Analysis of xx-top500-466-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .....1.6....4.2....8......3......12..4..3..........7..2.1...5.....74....6........ initial

Autosolve

position: ...3.1.6....4.2....8......3......12..4..3..........73.2.1...54....74....6.4...... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # G1: 8,9 => SOL
* DIS # I1: 8,9 => CTR => I1: 2,5,7
* DIS # H2: 8,9 => CTR => H2: 1,5,7
* DIS # I2: 8,9 => CTR => I2: 1,5,7
* DIS # G5: 8,9 => CTR => G5: 6
* DIS # G9: 8,9 => CTR => G9: 3
* DIS # D6: 1,2 => CTR => D6: 5,6,8,9
* DIS # B6: 5,6,9 => CTR => B6: 1,2
* DIS # D7: 6,9 => CTR => D7: 8
* DIS # F7: 6,9 => CTR => F7: 3,8
* DIS # I7: 7,8 => CTR => I7: 6,9
* DIS # D6: 1,2 => CTR => D6: 5,6,8,9
* PRF # I8: 1,9 => SOL
* DIS # I8: 2,6 => CTR => I8: 1,9
* DIS # H2: 1,9 => CTR => H2: 5,7,8
* CNT  15 HDP CHAINS /  37 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 # G1: 8,9 => SOL
* STA G1: 8,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

.....1.6....4.2....8......3......12..4..3..........7..2.1...5.....74....6........ initial
...3.1.6....4.2....8......3......12..4..3..........73.2.1...54....74....6.4...... autosolve
459371862316482975782569413863957124147238659925614738271893546538746291694125387 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (6)
G2: 8,9
E6: 1,2
E7: 6,9
D9: 1,2
E9: 1,2
H8: 1,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D9,E9: 1.. / D9 = 1  =>  0 pairs (*) / E9 = 1  =>  0 pairs (X)
H8,I8: 1.. / H8 = 1  =>  0 pairs (X) / I8 = 1  =>  0 pairs (_)
A3,H3: 1.. / A3 = 1  =>  0 pairs (X) / H3 = 1  =>  0 pairs (_)
A5,D5: 1.. / A5 = 1  =>  0 pairs (*) / D5 = 1  =>  0 pairs (X)
B2,B6: 1.. / B2 = 1  =>  0 pairs (*) / B6 = 1  =>  0 pairs (X)
E6,E9: 1.. / E6 = 1  =>  0 pairs (*) / E9 = 1  =>  0 pairs (X)
I2,I8: 1.. / I2 = 1  =>  0 pairs (X) / I8 = 1  =>  0 pairs (_)
D9,E9: 2.. / D9 = 2  =>  0 pairs (X) / E9 = 2  =>  0 pairs (_)
G8,I8: 2.. / G8 = 2  =>  0 pairs (*) / I8 = 2  =>  0 pairs (X)
C3,G3: 2.. / C3 = 2  =>  0 pairs (*) / G3 = 2  =>  0 pairs (X)
C5,D5: 2.. / C5 = 2  =>  0 pairs (X) / D5 = 2  =>  0 pairs (_)
B1,B6: 2.. / B1 = 2  =>  0 pairs (X) / B6 = 2  =>  0 pairs (_)
E6,E9: 2.. / E6 = 2  =>  0 pairs (X) / E9 = 2  =>  0 pairs (_)
I1,I8: 2.. / I1 = 2  =>  0 pairs (*) / I8 = 2  =>  0 pairs (X)
G8,G9: 3.. / G8 = 3  =>  0 pairs (X) / G9 = 3  =>  6 pairs (_)
B7,F7: 3.. / B7 = 3  =>  0 pairs (X) / F7 = 3  =>  7 pairs (_)
A1,A3: 4.. / A1 = 4  =>  0 pairs (*) / A3 = 4  =>  0 pairs (X)
G1,G3: 4.. / G1 = 4  =>  0 pairs (X) / G3 = 4  =>  0 pairs (_)
F4,F6: 4.. / F4 = 4  =>  6 pairs (_) / F6 = 4  =>  6 pairs (_)
I4,I6: 4.. / I4 = 4  =>  6 pairs (_) / I6 = 4  =>  6 pairs (_)
A1,G1: 4.. / A1 = 4  =>  0 pairs (*) / G1 = 4  =>  0 pairs (X)
A3,G3: 4.. / A3 = 4  =>  0 pairs (X) / G3 = 4  =>  0 pairs (_)
F4,I4: 4.. / F4 = 4  =>  6 pairs (_) / I4 = 4  =>  6 pairs (_)
F6,I6: 4.. / F6 = 4  =>  6 pairs (_) / I6 = 4  =>  6 pairs (_)
F8,F9: 5.. / F8 = 5  =>  0 pairs (X) / F9 = 5  =>  6 pairs (_)
B9,F9: 5.. / B9 = 5  =>  0 pairs (X) / F9 = 5  =>  6 pairs (_)
G5,G8: 6.. / G5 = 6  =>  6 pairs (_) / G8 = 6  =>  0 pairs (X)
B7,B9: 7.. / B7 = 7  =>  6 pairs (_) / B9 = 7  =>  0 pairs (X)
B7,I7: 7.. / B7 = 7  =>  6 pairs (_) / I7 = 7  =>  0 pairs (X)
E1,E2: 8.. / E1 = 8  =>  6 pairs (_) / E2 = 8  =>  9 pairs (_)
A8,C8: 8.. / A8 = 8  =>  6 pairs (_) / C8 = 8  =>  6 pairs (_)
* DURATION: 0:00:53.462703  START: 18:38:09.130417  END: 18:39:02.593120 2017-05-04
* CP COUNT: (31)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D9,E6,E7,E9,G2,H8)
* ...3.1.6....4.2....8......3......12..4..3..........73.2.1...54....74....6.4......
* PAIR G2: 8,9 BLK 3
G1: 8,9,2,4                              # reduction candidate for 8,9
G1: 8,9 => SOLVED
* 459371862316482975782569413863957124147238659925614738271893546538746291694125387
G1: 2,4                                  #  7 pairs
I1: 8,9,2,5,7                            # reduction candidate for 8,9
I1: 8,9 => CTR
* 42.3.1.6....4.2..118....4.3......12..4213.....1..2.73.2.1...54....74..126.421....
I1: 2,5,7                                #  6 pairs
H2: 8,9,1,5,7                            # reduction candidate for 8,9
H2: 8,9 => CTR
* 42.381.6....4.2..118....4.3......12..4.13.....1..2.73.2.1...54....74..126.421....
H2: 1,5,7                                #  6 pairs
I2: 8,9,1,5,7                            # reduction candidate for 8,9
I2: 8,9 => CTR
* ...3.1.62.164.2....82....13.6....12.14.23.6...2..1.73.2.1...546...7462916.41253.7
I2: 1,5,7                                #  6 pairs
* PAIR G2: 8,9 ROW 2
E2: 8,9,5,6,7                            # reduction candidate for 8,9
E2: 8,9                                  #  7 pairs
E2: 5,6,7                                #  7 pairs
* PAIR G2: 8,9 COL G
G5: 8,9,6                                # reduction candidate for 8,9
G5: 8,9 => CTR
* 42.3.1.6....4.2..118....4.3......12..4213.....1..2.73.2.1...54....74.6126.421.3..
G5: 6                                    #  6 pairs
G9: 8,9,3                                # reduction candidate for 8,9
G9: 8,9 => CTR
* 42.3.1.6....4.2..118....4.3......12..4213.6...1..2.73.271.93546...746312634215...
G9: 3                                    #  6 pairs
* PAIR E6: 1,2 BLK 5
D5: 1,2,5,6,8,9                          # reduction candidate for 1,2
D5: 1,2                                  #  7 pairs
D6: 1,2,5,6,8,9                          # reduction candidate for 1,2
D6: 1,2 => CTR
* .2.3.1.6..1.4.2....8....213......12.142.37.........73.2.1...54....74..9.6.4......
D6: 5,6,8,9                              #  7 pairs
* PAIR E6: 1,2 ROW 6
B6: 1,2,5,6,9                            # reduction candidate for 1,2
B6: 5,6,9 => CTR
* .2.3.1.6..1.4.2....8....213......12..4..3..........73.2.1...54....74..9.6.4......
B6: 1,2                                  #  8 pairs
* PAIR E7: 6,9 BLK 8
D7: 6,9,8                                # reduction candidate for 6,9
D7: 6,9 => CTR
* 42.3.1.6....4.2..118....4.3......12..4213.....1..2.73.2.1...54....74.2166.421.3..
D7: 8                                    #  6 pairs
F7: 6,9,3,8                              # reduction candidate for 6,9
F7: 6,9 => CTR
* 42.3.1.6....4.2..118....4.3......12..4213.....1..2.73.2318..547...7432166742153..
F7: 3,8                                  #  7 pairs
F8: 6,9,3,5                              # reduction candidate for 6,9
F8: 6,9                                  #  8 pairs
* PAIR E7: 6,9 ROW 7
I7: 6,9,7,8                              # reduction candidate for 6,9
I7: 7,8 => CTR
* 42.3.1.6....4.2..118....4.3......12..4213.....1..2.73.2.1...54....74.2166.421.3..
I7: 6,9                                  #  8 pairs
* PAIR E7: 6,9 COL E
E2: 6,9,5,7,8                            # reduction candidate for 6,9
E2: 6,9                                  # 12 pairs
E3: 6,9,5,7                              # reduction candidate for 6,9
E3: 6,9                                  #  9 pairs
E4: 6,9,5,7                              # reduction candidate for 6,9
E4: 6,9                                  # 11 pairs
* PAIR D9: 1,2 COL D
D5: 1,2,5,6,8,9                          # reduction candidate for 1,2
D5: 1,2                                  #  7 pairs
D6: 1,2,5,6,8,9                          # reduction candidate for 1,2
D6: 1,2 => CTR
* .2.3.1.6..1.4.2....8....213......12.142.37.........73.2.1...54....74..9.6.4......
D6: 5,6,8,9                              #  7 pairs
* PAIR H8: 1,9 BLK 9
I8: 1,9,2,6                              # reduction candidate for 1,9
I8: 1,9 => SOLVED
* 459371862316482975782569413863957124147238659925614738271893546538746291694125387
I8: 2,6 => CTR
* 42.3.1.6....4.2..118....4.3......12..4213.....1..2.73.2.1...54....74.2166.421.3..
* PAIR H8: 1,9 COL H
H2: 1,9,5,7,8                            # reduction candidate for 1,9
H2: 1,9 => CTR
* 42.3.1.6....4.2...18....4.3......12..4213.....1..2.73.2.1...54....74.2..6.421.3..
H2: 5,7,8                                #  6 pairs
H3: 1,9,5,7                              # reduction candidate for 1,9
H3: 1,9                                  #  9 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-466-base-pr-000.dot
* REASONING
* PRF # G1: 8,9 => SOL
* DIS # I1: 8,9 => CTR => I1: 2,5,7
* DIS # H2: 8,9 => CTR => H2: 1,5,7
* DIS # I2: 8,9 => CTR => I2: 1,5,7
* DIS # G5: 8,9 => CTR => G5: 6
* DIS # G9: 8,9 => CTR => G9: 3
* DIS # D6: 1,2 => CTR => D6: 5,6,8,9
* DIS # B6: 5,6,9 => CTR => B6: 1,2
* DIS # D7: 6,9 => CTR => D7: 8
* DIS # F7: 6,9 => CTR => F7: 3,8
* DIS # I7: 7,8 => CTR => I7: 6,9
* DIS # D6: 1,2 => CTR => D6: 5,6,8,9
* PRF # I8: 1,9 => SOL
* DIS # I8: 2,6 => CTR => I8: 1,9
* DIS # H2: 1,9 => CTR => H2: 5,7,8
* CNT  15 HDP CHAINS /  37 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D9,E6,E7,E9,G2,H8)
* ...3.1.6....4.2....8......3......12..4..3..........73.2.1...54....74....6.4......
* PAIR G2: 8,9 BLK 3
G1: 8,9,2,4                              # reduction candidate for 8,9
G1: 8,9 => SOLVED
* 459371862316482975782569413863957124147238659925614738271893546538746291694125387
* DURATION: 0:00:02.860356  START: 18:39:32.789711  END: 18:39:35.650067 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-466-base-pr-001.dot
* REASONING
* PRF # G1: 8,9 => SOL
* STA G1: 8,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 466

solution: 459371862316482975782569413863957124147238659925614738271893546538746291694125387
info: 95591    FNBTHYK  S8.f     1796

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

Solution

position: 459371862316482975782569413863957124147238659925614738271893546538746291694125387 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 # G1: 8,9 => SOL
* INC # G1: 2,4 => UNS
* DIS # I1: 8,9 => CTR => I1: 2,5,7
* INC # I1: 2,5,7 => UNS
* DIS # H2: 8,9 => CTR => H2: 1,5,7
* INC # H2: 1,5,7 => UNS
* DIS # I2: 8,9 => CTR => I2: 1,5,7
* INC # I2: 1,5,7 => UNS
* INC # E2: 8,9 => UNS
* INC # E2: 5,6,7 => UNS
* DIS # G5: 8,9 => CTR => G5: 6
* INC # G5: 6 => UNS
* DIS # G9: 8,9 => CTR => G9: 3
* INC # G9: 3 => UNS
* INC # D5: 1,2 => UNS
* DIS # D6: 1,2 => CTR => D6: 5,6,8,9
* INC # D6: 5,6,8,9 => UNS
* INC # B6: 1,2 => UNS
* DIS # B6: 5,6,9 => CTR => B6: 1,2
* DIS # D7: 6,9 => CTR => D7: 8
* INC # D7: 8 => UNS
* DIS # F7: 6,9 => CTR => F7: 3,8
* INC # F7: 3,8 => UNS
* INC # F8: 6,9 => UNS
* INC # I7: 6,9 => UNS
* DIS # I7: 7,8 => CTR => I7: 6,9
* INC # E2: 6,9 => UNS
* INC # E3: 6,9 => UNS
* INC # E4: 6,9 => UNS
* INC # D5: 1,2 => UNS
* DIS # D6: 1,2 => CTR => D6: 5,6,8,9
* INC # D6: 5,6,8,9 => UNS
* PRF # I8: 1,9 => SOL
* DIS # I8: 2,6 => CTR => I8: 1,9
* DIS # H2: 1,9 => CTR => H2: 5,7,8
* INC # H2: 5,7,8 => UNS
* INC # H3: 1,9 => UNS
* CNT  37 HDP CHAINS /  37 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # G1: 8,9 => SOL
* STA G1: 8,9
* CNT   1 HDP CHAINS /   1 HYP OPENED