Analysis of xx-top500-340-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 17..........8...2..45..........14..53......6.....7.1........4.72..3.............. initial

Autosolve

position: 172.........8...2.845..........14..53......6.....731........4.72..3.............. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # A4: 6,9 => SOL
* DIS # A4: 7 => CTR => A4: 6,9
* DIS # A6: 6,9 => CTR => A6: 4,5
* DIS # A7: 6,9 => CTR => A7: 5
* DIS # A9: 6,9 => CTR => A9: 4,5,7
* DIS # E1: 4,5 => CTR => E1: 3,6,9
* DIS # E9: 4,5 => CTR => E9: 6,8,9
* PRF # F2: 5,7 => SOL
* DIS # F2: 1 => CTR => F2: 5,7
* CNT   9 HDP CHAINS /  18 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 # A4: 6,9 => SOL
* STA A4: 6,9
* CNT   1 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

17..........8...2..45..........14..53......6.....7.1........4.72..3.............. initial
172.........8...2.845..........14..53......6.....731........4.72..3.............. autosolve
172936548693845721845721693928614375317598264456273189569182437284357916731469852 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (4)
A2: 6,9
E2: 4,5
G2: 5,7
I2: 1,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B5,C5: 1.. / B5 = 1  =>  4 pairs (_) / C5 = 1  =>  0 pairs (X)
F2,I2: 1.. / F2 = 1  =>  0 pairs (X) / I2 = 1  =>  0 pairs (_)
G9,I9: 2.. / G9 = 2  =>  5 pairs (_) / I9 = 2  =>  7 pairs (_)
B2,C2: 3.. / B2 = 3  =>  5 pairs (_) / C2 = 3  =>  5 pairs (_)
E1,E3: 3.. / E1 = 3  =>  4 pairs (_) / E3 = 3  =>  5 pairs (_)
G4,H4: 3.. / G4 = 3  =>  4 pairs (_) / H4 = 3  =>  0 pairs (X)
E2,I2: 4.. / E2 = 4  =>  0 pairs (*) / I2 = 4  =>  0 pairs (X)
C5,I5: 4.. / C5 = 4  =>  0 pairs (X) / I5 = 4  =>  0 pairs (_)
C8,E8: 4.. / C8 = 4  =>  0 pairs (*) / E8 = 4  =>  0 pairs (X)
A6,A9: 4.. / A6 = 4  =>  0 pairs (*) / A9 = 4  =>  0 pairs (X)
D1,D9: 4.. / D1 = 4  =>  0 pairs (X) / D9 = 4  =>  0 pairs (_)
H1,H6: 4.. / H1 = 4  =>  0 pairs (*) / H6 = 4  =>  0 pairs (X)
D4,D6: 6.. / D4 = 6  =>  5 pairs (_) / D6 = 6  =>  5 pairs (_)
F2,G2: 7.. / F2 = 7  =>  0 pairs (X) / G2 = 7  =>  0 pairs (_)
C5,G5: 7.. / C5 = 7  =>  0 pairs (*) / G5 = 7  =>  0 pairs (X)
C8,F8: 7.. / C8 = 7  =>  0 pairs (X) / F8 = 7  =>  0 pairs (_)
A4,A9: 7.. / A4 = 7  =>  0 pairs (X) / A9 = 7  =>  0 pairs (_)
D3,D9: 7.. / D3 = 7  =>  0 pairs (*) / D9 = 7  =>  0 pairs (X)
H3,H4: 7.. / H3 = 7  =>  0 pairs (X) / H4 = 7  =>  0 pairs (_)
E5,F5: 8.. / E5 = 8  =>  4 pairs (_) / F5 = 8  =>  4 pairs (_)
* DURATION: 0:00:30.082804  START: 14:22:17.873904  END: 14:22:47.956708 2017-05-04
* CP COUNT: (20)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,E2,G2,I2)
* 172.........8...2.845..........14..53......6.....731........4.72..3..............
* PAIR A2: 6,9 BLK 1
B2: 6,9,3                                # reduction candidate for 6,9
B2: 6,9                                  #  5 pairs
C2: 6,9,3                                # reduction candidate for 6,9
C2: 6,9                                  #  5 pairs
* PAIR A2: 6,9 COL A
A4: 6,9,7                                # reduction candidate for 6,9
A4: 6,9 => SOLVED
* 172936548693845721845721693928614375317598264456273189569182437284357916731469852
A4: 7 => CTR
* 172.........8.7521845....7.7...14..53.....76.....731........4.72.734.............
A6: 6,9,4,5                              # reduction candidate for 6,9
A6: 6,9 => CTR
* 1724........85.724845......7...14..53......6.....731........4.72..3.....4........
A6: 4,5                                  #  5 pairs
A7: 6,9,5                                # reduction candidate for 6,9
A7: 6,9 => CTR
* 172.........8.7521845....7.7...14..53.....76.....731........4.72.734.............
A7: 5                                    #  4 pairs
A9: 6,9,4,5,7                            # reduction candidate for 6,9
A9: 6,9 => CTR
* 172....4....847521845....7.7...14..53.....7644...731..5.....4.72..3..............
A9: 4,5,7                                #  4 pairs
* PAIR E2: 4,5 BLK 2
D1: 4,5,9                                # reduction candidate for 4,5
D1: 4,5                                  #  7 pairs
E1: 4,5,3,6,9                            # reduction candidate for 4,5
E1: 4,5 => CTR
* 1729.6......8.1724845732.......14.753.7....6.4...731.....12.4.72.43.7...7.14.....
E1: 3,6,9                                #  4 pairs
* PAIR E2: 4,5 COL E
E8: 4,5,6,8,9                            # reduction candidate for 4,5
E8: 4,5                                  #  5 pairs
E9: 4,5,6,8,9                            # reduction candidate for 4,5
E9: 4,5 => CTR
* 172....4....8457218457.1.......143753175...6445..731..5.....4.72.43.7.1.7..45....
E9: 6,8,9                                #  4 pairs
* PAIR G2: 5,7 ROW 2
F2: 5,7,1                                # reduction candidate for 5,7
F2: 5,7 => SOLVED
* 172936548693845721845721693928614375317598264456273189569182437284357916731469852
F2: 1 => CTR
* 172.........8.1724845..........14.753......6.....731........4.72..3..............
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-340-base-pr-000.dot
* REASONING
* PRF # A4: 6,9 => SOL
* DIS # A4: 7 => CTR => A4: 6,9
* DIS # A6: 6,9 => CTR => A6: 4,5
* DIS # A7: 6,9 => CTR => A7: 5
* DIS # A9: 6,9 => CTR => A9: 4,5,7
* DIS # E1: 4,5 => CTR => E1: 3,6,9
* DIS # E9: 4,5 => CTR => E9: 6,8,9
* PRF # F2: 5,7 => SOL
* DIS # F2: 1 => CTR => F2: 5,7
* CNT   9 HDP CHAINS /  18 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,E2,G2,I2)
* 172.........8...2.845..........14..53......6.....731........4.72..3..............
* PAIR A2: 6,9 BLK 1
B2: 6,9,3                                # reduction candidate for 6,9
B2: 6,9                                  #  5 pairs
C2: 6,9,3                                # reduction candidate for 6,9
C2: 6,9                                  #  5 pairs
* PAIR A2: 6,9 COL A
A4: 6,9,7                                # reduction candidate for 6,9
A4: 6,9 => SOLVED
* 172936548693845721845721693928614375317598264456273189569182437284357916731469852
* DURATION: 0:00:03.866397  START: 14:23:01.873215  END: 14:23:05.739612 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-340-base-pr-001.dot
* REASONING
* PRF # A4: 6,9 => SOL
* STA A4: 6,9
* CNT   1 HDP CHAINS /   3 HYP OPENED

Header Info

Top 500 Minimum 17 340

solution: 172936548693845721845721693928614375317598264456273189569182437284357916731469852
info: 3225     FNBHWXY  S8.f     26568

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

Solution

position: 172936548693845721845721693928614375317598264456273189569182437284357916731469852 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 # B2: 6,9 => UNS
* INC # C2: 6,9 => UNS
* PRF # A4: 6,9 => SOL
* DIS # A4: 7 => CTR => A4: 6,9
* DIS # A6: 6,9 => CTR => A6: 4,5
* INC # A6: 4,5 => UNS
* DIS # A7: 6,9 => CTR => A7: 5
* INC # A7: 5 => UNS
* DIS # A9: 6,9 => CTR => A9: 4,5,7
* INC # A9: 4,5,7 => UNS
* INC # D1: 4,5 => UNS
* DIS # E1: 4,5 => CTR => E1: 3,6,9
* INC # E1: 3,6,9 => UNS
* INC # E8: 4,5 => UNS
* DIS # E9: 4,5 => CTR => E9: 6,8,9
* INC # E9: 6,8,9 => UNS
* PRF # F2: 5,7 => SOL
* DIS # F2: 1 => CTR => F2: 5,7
* CNT  18 HDP CHAINS /  18 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B2: 6,9 => UNS
* INC # C2: 6,9 => UNS
* PRF # A4: 6,9 => SOL
* STA A4: 6,9
* CNT   3 HDP CHAINS /   3 HYP OPENED