Analysis of xx-top500-264-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .53..8.7..4....2....1......6...4............1.......9.2...6.4.....1.9......3..... initial

Autosolve

position: 953218674.46..321..214.69..6.5.413..3.26...411.4.32.9621..6.4..43.1.9.6.56.3.41.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # E2: 5,7 => SOL
* DIS # E5: 5,7 => CTR => E5: 8,9
* DIS # I3: 5,8 => CTR => I3: 3
* DIS # I3: 8 => CTR => I3: 3,5
* PRF # B5: 7,8 => SOL
* DIS # G6: 7,8 => CTR => G6: 5
* DIS # E5: 5,7 => CTR => E5: 8,9
* DIS # G5: 8 => CTR => G5: 5,7
* PRF # I9: 2,7 => SOL
* PRF # C7: 7,8 => SOL
* PRF # D7: 5,7 => SOL
* DIS # I7: 5,7 => CTR => I7: 3,9
* DIS # I7: 3,5 => CTR => I7: 7,9
* PRF # I7: 7,9 => SOL
* DIS # G6: 7,8 => CTR => G6: 5
* DIS # E9: 7 => CTR => E9: 2,8
* CNT  16 HDP CHAINS /  36 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 # E2: 5,7 => SOL
* STA E2: 5,7
* CNT   1 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

.53..8.7..4....2....1......6...4............1.......9.2...6.4.....1.9......3..... initial
953218674.46..321..214.69..6.5.413..3.26...411.4.32.9621..6.4..43.1.9.6.56.3.41.. autosolve
953218674746953218821476953695741382382695741174832596218567439437129865569384127 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (16)
A2: 7,8
A3: 7,8
E3: 5,7
I2: 5,8
H3: 3,5
B6: 7,8
F5: 5,7
H4: 2,8
I4: 2,7
C8: 7,8
F7: 5,7
E8: 2,5
H7: 3,5
G8: 7,8
I8: 2,5
H9: 2,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H4,I4: 2.. / H4 = 2  =>  0 pairs (X) / I4 = 2  =>  0 pairs (_)
E8,E9: 2.. / E8 = 2  =>  0 pairs (*) / E9 = 2  =>  0 pairs (X)
E8,I8: 2.. / E8 = 2  =>  0 pairs (*) / I8 = 2  =>  0 pairs (X)
H4,H9: 2.. / H4 = 2  =>  0 pairs (X) / H9 = 2  =>  0 pairs (_)
H3,I3: 3.. / H3 = 3  =>  0 pairs (X) / I3 = 3  => 17 pairs (_)
H7,I7: 3.. / H7 = 3  => 17 pairs (_) / I7 = 3  =>  0 pairs (X)
H3,H7: 3.. / H3 = 3  =>  0 pairs (X) / H7 = 3  => 17 pairs (_)
I3,I7: 3.. / I3 = 3  => 17 pairs (_) / I7 = 3  =>  0 pairs (X)
G5,G6: 5.. / G5 = 5  =>  0 pairs (X) / G6 = 5  => 18 pairs (_)
D6,G6: 5.. / D6 = 5  =>  0 pairs (X) / G6 = 5  => 18 pairs (_)
E8,I8: 5.. / E8 = 5  =>  0 pairs (X) / I8 = 5  =>  0 pairs (_)
F5,F7: 5.. / F5 = 5  => 21 pairs (_) / F7 = 5  =>  0 pairs (X)
H3,H7: 5.. / H3 = 5  => 17 pairs (_) / H7 = 5  =>  0 pairs (X)
A2,A3: 7.. / A2 = 7  => 19 pairs (_) / A3 = 7  =>  0 pairs (X)
A3,E3: 7.. / A3 = 7  =>  0 pairs (X) / E3 = 7  => 19 pairs (_)
C8,G8: 7.. / C8 = 7  =>  0 pairs (*) / G8 = 7  =>  0 pairs (X)
F5,F7: 7.. / F5 = 7  =>  0 pairs (X) / F7 = 7  => 21 pairs (_)
A2,A3: 8.. / A2 = 8  =>  0 pairs (X) / A3 = 8  => 19 pairs (_)
I2,I3: 8.. / I2 = 8  => 19 pairs (_) / I3 = 8  =>  0 pairs (X)
D7,E9: 8.. / D7 = 8  => 22 pairs (_) / E9 = 8  =>  0 pairs (*)
G8,H9: 8.. / G8 = 8  =>  0 pairs (*) / H9 = 8  =>  0 pairs (X)
A2,I2: 8.. / A2 = 8  =>  0 pairs (X) / I2 = 8  => 19 pairs (_)
A3,I3: 8.. / A3 = 8  => 19 pairs (_) / I3 = 8  =>  0 pairs (X)
C7,D7: 8.. / C7 = 8  =>  0 pairs (*) / D7 = 8  =>  0 pairs (X)
C8,G8: 8.. / C8 = 8  =>  0 pairs (X) / G8 = 8  =>  0 pairs (_)
E5,E9: 8.. / E5 = 8  => 22 pairs (_) / E9 = 8  =>  0 pairs (*)
H4,H9: 8.. / H4 = 8  =>  0 pairs (*) / H9 = 8  =>  0 pairs (X)
D2,E2: 9.. / D2 = 9  =>  0 pairs (*) / E2 = 9  =>  0 pairs (X)
B4,B5: 9.. / B4 = 9  =>  0 pairs (*) / B5 = 9  =>  0 pairs (X)
D4,E5: 9.. / D4 = 9  => 18 pairs (_) / E5 = 9  =>  0 pairs (*)
C7,C9: 9.. / C7 = 9  => 22 pairs (_) / C9 = 9  =>  0 pairs (*)
I7,I9: 9.. / I7 = 9  =>  0 pairs (*) / I9 = 9  =>  0 pairs (X)
B4,D4: 9.. / B4 = 9  =>  0 pairs (*) / D4 = 9  =>  0 pairs (X)
B5,E5: 9.. / B5 = 9  => 18 pairs (_) / E5 = 9  =>  0 pairs (*)
C7,I7: 9.. / C7 = 9  => 22 pairs (_) / I7 = 9  =>  0 pairs (*)
C9,I9: 9.. / C9 = 9  =>  0 pairs (*) / I9 = 9  =>  0 pairs (X)
D2,D4: 9.. / D2 = 9  =>  0 pairs (*) / D4 = 9  =>  0 pairs (X)
E2,E5: 9.. / E2 = 9  => 18 pairs (_) / E5 = 9  =>  0 pairs (*)
* DURATION: 0:01:16.201693  START: 11:53:15.479928  END: 11:54:31.681621 2017-05-04
* CP COUNT: (38)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,B6,C8,E3,E8,F5,F7,G8,H3,H4,H7,H9,I2,I4,I8)
* 953218674.46..321..214.69..6.5.413..3.26...411.4.32.9621..6.4..43.1.9.6.56.3.41..
* PAIR E3: 5,7 BLK 2
D2: 5,7,9                                # reduction candidate for 5,7
D2: 5,7                                  # 18 pairs
E2: 5,7,9                                # reduction candidate for 5,7
E2: 5,7 => SOLVED
* 953218674746953218821476953695741382382695741174832596218567439437129865569384127
E2: 9                                    # 18 pairs
* PAIR E3: 5,7 COL E
E5: 5,7,8,9                              # reduction candidate for 5,7
E5: 5,7 => CTR
* 953218674.46.9321..214.69..6.59413..3926..8411.4832596218.6.4.94371.9.6.56.3.41..
E5: 8,9                                  # 17 pairs
* PAIR I2: 5,8 BLK 3
I3: 5,8,3                                # reduction candidate for 5,8
I3: 5,8 => CTR
* 953218674.465932188214769356.594132739268..411.4.32.9621..6.45343.159.6256.324189
I3: 3                                    # 17 pairs
* PAIR H3: 3,5 BLK 3
I3: 3,5,8                                # reduction candidate for 3,5
I3: 8 => CTR
* 953218674.46..321..214.69386.5.413..3.26...411.4.32.9621..6.45343.159.6256.324189
I3: 3,5                                  # 19 pairs
* PAIR B6: 7,8 BLK 4
B4: 7,8,9                                # reduction candidate for 7,8
B4: 7,8                                  # 18 pairs
B5: 7,8,9                                # reduction candidate for 7,8
B5: 7,8 => SOLVED
* 953218674746953218821476953695741382382695741174832596218567439437129865569384127
B5: 9                                    # 18 pairs
* PAIR B6: 7,8 ROW 6
D6: 7,8,5                                # reduction candidate for 7,8
D6: 7,8                                  # 18 pairs
G6: 7,8,5                                # reduction candidate for 7,8
G6: 7,8 => CTR
* 953218674.46.532188214769536.5.413..3.26975411.4532.9621.76543943.129.65569384127
G6: 5                                    # 18 pairs
* PAIR F5: 5,7 BLK 5
E5: 5,7,8,9                              # reduction candidate for 5,7
E5: 5,7 => CTR
* 953218674.46.9321..214.69..6.59413..3926..8411.4832596218.6.4.94371.9.6.56.3.41..
E5: 8,9                                  # 17 pairs
D6: 5,7,8                                # reduction candidate for 5,7
D6: 5,7                                  # 19 pairs
* PAIR F5: 5,7 ROW 5
G5: 5,7,8                                # reduction candidate for 5,7
G5: 8 => CTR
* 953218674.46..321..214.69..6.5.413..3.26..8411.4.3259621..6.4..4381.976.56.38412.
G5: 5,7                                  # 19 pairs
* PAIR I4: 2,7 COL I
I9: 2,7,9                                # reduction candidate for 2,7
I9: 2,7 => SOLVED
* 953218674746953218821476953695741382382695741174832596218567439437129865569384127
I9: 9                                    # 22 pairs
* PAIR C8: 7,8 BLK 7
C7: 7,8,9                                # reduction candidate for 7,8
C7: 7,8 => SOLVED
* 953218674746953218821476953695741382382695741174832596218567439437129865569384127
C7: 9                                    # 22 pairs
C9: 7,8,9                                # reduction candidate for 7,8
C9: 7,8                                  # 22 pairs
* PAIR F7: 5,7 BLK 8
D7: 5,7,8                                # reduction candidate for 5,7
D7: 5,7 => SOLVED
* 953218674746953218821476953695741382382695741174832596218567439437129865569384127
D7: 8                                    # 22 pairs
* PAIR F7: 5,7 ROW 7
I7: 5,7,3,9                              # reduction candidate for 5,7
I7: 5,7 => CTR
* 953218674.46..32188214769536.5.413..3.268..411.4.32.9621986743543.159762567324189
I7: 3,9                                  # 17 pairs
* PAIR H7: 3,5 BLK 9
I7: 3,5,7,9                              # reduction candidate for 3,5
I7: 3,5 => CTR
* 953218674.465932188214769..68594132.3.26...411.4.32.962198674..43.159.6256.324189
I7: 7,9 => SOLVED
* 953218674746953218821476953695741382382695741174832596218567439437129865569384127
* PAIR G8: 7,8 COL G
G5: 7,8,5                                # reduction candidate for 7,8
G5: 7,8                                  # 18 pairs
G6: 7,8,5                                # reduction candidate for 7,8
G6: 7,8 => CTR
* 953218674.46.532188214769536.5.413..3.26975411.4532.9621.76543943.129.65569384127
G6: 5                                    # 18 pairs
* PAIR H9: 2,8 ROW 9
E9: 2,8,7                                # reduction candidate for 2,8
E9: 7 => CTR
* 953218674.467.321..214.69..6.5.413..3.268..411.4.32.9621.86.4..43.129.6556.3741..
E9: 2,8                                  # 20 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-264-base-pr-000.dot
* REASONING
* PRF # E2: 5,7 => SOL
* DIS # E5: 5,7 => CTR => E5: 8,9
* DIS # I3: 5,8 => CTR => I3: 3
* DIS # I3: 8 => CTR => I3: 3,5
* PRF # B5: 7,8 => SOL
* DIS # G6: 7,8 => CTR => G6: 5
* DIS # E5: 5,7 => CTR => E5: 8,9
* DIS # G5: 8 => CTR => G5: 5,7
* PRF # I9: 2,7 => SOL
* PRF # C7: 7,8 => SOL
* PRF # D7: 5,7 => SOL
* DIS # I7: 5,7 => CTR => I7: 3,9
* DIS # I7: 3,5 => CTR => I7: 7,9
* PRF # I7: 7,9 => SOL
* DIS # G6: 7,8 => CTR => G6: 5
* DIS # E9: 7 => CTR => E9: 2,8
* CNT  16 HDP CHAINS /  36 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,B6,C8,E3,E8,F5,F7,G8,H3,H4,H7,H9,I2,I4,I8)
* 953218674.46..321..214.69..6.5.413..3.26...411.4.32.9621..6.4..43.1.9.6.56.3.41..
* PAIR E3: 5,7 BLK 2
D2: 5,7,9                                # reduction candidate for 5,7
D2: 5,7                                  # 18 pairs
E2: 5,7,9                                # reduction candidate for 5,7
E2: 5,7 => SOLVED
* 953218674746953218821476953695741382382695741174832596218567439437129865569384127
* DURATION: 0:00:03.430986  START: 11:55:14.091355  END: 11:55:17.522341 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-264-base-pr-001.dot
* REASONING
* PRF # E2: 5,7 => SOL
* STA E2: 5,7
* CNT   1 HDP CHAINS /   2 HYP OPENED

Header Info

Top 500 Minimum 17 264

solution: 953218674746953218821476953695741382382695741174832596218567439437129865569384127
info: 2117     FNBTWXY  S8.f     20601

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

Solution

position: 953218674746953218821476953695741382382695741174832596218567439437129865569384127 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:

* INC # D2: 5,7 => UNS
* PRF # E2: 5,7 => SOL
* INC # E2: 9 => UNS
* DIS # E5: 5,7 => CTR => E5: 8,9
* INC # E5: 8,9 => UNS
* DIS # I3: 5,8 => CTR => I3: 3
* INC # I3: 3 => UNS
* INC # I3: 3,5 => UNS
* DIS # I3: 8 => CTR => I3: 3,5
* INC # B4: 7,8 => UNS
* PRF # B5: 7,8 => SOL
* INC # B5: 9 => UNS
* INC # D6: 7,8 => UNS
* DIS # G6: 7,8 => CTR => G6: 5
* INC # G6: 5 => UNS
* DIS # E5: 5,7 => CTR => E5: 8,9
* INC # E5: 8,9 => UNS
* INC # D6: 5,7 => UNS
* INC # G5: 5,7 => UNS
* DIS # G5: 8 => CTR => G5: 5,7
* PRF # I9: 2,7 => SOL
* INC # I9: 9 => UNS
* PRF # C7: 7,8 => SOL
* INC # C7: 9 => UNS
* INC # C9: 7,8 => UNS
* PRF # D7: 5,7 => SOL
* INC # D7: 8 => UNS
* DIS # I7: 5,7 => CTR => I7: 3,9
* INC # I7: 3,9 => UNS
* DIS # I7: 3,5 => CTR => I7: 7,9
* PRF # I7: 7,9 => SOL
* INC # G5: 7,8 => UNS
* DIS # G6: 7,8 => CTR => G6: 5
* INC # G6: 5 => UNS
* INC # E9: 2,8 => UNS
* DIS # E9: 7 => CTR => E9: 2,8
* CNT  36 HDP CHAINS /  36 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # D2: 5,7 => UNS
* PRF # E2: 5,7 => SOL
* STA E2: 5,7
* CNT   2 HDP CHAINS /   2 HYP OPENED