Analysis of xx-top500-052-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 53.9...........6.1.........2.1...7..6...35..........9..8.4...7.....6.....5....... initial

Autosolve

position: 534916287829...6.1167.....92416..7..698735412375...8969864...7..13.6..2..52....6. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D3: 3,5 => CTR => D3: 2,8
* DIS # D3: 3,5 => CTR => D3: 2,8
* PRF # G7: 3,5 => SOL
* DIS # E9: 7 => CTR => E9: 8,9
* DIS # F9: 8,9 => CTR => F9: 1,3,7
* DIS # F6: 4 => CTR => F6: 1,2
* DIS # E3: 2,4 => CTR => E3: 5,8
* PRF # G7: 3,5 => SOL
* CNT   8 HDP CHAINS /  29 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 # D3: 3,5 => CTR => D3: 2,8
* PRF D3: 2,8 # G7: 3,5 => SOL
* STA D3: 2,8 + G7: 3,5
* CNT   2 HDP CHAINS /   6 HYP OPENED

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

Details

Positions

53.9...........6.1.........2.1...7..6...35..........9..8.4...7.....6.....5....... initial
534916287829...6.1167.....92416..7..698735412375...8969864...7..13.6..2..52....6. autosolve
534916287829374651167258349241689735698735412375142896986421573413567928752893164 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (16)
D2: 3,5
G3: 3,5
E4: 8,9
F4: 8,9
D6: 1,2
E6: 2,4
H4: 3,5
I4: 3,5
A8: 4,7
A9: 4,7
E7: 2,5
D8: 5,8
I7: 3,5
G8: 5,9
I8: 4,8
I9: 4,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D6,F6: 1.. / D6 = 1  => 20 pairs (_) / F6 = 1  => 18 pairs (_)
G7,G9: 1.. / G7 = 1  => 18 pairs (_) / G9 = 1  =>  0 pairs (*)
F7,G7: 1.. / F7 = 1  =>  0 pairs (*) / G7 = 1  =>  0 pairs (X)
D6,D9: 1.. / D6 = 1  => 20 pairs (_) / D9 = 1  => 18 pairs (_)
E7,F7: 2.. / E7 = 2  => 21 pairs (_) / F7 = 2  =>  0 pairs (X)
D3,D6: 2.. / D3 = 2  => 20 pairs (_) / D6 = 2  => 18 pairs (_)
H4,I4: 3.. / H4 = 3  => 17 pairs (_) / I4 = 3  =>  0 pairs (X)
I4,I7: 3.. / I4 = 3  =>  0 pairs (X) / I7 = 3  => 17 pairs (_)
H2,H3: 4.. / H2 = 4  => 20 pairs (_) / H3 = 4  => 19 pairs (_)
E6,F6: 4.. / E6 = 4  => 17 pairs (_) / F6 = 4  =>  0 pairs (X)
A8,A9: 4.. / A8 = 4  =>  0 pairs (*) / A9 = 4  =>  0 pairs (X)
I8,I9: 4.. / I8 = 4  => 15 pairs (_) / I9 = 4  =>  0 pairs (*)
A8,I8: 4.. / A8 = 4  =>  0 pairs (*) / I8 = 4  =>  0 pairs (X)
A9,I9: 4.. / A9 = 4  => 15 pairs (_) / I9 = 4  =>  0 pairs (*)
H4,I4: 5.. / H4 = 5  =>  0 pairs (X) / I4 = 5  => 17 pairs (_)
E7,D8: 5.. / E7 = 5  =>  0 pairs (X) / D8 = 5  => 21 pairs (_)
D8,G8: 5.. / D8 = 5  => 21 pairs (_) / G8 = 5  =>  0 pairs (X)
I4,I7: 5.. / I4 = 5  => 17 pairs (_) / I7 = 5  =>  0 pairs (X)
E2,F2: 7.. / E2 = 7  => 18 pairs (_) / F2 = 7  =>  0 pairs (X)
A8,A9: 7.. / A8 = 7  => 15 pairs (_) / A9 = 7  =>  0 pairs (*)
A8,F8: 7.. / A8 = 7  => 15 pairs (_) / F8 = 7  =>  0 pairs (*)
E2,E9: 7.. / E2 = 7  => 18 pairs (_) / E9 = 7  =>  0 pairs (X)
E4,F4: 8.. / E4 = 8  =>  0 pairs (*) / F4 = 8  =>  0 pairs (X)
I8,I9: 8.. / I8 = 8  =>  0 pairs (*) / I9 = 8  =>  0 pairs (X)
E4,F4: 9.. / E4 = 9  => 16 pairs (_) / F4 = 9  =>  0 pairs (*)
G8,G9: 9.. / G8 = 9  => 21 pairs (_) / G9 = 9  =>  0 pairs (X)
F8,G8: 9.. / F8 = 9  =>  0 pairs (X) / G8 = 9  => 21 pairs (_)
E4,E9: 9.. / E4 = 9  => 16 pairs (_) / E9 = 9  =>  0 pairs (*)
* DURATION: 0:01:06.968284  START: 04:25:59.836349  END: 04:27:06.804633 2017-05-04
* CP COUNT: (28)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,D2,D6,D8,E4,E6,E7,F4,G3,G8,H4,I4,I7,I8,I9)
* 534916287829...6.1167.....92416..7..698735412375...8969864...7..13.6..2..52....6.
* PAIR D2: 3,5 BLK 2
D3: 3,5,2,8                              # reduction candidate for 3,5
D3: 3,5 => CTR
* 534916287829...6.1167...3.924169873569873541237524189698645217371386952445217.968
D3: 2,8                                  # 17 pairs
* PAIR D2: 3,5 ROW 2
H2: 3,5,4                                # reduction candidate for 3,5
H2: 4                                    # 20 pairs
H2: 3,5                                  # 19 pairs
* PAIR G3: 3,5 BLK 3
H2: 3,5,4                                # reduction candidate for 3,5
H2: 3,5                                  # 19 pairs
H3: 3,5,4                                # reduction candidate for 3,5
H3: 3,5                                  # 20 pairs
* PAIR G3: 3,5 ROW 3
D3: 3,5,2,8                              # reduction candidate for 3,5
D3: 3,5 => CTR
* 534916287829...6.1167...3.924169873569873541237524189698645217371386952445217.968
D3: 2,8                                  # 17 pairs
* PAIR G3: 3,5 COL G
G7: 3,5,1                                # reduction candidate for 3,5
G7: 3,5 => SOLVED
* 534916287829374651167258349241689735698735412375142896986421573413567928752893164
G7: 1                                    # 18 pairs
* PAIR E4: 8,9 COL E
E9: 8,9,7                                # reduction candidate for 8,9
E9: 7 => CTR
* 534916287829..76.1167.8.3.9241698735698735412375...896986452173713869524452.73968
E9: 8,9                                  # 18 pairs
* PAIR F4: 8,9 COL F
F8: 8,9,7                                # reduction candidate for 8,9
F8: 8,9                                  # 15 pairs
F9: 8,9,1,3,7                            # reduction candidate for 8,9
F9: 8,9 => CTR
* 534916287829...6.11678....92416..7..698735412375241896986423175.135679287521..364
F9: 1,3,7                                # 16 pairs
* PAIR D6: 1,2 BLK 5
F6: 1,2,4                                # reduction candidate for 1,2
F6: 4 => CTR
* 5349162878295..6.11672..3592416987..698735412375124896986452173.1386.5244523.1968
F6: 1,2                                  # 17 pairs
* PAIR E6: 2,4 BLK 5
F6: 2,4,1                                # reduction candidate for 2,4
F6: 2,4                                  # 20 pairs
F6: 1                                    # 18 pairs
* PAIR E6: 2,4 COL E
E3: 2,4,5,8                              # reduction candidate for 2,4
E3: 2,4 => CTR
* 534916287829.7.6.1167.....92416..7..698735412375...896986452173.1386.524452.9..6.
E3: 5,8                                  # 17 pairs
* PAIR H4: 3,5 COL H
H2: 3,5,4                                # reduction candidate for 3,5
H2: 3,5                                  # 19 pairs
H3: 3,5,4                                # reduction candidate for 3,5
H3: 3,5                                  # 20 pairs
* PAIR E7: 2,5 COL E
E3: 2,5,4,8                              # reduction candidate for 2,5
E3: 2,5                                  # 19 pairs
E3: 4,8                                  # 17 pairs
* PAIR D8: 5,8 COL D
D3: 5,8,2,3                              # reduction candidate for 5,8
D3: 2,3                                  # 20 pairs
D3: 5,8                                  # 19 pairs
* PAIR I7: 3,5 BLK 9
G7: 3,5,1                                # reduction candidate for 3,5
G7: 3,5 => SOLVED
* 534916287829374651167258349241689735698735412375142896986421573413567928752893164
G7: 1                                    # 18 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-052-base-pr-000.dot
* REASONING
* DIS # D3: 3,5 => CTR => D3: 2,8
* DIS # D3: 3,5 => CTR => D3: 2,8
* PRF # G7: 3,5 => SOL
* DIS # E9: 7 => CTR => E9: 8,9
* DIS # F9: 8,9 => CTR => F9: 1,3,7
* DIS # F6: 4 => CTR => F6: 1,2
* DIS # E3: 2,4 => CTR => E3: 5,8
* PRF # G7: 3,5 => SOL
* CNT   8 HDP CHAINS /  29 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,D2,D6,D8,E4,E6,E7,F4,G3,G8,H4,I4,I7,I8,I9)
* 534916287829...6.1167.....92416..7..698735412375...8969864...7..13.6..2..52....6.
* PAIR D2: 3,5 BLK 2
D3: 3,5,2,8                              # reduction candidate for 3,5
D3: 3,5 => CTR
* 534916287829...6.1167...3.924169873569873541237524189698645217371386952445217.968
* PAIR D2: 3,5 ROW 2
H2: 3,5,4                                # reduction candidate for 3,5
H2: 4                                    # 20 pairs
H2: 3,5                                  # 20 pairs
* PAIR G3: 3,5 BLK 3
H2: 3,5,4                                # reduction candidate for 3,5
H2: 3,5                                  # 20 pairs
H3: 3,5,4                                # reduction candidate for 3,5
H3: 3,5                                  # 20 pairs
* PAIR G3: 3,5 COL G
G7: 3,5,1                                # reduction candidate for 3,5
G7: 3,5 => SOLVED
* 534916287829374651167258349241689735698735412375142896986421573413567928752893164
* DURATION: 0:00:09.997755  START: 04:27:44.634695  END: 04:27:54.632450 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-052-base-pr-001.dot
* REASONING
* DIS # D3: 3,5 => CTR => D3: 2,8
* PRF D3: 2,8 # G7: 3,5 => SOL
* STA D3: 2,8 + G7: 3,5
* CNT   2 HDP CHAINS /   6 HYP OPENED

Header Info

Top 500 Minimum 17 052

solution: 534916287829374651167258349241689735698735412375142896986421573413567928752893164
info: 1396     FNBTHY   S8.f     43019

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

Solution

position: 534916287829374651167258349241689735698735412375142896986421573413567928752893164 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 # D3: 3,5 => CTR => D3: 2,8
* INC # D3: 2,8 => UNS
* INC # H2: 3,5 => UNS
* INC # H2: 4 => UNS
* INC # H2: 3,5 => UNS
* INC # H3: 3,5 => UNS
* DIS # D3: 3,5 => CTR => D3: 2,8
* INC # D3: 2,8 => UNS
* PRF # G7: 3,5 => SOL
* INC # G7: 1 => UNS
* INC # E9: 8,9 => UNS
* DIS # E9: 7 => CTR => E9: 8,9
* INC # F8: 8,9 => UNS
* DIS # F9: 8,9 => CTR => F9: 1,3,7
* INC # F9: 1,3,7 => UNS
* INC # F6: 1,2 => UNS
* DIS # F6: 4 => CTR => F6: 1,2
* INC # F6: 2,4 => UNS
* INC # F6: 1 => UNS
* DIS # E3: 2,4 => CTR => E3: 5,8
* INC # E3: 5,8 => UNS
* INC # H2: 3,5 => UNS
* INC # H3: 3,5 => UNS
* INC # E3: 2,5 => UNS
* INC # E3: 4,8 => UNS
* INC # D3: 5,8 => UNS
* INC # D3: 2,3 => UNS
* PRF # G7: 3,5 => SOL
* INC # G7: 1 => UNS
* CNT  29 HDP CHAINS /  29 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # D3: 3,5 => CTR => D3: 2,8
* INC D3: 2,8 # H2: 3,5 => UNS
* INC D3: 2,8 # H2: 4 => UNS
* INC D3: 2,8 # H2: 3,5 => UNS
* INC D3: 2,8 # H3: 3,5 => UNS
* PRF D3: 2,8 # G7: 3,5 => SOL
* STA D3: 2,8 + G7: 3,5
* CNT   6 HDP CHAINS /   6 HYP OPENED