Analysis of xx-top95-028-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 6..3.2....4.....8..........7.26............543.........8.15........8.2........7.. initial

Autosolve

position: 6.83.25...4.....82.2.......7.26.....8......543.4....2728.15........8.2.5......7.8 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # G2: 1,9 => SOL
* DIS # G2: 3 => CTR => G2: 1,9
* DIS # G3: 1,9 => CTR => G3: 3,4
* DIS # I3: 1,9 => CTR => I3: 3,6
* PRF # B1: 1,9 => SOL
* DIS # B1: 7 => CTR => B1: 1,9
* DIS # E1: 1,9 => CTR => E1: 4,7
* DIS # I4: 3 => CTR => I4: 1,9
* DIS # E4: 1,9 => CTR => E4: 3,4
* DIS # F4: 1,9 => CTR => F4: 3,4,5,8
* DIS # E5: 1,9 => CTR => E5: 2,3,7
* PRF # F5: 1,9 => SOL
* DIS # F6: 1,9 => CTR => F6: 5,8
* DIS # G6: 1,9 => CTR => G6: 6,8
* DIS # E1: 1,9 => CTR => E1: 4,7
* DIS # E2: 1,9 => CTR => E2: 6,7
* DIS # G4: 3,9 => CTR => G4: 1,8
* DIS # I4: 3,9 => CTR => I4: 1
* DIS # F4: 3,9 => CTR => F4: 1,4,5,8
* PRF # H3: 3,9 => SOL
* CNT  20 HDP CHAINS /  43 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* PRF # G2: 1,9 => SOL
* STA G2: 1,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

6..3.2....4.....8..........7.26............543.........8.15........8.2........7.. initial
6.83.25...4.....82.2.......7.26.....8......543.4....2728.15........8.2.5......7.8 autosolve
618342579943765182527891436752634891861279354394518627286157943179483265435926718 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (3)
I1: 1,9
E6: 1,9
H4: 3,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H8,H9: 1.. / H8 = 1  =>  4 pairs (_) / H9 = 1  =>  3 pairs (_)
D5,E5: 2.. / D5 = 2  =>  4 pairs (_) / E5 = 2  =>  5 pairs (_)
D9,E9: 2.. / D9 = 2  =>  5 pairs (_) / E9 = 2  =>  4 pairs (_)
D5,D9: 2.. / D5 = 2  =>  4 pairs (_) / D9 = 2  =>  5 pairs (_)
E5,E9: 2.. / E5 = 2  =>  5 pairs (_) / E9 = 2  =>  4 pairs (_)
C2,C3: 3.. / C2 = 3  =>  0 pairs (*) / C3 = 3  =>  0 pairs (X)
B8,B9: 3.. / B8 = 3  =>  0 pairs (X) / B9 = 3  =>  3 pairs (_)
C2,G2: 3.. / C2 = 3  =>  0 pairs (*) / G2 = 3  =>  0 pairs (X)
E4,F4: 4.. / E4 = 4  =>  0 pairs (X) / F4 = 4  =>  5 pairs (_)
A8,A9: 4.. / A8 = 4  =>  4 pairs (_) / A9 = 4  =>  5 pairs (_)
E1,H1: 4.. / E1 = 4  =>  6 pairs (_) / H1 = 4  =>  0 pairs (X)
G3,G7: 4.. / G3 = 4  =>  7 pairs (_) / G7 = 4  =>  0 pairs (X)
B4,B6: 5.. / B4 = 5  =>  3 pairs (_) / B6 = 5  =>  0 pairs (X)
A9,C9: 5.. / A9 = 5  =>  0 pairs (X) / C9 = 5  =>  3 pairs (_)
B4,F4: 5.. / B4 = 5  =>  3 pairs (_) / F4 = 5  =>  0 pairs (X)
E2,F2: 6.. / E2 = 6  =>  3 pairs (_) / F2 = 6  =>  0 pairs (X)
H3,I3: 6.. / H3 = 6  =>  0 pairs (X) / I3 = 6  =>  4 pairs (_)
G5,G6: 6.. / G5 = 6  =>  0 pairs (X) / G6 = 6  =>  3 pairs (_)
B6,G6: 6.. / B6 = 6  =>  0 pairs (X) / G6 = 6  =>  3 pairs (_)
E2,E9: 6.. / E2 = 6  =>  3 pairs (_) / E9 = 6  =>  0 pairs (X)
I3,I7: 6.. / I3 = 6  =>  4 pairs (_) / I7 = 6  =>  0 pairs (X)
H1,H3: 7.. / H1 = 7  =>  0 pairs (*) / H3 = 7  =>  0 pairs (X)
C7,F7: 7.. / C7 = 7  =>  0 pairs (X) / F7 = 7  =>  7 pairs (_)
B1,B8: 7.. / B1 = 7  =>  0 pairs (X) / B8 = 7  =>  0 pairs (_)
D3,F3: 8.. / D3 = 8  =>  4 pairs (_) / F3 = 8  =>  3 pairs (_)
G4,G6: 8.. / G4 = 8  =>  3 pairs (_) / G6 = 8  =>  0 pairs (X)
F4,G4: 8.. / F4 = 8  =>  0 pairs (X) / G4 = 8  =>  3 pairs (_)
D3,D6: 8.. / D3 = 8  =>  4 pairs (_) / D6 = 8  =>  3 pairs (_)
* DURATION: 0:00:38.166270  START: 23:23:58.839641  END: 23:24:37.005911 2017-05-03
* CP COUNT: (28)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (E6,H4,I1)
* 6.83.25...4.....82.2.......7.26.....8......543.4....2728.15........8.2.5......7.8
* PAIR I1: 1,9 BLK 3
G2: 1,9,3                                # reduction candidate for 1,9
G2: 1,9 => SOLVED
* 618342579943765182527891436752634891861279354394518627286157943179483265435926718
G2: 3 => CTR
* 6.83.25...47.6.382.23......7.26.....8......543.4....2728.157....7..8.2.5.35.2.7.8
G3: 1,9,3,4                              # reduction candidate for 1,9
G3: 1,9 => CTR
* 6.83.25...47.6.382.23.....67.26.....8......543.4....2728.1574...7..8.2.5.35.2.7.8
G3: 3,4                                  #  4 pairs
I3: 1,9,3,6                              # reduction candidate for 1,9
I3: 1,9 => CTR
* 6.834257..4....382.23...46.7.26.48938...3..543.4....2728915...6.7..8.2.5.3....7.8
I3: 3,6                                  #  4 pairs
* PAIR I1: 1,9 ROW 1
B1: 1,9,7                                # reduction candidate for 1,9
B1: 1,9 => SOLVED
* 618342579943765182527891436752634891861279354394518627286157943179483265435926718
B1: 7 => CTR
* 6783.25...4.....82.2.....767.26.....8......543.4....2728.15........8.2.5......7.8
E1: 1,9,4,7                              # reduction candidate for 1,9
E1: 1,9 => CTR
* 6783.254..4.....82.2.....767.26.....8......543.4....2728.15.4......8.2.5......7.8
E1: 4,7                                  #  4 pairs
* PAIR I1: 1,9 COL I
I4: 1,9,3                                # reduction candidate for 1,9
I4: 3 => CTR
* 6.83.25...47.6.382.23......7.26...938......543.4....27286157.39.7..832.5......7.8
I4: 1,9                                  #  6 pairs
* PAIR E6: 1,9 BLK 5
E4: 1,9,3,4                              # reduction candidate for 1,9
E4: 1,9 => CTR
* 6.83.25...47.6.382.23......7526.48..8......543.4....2728.157....7.48.2.54352..7.8
E4: 3,4                                  #  4 pairs
F4: 1,9,3,4,5,8                          # reduction candidate for 1,9
F4: 1,9 => CTR
* 6.837254..47.6.382.23....7675264.8..8......543.4....2728.1574...7..8.2.5.35.2.7.8
F4: 3,4,5,8                              #  3 pairs
E5: 1,9,2,3,7                            # reduction candidate for 1,9
E5: 1,9 => CTR
* 6.83.25...4.....82.2.......7.26.....8..2.73543.4...62728715.......78.2.5....2.7.8
E5: 2,3,7                                #  3 pairs
F5: 1,9,3,7                              # reduction candidate for 1,9
F5: 1,9 => SOLVED
* 618342579943765182527891436752634891861279354394518627286157943179483265435926718
F5: 3,7                                  #  4 pairs
F6: 1,9,5,8                              # reduction candidate for 1,9
F6: 1,9 => CTR
* 6.837254..47.6.382.23....767.264....8......543.4....2728.1574...7..8.2.5.35.2.7.8
F6: 5,8                                  #  4 pairs
* PAIR E6: 1,9 ROW 6
B6: 1,9,5,6                              # reduction candidate for 1,9
B6: 1,9                                  #  6 pairs
G6: 1,9,6,8                              # reduction candidate for 1,9
G6: 1,9 => CTR
* 6.83.25...47.6.382.23......7526..8..8.....654364....2728.157....7..8.2.5.35.2.7.8
G6: 6,8                                  #  4 pairs
* PAIR E6: 1,9 COL E
E1: 1,9,4,7                              # reduction candidate for 1,9
E1: 1,9 => CTR
* 6783.254..4.....82.2.....767.26.....8......543.4....2728.15.4......8.2.5......7.8
E1: 4,7                                  #  4 pairs
E2: 1,9,6,7                              # reduction candidate for 1,9
E2: 1,9 => CTR
* 6.83.25.9.437.6182.2....4..7526348918..927354394.1.62728715.946...48.2.54.52697.8
E2: 6,7                                  #  4 pairs
E3: 1,9,4,7                              # reduction candidate for 1,9
E3: 1,9                                  #  7 pairs
* PAIR H4: 3,9 BLK 6
G4: 3,9,1,8                              # reduction candidate for 3,9
G4: 3,9 => CTR
* 618372549947561382523894176752648931891...65436491582728.1574.3.7.4832.5......7.8
G4: 1,8                                  #  4 pairs
I4: 3,9,1                                # reduction candidate for 3,9
I4: 3,9 => CTR
* 6.83.25...47.6.382.23......7.26.....8......543.4....2728.157....7..8.2.5.35.2.7.8
I4: 1                                    #  8 pairs
G5: 3,9,1,6                              # reduction candidate for 3,9
G5: 3,9                                  #  9 pairs
* PAIR H4: 3,9 ROW 4
E4: 3,9,1,4                              # reduction candidate for 3,9
E4: 3,9                                  # 11 pairs
F4: 3,9,1,4,5,8                          # reduction candidate for 3,9
F4: 3,9 => CTR
* 618372549.47...382.23.9.1767526498318.1....543.4.1..2728.1574.3.7..832.5......7.8
F4: 1,4,5,8                              #  3 pairs
* PAIR H4: 3,9 COL H
H3: 3,9,4,6,7                            # reduction candidate for 3,9
H3: 3,9 => SOLVED
* 618342579943765182527891436752634891861279354394518627286157943179483265435926718
H3: 4,6,7                                #  3 pairs
H7: 3,9,4,6                              # reduction candidate for 3,9
H7: 3,9                                  #  6 pairs
H8: 3,9,1,4,6                            # reduction candidate for 3,9
H8: 3,9                                  #  7 pairs
H9: 3,9,1,4,6                            # reduction candidate for 3,9
H9: 3,9                                  #  8 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top95-028-base-pr-000.dot
* REASONING
* PRF # G2: 1,9 => SOL
* DIS # G2: 3 => CTR => G2: 1,9
* DIS # G3: 1,9 => CTR => G3: 3,4
* DIS # I3: 1,9 => CTR => I3: 3,6
* PRF # B1: 1,9 => SOL
* DIS # B1: 7 => CTR => B1: 1,9
* DIS # E1: 1,9 => CTR => E1: 4,7
* DIS # I4: 3 => CTR => I4: 1,9
* DIS # E4: 1,9 => CTR => E4: 3,4
* DIS # F4: 1,9 => CTR => F4: 3,4,5,8
* DIS # E5: 1,9 => CTR => E5: 2,3,7
* PRF # F5: 1,9 => SOL
* DIS # F6: 1,9 => CTR => F6: 5,8
* DIS # G6: 1,9 => CTR => G6: 6,8
* DIS # E1: 1,9 => CTR => E1: 4,7
* DIS # E2: 1,9 => CTR => E2: 6,7
* DIS # G4: 3,9 => CTR => G4: 1,8
* DIS # I4: 3,9 => CTR => I4: 1
* DIS # F4: 3,9 => CTR => F4: 1,4,5,8
* PRF # H3: 3,9 => SOL
* CNT  20 HDP CHAINS /  43 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (E6,H4,I1)
* 6.83.25...4.....82.2.......7.26.....8......543.4....2728.15........8.2.5......7.8
* PAIR I1: 1,9 BLK 3
G2: 1,9,3                                # reduction candidate for 1,9
G2: 1,9 => SOLVED
* 618342579943765182527891436752634891861279354394518627286157943179483265435926718
* DURATION: 0:00:02.571853  START: 23:25:10.083465  END: 23:25:12.655318 2017-05-03
* SOLUTION FOUND
* SAVE PR GRAPH xx-top95-028-base-pr-001.dot
* REASONING
* PRF # G2: 1,9 => SOL
* STA G2: 1,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

Top 95 Sudokus 028
[sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt

Solution

position: 618342579943765182527891436752634891861279354394518627286157943179483265435926718 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:

* PRF # G2: 1,9 => SOL
* DIS # G2: 3 => CTR => G2: 1,9
* DIS # G3: 1,9 => CTR => G3: 3,4
* INC # G3: 3,4 => UNS
* DIS # I3: 1,9 => CTR => I3: 3,6
* INC # I3: 3,6 => UNS
* PRF # B1: 1,9 => SOL
* DIS # B1: 7 => CTR => B1: 1,9
* DIS # E1: 1,9 => CTR => E1: 4,7
* INC # E1: 4,7 => UNS
* INC # I4: 1,9 => UNS
* DIS # I4: 3 => CTR => I4: 1,9
* DIS # E4: 1,9 => CTR => E4: 3,4
* INC # E4: 3,4 => UNS
* DIS # F4: 1,9 => CTR => F4: 3,4,5,8
* INC # F4: 3,4,5,8 => UNS
* DIS # E5: 1,9 => CTR => E5: 2,3,7
* INC # E5: 2,3,7 => UNS
* PRF # F5: 1,9 => SOL
* INC # F5: 3,7 => UNS
* DIS # F6: 1,9 => CTR => F6: 5,8
* INC # F6: 5,8 => UNS
* INC # B6: 1,9 => UNS
* DIS # G6: 1,9 => CTR => G6: 6,8
* INC # G6: 6,8 => UNS
* DIS # E1: 1,9 => CTR => E1: 4,7
* INC # E1: 4,7 => UNS
* DIS # E2: 1,9 => CTR => E2: 6,7
* INC # E2: 6,7 => UNS
* INC # E3: 1,9 => UNS
* DIS # G4: 3,9 => CTR => G4: 1,8
* INC # G4: 1,8 => UNS
* DIS # I4: 3,9 => CTR => I4: 1
* INC # I4: 1 => UNS
* INC # G5: 3,9 => UNS
* INC # E4: 3,9 => UNS
* DIS # F4: 3,9 => CTR => F4: 1,4,5,8
* INC # F4: 1,4,5,8 => UNS
* PRF # H3: 3,9 => SOL
* INC # H3: 4,6,7 => UNS
* INC # H7: 3,9 => UNS
* INC # H8: 3,9 => UNS
* INC # H9: 3,9 => UNS
* CNT  43 HDP CHAINS /  43 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # G2: 1,9 => SOL
* STA G2: 1,9
* CNT   1 HDP CHAINS /   1 HYP OPENED