Analysis of xx-top500-213-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .45....8...92........3.....2..7..4..6...8..5..........3.....2...7..5.........1... initial

Autosolve

position: .45...382.392......263.....25.7..4..6...82.5....5...2.3.....2.5.72.53...5...21... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # E1: 1,7 => CTR => E1: 6,9
* DIS # B6: 1,9 => CTR => B6: 8
* PRF # D5: 1,9 => SOL
* DIS # D5: 4 => CTR => D5: 1,9
* DIS # G5: 1,9 => CTR => G5: 7
* DIS # I5: 1,9 => CTR => I5: 3,7
* DIS # F6: 6 => CTR => F6: 4,9
* DIS # E4: 6,9 => CTR => E4: 1,3
* DIS # E6: 6,9 => CTR => E6: 1,3
* DIS # F6: 6,9 => CTR => F6: 4
* PRF # F6: 4 => SOL
* DIS # I4: 6,9 => CTR => I4: 1,3,8
* PRF # F1: 6,9 => SOL
* DIS # F1: 7 => CTR => F1: 6,9
* DIS # F7: 6,9 => CTR => F7: 4,7
* DIS # C7: 4,8 => CTR => C7: 1
* DIS # I9: 4,8 => CTR => I9: 3,6,7,9
* DIS # C6: 4,8 => CTR => C6: 1,3,7
* CNT  18 HDP CHAINS /  39 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 # E1: 1,7 => CTR => E1: 6,9
* DIS E1: 6,9 # B6: 1,9 => CTR => B6: 8
* PRF E1: 6,9 + B6: 8 # D5: 1,9 => SOL
* STA E1: 6,9 + B6: 8 + D5: 1,9
* CNT   3 HDP CHAINS /   7 HYP OPENED

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

Details

Positions

.45....8...92........3.....2..7..4..6...8..5..........3.....2...7..5.........1... initial
.45...382.392......263.....25.7..4..6...82.5....5...2.3.....2.5.72.53...5...21... autosolve
745169382139278564826345971253716498614982753987534126361897245472653819598421637 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
A1: 1,7
F2: 5,8
F3: 5,8
B5: 1,9
A6: 4,9
F4: 6,9
A8: 4,9
C9: 4,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B7,C7: 1.. / B7 = 1  =>  0 pairs (X) / C7 = 1  =>  9 pairs (_)
D1,D5: 1.. / D1 = 1  =>  0 pairs (*) / D5 = 1  =>  0 pairs (X)
E4,E6: 3.. / E4 = 3  =>  0 pairs (X) / E6 = 3  =>  8 pairs (_)
H9,I9: 3.. / H9 = 3  =>  8 pairs (_) / I9 = 3  =>  0 pairs (X)
C5,I5: 3.. / C5 = 3  =>  0 pairs (X) / I5 = 3  =>  8 pairs (_)
H4,H9: 3.. / H4 = 3  =>  0 pairs (X) / H9 = 3  =>  8 pairs (_)
E2,E3: 4.. / E2 = 4  =>  9 pairs (_) / E3 = 4  =>  9 pairs (_)
D5,F6: 4.. / D5 = 4  =>  0 pairs (X) / F6 = 4  =>  0 pairs (_)
C5,D5: 4.. / C5 = 4  =>  0 pairs (*) / D5 = 4  =>  0 pairs (X)
A6,A8: 4.. / A6 = 4  =>  0 pairs (X) / A8 = 4  =>  0 pairs (_)
F6,F7: 4.. / F6 = 4  =>  0 pairs (*) / F7 = 4  =>  0 pairs (X)
F2,F3: 5.. / F2 = 5  =>  7 pairs (_) / F3 = 5  =>  7 pairs (_)
G2,G3: 5.. / G2 = 5  =>  7 pairs (_) / G3 = 5  =>  7 pairs (_)
F2,G2: 5.. / F2 = 5  =>  7 pairs (_) / G2 = 5  =>  7 pairs (_)
F3,G3: 5.. / F3 = 5  =>  7 pairs (_) / G3 = 5  =>  7 pairs (_)
B7,B9: 6.. / B7 = 6  => 13 pairs (_) / B9 = 6  =>  8 pairs (_)
C5,C6: 7.. / C5 = 7  =>  0 pairs (X) / C6 = 7  =>  8 pairs (_)
E7,F7: 7.. / E7 = 7  =>  0 pairs (X) / F7 = 7  =>  0 pairs (_)
F1,F7: 7.. / F1 = 7  =>  0 pairs (X) / F7 = 7  =>  0 pairs (_)
A2,A3: 8.. / A2 = 8  =>  7 pairs (_) / A3 = 8  =>  7 pairs (_)
F2,F3: 8.. / F2 = 8  =>  7 pairs (_) / F3 = 8  =>  7 pairs (_)
A2,F2: 8.. / A2 = 8  =>  7 pairs (_) / F2 = 8  =>  7 pairs (_)
A3,F3: 8.. / A3 = 8  =>  7 pairs (_) / F3 = 8  =>  7 pairs (_)
C4,I4: 8.. / C4 = 8  =>  0 pairs (X) / I4 = 8  =>  9 pairs (_)
A6,A8: 9.. / A6 = 9  =>  0 pairs (*) / A8 = 9  =>  0 pairs (X)
* DURATION: 0:00:36.544990  START: 10:05:52.649540  END: 10:06:29.194530 2017-05-04
* CP COUNT: (25)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,A8,B5,C9,F2,F3,F4)
* .45...382.392......263.....25.7..4..6...82.5....5...2.3.....2.5.72.53...5...21...
* PAIR A1: 1,7 BLK 1
A2: 1,7,8                                # reduction candidate for 1,7
A2: 1,7                                  #  7 pairs
A3: 1,7,8                                # reduction candidate for 1,7
A3: 1,7                                  #  7 pairs
* PAIR A1: 1,7 ROW 1
E1: 1,7,6,9                              # reduction candidate for 1,7
E1: 1,7 => CTR
* .45...382.392......263.....25.7..4..6..182.5....5.4.2.3....72.5472.53...5.8.21...
E1: 6,9                                  #  9 pairs
* PAIR B5: 1,9 BLK 4
B6: 1,9,8                                # reduction candidate for 1,9
B6: 1,9 => CTR
* .451.7382.392......263.....25.7..4..6..482.5.4..5...2.3.1..42.5972.53...5.4.21...
B6: 8                                    # 10 pairs
* PAIR B5: 1,9 ROW 5
D5: 1,9,4                                # reduction candidate for 1,9
D5: 1,9 => SOLVED
* 745169382139278564826345971253716498614982753987534126361897245472653819598421637
D5: 4 => CTR
* 7451..382.392......263.....25.7..4..6..482.5....5...2.3...742.5.72.53...5...21...
G5: 1,9,7                                # reduction candidate for 1,9
G5: 1,9 => CTR
* 7451..382.392......263.....25.7..4..6..482.5....5...2.3...742.5.72.53...5...21...
G5: 7                                    # 10 pairs
I5: 1,9,3,7                              # reduction candidate for 1,9
I5: 1,9 => CTR
* .451.7382.392......263.....25.7..4..6.348275...75...2.3....42.5.72.53...5.4.21...
I5: 3,7                                  #  9 pairs
* PAIR B5: 1,9 COL B
B7: 1,9,6,8                              # reduction candidate for 1,9
B7: 6,8                                  # 10 pairs
B7: 1,9                                  # 10 pairs
* PAIR A6: 4,9 ROW 6
F6: 4,9,6                                # reduction candidate for 4,9
F6: 6 => CTR
* .4516.382.392......263.....25.7..4..6..482.5....5.6.2.3....42.5.72.53...5...21...
F6: 4,9                                  # 10 pairs
* PAIR F4: 6,9 BLK 5
E4: 6,9,1,3                              # reduction candidate for 6,9
E4: 6,9 => CTR
* .45...382.392......263.....25.7..4..6..182.5....534.2.3.....2.5472.53...5.8.21...
E4: 1,3                                  #  9 pairs
E6: 6,9,1,3                              # reduction candidate for 6,9
E6: 6,9 => CTR
* .45...382.392......263.....25.73.4..6..182.5....5.4.2.3.....2.5472.53...5.8.21.3.
E6: 1,3                                  #  9 pairs
F6: 6,9,4                                # reduction candidate for 6,9
F6: 6,9 => CTR
* .451.7382.392......263.....25.7..4..6..482.5....5...2.3....42.5.72.53...5...21...
F6: 4 => SOLVED
* 745169382139278564826345971253716498614982753987534126361897245472653819598421637
* PAIR F4: 6,9 ROW 4
H4: 6,9,1,3                              # reduction candidate for 6,9
H4: 6,9                                  # 10 pairs
I4: 6,9,1,3,8                            # reduction candidate for 6,9
I4: 6,9 => CTR
* .451.7382.392......263.....2587..4..6..482.5.4..5...2.3.1..42.5972.53...5.4.21...
I4: 1,3,8                                #  8 pairs
* PAIR F4: 6,9 COL F
F1: 6,9,7                                # reduction candidate for 6,9
F1: 6,9 => SOLVED
* 745169382139278564826345971253716498614982753987534126361897245472653819598421637
F1: 7 => CTR
* 145..7382.392......263.....25.7..4..6..182.5....5.4.2.3...7.2.5472.53...5.8.21...
F7: 6,9,4,7                              # reduction candidate for 6,9
F7: 6,9 => CTR
* 145..7382.392......263.....25.7..4.86.4182.539..5.4.2.3...7.2.5472.53...5.8.21...
F7: 4,7                                  #  9 pairs
* PAIR A8: 4,9 ROW 8
D8: 4,9,6,8                              # reduction candidate for 4,9
D8: 4,9                                  # 12 pairs
H8: 4,9,1,6                              # reduction candidate for 4,9
H8: 4,9                                  # 10 pairs
I8: 4,9,1,6,8                            # reduction candidate for 4,9
I8: 4,9                                  # 11 pairs
* PAIR C9: 4,8 BLK 7
C7: 4,8,1                                # reduction candidate for 4,8
C7: 4,8 => CTR
* 145..7382.392......263.....25.7..4.869.482.5.48.5...2.318.742.5972.53...564.21...
C7: 1                                    #  9 pairs
* PAIR C9: 4,8 ROW 9
D9: 4,8,6,9                              # reduction candidate for 4,8
D9: 4,8                                  # 10 pairs
I9: 4,8,3,6,7,9                          # reduction candidate for 4,8
I9: 4,8 => CTR
* 7451..382.392......263.....25.7..4..6..482.5....5...2.3...742.5.72.53...5...2173.
I9: 3,6,7,9                              #  8 pairs
* PAIR C9: 4,8 COL C
C6: 4,8,1,3,7                            # reduction candidate for 4,8
C6: 4,8 => CTR
* .451.7382.392......263.....25.7..4..6.7482.53...53..2.3....42.5.72.53...5...21.3.
C6: 1,3,7                                #  8 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-213-base-pr-000.dot
* REASONING
* DIS # E1: 1,7 => CTR => E1: 6,9
* DIS # B6: 1,9 => CTR => B6: 8
* PRF # D5: 1,9 => SOL
* DIS # D5: 4 => CTR => D5: 1,9
* DIS # G5: 1,9 => CTR => G5: 7
* DIS # I5: 1,9 => CTR => I5: 3,7
* DIS # F6: 6 => CTR => F6: 4,9
* DIS # E4: 6,9 => CTR => E4: 1,3
* DIS # E6: 6,9 => CTR => E6: 1,3
* DIS # F6: 6,9 => CTR => F6: 4
* PRF # F6: 4 => SOL
* DIS # I4: 6,9 => CTR => I4: 1,3,8
* PRF # F1: 6,9 => SOL
* DIS # F1: 7 => CTR => F1: 6,9
* DIS # F7: 6,9 => CTR => F7: 4,7
* DIS # C7: 4,8 => CTR => C7: 1
* DIS # I9: 4,8 => CTR => I9: 3,6,7,9
* DIS # C6: 4,8 => CTR => C6: 1,3,7
* CNT  18 HDP CHAINS /  39 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,A8,B5,C9,F2,F3,F4)
* .45...382.392......263.....25.7..4..6...82.5....5...2.3.....2.5.72.53...5...21...
* PAIR A1: 1,7 BLK 1
A2: 1,7,8                                # reduction candidate for 1,7
A2: 1,7                                  #  7 pairs
A3: 1,7,8                                # reduction candidate for 1,7
A3: 1,7                                  #  7 pairs
* PAIR A1: 1,7 ROW 1
E1: 1,7,6,9                              # reduction candidate for 1,7
E1: 1,7 => CTR
* .45...382.392......263.....25.7..4..6..182.5....5.4.2.3....72.5472.53...5.8.21...
* PAIR RESTART
* PAIR A1: 1,7 BLK 1
A2: 1,7,8                                # reduction candidate for 1,7
A2: 1,7                                  #  8 pairs
A3: 1,7,8                                # reduction candidate for 1,7
A3: 1,7                                  #  8 pairs
* PAIR B5: 1,9 BLK 4
B6: 1,9,8                                # reduction candidate for 1,9
B6: 1,9 => CTR
* .451.7382.392......263.....25.7..4..6..482.5.4..5...2.3.1..42.5972.53...5.4.21...
* PAIR B5: 1,9 ROW 5
D5: 1,9,4                                # reduction candidate for 1,9
D5: 1,9 => SOLVED
* 745169382139278564826345971253716498614982753987534126361897245472653819598421637
* DURATION: 0:00:08.429650  START: 10:06:59.584442  END: 10:07:08.014092 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-213-base-pr-001.dot
* REASONING
* DIS # E1: 1,7 => CTR => E1: 6,9
* DIS E1: 6,9 # B6: 1,9 => CTR => B6: 8
* PRF E1: 6,9 + B6: 8 # D5: 1,9 => SOL
* STA E1: 6,9 + B6: 8 + D5: 1,9
* CNT   3 HDP CHAINS /   7 HYP OPENED

Header Info

Top 500 Minimum 17 213

solution: 745169382139278564826345971253716498614982753987534126361897245472653819598421637
info: 1945     FNBHWXY  S8.f     19452

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

Solution

position: 745169382139278564826345971253716498614982753987534126361897245472653819598421637 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: 1,7 => UNS
* INC # A3: 1,7 => UNS
* DIS # E1: 1,7 => CTR => E1: 6,9
* INC # E1: 6,9 => UNS
* DIS # B6: 1,9 => CTR => B6: 8
* INC # B6: 8 => UNS
* PRF # D5: 1,9 => SOL
* DIS # D5: 4 => CTR => D5: 1,9
* DIS # G5: 1,9 => CTR => G5: 7
* INC # G5: 7 => UNS
* DIS # I5: 1,9 => CTR => I5: 3,7
* INC # I5: 3,7 => UNS
* INC # B7: 1,9 => UNS
* INC # B7: 6,8 => UNS
* INC # F6: 4,9 => UNS
* DIS # F6: 6 => CTR => F6: 4,9
* DIS # E4: 6,9 => CTR => E4: 1,3
* INC # E4: 1,3 => UNS
* DIS # E6: 6,9 => CTR => E6: 1,3
* INC # E6: 1,3 => UNS
* DIS # F6: 6,9 => CTR => F6: 4
* PRF # F6: 4 => SOL
* INC # H4: 6,9 => UNS
* DIS # I4: 6,9 => CTR => I4: 1,3,8
* INC # I4: 1,3,8 => UNS
* PRF # F1: 6,9 => SOL
* DIS # F1: 7 => CTR => F1: 6,9
* DIS # F7: 6,9 => CTR => F7: 4,7
* INC # F7: 4,7 => UNS
* INC # D8: 4,9 => UNS
* INC # H8: 4,9 => UNS
* INC # I8: 4,9 => UNS
* DIS # C7: 4,8 => CTR => C7: 1
* INC # C7: 1 => UNS
* INC # D9: 4,8 => UNS
* DIS # I9: 4,8 => CTR => I9: 3,6,7,9
* INC # I9: 3,6,7,9 => UNS
* DIS # C6: 4,8 => CTR => C6: 1,3,7
* INC # C6: 1,3,7 => UNS
* CNT  39 HDP CHAINS /  39 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A2: 1,7 => UNS
* INC # A3: 1,7 => UNS
* DIS # E1: 1,7 => CTR => E1: 6,9
* INC E1: 6,9 # A2: 1,7 => UNS
* INC E1: 6,9 # A3: 1,7 => UNS
* DIS E1: 6,9 # B6: 1,9 => CTR => B6: 8
* PRF E1: 6,9 + B6: 8 # D5: 1,9 => SOL
* STA E1: 6,9 + B6: 8 + D5: 1,9
* CNT   7 HDP CHAINS /   7 HYP OPENED