Analysis of xx-top500-103-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 3.......1...7.4......2......2.5..4..6.7..........8..3.1...3..........25.......7.. initial

Autosolve

position: 3.......1...7.43.....2.3....235.14..6.73.........8..3.1...3.......1..25.......71. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A3: 4,7 => CTR => A3: 5,8,9
* PRF # A3: 5,8,9 => SOL
* DIS # B3: 4,7 => CTR => B3: 1,5,6,8,9
* DIS # H1: 4,7 => CTR => H1: 2
* PRF # H1: 2 => SOL
* PRF # B8: 4,7 => SOL
* PRF # H1: 2,4 => SOL
* DIS # H1: 7 => CTR => H1: 2,4
* DIS # C9: 2,4 => CTR => C9: 5,6,8,9
* DIS # B5: 8,9 => CTR => B5: 1,4,5
* DIS # A2: 8,9 => CTR => A2: 2,5
* DIS # A3: 8,9 => CTR => A3: 4,5,7
* DIS # A8: 8,9 => CTR => A8: 4,7
* PRF # A9: 8,9 => SOL
* DIS # E5: 2,9 => CTR => E5: 4
* PRF # E5: 4 => SOL
* DIS # H5: 2,9 => CTR => H5: 8
* PRF # I5: 2,9 => SOL
* DIS # F9: 2,9 => CTR => F9: 5,6,8
* DIS # F7: 5 => CTR => F7: 2,7
* PRF # F7: 5,7 => SOL
* DIS # F7: 2 => CTR => F7: 5,7
* DIS # B3: 5,7 => CTR => B3: 1,4,6,8,9
* DIS # A9: 2,5 => CTR => A9: 4,8,9
* PRF # A9: 4,8,9 => SOL
* DIS # C9: 2,5 => CTR => C9: 4,6,8,9
* DIS # F7: 2,5 => CTR => F7: 7
* PRF # F7: 7 => SOL
* DIS # C2: 2,5 => CTR => C2: 1,6,8,9
* CNT  29 HDP CHAINS /  46 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: 4,7 => CTR => A3: 5,8,9
* PRF A3: 5,8,9 => SOL
* STA A3: 5,8,9
* CNT   2 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

3.......1...7.4......2......2.5..4..6.7..........8..3.1...3..........25.......7.. initial
3.......1...7.43.....2.3....235.14..6.73.........8..3.1...3.......1..25.......71. autosolve
374958621281764395569213874823571469617349582495682137152837946748196253936425718 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
B1: 4,7
C1: 2,4
A4: 8,9
F5: 2,9
F6: 2,7
I6: 2,7
B7: 5,7
C7: 2,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E2,E3: 1.. / E2 = 1  =>  8 pairs (_) / E3 = 1  =>  8 pairs (_)
G5,G6: 1.. / G5 = 1  =>  8 pairs (_) / G6 = 1  =>  0 pairs (*)
B5,G5: 1.. / B5 = 1  =>  0 pairs (*) / G5 = 1  =>  0 pairs (X)
C1,H1: 2.. / C1 = 2  =>  0 pairs (X) / H1 = 2  =>  0 pairs (_)
F6,I6: 2.. / F6 = 2  =>  0 pairs (*) / I6 = 2  =>  0 pairs (X)
C7,F7: 2.. / C7 = 2  =>  0 pairs (*) / F7 = 2  =>  0 pairs (X)
A2,A9: 2.. / A2 = 2  =>  0 pairs (*) / A9 = 2  =>  0 pairs (X)
E5,E9: 2.. / E5 = 2  =>  0 pairs (X) / E9 = 2  =>  0 pairs (_)
B8,B9: 3.. / B8 = 3  =>  8 pairs (_) / B9 = 3  =>  8 pairs (_)
I8,I9: 3.. / I8 = 3  =>  8 pairs (_) / I9 = 3  =>  8 pairs (_)
B8,I8: 3.. / B8 = 3  =>  8 pairs (_) / I8 = 3  =>  8 pairs (_)
B9,I9: 3.. / B9 = 3  =>  8 pairs (_) / I9 = 3  =>  8 pairs (_)
E5,D6: 4.. / E5 = 4  =>  0 pairs (*) / D6 = 4  =>  0 pairs (X)
B5,E5: 4.. / B5 = 4  =>  0 pairs (X) / E5 = 4  =>  0 pairs (_)
E4,D6: 6.. / E4 = 6  =>  0 pairs (X) / D6 = 6  =>  0 pairs (_)
D6,G6: 6.. / D6 = 6  =>  0 pairs (*) / G6 = 6  =>  0 pairs (X)
E4,F6: 7.. / E4 = 7  =>  0 pairs (*) / F6 = 7  =>  0 pairs (X)
B1,H1: 7.. / B1 = 7  =>  0 pairs (*) / H1 = 7  =>  0 pairs (X)
F6,I6: 7.. / F6 = 7  =>  0 pairs (X) / I6 = 7  =>  0 pairs (_)
B7,F7: 7.. / B7 = 7  =>  0 pairs (X) / F7 = 7  =>  0 pairs (_)
A3,A8: 7.. / A3 = 7  =>  0 pairs (X) / A8 = 7  =>  0 pairs (_)
E4,E8: 7.. / E4 = 7  =>  0 pairs (*) / E8 = 7  =>  0 pairs (X)
D1,F1: 8.. / D1 = 8  =>  8 pairs (_) / F1 = 8  =>  9 pairs (_)
A4,B5: 8.. / A4 = 8  =>  7 pairs (_) / B5 = 8  =>  0 pairs (X)
* DURATION: 0:00:42.609743  START: 06:17:49.169547  END: 06:18:31.779290 2017-05-04
* CP COUNT: (24)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B1,B7,C1,C7,F5,F6,I6)
* 3.......1...7.43.....2.3....235.14..6.73.........8..3.1...3.......1..25.......71.
* PAIR B1: 4,7 BLK 1
A3: 4,7,5,8,9                            # reduction candidate for 4,7
A3: 4,7 => CTR
* 342....71...7.432.7..2.3...823561497617329.85...487632175.32......17.25.2...4571.
A3: 5,8,9 => SOLVED
* 374958621281764395569213874823571469617349582495682137152837946748196253936425718
B3: 4,7,1,5,6,8,9                        # reduction candidate for 4,7
B3: 4,7 => CTR
* 3.2.....1...7.43.....2.3....235.14..6.734........8..3.15..3.......1..25.......71.
B3: 1,5,6,8,9                            #  8 pairs
* PAIR B1: 4,7 ROW 1
H1: 4,7,2                                # reduction candidate for 4,7
H1: 4,7 => CTR
* 342....71...7.432.7..2.3...823561497617329.85...487632175.32......17.25.2...4571.
H1: 2 => SOLVED
* 374958621281764395569213874823571469617349582495682137152837946748196253936425718
* PAIR B1: 4,7 COL B
B8: 4,7,3,6,8,9                          # reduction candidate for 4,7
B8: 4,7 => SOLVED
* 374958621281764395569213874823571469617349582495682137152837946748196253936425718
B8: 3,6,8,9                              #  8 pairs
* PAIR C1: 2,4 ROW 1
H1: 2,4,7                                # reduction candidate for 2,4
H1: 2,4 => SOLVED
* 374958621281764395569213874823571469617349582495682137152837946748196253936425718
H1: 7 => CTR
* 342....71...7.43.....2.3....235.14..6.73.........8..3.1.5.32......1..25.2.....71.
* PAIR C1: 2,4 COL C
C9: 2,4,5,6,8,9                          # reduction candidate for 2,4
C9: 2,4 => CTR
* 342.....1...7.43.....2.3....235.14..6.7329.85...487632175.32......17.25.....4571.
C9: 5,6,8,9                              #  8 pairs
* PAIR A4: 8,9 BLK 4
B5: 8,9,1,4,5                            # reduction candidate for 8,9
B5: 8,9 => CTR
* 3.4....212..7.43.....2.3....235.14..6.73421.5....87.32172.3.......1..25.....2.71.
B5: 1,4,5                                #  8 pairs
* PAIR A4: 8,9 ROW 4
H4: 8,9,6,7                              # reduction candidate for 8,9
H4: 8,9                                  # 11 pairs
I4: 8,9,6,7                              # reduction candidate for 8,9
I4: 8,9                                  # 11 pairs
* PAIR A4: 8,9 COL A
A2: 8,9,2,5                              # reduction candidate for 8,9
A2: 8,9 => CTR
* 342....71...7.432.7..2.3...823561497617329.85...487632175.32......17.25.2...4571.
A2: 2,5                                  #  9 pairs
A3: 8,9,4,5,7                            # reduction candidate for 8,9
A3: 8,9 => CTR
* 3.4....212..7.43.....2.3.74.235714..6.7349.8254.682.37152.37.4.7..1..25.4...2571.
A3: 4,5,7                                #  8 pairs
A8: 8,9,4,7                              # reduction candidate for 8,9
A8: 8,9 => CTR
* 342....71...7.43..7..2.3....235.14..6.734........8..3.1.5.32......1..25.2.....71.
A8: 4,7                                  #  9 pairs
A9: 8,9,2,4,5                            # reduction candidate for 8,9
A9: 8,9 => SOLVED
* 374958621281764395569213874823571469617349582495682137152837946748196253936425718
A9: 2,4,5                                #  8 pairs
* PAIR F5: 2,9 BLK 5
E5: 2,9,4                                # reduction candidate for 2,9
E5: 2,9 => CTR
* 37......1...7.43.....2.3...8235614..6473..185...487632152.3.......1..25.......71.
E5: 4 => SOLVED
* 374958621281764395569213874823571469617349582495682137152837946748196253936425718
* PAIR F5: 2,9 ROW 5
H5: 2,9,8                                # reduction candidate for 2,9
H5: 2,9 => CTR
* 3.4....212..7.43.....2.3....235.14..6.7342.9.....87.32172.3.......1..25.....2.71.
H5: 8                                    #  7 pairs
I5: 2,9,5,8                              # reduction candidate for 2,9
I5: 2,9 => SOLVED
* 374958621281764395569213874823571469617349582495682137152837946748196253936425718
I5: 5,8                                  #  9 pairs
* PAIR F5: 2,9 COL F
F9: 2,9,5,6,8                            # reduction candidate for 2,9
F9: 2,9 => CTR
* 3.......1...7.43.....2.3....235.14..6.73.........87.32172.35......17.25.......71.
F9: 5,6,8                                #  8 pairs
* PAIR F6: 2,7 COL F
F7: 2,7,5                                # reduction candidate for 2,7
F7: 5 => CTR
* 3.......1...7.43.....2.3....235.14..6.73.........8..3.172.35......1..25.......71.
F7: 2,7                                  # 13 pairs
* PAIR B7: 5,7 ROW 7
F7: 5,7,2                                # reduction candidate for 5,7
F7: 5,7 => SOLVED
* 374958621281764395569213874823571469617349582495682137152837946748196253936425718
F7: 2 => CTR
* 342....71...7.43..7..2.3....235.14..6.73.........8..3.175.32......1..25.......71.
* PAIR B7: 5,7 COL B
B3: 5,7,1,4,6,8,9                        # reduction candidate for 5,7
B3: 5,7 => CTR
* 342....71...7.43.....2.3....235.14..6.734........8..3.1.5.32......1..25.2.....71.
B3: 1,4,6,8,9                            #  8 pairs
* PAIR C7: 2,5 BLK 7
A9: 2,5,4,8,9                            # reduction candidate for 2,5
A9: 2,5 => CTR
* 342....71...7.43..7..2.3....235.14..6.734........8..3.175.32......1..25.2.....71.
A9: 4,8,9 => SOLVED
* 374958621281764395569213874823571469617349582495682137152837946748196253936425718
C9: 2,5,4,6,8,9                          # reduction candidate for 2,5
C9: 2,5 => CTR
* 3.4....212..7.43.....2.3....235.14..6.73.........8..3.17..3.......1..25.......71.
C9: 4,6,8,9                              #  8 pairs
* PAIR C7: 2,5 ROW 7
F7: 2,5,7                                # reduction candidate for 2,5
F7: 2,5 => CTR
* 342....71...7.43..7..2.3....235.14..6.734........8..3.175.32......1..25.2.....71.
F7: 7 => SOLVED
* 374958621281764395569213874823571469617349582495682137152837946748196253936425718
* PAIR C7: 2,5 COL C
C2: 2,5,1,6,8,9                          # reduction candidate for 2,5
C2: 2,5 => CTR
* 374....212.57.43.....2.3.74.235714..6.734....5..682.37152.37...7..1..25.4...2571.
C2: 1,6,8,9                              #  8 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-103-base-pr-000.dot
* REASONING
* DIS # A3: 4,7 => CTR => A3: 5,8,9
* PRF # A3: 5,8,9 => SOL
* DIS # B3: 4,7 => CTR => B3: 1,5,6,8,9
* DIS # H1: 4,7 => CTR => H1: 2
* PRF # H1: 2 => SOL
* PRF # B8: 4,7 => SOL
* PRF # H1: 2,4 => SOL
* DIS # H1: 7 => CTR => H1: 2,4
* DIS # C9: 2,4 => CTR => C9: 5,6,8,9
* DIS # B5: 8,9 => CTR => B5: 1,4,5
* DIS # A2: 8,9 => CTR => A2: 2,5
* DIS # A3: 8,9 => CTR => A3: 4,5,7
* DIS # A8: 8,9 => CTR => A8: 4,7
* PRF # A9: 8,9 => SOL
* DIS # E5: 2,9 => CTR => E5: 4
* PRF # E5: 4 => SOL
* DIS # H5: 2,9 => CTR => H5: 8
* PRF # I5: 2,9 => SOL
* DIS # F9: 2,9 => CTR => F9: 5,6,8
* DIS # F7: 5 => CTR => F7: 2,7
* PRF # F7: 5,7 => SOL
* DIS # F7: 2 => CTR => F7: 5,7
* DIS # B3: 5,7 => CTR => B3: 1,4,6,8,9
* DIS # A9: 2,5 => CTR => A9: 4,8,9
* PRF # A9: 4,8,9 => SOL
* DIS # C9: 2,5 => CTR => C9: 4,6,8,9
* DIS # F7: 2,5 => CTR => F7: 7
* PRF # F7: 7 => SOL
* DIS # C2: 2,5 => CTR => C2: 1,6,8,9
* CNT  29 HDP CHAINS /  46 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B1,B7,C1,C7,F5,F6,I6)
* 3.......1...7.43.....2.3....235.14..6.73.........8..3.1...3.......1..25.......71.
* PAIR B1: 4,7 BLK 1
A3: 4,7,5,8,9                            # reduction candidate for 4,7
A3: 4,7 => CTR
* 342....71...7.432.7..2.3...823561497617329.85...487632175.32......17.25.2...4571.
A3: 5,8,9 => SOLVED
* 374958621281764395569213874823571469617349582495682137152837946748196253936425718
* DURATION: 0:00:02.151520  START: 06:19:17.164985  END: 06:19:19.316505 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-103-base-pr-001.dot
* REASONING
* DIS # A3: 4,7 => CTR => A3: 5,8,9
* PRF A3: 5,8,9 => SOL
* STA A3: 5,8,9
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 103

solution: 374958621281764395569213874823571469617349582495682137152837946748196253936425718
info: 1613     FNBHXY   S8.f     28614

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

Solution

position: 374958621281764395569213874823571469617349582495682137152837946748196253936425718 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:

* DIS # A3: 4,7 => CTR => A3: 5,8,9
* PRF # A3: 5,8,9 => SOL
* DIS # B3: 4,7 => CTR => B3: 1,5,6,8,9
* INC # B3: 1,5,6,8,9 => UNS
* DIS # H1: 4,7 => CTR => H1: 2
* PRF # H1: 2 => SOL
* PRF # B8: 4,7 => SOL
* INC # B8: 3,6,8,9 => UNS
* PRF # H1: 2,4 => SOL
* DIS # H1: 7 => CTR => H1: 2,4
* DIS # C9: 2,4 => CTR => C9: 5,6,8,9
* INC # C9: 5,6,8,9 => UNS
* DIS # B5: 8,9 => CTR => B5: 1,4,5
* INC # B5: 1,4,5 => UNS
* INC # H4: 8,9 => UNS
* INC # I4: 8,9 => UNS
* DIS # A2: 8,9 => CTR => A2: 2,5
* INC # A2: 2,5 => UNS
* DIS # A3: 8,9 => CTR => A3: 4,5,7
* INC # A3: 4,5,7 => UNS
* DIS # A8: 8,9 => CTR => A8: 4,7
* INC # A8: 4,7 => UNS
* PRF # A9: 8,9 => SOL
* INC # A9: 2,4,5 => UNS
* DIS # E5: 2,9 => CTR => E5: 4
* PRF # E5: 4 => SOL
* DIS # H5: 2,9 => CTR => H5: 8
* INC # H5: 8 => UNS
* PRF # I5: 2,9 => SOL
* INC # I5: 5,8 => UNS
* DIS # F9: 2,9 => CTR => F9: 5,6,8
* INC # F9: 5,6,8 => UNS
* INC # F7: 2,7 => UNS
* DIS # F7: 5 => CTR => F7: 2,7
* PRF # F7: 5,7 => SOL
* DIS # F7: 2 => CTR => F7: 5,7
* DIS # B3: 5,7 => CTR => B3: 1,4,6,8,9
* INC # B3: 1,4,6,8,9 => UNS
* DIS # A9: 2,5 => CTR => A9: 4,8,9
* PRF # A9: 4,8,9 => SOL
* DIS # C9: 2,5 => CTR => C9: 4,6,8,9
* INC # C9: 4,6,8,9 => UNS
* DIS # F7: 2,5 => CTR => F7: 7
* PRF # F7: 7 => SOL
* DIS # C2: 2,5 => CTR => C2: 1,6,8,9
* INC # C2: 1,6,8,9 => UNS
* CNT  46 HDP CHAINS /  46 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A3: 4,7 => CTR => A3: 5,8,9
* PRF A3: 5,8,9 => SOL
* STA A3: 5,8,9
* CNT   2 HDP CHAINS /   1 HYP OPENED