* STA A3: 9
* CNT   2 HDP CHAINS /   1 HYP OPENED