Analysis of xx-top500-021-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 1......727..5........3........6..8.34...1...............3...5...2...4.......7..4. initial

Autosolve

position: 1354...727..5.143...43.71.5.7164.85345..13...3...5..14.431..527527.34..1.1.27534. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # I2: 6,9 => SOL
* DIS # I2: 8 => CTR => I2: 6,9
* DIS # H3: 6,9 => CTR => H3: 8
* PRF # H3: 8 => SOL
* DIS # E1: 6,9 => CTR => E1: 8
* PRF # A3: 2,9 => SOL
* DIS # A3: 6,8 => CTR => A3: 2,9
* PRF # C6: 2,8 => SOL
* PRF # C2: 6,9 => SOL
* DIS # F6: 2,9 => CTR => F6: 8
* PRF # F6: 8 => SOL
* DIS # D6: 7,8 => CTR => D6: 9
* PRF # D6: 9 => SOL
* DIS # H3: 6,9 => CTR => H3: 8
* PRF # H3: 8 => SOL
* PRF # H8: 6,9 => SOL
* DIS # H8: 8 => CTR => H8: 6,9
* PRF # I2: 6,9 => SOL
* DIS # I2: 8 => CTR => I2: 6,9
* DIS # A9: 8,9 => CTR => A9: 6
* DIS # A3: 8,9 => CTR => A3: 2,6
* PRF # H8: 6 => SOL
* DIS # D6: 7 => CTR => D6: 8,9
* PRF # H8: 6,9 => SOL
* DIS # H8: 8 => CTR => H8: 6,9
* PRF # H8: 6 => SOL
* DIS # A9: 8,9 => CTR => A9: 6
* DIS # I2: 6 => CTR => I2: 8,9
* CNT  28 HDP CHAINS /  47 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 # I2: 6,9 => SOL
* STA I2: 6,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

1......727..5........3........6..8.34...1...............3...5...2...4.......7..4. initial
1354...727..5.143...43.71.5.7164.85345..13...3...5..14.431..527527.34..1.1.27534. autosolve
135489672786521439294367185971642853458713296362958714843196527527834961619275348 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
G1: 6,9
A4: 2,9
C5: 2,8
F4: 2,9
D5: 7,8
G5: 2,7
H5: 6,9
I5: 6,9
G6: 2,7
A7: 8,9
D8: 8,9
G8: 6,9
I9: 8,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C2,A3: 2.. / C2 = 2  =>  0 pairs (X) / A3 = 2  =>  0 pairs (_)
E2,E3: 2.. / E2 = 2  =>  0 pairs (*) / E3 = 2  =>  0 pairs (X)
F4,F6: 2.. / F4 = 2  =>  0 pairs (*) / F6 = 2  =>  0 pairs (X)
G5,G6: 2.. / G5 = 2  => 12 pairs (_) / G6 = 2  =>  0 pairs (X)
C2,E2: 2.. / C2 = 2  =>  0 pairs (X) / E2 = 2  =>  0 pairs (_)
A3,E3: 2.. / A3 = 2  =>  0 pairs (*) / E3 = 2  =>  0 pairs (X)
A4,F4: 2.. / A4 = 2  =>  0 pairs (X) / F4 = 2  =>  0 pairs (_)
C5,G5: 2.. / C5 = 2  =>  0 pairs (X) / G5 = 2  => 12 pairs (_)
A3,A4: 2.. / A3 = 2  =>  0 pairs (*) / A4 = 2  =>  0 pairs (X)
B6,C6: 6.. / B6 = 6  => 18 pairs (_) / C6 = 6  => 15 pairs (_)
H5,I5: 6.. / H5 = 6  =>  0 pairs (X) / I5 = 6  => 14 pairs (_)
A9,C9: 6.. / A9 = 6  => 14 pairs (_) / C9 = 6  =>  0 pairs (X)
E7,F7: 6.. / E7 = 6  => 17 pairs (_) / F7 = 6  => 15 pairs (_)
G8,H8: 6.. / G8 = 6  => 19 pairs (_) / H8 = 6  =>  0 pairs (*)
A3,A9: 6.. / A3 = 6  =>  0 pairs (X) / A9 = 6  => 14 pairs (_)
F1,F7: 6.. / F1 = 6  => 17 pairs (_) / F7 = 6  => 15 pairs (_)
G1,G8: 6.. / G1 = 6  =>  0 pairs (*) / G8 = 6  =>  0 pairs (X)
I2,I5: 6.. / I2 = 6  =>  0 pairs (X) / I5 = 6  => 14 pairs (_)
D5,D6: 7.. / D5 = 7  => 12 pairs (_) / D6 = 7  =>  0 pairs (X)
G5,G6: 7.. / G5 = 7  =>  0 pairs (X) / G6 = 7  => 12 pairs (_)
D5,G5: 7.. / D5 = 7  => 12 pairs (_) / G5 = 7  =>  0 pairs (X)
D6,G6: 7.. / D6 = 7  =>  0 pairs (X) / G6 = 7  => 12 pairs (_)
E1,F1: 8.. / E1 = 8  => 15 pairs (_) / F1 = 8  =>  0 pairs (X)
I2,H3: 8.. / I2 = 8  =>  0 pairs (X) / H3 = 8  =>  0 pairs (_)
H8,I9: 8.. / H8 = 8  =>  0 pairs (X) / I9 = 8  =>  0 pairs (_)
C5,D5: 8.. / C5 = 8  => 12 pairs (_) / D5 = 8  =>  0 pairs (X)
D8,H8: 8.. / D8 = 8  =>  0 pairs (*) / H8 = 8  =>  0 pairs (X)
E1,E7: 8.. / E1 = 8  => 15 pairs (_) / E7 = 8  =>  0 pairs (X)
H3,H8: 8.. / H3 = 8  =>  0 pairs (*) / H8 = 8  =>  0 pairs (X)
I2,I9: 8.. / I2 = 8  =>  0 pairs (X) / I9 = 8  =>  0 pairs (_)
H5,I5: 9.. / H5 = 9  => 14 pairs (_) / I5 = 9  =>  0 pairs (X)
A4,F4: 9.. / A4 = 9  =>  0 pairs (*) / F4 = 9  =>  0 pairs (X)
D6,D8: 9.. / D6 = 9  =>  0 pairs (*) / D8 = 9  =>  0 pairs (X)
G1,G8: 9.. / G1 = 9  => 19 pairs (_) / G8 = 9  =>  0 pairs (*)
* DURATION: 0:01:05.816725  START: 03:17:51.069939  END: 03:18:56.886664 2017-05-04
* CP COUNT: (34)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,C5,D5,D8,F4,G1,G5,G6,G8,H5,I5,I9)
* 1354...727..5.143...43.71.5.7164.85345..13...3...5..14.431..527527.34..1.1.27534.
* PAIR G1: 6,9 BLK 3
I2: 6,9,8                                # reduction candidate for 6,9
I2: 6,9 => SOLVED
* 135489672786521439294367185971642853458713296362958714843196527527834961619275348
I2: 8 => CTR
* 1354..9727..5.1438..43.7165.7164.85345..13.963...5..149431..527527934681618275349
H3: 6,9,8                                # reduction candidate for 6,9
H3: 6,9 => CTR
* 1354..9727..5.1438..43.7165.7164.85345..13.963...5..149431..527527934681618275349
H3: 8 => SOLVED
* 135489672786521439294367185971642853458713296362958714843196527527834961619275348
* PAIR G1: 6,9 ROW 1
E1: 6,9,8                                # reduction candidate for 6,9
E1: 6,9 => CTR
* 1354689727..5.1438..43.7165.7164.85345..13.963...5..14943186527527934681618275349
E1: 8                                    # 15 pairs
F1: 6,9,8                                # reduction candidate for 6,9
F1: 6,9                                  # 15 pairs
* PAIR A4: 2,9 BLK 4
C6: 2,9,6,8                              # reduction candidate for 2,9
C6: 2,9                                  # 16 pairs
C6: 6,8                                  # 14 pairs
* PAIR A4: 2,9 COL A
A3: 2,9,6,8                              # reduction candidate for 2,9
A3: 2,9 => SOLVED
* 135489672786521439294367185971642853458713296362958714843196527527834961619275348
A3: 6,8 => CTR
* 1354..9727.25914386.43271.52716498534587132..3..852714.431..527527934681816275349
* PAIR C5: 2,8 BLK 4
C6: 2,8,6,9                              # reduction candidate for 2,8
C6: 2,8 => SOLVED
* 135489672786521439294367185971642853458713296362958714843196527527834961619275348
C6: 6,9                                  # 14 pairs
* PAIR C5: 2,8 COL C
C2: 2,8,6,9                              # reduction candidate for 2,8
C2: 6,9 => SOLVED
* 135489672786521439294367185971642853458713296362958714843196527527834961619275348
C2: 2,8                                  # 16 pairs
* PAIR F4: 2,9 BLK 5
F6: 2,9,8                                # reduction candidate for 2,9
F6: 2,9 => CTR
* 1354..9727..5.1438..43.7165.7164.85345..13.963...5..149431..527527934681618275349
F6: 8 => SOLVED
* 135489672786521439294367185971642853458713296362958714843196527527834961619275348
* PAIR D5: 7,8 BLK 5
D6: 7,8,9                                # reduction candidate for 7,8
D6: 7,8 => CTR
* 1354..9727..5.1438..43.7165.7164.85345..13.963...5..149431..527527934681618275349
D6: 9 => SOLVED
* 135489672786521439294367185971642853458713296362958714843196527527834961619275348
* PAIR H5: 6,9 COL H
H3: 6,9,8                                # reduction candidate for 6,9
H3: 6,9 => CTR
* 1354..9727..5.1438..43.7165.7164.85345..13.963...5..149431..527527934681618275349
H3: 8 => SOLVED
* 135489672786521439294367185971642853458713296362958714843196527527834961619275348
H8: 6,9,8                                # reduction candidate for 6,9
H8: 6,9 => SOLVED
* 135489672786521439294367185971642853458713296362958714843196527527834961619275348
H8: 8 => CTR
* 1354..9727..5.1438..43.7165.7164.85345..13.963...5..149431..527527934681618275349
* PAIR I5: 6,9 COL I
I2: 6,9,8                                # reduction candidate for 6,9
I2: 6,9 => SOLVED
* 135489672786521439294367185971642853458713296362958714843196527527834961619275348
I2: 8 => CTR
* 1354..9727..5.1438..43.7165.7164.85345..13.963...5..149431..527527934681618275349
* PAIR A7: 8,9 BLK 7
A9: 8,9,6                                # reduction candidate for 8,9
A9: 8,9 => CTR
* 1354...727..5.143.6.43271.52716498534587132..369852714.431..527527934681816275349
A9: 6                                    # 14 pairs
C9: 8,9,6                                # reduction candidate for 8,9
C9: 8,9                                  # 14 pairs
* PAIR A7: 8,9 ROW 7
E7: 8,9,6                                # reduction candidate for 8,9
E7: 8,9                                  # 15 pairs
F7: 8,9,6                                # reduction candidate for 8,9
F7: 8,9                                  # 17 pairs
* PAIR A7: 8,9 COL A
A3: 8,9,2,6                              # reduction candidate for 8,9
A3: 8,9 => CTR
* 1354...727.25.143...43271.52716498534587132..3..852714.431..527527934681.1.27534.
A3: 2,6                                  # 15 pairs
* PAIR D8: 8,9 BLK 8
E7: 8,9,6                                # reduction candidate for 8,9
E7: 8,9                                  # 15 pairs
F7: 8,9,6                                # reduction candidate for 8,9
F7: 8,9                                  # 17 pairs
* PAIR D8: 8,9 ROW 8
H8: 8,9,6                                # reduction candidate for 8,9
H8: 6 => SOLVED
* 135489672786521439294367185971642853458713296362958714843196527527834961619275348
H8: 8,9                                  # 19 pairs
* PAIR D8: 8,9 COL D
D6: 8,9,7                                # reduction candidate for 8,9
D6: 7 => CTR
* 1354..9727..5.1438..43.7165.716428534528137963..7592149431..527527934681.1.275349
D6: 8,9                                  # 12 pairs
* PAIR G8: 6,9 BLK 9
H8: 6,9,8                                # reduction candidate for 6,9
H8: 6,9 => SOLVED
* 135489672786521439294367185971642853458713296362958714843196527527834961619275348
H8: 8 => CTR
* 1354..9727..5.1438..43.7165.7164.85345..13.963...5..149431..527527934681618275349
* PAIR I9: 8,9 BLK 9
H8: 8,9,6                                # reduction candidate for 8,9
H8: 6 => SOLVED
* 135489672786521439294367185971642853458713296362958714843196527527834961619275348
H8: 8,9                                  # 19 pairs
* PAIR I9: 8,9 ROW 9
A9: 8,9,6                                # reduction candidate for 8,9
A9: 8,9 => CTR
* 1354...727..5.143.6.43271.52716498534587132..369852714.431..527527934681816275349
A9: 6                                    # 14 pairs
C9: 8,9,6                                # reduction candidate for 8,9
C9: 8,9                                  # 14 pairs
* PAIR I9: 8,9 COL I
I2: 8,9,6                                # reduction candidate for 8,9
I2: 6 => CTR
* 13548697278.5.1436.94327185.7164.8534587132693..958714843169527527834691.1.275348
I2: 8,9                                  # 14 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-021-base-pr-000.dot
* REASONING
* PRF # I2: 6,9 => SOL
* DIS # I2: 8 => CTR => I2: 6,9
* DIS # H3: 6,9 => CTR => H3: 8
* PRF # H3: 8 => SOL
* DIS # E1: 6,9 => CTR => E1: 8
* PRF # A3: 2,9 => SOL
* DIS # A3: 6,8 => CTR => A3: 2,9
* PRF # C6: 2,8 => SOL
* PRF # C2: 6,9 => SOL
* DIS # F6: 2,9 => CTR => F6: 8
* PRF # F6: 8 => SOL
* DIS # D6: 7,8 => CTR => D6: 9
* PRF # D6: 9 => SOL
* DIS # H3: 6,9 => CTR => H3: 8
* PRF # H3: 8 => SOL
* PRF # H8: 6,9 => SOL
* DIS # H8: 8 => CTR => H8: 6,9
* PRF # I2: 6,9 => SOL
* DIS # I2: 8 => CTR => I2: 6,9
* DIS # A9: 8,9 => CTR => A9: 6
* DIS # A3: 8,9 => CTR => A3: 2,6
* PRF # H8: 6 => SOL
* DIS # D6: 7 => CTR => D6: 8,9
* PRF # H8: 6,9 => SOL
* DIS # H8: 8 => CTR => H8: 6,9
* PRF # H8: 6 => SOL
* DIS # A9: 8,9 => CTR => A9: 6
* DIS # I2: 6 => CTR => I2: 8,9
* CNT  28 HDP CHAINS /  47 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,C5,D5,D8,F4,G1,G5,G6,G8,H5,I5,I9)
* 1354...727..5.143...43.71.5.7164.85345..13...3...5..14.431..527527.34..1.1.27534.
* PAIR G1: 6,9 BLK 3
I2: 6,9,8                                # reduction candidate for 6,9
I2: 6,9 => SOLVED
* 135489672786521439294367185971642853458713296362958714843196527527834961619275348
* DURATION: 0:00:02.255854  START: 03:19:51.879123  END: 03:19:54.134977 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-021-base-pr-001.dot
* REASONING
* PRF # I2: 6,9 => SOL
* STA I2: 6,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 021

solution: 135489672786521439294367185971642853458713296362958714843196527527834961619275348
info: 1312     FNBTXY   S8.f     24861

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

Solution

position: 135489672786521439294367185971642853458713296362958714843196527527834961619275348 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 # I2: 6,9 => SOL
* DIS # I2: 8 => CTR => I2: 6,9
* DIS # H3: 6,9 => CTR => H3: 8
* PRF # H3: 8 => SOL
* DIS # E1: 6,9 => CTR => E1: 8
* INC # E1: 8 => UNS
* INC # F1: 6,9 => UNS
* INC # C6: 2,9 => UNS
* INC # C6: 6,8 => UNS
* PRF # A3: 2,9 => SOL
* DIS # A3: 6,8 => CTR => A3: 2,9
* PRF # C6: 2,8 => SOL
* INC # C6: 6,9 => UNS
* INC # C2: 2,8 => UNS
* PRF # C2: 6,9 => SOL
* DIS # F6: 2,9 => CTR => F6: 8
* PRF # F6: 8 => SOL
* DIS # D6: 7,8 => CTR => D6: 9
* PRF # D6: 9 => SOL
* DIS # H3: 6,9 => CTR => H3: 8
* PRF # H3: 8 => SOL
* PRF # H8: 6,9 => SOL
* DIS # H8: 8 => CTR => H8: 6,9
* PRF # I2: 6,9 => SOL
* DIS # I2: 8 => CTR => I2: 6,9
* DIS # A9: 8,9 => CTR => A9: 6
* INC # A9: 6 => UNS
* INC # C9: 8,9 => UNS
* INC # E7: 8,9 => UNS
* INC # F7: 8,9 => UNS
* DIS # A3: 8,9 => CTR => A3: 2,6
* INC # A3: 2,6 => UNS
* INC # E7: 8,9 => UNS
* INC # F7: 8,9 => UNS
* INC # H8: 8,9 => UNS
* PRF # H8: 6 => SOL
* INC # D6: 8,9 => UNS
* DIS # D6: 7 => CTR => D6: 8,9
* PRF # H8: 6,9 => SOL
* DIS # H8: 8 => CTR => H8: 6,9
* INC # H8: 8,9 => UNS
* PRF # H8: 6 => SOL
* DIS # A9: 8,9 => CTR => A9: 6
* INC # A9: 6 => UNS
* INC # C9: 8,9 => UNS
* INC # I2: 8,9 => UNS
* DIS # I2: 6 => CTR => I2: 8,9
* CNT  47 HDP CHAINS /  47 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # I2: 6,9 => SOL
* STA I2: 6,9
* CNT   1 HDP CHAINS /   1 HYP OPENED