Analysis of xx-top500-444-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 5.1.........6...8....2........4..62.3...8....9.........4..7.....2....4.......3..9 initial

Autosolve

position: 5.1..4.622.76...844.62...9....4..6233.2.8.94.9.432.....4..72..6.2..6.4..6...432.9 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B1: 3,9 => CTR => B1: 8
* DIS # B1: 9 => CTR => B1: 3,8
* DIS # B1: 3,9 => CTR => B1: 8
* DIS # D7: 1,8 => CTR => D7: 5,9
* DIS # D7: 1,8 => CTR => D7: 5,9
* DIS # D8: 1,8 => CTR => D8: 5,9
* CNT   6 HDP CHAINS /  30 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 # B1: 3,9 => CTR => B1: 8
* DIS B1: 8 # D7: 1,8 => CTR => D7: 5,9
* PRF B1: 8 + D7: 5,9 # G7: 5 => SOL
* STA B1: 8 + D7: 5,9 + G7: 5
* CNT   3 HDP CHAINS /   7 HYP OPENED

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

Details

Positions

5.1.........6...8....2........4..62.3...8....9.........4..7.....2....4.......3..9 initial
5.1..4.622.76...844.62...9....4..6233.2.8.94.9.432.....4..72..6.2..6.4..6...432.9 autosolve
581794362297635184436218795178459623352186947964327851843972516729561438615843279 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
B2: 3,9
B3: 3,8
D1: 7,8
E1: 3,9
F3: 7,8
G1: 3,7
C4: 5,8
A7: 1,8
C7: 3,9
C8: 3,9
C9: 5,8
D9: 1,8
H9: 1,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C7,C8: 3.. / C7 = 3  => 12 pairs (_) / C8 = 3  => 11 pairs (_)
H7,H8: 3.. / H7 = 3  => 11 pairs (_) / H8 = 3  => 12 pairs (_)
C7,H7: 3.. / C7 = 3  => 12 pairs (_) / H7 = 3  => 11 pairs (_)
C8,H8: 3.. / C8 = 3  => 11 pairs (_) / H8 = 3  => 12 pairs (_)
B9,C9: 5.. / B9 = 5  => 16 pairs (_) / C9 = 5  => 14 pairs (_)
C4,C9: 5.. / C4 = 5  => 16 pairs (_) / C9 = 5  => 14 pairs (_)
B5,B6: 6.. / B5 = 6  => 13 pairs (_) / B6 = 6  => 13 pairs (_)
F5,F6: 6.. / F5 = 6  => 13 pairs (_) / F6 = 6  => 13 pairs (_)
B5,F5: 6.. / B5 = 6  => 13 pairs (_) / F5 = 6  => 13 pairs (_)
B6,F6: 6.. / B6 = 6  => 13 pairs (_) / F6 = 6  => 13 pairs (_)
D1,F3: 7.. / D1 = 7  => 15 pairs (_) / F3 = 7  =>  0 pairs (X)
A8,B9: 7.. / A8 = 7  => 15 pairs (_) / B9 = 7  => 16 pairs (_)
D1,G1: 7.. / D1 = 7  => 15 pairs (_) / G1 = 7  =>  0 pairs (X)
B9,H9: 7.. / B9 = 7  => 16 pairs (_) / H9 = 7  => 15 pairs (_)
A4,A8: 7.. / A4 = 7  => 16 pairs (_) / A8 = 7  => 15 pairs (_)
D1,D5: 7.. / D1 = 7  => 15 pairs (_) / D5 = 7  =>  0 pairs (X)
B1,B3: 8.. / B1 = 8  => 15 pairs (_) / B3 = 8  =>  0 pairs (X)
D1,F3: 8.. / D1 = 8  =>  0 pairs (X) / F3 = 8  => 15 pairs (_)
A4,C4: 8.. / A4 = 8  => 16 pairs (_) / C4 = 8  => 14 pairs (_)
G6,I6: 8.. / G6 = 8  => 19 pairs (_) / I6 = 8  => 17 pairs (_)
G7,I8: 8.. / G7 = 8  => 17 pairs (_) / I8 = 8  => 19 pairs (_)
B1,D1: 8.. / B1 = 8  => 15 pairs (_) / D1 = 8  =>  0 pairs (X)
B3,F3: 8.. / B3 = 8  =>  0 pairs (X) / F3 = 8  => 15 pairs (_)
C9,D9: 8.. / C9 = 8  => 16 pairs (_) / D9 = 8  => 14 pairs (_)
C4,C9: 8.. / C4 = 8  => 14 pairs (_) / C9 = 8  => 16 pairs (_)
F3,F8: 8.. / F3 = 8  => 15 pairs (_) / F8 = 8  =>  0 pairs (X)
G6,G7: 8.. / G6 = 8  => 19 pairs (_) / G7 = 8  => 17 pairs (_)
I6,I8: 8.. / I6 = 8  => 17 pairs (_) / I8 = 8  => 19 pairs (_)
B1,B2: 9.. / B1 = 9  =>  0 pairs (X) / B2 = 9  => 14 pairs (_)
E4,F4: 9.. / E4 = 9  =>  0 pairs (X) / F4 = 9  => 15 pairs (_)
C7,C8: 9.. / C7 = 9  => 11 pairs (_) / C8 = 9  => 12 pairs (_)
D7,D8: 9.. / D7 = 9  => 12 pairs (_) / D8 = 9  => 11 pairs (_)
B1,E1: 9.. / B1 = 9  =>  0 pairs (X) / E1 = 9  => 14 pairs (_)
C7,D7: 9.. / C7 = 9  => 11 pairs (_) / D7 = 9  => 12 pairs (_)
C8,D8: 9.. / C8 = 9  => 12 pairs (_) / D8 = 9  => 11 pairs (_)
F2,F4: 9.. / F2 = 9  =>  0 pairs (X) / F4 = 9  => 15 pairs (_)
* DURATION: 0:01:08.423454  START: 17:55:05.197314  END: 17:56:13.620768 2017-05-04
* CP COUNT: (36)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B2,B3,C4,C7,C8,C9,D1,D9,E1,F3,G1,H9)
* 5.1..4.622.76...844.62...9....4..6233.2.8.94.9.432.....4..72..6.2..6.4..6...432.9
* PAIR B2: 3,9 BLK 1
B1: 3,9,8                                # reduction candidate for 3,9
B1: 3,9 => CTR
* 5.18.47622.76...844862.7.9....4..6233.278.94.9.432.....4..72..6.2..684..6.8143279
B1: 8                                    # 15 pairs
* PAIR B2: 3,9 ROW 2
E2: 3,9,1,5                              # reduction candidate for 3,9
E2: 3,9                                  # 18 pairs
E2: 1,5                                  # 14 pairs
* PAIR B3: 3,8 BLK 1
B1: 3,8,9                                # reduction candidate for 3,8
B1: 9 => CTR
* 5918347622376...844862.739....4..6233.278.94.9.432.....4..72..6.2..684..6.8143279
B1: 3,8                                  # 14 pairs
* PAIR E1: 3,9 BLK 2
E2: 3,9,1,5                              # reduction candidate for 3,9
E2: 3,9                                  # 18 pairs
E2: 1,5                                  # 14 pairs
* PAIR E1: 3,9 ROW 1
B1: 3,9,8                                # reduction candidate for 3,9
B1: 3,9 => CTR
* 5.18.47622.76...844862.7.9....4..6233.278.94.9.432.....4..72..6.2..684..6.8143279
B1: 8                                    # 15 pairs
* PAIR G1: 3,7 BLK 3
G3: 3,7,1,5                              # reduction candidate for 3,7
G3: 3,7                                  # 17 pairs
G3: 1,5                                  # 14 pairs
* PAIR A7: 1,8 BLK 7
A8: 1,8,7                                # reduction candidate for 1,8
A8: 1,8                                  # 16 pairs
A8: 7                                    # 15 pairs
* PAIR A7: 1,8 ROW 7
D7: 1,8,5,9                              # reduction candidate for 1,8
D7: 1,8 => CTR
* 5817943622976...844.62.8.9....4..6233.258.94.9.432..5..49.72536.239654.86...432.9
D7: 5,9                                  # 14 pairs
G7: 1,8,5                                # reduction candidate for 1,8
G7: 1,8                                  # 16 pairs
* PAIR A7: 1,8 COL A
A4: 1,8,7                                # reduction candidate for 1,8
A4: 7                                    # 16 pairs
A4: 1,8                                  # 15 pairs
* PAIR D9: 1,8 BLK 8
D7: 1,8,5,9                              # reduction candidate for 1,8
D7: 1,8 => CTR
* 5817943622976...844.62.8.9....4..6233.258.94.9.432..5..49.72536.239654.86...432.9
D7: 5,9                                  # 14 pairs
D8: 1,8,5,9                              # reduction candidate for 1,8
D8: 1,8 => CTR
* 581794362297631584436258.9...84196233.258.94.9.432.815843972156.29.654386..843279
D8: 5,9                                  # 14 pairs
F8: 1,8,5                                # reduction candidate for 1,8
F8: 1,8                                  # 17 pairs
* PAIR H9: 1,7 BLK 9
H8: 1,7,3,5                              # reduction candidate for 1,7
H8: 1,7                                  # 15 pairs
I8: 1,7,5,8                              # reduction candidate for 1,7
I8: 1,7                                  # 20 pairs
* PAIR H9: 1,7 ROW 9
B9: 1,7,5                                # reduction candidate for 1,7
B9: 5                                    # 16 pairs
B9: 1,7                                  # 14 pairs
* PAIR H9: 1,7 COL H
H6: 1,7,5                                # reduction candidate for 1,7
H6: 1,7                                  # 18 pairs
H6: 5                                    # 17 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-444-base-pr-000.dot
* REASONING
* DIS # B1: 3,9 => CTR => B1: 8
* DIS # B1: 9 => CTR => B1: 3,8
* DIS # B1: 3,9 => CTR => B1: 8
* DIS # D7: 1,8 => CTR => D7: 5,9
* DIS # D7: 1,8 => CTR => D7: 5,9
* DIS # D8: 1,8 => CTR => D8: 5,9
* CNT   6 HDP CHAINS /  30 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B2,B3,C4,C7,C8,C9,D1,D9,E1,F3,G1,H9)
* 5.1..4.622.76...844.62...9....4..6233.2.8.94.9.432.....4..72..6.2..6.4..6...432.9
* PAIR B2: 3,9 BLK 1
B1: 3,9,8                                # reduction candidate for 3,9
B1: 3,9 => CTR
* 5.18.47622.76...844862.7.9....4..6233.278.94.9.432.....4..72..6.2..684..6.8143279
* PAIR A7: 1,8 BLK 7
A8: 1,8,7                                # reduction candidate for 1,8
A8: 7                                    # 17 pairs
A8: 1,8                                  # 16 pairs
* PAIR A7: 1,8 ROW 7
D7: 1,8,5,9                              # reduction candidate for 1,8
D7: 1,8 => CTR
* 581794362297631584436258.9....4196233.258.94.9.432..5..49.72.36.239654..6...432.9
G7: 1,8,5                                # reduction candidate for 1,8
G7: 1,8                                  # 18 pairs
* RESTART
* PAIR A7: 1,8 ROW 7
G7: 1,8,5                                # reduction candidate for 1,8
G7: 5 => SOLVED
* 581794362297635184436218795178459623352186947964327851843972516729561438615843279
* DURATION: 0:00:11.111522  START: 17:56:43.874639  END: 17:56:54.986161 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-444-base-pr-001.dot
* REASONING
* DIS # B1: 3,9 => CTR => B1: 8
* DIS B1: 8 # D7: 1,8 => CTR => D7: 5,9
* PRF B1: 8 + D7: 5,9 # G7: 5 => SOL
* STA B1: 8 + D7: 5,9 + G7: 5
* CNT   3 HDP CHAINS /   7 HYP OPENED

Header Info

Top 500 Minimum 17 444

solution: 581794362297635184436218795178459623352186947964327851843972516729561438615843279
info: 95317    FNBTHYK  S8.f     46871

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

Solution

position: 581794362297635184436218795178459623352186947964327851843972516729561438615843279 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 # B1: 3,9 => CTR => B1: 8
* INC # B1: 8 => UNS
* INC # E2: 3,9 => UNS
* INC # E2: 1,5 => UNS
* INC # B1: 3,8 => UNS
* DIS # B1: 9 => CTR => B1: 3,8
* INC # E2: 3,9 => UNS
* INC # E2: 1,5 => UNS
* DIS # B1: 3,9 => CTR => B1: 8
* INC # B1: 8 => UNS
* INC # G3: 3,7 => UNS
* INC # G3: 1,5 => UNS
* INC # A8: 1,8 => UNS
* INC # A8: 7 => UNS
* DIS # D7: 1,8 => CTR => D7: 5,9
* INC # D7: 5,9 => UNS
* INC # G7: 1,8 => UNS
* INC # A4: 1,8 => UNS
* INC # A4: 7 => UNS
* DIS # D7: 1,8 => CTR => D7: 5,9
* INC # D7: 5,9 => UNS
* DIS # D8: 1,8 => CTR => D8: 5,9
* INC # D8: 5,9 => UNS
* INC # F8: 1,8 => UNS
* INC # H8: 1,7 => UNS
* INC # I8: 1,7 => UNS
* INC # B9: 1,7 => UNS
* INC # B9: 5 => UNS
* INC # H6: 1,7 => UNS
* INC # H6: 5 => UNS
* CNT  30 HDP CHAINS /  30 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B1: 3,9 => CTR => B1: 8
* INC B1: 8 # A8: 1,8 => UNS
* INC B1: 8 # A8: 7 => UNS
* DIS B1: 8 # D7: 1,8 => CTR => D7: 5,9
* INC B1: 8 + D7: 5,9 # G7: 1,8 => UNS
* INC B1: 8 + D7: 5,9 # G7: 1,8 => UNS
* PRF B1: 8 + D7: 5,9 # G7: 5 => SOL
* STA B1: 8 + D7: 5,9 + G7: 5
* CNT   7 HDP CHAINS /   7 HYP OPENED