Analysis of xx-top500-441-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ....3...26.....5...1.4.........527...74...........1......8...1.2.3......5........ initial

Autosolve

position: ....3...26.....5...1.4.........527...74.........741......8...1.2.3......5.1...... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C3: 7,8,9 => CTR => C3: 2,5
* DIS # A4: 3,9 => CTR => A4: 1,8
* DIS # H4: 3,9 => CTR => H4: 4,8
* DIS # I4: 3,9 => CTR => I4: 1,4,8
* DIS # D9: 3,9 => CTR => D9: 2,6
* CNT   5 HDP CHAINS /  13 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 # C3: 7,8,9 => CTR => C3: 2,5
* DIS C3: 2,5 # A4: 3,9 => CTR => A4: 1,8
* DIS C3: 2,5 + A4: 1,8 # H4: 3,9 => CTR => H4: 4,8
* DIS C3: 2,5 + A4: 1,8 + H4: 4,8 # I4: 3,9 => CTR => I4: 1,4,8
* DIS C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 # B4: 6 => CTR => B4: 3,9
* DIS C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 # D9: 3,9 => CTR => D9: 2,6
* DIS C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 # D5: 6 => CTR => D5: 3,9
* DIS C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 + D5: 3,9 # E2: 1,2 => CTR => E2: 7,8,9
* PRF C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 + D5: 3,9 + E2: 7,8,9 # A6: 3,9 => SOL
* STA C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 + D5: 3,9 + E2: 7,8,9 + A6: 3,9
* CNT   9 HDP CHAINS /  18 HYP OPENED

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

Details

Positions

....3...26.....5...1.4.........527...74...........1......8...1.2.3......5........ initial
....3...26.....5...1.4.........527...74.........741......8...1.2.3......5.1...... autosolve
748536192629187534315429678836952741174368925952741386467895213293614857581273469 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (3)
B6: 2,5
C6: 2,5
D4: 3,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G1,I2: 1.. / G1 = 1  =>  3 pairs (_) / I2 = 1  =>  0 pairs (X)
A4,A5: 1.. / A4 = 1  =>  7 pairs (_) / A5 = 1  =>  4 pairs (_)
D8,E8: 1.. / D8 = 1  =>  0 pairs (X) / E8 = 1  =>  3 pairs (_)
D1,G1: 1.. / D1 = 1  =>  0 pairs (X) / G1 = 1  =>  3 pairs (_)
A4,I4: 1.. / A4 = 1  =>  7 pairs (_) / I4 = 1  =>  4 pairs (_)
E2,E8: 1.. / E2 = 1  =>  0 pairs (X) / E8 = 1  =>  3 pairs (_)
G1,G5: 1.. / G1 = 1  =>  3 pairs (_) / G5 = 1  =>  0 pairs (X)
B6,C6: 2.. / B6 = 2  =>  0 pairs (X) / C6 = 2  =>  0 pairs (_)
G5,H5: 2.. / G5 = 2  =>  0 pairs (X) / H5 = 2  =>  0 pairs (_)
C3,E3: 2.. / C3 = 2  =>  0 pairs (X) / E3 = 2  =>  0 pairs (_)
E7,G7: 2.. / E7 = 2  =>  0 pairs (X) / G7 = 2  =>  0 pairs (_)
B2,B6: 2.. / B2 = 2  =>  0 pairs (*) / B6 = 2  =>  0 pairs (X)
D2,D9: 2.. / D2 = 2  =>  0 pairs (X) / D9 = 2  =>  0 pairs (_)
H5,H9: 2.. / H5 = 2  =>  0 pairs (*) / H9 = 2  =>  0 pairs (X)
B2,A3: 3.. / B2 = 3  =>  0 pairs (X) / A3 = 3  => 12 pairs (_)
B2,B4: 3.. / B2 = 3  =>  0 pairs (X) / B4 = 3  => 12 pairs (_)
H4,I4: 4.. / H4 = 4  =>  5 pairs (_) / I4 = 4  =>  7 pairs (_)
A1,A7: 4.. / A1 = 4  =>  5 pairs (_) / A7 = 4  => 12 pairs (_)
B6,C6: 5.. / B6 = 5  =>  0 pairs (*) / C6 = 5  =>  0 pairs (X)
H5,I5: 5.. / H5 = 5  =>  0 pairs (X) / I5 = 5  =>  0 pairs (_)
C3,F3: 5.. / C3 = 5  =>  0 pairs (*) / F3 = 5  =>  0 pairs (X)
F7,I7: 5.. / F7 = 5  =>  0 pairs (*) / I7 = 5  =>  0 pairs (X)
B1,B6: 5.. / B1 = 5  =>  0 pairs (X) / B6 = 5  =>  0 pairs (_)
D1,D8: 5.. / D1 = 5  =>  0 pairs (*) / D8 = 5  =>  0 pairs (X)
H5,H8: 5.. / H5 = 5  =>  0 pairs (X) / H8 = 5  =>  0 pairs (_)
B4,C4: 6.. / B4 = 6  =>  0 pairs (X) / C4 = 6  =>  7 pairs (_)
C4,C7: 6.. / C4 = 6  =>  7 pairs (_) / C7 = 6  =>  0 pairs (X)
A7,C7: 7.. / A7 = 7  =>  5 pairs (_) / C7 = 7  => 10 pairs (_)
E5,F5: 8.. / E5 = 8  =>  3 pairs (_) / F5 = 8  =>  5 pairs (_)
B8,B9: 8.. / B8 = 8  =>  3 pairs (_) / B9 = 8  =>  3 pairs (_)
* DURATION: 0:00:47.477465  START: 17:50:39.494246  END: 17:51:26.971711 2017-05-04
* CP COUNT: (30)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,C6,D4)
* ....3...26.....5...1.4.........527...74.........741......8...1.2.3......5.1......
* PAIR C6: 2,5 COL C
C3: 2,5,7,8,9                            # reduction candidate for 2,5
C3: 7,8,9 => CTR
* ....3...26.....5...1.425.......527...74.........741......8..2152.351....5.12.....
C3: 2,5                                  #  4 pairs
* PAIR D4: 3,9 BLK 5
D5: 3,9,6                                # reduction candidate for 3,9
D5: 3,9                                  #  8 pairs
F5: 3,9,6,8                              # reduction candidate for 3,9
F5: 3,9                                  #  4 pairs
* PAIR D4: 3,9 ROW 4
A4: 3,9,1,8                              # reduction candidate for 3,9
A4: 3,9 => CTR
* 45..3.1.263.1..5.481.4.5....68.52741174....5..25741...7.68...152.351....5.12.....
A4: 1,8                                  #  4 pairs
B4: 3,9,6                                # reduction candidate for 3,9
B4: 3,9                                  #  7 pairs
H4: 3,9,4,8                              # reduction candidate for 3,9
H4: 3,9 => CTR
* 45..3...263.2..5418124.5...168.527.4.74....5..25741...7.68...152.351....5.1....2.
H4: 4,8                                  #  4 pairs
I4: 3,9,1,4,8                            # reduction candidate for 3,9
I4: 3,9 => CTR
* 45..3.1.263....5.481.4.5...168.5274..74....51.25741...7.68...152.351....5.1....2.
I4: 1,4,8                                #  3 pairs
* PAIR D4: 3,9 COL D
D9: 3,9,2,6                              # reduction candidate for 3,9
D9: 3,9 => CTR
* .5.13...26..2..5.1.124.5...1...527...746..1...25741......8...152.351....5.1......
D9: 2,6                                  #  4 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-441-base-pr-000.dot
* REASONING
* DIS # C3: 7,8,9 => CTR => C3: 2,5
* DIS # A4: 3,9 => CTR => A4: 1,8
* DIS # H4: 3,9 => CTR => H4: 4,8
* DIS # I4: 3,9 => CTR => I4: 1,4,8
* DIS # D9: 3,9 => CTR => D9: 2,6
* CNT   5 HDP CHAINS /  13 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,C6,D4)
* ....3...26.....5...1.4.........527...74.........741......8...1.2.3......5.1......
* PAIR C6: 2,5 COL C
C3: 2,5,7,8,9                            # reduction candidate for 2,5
C3: 7,8,9 => CTR
* ....3...26.....5...1.425.......527...74.........741......8..2152.351....5.12.....
* PAIR RESTART
* PAIR D4: 3,9 BLK 5
D5: 3,9,6                                # reduction candidate for 3,9
D5: 3,9                                  #  9 pairs
F5: 3,9,6,8                              # reduction candidate for 3,9
F5: 3,9                                  #  5 pairs
* PAIR D4: 3,9 ROW 4
A4: 3,9,1,8                              # reduction candidate for 3,9
A4: 3,9 => CTR
* 45..3.1.263.12.5.48124.5....68.52741174.8..5..25741...7.689.2152.351....5.12.....
B4: 3,9,6                                # reduction candidate for 3,9
B4: 3,9                                  #  8 pairs
H4: 3,9,4,8                              # reduction candidate for 3,9
H4: 3,9 => CTR
* 45..3...263.2..5418124.5...168.527.4.74....5..25741...7.68...152.351....5.1....2.
I4: 3,9,1,4,8                            # reduction candidate for 3,9
I4: 3,9 => CTR
* 45..3.1.263.12.5.48124.5...168.5274..74.8..51.25741...7.689.2152.351....5.12.....
* RESTART
* PAIR D4: 3,9 ROW 4
B4: 3,9,6                                # reduction candidate for 3,9
B4: 6 => CTR
* 45..3...263.2..5.19124.5...1693527..374....5..25741...7.68...152.351....5.1....2.
* PAIR D4: 3,9 COL D
D9: 3,9,2,6                              # reduction candidate for 3,9
D9: 3,9 => CTR
* .5.13...26..2..5.1.124.5...1.6.527...746..1...25741......8...152.351....5.1......
* PAIR RESTART
* PAIR D4: 3,9 BLK 5
D5: 3,9,6                                # reduction candidate for 3,9
D5: 6 => CTR
* ....3...263..2.5...124.5....963527...746...25.25741......8..21.2.351....5.12.....

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A4,B4,B6,C3,C6,C7,D2,D4,D5,D9,E5,F5,H4)
* ....3...26.....5...1.4.......6.527...74.........741......8...1.2.3......5.1......
* PAIR D2: 1,2 BLK 2
E2: 1,2,7,8,9                            # reduction candidate for 1,2
E2: 1,2 => CTR
* .5.63.1.26..12.5...124.5.....6.527...74....5..25741......8..2152.351....5.12.....
* PAIR A4: 1,8 ROW 4
I4: 1,8,4                                # reduction candidate for 1,8
I4: 4                                    # 18 pairs
I4: 1,8                                  # 18 pairs
* PAIR B4: 3,9 BLK 4
A5: 3,9,1                                # reduction candidate for 3,9
A5: 3,9                                  # 19 pairs
A6: 3,9,8                                # reduction candidate for 3,9
A6: 3,9 => SOLVED
* 748536192629187534315429678836952741174368925952741386467895213293614857581273469
* DURATION: 0:00:20.597232  START: 17:51:36.869219  END: 17:51:57.466451 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-441-base-pr-001.dot
* REASONING
* DIS # C3: 7,8,9 => CTR => C3: 2,5
* DIS C3: 2,5 # A4: 3,9 => CTR => A4: 1,8
* DIS C3: 2,5 + A4: 1,8 # H4: 3,9 => CTR => H4: 4,8
* DIS C3: 2,5 + A4: 1,8 + H4: 4,8 # I4: 3,9 => CTR => I4: 1,4,8
* DIS C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 # B4: 6 => CTR => B4: 3,9
* DIS C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 # D9: 3,9 => CTR => D9: 2,6
* DIS C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 # D5: 6 => CTR => D5: 3,9
* DIS C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 + D5: 3,9 # E2: 1,2 => CTR => E2: 7,8,9
* PRF C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 + D5: 3,9 + E2: 7,8,9 # A6: 3,9 => SOL
* STA C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 + D5: 3,9 + E2: 7,8,9 + A6: 3,9
* CNT   9 HDP CHAINS /  18 HYP OPENED

Header Info

Top 500 Minimum 17 441

solution: 748536192629187534315429678836952741174368925952741386467895213293614857581273469
info: 95272    FNBHYK   S8.f     40763

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

Solution

position: 748536192629187534315429678836952741174368925952741386467895213293614857581273469 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 # C3: 2,5 => UNS
* DIS # C3: 7,8,9 => CTR => C3: 2,5
* INC # D5: 3,9 => UNS
* INC # F5: 3,9 => UNS
* DIS # A4: 3,9 => CTR => A4: 1,8
* INC # A4: 1,8 => UNS
* INC # B4: 3,9 => UNS
* DIS # H4: 3,9 => CTR => H4: 4,8
* INC # H4: 4,8 => UNS
* DIS # I4: 3,9 => CTR => I4: 1,4,8
* INC # I4: 1,4,8 => UNS
* DIS # D9: 3,9 => CTR => D9: 2,6
* INC # D9: 2,6 => UNS
* CNT  13 HDP CHAINS /  13 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C3: 2,5 => UNS
* DIS # C3: 7,8,9 => CTR => C3: 2,5
* INC C3: 2,5 # D5: 3,9 => UNS
* INC C3: 2,5 # F5: 3,9 => UNS
* DIS C3: 2,5 # A4: 3,9 => CTR => A4: 1,8
* INC C3: 2,5 + A4: 1,8 # B4: 3,9 => UNS
* DIS C3: 2,5 + A4: 1,8 # H4: 3,9 => CTR => H4: 4,8
* DIS C3: 2,5 + A4: 1,8 + H4: 4,8 # I4: 3,9 => CTR => I4: 1,4,8
* INC C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 # B4: 3,9 => UNS
* DIS C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 # B4: 6 => CTR => B4: 3,9
* DIS C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 # D9: 3,9 => CTR => D9: 2,6
* INC C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 # D5: 3,9 => UNS
* DIS C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 # D5: 6 => CTR => D5: 3,9
* DIS C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 + D5: 3,9 # E2: 1,2 => CTR => E2: 7,8,9
* INC C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 + D5: 3,9 + E2: 7,8,9 # I4: 1,8 => UNS
* INC C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 + D5: 3,9 + E2: 7,8,9 # I4: 4 => UNS
* INC C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 + D5: 3,9 + E2: 7,8,9 # A5: 3,9 => UNS
* PRF C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 + D5: 3,9 + E2: 7,8,9 # A6: 3,9 => SOL
* STA C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 + D5: 3,9 + E2: 7,8,9 + A6: 3,9
* CNT  18 HDP CHAINS /  18 HYP OPENED