Analysis of xx-top500-354-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 9..6.1....3......8.......4..4..8..3....3..1..2...........52....1.....9......4.... initial

Autosolve

position: 9846.12.3.3249..18.1.238.49.41982.3.8..3.419229371.48.4.85293.11..8.39.43.914.8.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A3: 5,6 => CTR => A3: 7
* DIS # G3: 7 => CTR => G3: 5,6
* DIS # C5: 5,6 => CTR => C5: 7
* DIS # G2: 5,7 => CTR => G2: 6
* DIS # G2: 5,7 => CTR => G2: 6
* PRF # H9: 5,7 => SOL
* DIS # C5: 5,6 => CTR => C5: 7
* PRF # I4: 5,6 => SOL
* DIS # I4: 7 => CTR => I4: 5,6
* DIS # A3: 5,6 => CTR => A3: 7
* DIS # C5: 5,6 => CTR => C5: 7
* PRF # I4: 5,7 => SOL
* DIS # I4: 6 => CTR => I4: 5,7
* DIS # G2: 5,7 => CTR => G2: 6
* PRF # I4: 5,6 => SOL
* DIS # I4: 7 => CTR => I4: 5,6
* PRF # B8: 6,7 => SOL
* DIS # B9: 6,7 => CTR => B9: 2,5
* PRF # B5: 5 => SOL
* PRF # B8: 6,7 => SOL
* DIS # H8: 6,7 => CTR => H8: 2,5
* DIS # B9: 6,7 => CTR => B9: 2,5
* DIS # H9: 6,7 => CTR => H9: 2,5
* DIS # H8: 6,7 => CTR => H8: 2,5
* DIS # H9: 6,7 => CTR => H9: 2,5
* PRF # H9: 5,7 => SOL
* DIS # B9: 5,7 => CTR => B9: 2,6
* PRF # I4: 5,7 => SOL
* DIS # I4: 6 => CTR => I4: 5,7
* CNT  29 HDP CHAINS /  62 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: 5,6 => CTR => A3: 7
* DIS A3: 7 # C5: 5,6 => CTR => C5: 7
* DIS A3: 7 + C5: 7 # G2: 5,7 => CTR => G2: 6
* PRF A3: 7 + C5: 7 + G2: 6 => SOL
* STA A3: 7 + C5: 7 + G2: 6
* CNT   4 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

9..6.1....3......8.......4..4..8..3....3..1..2...........52....1.....9......4.... initial
9846.12.3.3249..18.1.238.49.41982.3.8..3.419229371.48.4.85293.11..8.39.43.914.8.. autosolve
984651273532497618716238549641982735857364192293715486478529361165873924329146857 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
C3: 5,6
E1: 5,7
F2: 5,7
H1: 5,7
A4: 5,6
E5: 5,6
F6: 5,6
G4: 5,7
I6: 5,6
B7: 6,7
E8: 6,7
F9: 6,7
H7: 6,7
I9: 5,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B8,B9: 2.. / B8 = 2  => 14 pairs (_) / B9 = 2  => 14 pairs (_)
H8,H9: 2.. / H8 = 2  => 14 pairs (_) / H9 = 2  => 14 pairs (_)
B8,H8: 2.. / B8 = 2  => 14 pairs (_) / H8 = 2  => 14 pairs (_)
B9,H9: 2.. / B9 = 2  => 14 pairs (_) / H9 = 2  => 14 pairs (_)
E1,F2: 5.. / E1 = 5  =>  0 pairs (*) / F2 = 5  =>  0 pairs (X)
E5,F6: 5.. / E5 = 5  =>  0 pairs (X) / F6 = 5  =>  0 pairs (_)
E1,H1: 5.. / E1 = 5  =>  0 pairs (*) / H1 = 5  =>  0 pairs (X)
F6,I6: 5.. / F6 = 5  =>  0 pairs (*) / I6 = 5  =>  0 pairs (X)
E1,E5: 5.. / E1 = 5  =>  0 pairs (*) / E5 = 5  =>  0 pairs (X)
F2,F6: 5.. / F2 = 5  =>  0 pairs (X) / F6 = 5  =>  0 pairs (_)
G2,G3: 6.. / G2 = 6  => 16 pairs (_) / G3 = 6  =>  0 pairs (X)
E5,F6: 6.. / E5 = 6  =>  0 pairs (*) / F6 = 6  =>  0 pairs (X)
I4,I6: 6.. / I4 = 6  =>  0 pairs (X) / I6 = 6  =>  0 pairs (_)
E8,F9: 6.. / E8 = 6  =>  0 pairs (X) / F9 = 6  =>  0 pairs (_)
A2,G2: 6.. / A2 = 6  =>  0 pairs (X) / G2 = 6  => 16 pairs (_)
A4,I4: 6.. / A4 = 6  =>  0 pairs (*) / I4 = 6  =>  0 pairs (X)
F6,I6: 6.. / F6 = 6  =>  0 pairs (X) / I6 = 6  =>  0 pairs (_)
B7,H7: 6.. / B7 = 6  =>  0 pairs (X) / H7 = 6  => 14 pairs (_)
E5,E8: 6.. / E5 = 6  =>  0 pairs (*) / E8 = 6  =>  0 pairs (X)
F6,F9: 6.. / F6 = 6  =>  0 pairs (X) / F9 = 6  =>  0 pairs (_)
A2,A3: 7.. / A2 = 7  =>  0 pairs (X) / A3 = 7  => 16 pairs (_)
E1,F2: 7.. / E1 = 7  =>  0 pairs (X) / F2 = 7  =>  0 pairs (_)
B5,C5: 7.. / B5 = 7  =>  0 pairs (X) / C5 = 7  => 16 pairs (_)
G4,I4: 7.. / G4 = 7  =>  0 pairs (*) / I4 = 7  =>  0 pairs (X)
E8,F9: 7.. / E8 = 7  =>  0 pairs (*) / F9 = 7  =>  0 pairs (X)
E1,H1: 7.. / E1 = 7  =>  0 pairs (X) / H1 = 7  =>  0 pairs (_)
A3,G3: 7.. / A3 = 7  => 16 pairs (_) / G3 = 7  =>  0 pairs (X)
B7,H7: 7.. / B7 = 7  => 14 pairs (_) / H7 = 7  =>  0 pairs (X)
C5,C8: 7.. / C5 = 7  => 16 pairs (_) / C8 = 7  =>  0 pairs (X)
E1,E8: 7.. / E1 = 7  =>  0 pairs (X) / E8 = 7  =>  0 pairs (_)
F2,F9: 7.. / F2 = 7  =>  0 pairs (*) / F9 = 7  =>  0 pairs (X)
I4,I9: 7.. / I4 = 7  =>  0 pairs (X) / I9 = 7  =>  0 pairs (_)
* DURATION: 0:00:54.106478  START: 14:50:55.475033  END: 14:51:49.581511 2017-05-04
* CP COUNT: (32)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B7,C3,E1,E5,E8,F2,F6,F9,G4,H1,H7,I6,I9)
* 9846.12.3.3249..18.1.238.49.41982.3.8..3.419229371.48.4.85293.11..8.39.43.914.8..
* PAIR C3: 5,6 BLK 1
A2: 5,6,7                                # reduction candidate for 5,6
A2: 5,6                                  # 16 pairs
A3: 5,6,7                                # reduction candidate for 5,6
A3: 5,6 => CTR
* 9846.12.3732495618.1.238749.419825378..35419229371648.4.85293.11..8.39.43.914.8..
A3: 7                                    # 16 pairs
* PAIR C3: 5,6 ROW 3
G3: 5,6,7                                # reduction candidate for 5,6
G3: 7 => CTR
* 9846.12.3.3249.618.1.238749.419825378..3.41922937154864.85293.11..8.39.43.91468.5
G3: 5,6                                  # 16 pairs
* PAIR C3: 5,6 COL C
C5: 5,6,7                                # reduction candidate for 5,6
C5: 5,6 => CTR
* 9846.12.3.3249..18.1.238.49.41982.3.87.3.419229371.48.4685293711.78639.43.9147865
C5: 7                                    # 16 pairs
C8: 5,6,7                                # reduction candidate for 5,6
C8: 5,6                                  # 16 pairs
* PAIR F2: 5,7 ROW 2
A2: 5,7,6                                # reduction candidate for 5,7
A2: 5,7                                  # 16 pairs
G2: 5,7,6                                # reduction candidate for 5,7
G2: 5,7 => CTR
* 9846.12.363249..187152386495419827368..35419229371648.4.85293.11..8.39.43.914.8..
G2: 6                                    # 16 pairs
* PAIR H1: 5,7 BLK 3
G2: 5,7,6                                # reduction candidate for 5,7
G2: 5,7 => CTR
* 9846.12.363249..187152386495419827368..35419229371648.4.85293.11..8.39.43.914.8..
G2: 6                                    # 16 pairs
G3: 5,7,6                                # reduction candidate for 5,7
G3: 5,7                                  # 16 pairs
* PAIR H1: 5,7 COL H
H8: 5,7,2,6                              # reduction candidate for 5,7
H8: 5,7                                  # 16 pairs
H9: 5,7,2,6                              # reduction candidate for 5,7
H9: 5,7 => SOLVED
* 984651273532497618716238549641982735857364192293715486478529361165873924329146857
H9: 2,6                                  # 15 pairs
* PAIR A4: 5,6 BLK 4
B5: 5,6,7                                # reduction candidate for 5,6
B5: 5,6                                  # 16 pairs
C5: 5,6,7                                # reduction candidate for 5,6
C5: 5,6 => CTR
* 9846.12.3.3249..18.1.238.49.41982.3.87.3.419229371.48.4685293711.78639.43.9147865
C5: 7                                    # 16 pairs
* PAIR A4: 5,6 ROW 4
I4: 5,6,7                                # reduction candidate for 5,6
I4: 5,6 => SOLVED
* 984651273532497618716238549641982735857364192293715486478529361165873924329146857
I4: 7 => CTR
* 9846.12.3.3249..18.1.238.496419825378..3641922937154864.85293.11..8739.43.91468.5
* PAIR A4: 5,6 COL A
A2: 5,6,7                                # reduction candidate for 5,6
A2: 5,6                                  # 16 pairs
A3: 5,6,7                                # reduction candidate for 5,6
A3: 5,6 => CTR
* 9846.12.3732495618.1.238749.419825378..35419229371648.4.85293.11..8.39.43.914.8..
A3: 7                                    # 16 pairs
* PAIR E5: 5,6 ROW 5
B5: 5,6,7                                # reduction candidate for 5,6
B5: 5,6                                  # 16 pairs
C5: 5,6,7                                # reduction candidate for 5,6
C5: 5,6 => CTR
* 9846.12.3.3249..18.1.238.49.41982.3.87.3.419229371.48.4685293711.78639.43.9147865
C5: 7                                    # 16 pairs
* PAIR G4: 5,7 BLK 6
I4: 5,7,6                                # reduction candidate for 5,7
I4: 5,7 => SOLVED
* 984651273532497618716238549641982735857364192293715486478529361165873924329146857
I4: 6 => CTR
* 9846.12.3.3249..18.1.238.49.419827368..3.41922937164854.85293.11..8639.43.91478..
* PAIR G4: 5,7 COL G
G2: 5,7,6                                # reduction candidate for 5,7
G2: 5,7 => CTR
* 9846.12.363249..187152386495419827368..35419229371648.4.85293.11..8.39.43.914.8..
G2: 6                                    # 16 pairs
G3: 5,7,6                                # reduction candidate for 5,7
G3: 5,7                                  # 16 pairs
* PAIR I6: 5,6 BLK 6
I4: 5,6,7                                # reduction candidate for 5,6
I4: 5,6 => SOLVED
* 984651273532497618716238549641982735857364192293715486478529361165873924329146857
I4: 7 => CTR
* 9846.12.3.3249..18.1.238.496419825378..3641922937154864.85293.11..8739.43.91468.5
* PAIR B7: 6,7 BLK 7
B8: 6,7,2,5                              # reduction candidate for 6,7
B8: 6,7 => SOLVED
* 984651273532497618716238549641982735857364192293715486478529361165873924329146857
B8: 2,5                                  # 15 pairs
C8: 6,7,5                                # reduction candidate for 6,7
C8: 6,7                                  # 19 pairs
B9: 6,7,2,5                              # reduction candidate for 6,7
B9: 6,7 => CTR
* 9846.1253.32495.1851623874964198253785.3.419229371.48.4.85293.11258.39.43.914.825
B9: 2,5                                  # 15 pairs
* PAIR B7: 6,7 COL B
B5: 6,7,5                                # reduction candidate for 6,7
B5: 5 => SOLVED
* 984651273532497618716238549641982735857364192293715486478529361165873924329146857
B5: 6,7                                  # 19 pairs
* PAIR E8: 6,7 ROW 8
B8: 6,7,2,5                              # reduction candidate for 6,7
B8: 6,7 => SOLVED
* 984651273532497618716238549641982735857364192293715486478529361165873924329146857
B8: 2,5                                  # 15 pairs
C8: 6,7,5                                # reduction candidate for 6,7
C8: 6,7                                  # 19 pairs
H8: 6,7,2,5                              # reduction candidate for 6,7
H8: 6,7 => CTR
* 9846.1253.32495.1851623874964198253785.3.419229371.48.4.85293.11258.39.43.914.825
H8: 2,5                                  # 15 pairs
* PAIR F9: 6,7 ROW 9
B9: 6,7,2,5                              # reduction candidate for 6,7
B9: 6,7 => CTR
* 9846.1253.32495.1851623874964198253785.3.419229371.48.4.85293.11258.39.43.914.825
B9: 2,5                                  # 15 pairs
H9: 6,7,2,5                              # reduction candidate for 6,7
H9: 6,7 => CTR
* 9846.1253.32495.18.1.238.49.419825378..35419229371648.4.85293.11..8.392432914.8.5
H9: 2,5                                  # 15 pairs
* PAIR H7: 6,7 BLK 9
H8: 6,7,2,5                              # reduction candidate for 6,7
H8: 6,7 => CTR
* 9846.1253.32495.1851623874964198253785.3.419229371.48.4.85293.11258.39.43.914.825
H8: 2,5                                  # 15 pairs
H9: 6,7,2,5                              # reduction candidate for 6,7
H9: 6,7 => CTR
* 9846.1253.32495.18.1.238.49.419825378..35419229371648.4.85293.11..8.392432914.8.5
H9: 2,5                                  # 15 pairs
* PAIR I9: 5,7 BLK 9
H8: 5,7,2,6                              # reduction candidate for 5,7
H8: 5,7                                  # 16 pairs
H9: 5,7,2,6                              # reduction candidate for 5,7
H9: 5,7 => SOLVED
* 984651273532497618716238549641982735857364192293715486478529361165873924329146857
H9: 2,6                                  # 15 pairs
* PAIR I9: 5,7 ROW 9
B9: 5,7,2,6                              # reduction candidate for 5,7
B9: 5,7 => CTR
* 9846.12.3.32497.1871.238.49.4198273.8..36419229371548646852937112.873964379146825
B9: 2,6                                  # 15 pairs
* PAIR I9: 5,7 COL I
I4: 5,7,6                                # reduction candidate for 5,7
I4: 5,7 => SOLVED
* 984651273532497618716238549641982735857364192293715486478529361165873924329146857
I4: 6 => CTR
* 9846.12.3.3249..18.1.238.49.419827368..3.41922937164854.85293.11..8639.43.91478..
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-354-base-pr-000.dot
* REASONING
* DIS # A3: 5,6 => CTR => A3: 7
* DIS # G3: 7 => CTR => G3: 5,6
* DIS # C5: 5,6 => CTR => C5: 7
* DIS # G2: 5,7 => CTR => G2: 6
* DIS # G2: 5,7 => CTR => G2: 6
* PRF # H9: 5,7 => SOL
* DIS # C5: 5,6 => CTR => C5: 7
* PRF # I4: 5,6 => SOL
* DIS # I4: 7 => CTR => I4: 5,6
* DIS # A3: 5,6 => CTR => A3: 7
* DIS # C5: 5,6 => CTR => C5: 7
* PRF # I4: 5,7 => SOL
* DIS # I4: 6 => CTR => I4: 5,7
* DIS # G2: 5,7 => CTR => G2: 6
* PRF # I4: 5,6 => SOL
* DIS # I4: 7 => CTR => I4: 5,6
* PRF # B8: 6,7 => SOL
* DIS # B9: 6,7 => CTR => B9: 2,5
* PRF # B5: 5 => SOL
* PRF # B8: 6,7 => SOL
* DIS # H8: 6,7 => CTR => H8: 2,5
* DIS # B9: 6,7 => CTR => B9: 2,5
* DIS # H9: 6,7 => CTR => H9: 2,5
* DIS # H8: 6,7 => CTR => H8: 2,5
* DIS # H9: 6,7 => CTR => H9: 2,5
* PRF # H9: 5,7 => SOL
* DIS # B9: 5,7 => CTR => B9: 2,6
* PRF # I4: 5,7 => SOL
* DIS # I4: 6 => CTR => I4: 5,7
* CNT  29 HDP CHAINS /  62 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B7,C3,E1,E5,E8,F2,F6,F9,G4,H1,H7,I6,I9)
* 9846.12.3.3249..18.1.238.49.41982.3.8..3.419229371.48.4.85293.11..8.39.43.914.8..
* PAIR C3: 5,6 BLK 1
A2: 5,6,7                                # reduction candidate for 5,6
A2: 5,6                                  # 16 pairs
A3: 5,6,7                                # reduction candidate for 5,6
A3: 5,6 => CTR
* 9846.12.3732495618.1.238749.419825378..35419229371648.4.85293.11..8.39.43.914.8..
* RESTART
* PAIR C3: 5,6 COL C
C5: 5,6,7                                # reduction candidate for 5,6
C5: 5,6 => CTR
* 9846.12.3.3249..1871.238.49.41982.3.87.3.419229371.48.4685293711.78639.43.9147865
* RESTART
* PAIR RESTART
* PAIR F2: 5,7 ROW 2
G2: 5,7,6                                # reduction candidate for 5,7
G2: 5,7 => CTR
* 9846.12.363249..1871523864954198273686735419229371648.4.85293.11..8.39.43.914.8..
G2: 6 => SOLVED
* 984651273532497618716238549641982735857364192293715486478529361165873924329146857
* DURATION: 0:00:06.058202  START: 14:52:50.092642  END: 14:52:56.150844 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-354-base-pr-001.dot
* REASONING
* DIS # A3: 5,6 => CTR => A3: 7
* DIS A3: 7 # C5: 5,6 => CTR => C5: 7
* DIS A3: 7 + C5: 7 # G2: 5,7 => CTR => G2: 6
* PRF A3: 7 + C5: 7 + G2: 6 => SOL
* STA A3: 7 + C5: 7 + G2: 6
* CNT   4 HDP CHAINS /   4 HYP OPENED

Header Info

Top 500 Minimum 17 354

solution: 984651273532497618716238549641982735857364192293715486478529361165873924329146857
info: 4885     FNBWX    S8.f     39072

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

Solution

position: 984651273532497618716238549641982735857364192293715486478529361165873924329146857 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 # A2: 5,6 => UNS
* DIS # A3: 5,6 => CTR => A3: 7
* INC # A3: 7 => UNS
* INC # G3: 5,6 => UNS
* DIS # G3: 7 => CTR => G3: 5,6
* DIS # C5: 5,6 => CTR => C5: 7
* INC # C5: 7 => UNS
* INC # C8: 5,6 => UNS
* INC # A2: 5,7 => UNS
* DIS # G2: 5,7 => CTR => G2: 6
* INC # G2: 6 => UNS
* DIS # G2: 5,7 => CTR => G2: 6
* INC # G2: 6 => UNS
* INC # G3: 5,7 => UNS
* INC # H8: 5,7 => UNS
* PRF # H9: 5,7 => SOL
* INC # H9: 2,6 => UNS
* INC # B5: 5,6 => UNS
* DIS # C5: 5,6 => CTR => C5: 7
* INC # C5: 7 => UNS
* PRF # I4: 5,6 => SOL
* DIS # I4: 7 => CTR => I4: 5,6
* INC # A2: 5,6 => UNS
* DIS # A3: 5,6 => CTR => A3: 7
* INC # A3: 7 => UNS
* INC # B5: 5,6 => UNS
* DIS # C5: 5,6 => CTR => C5: 7
* INC # C5: 7 => UNS
* PRF # I4: 5,7 => SOL
* DIS # I4: 6 => CTR => I4: 5,7
* DIS # G2: 5,7 => CTR => G2: 6
* INC # G2: 6 => UNS
* INC # G3: 5,7 => UNS
* PRF # I4: 5,6 => SOL
* DIS # I4: 7 => CTR => I4: 5,6
* PRF # B8: 6,7 => SOL
* INC # B8: 2,5 => UNS
* INC # C8: 6,7 => UNS
* DIS # B9: 6,7 => CTR => B9: 2,5
* INC # B9: 2,5 => UNS
* INC # B5: 6,7 => UNS
* PRF # B5: 5 => SOL
* PRF # B8: 6,7 => SOL
* INC # B8: 2,5 => UNS
* INC # C8: 6,7 => UNS
* DIS # H8: 6,7 => CTR => H8: 2,5
* INC # H8: 2,5 => UNS
* DIS # B9: 6,7 => CTR => B9: 2,5
* INC # B9: 2,5 => UNS
* DIS # H9: 6,7 => CTR => H9: 2,5
* INC # H9: 2,5 => UNS
* DIS # H8: 6,7 => CTR => H8: 2,5
* INC # H8: 2,5 => UNS
* DIS # H9: 6,7 => CTR => H9: 2,5
* INC # H9: 2,5 => UNS
* INC # H8: 5,7 => UNS
* PRF # H9: 5,7 => SOL
* INC # H9: 2,6 => UNS
* DIS # B9: 5,7 => CTR => B9: 2,6
* INC # B9: 2,6 => UNS
* PRF # I4: 5,7 => SOL
* DIS # I4: 6 => CTR => I4: 5,7
* CNT  62 HDP CHAINS /  62 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A2: 5,6 => UNS
* DIS # A3: 5,6 => CTR => A3: 7
* DIS A3: 7 # C5: 5,6 => CTR => C5: 7
* DIS A3: 7 + C5: 7 # G2: 5,7 => CTR => G2: 6
* PRF A3: 7 + C5: 7 + G2: 6 => SOL
* STA A3: 7 + C5: 7 + G2: 6
* CNT   5 HDP CHAINS /   4 HYP OPENED