Analysis of xx-top500-221-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ....7..2...3...5..6........17.....4..4.8........3.....5.....8.3...24.........6... initial

Autosolve

position: 45..73.2...3...5..6......3.17....34.34.8.7....6.3.4...524791863.36248......536... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D2: 6,9 => CTR => D2: 1,4
* DIS # A9: 7,9 => CTR => A9: 8
* DIS # A9: 7,9 => CTR => A9: 8
* DIS # H6: 7,9 => CTR => H6: 1,5,8
* CNT   4 HDP CHAINS /  22 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 # D2: 6,9 => CTR => D2: 1,4
* DIS D2: 1,4 # D1: 1 => CTR => D1: 6,9
* DIS D2: 1,4 + D1: 6,9 # A9: 7,9 => CTR => A9: 8
* DIS D2: 1,4 + D1: 6,9 + A9: 8 # C9: 1 => CTR => C9: 7,9
* DIS D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 # H2: 7,9 => CTR => H2: 1
* DIS D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 + H2: 1 # H8: 5 => CTR => H8: 7,9
* PRF D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 + H2: 1 + H8: 7,9 # F3: 2,9 => SOL
* STA D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 + H2: 1 + H8: 7,9 + F3: 2,9
* CNT   7 HDP CHAINS /  22 HYP OPENED

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

Details

Positions

....7..2...3...5..6........17.....4..4.8........3.....5.....8.3...24.........6... initial
45..73.2...3...5..6......3.17....34.34.8.7....6.3.4...524791863.36248......536... autosolve
451673928793482516682159437178965342349827651265314789524791863936248175817536294 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
A2: 2,7
C3: 2,7
F2: 2,9
D4: 6,9
A8: 7,9
G9: 2,4
H9: 7,9
I9: 2,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E5,E6: 1.. / E5 = 1  => 10 pairs (_) / E6 = 1  =>  8 pairs (_)
B9,C9: 1.. / B9 = 1  => 16 pairs (_) / C9 = 1  =>  0 pairs (X)
C1,C9: 1.. / C1 = 1  => 16 pairs (_) / C9 = 1  =>  0 pairs (X)
A2,C3: 2.. / A2 = 2  =>  0 pairs (X) / C3 = 2  => 18 pairs (_)
G9,I9: 2.. / G9 = 2  =>  7 pairs (_) / I9 = 2  =>  6 pairs (_)
A2,A6: 2.. / A2 = 2  =>  0 pairs (X) / A6 = 2  => 18 pairs (_)
D2,D3: 4.. / D2 = 4  =>  9 pairs (_) / D3 = 4  =>  7 pairs (_)
G9,I9: 4.. / G9 = 4  =>  6 pairs (_) / I9 = 4  =>  7 pairs (_)
D2,I2: 4.. / D2 = 4  =>  9 pairs (_) / I2 = 4  =>  7 pairs (_)
G3,G9: 4.. / G3 = 4  =>  7 pairs (_) / G9 = 4  =>  6 pairs (_)
E3,F3: 5.. / E3 = 5  => 19 pairs (_) / F3 = 5  => 10 pairs (_)
H8,I8: 5.. / H8 = 5  =>  9 pairs (_) / I8 = 5  =>  8 pairs (_)
F3,F4: 5.. / F3 = 5  => 10 pairs (_) / F4 = 5  => 19 pairs (_)
G1,G5: 6.. / G1 = 6  =>  9 pairs (_) / G5 = 6  =>  9 pairs (_)
A2,C3: 7.. / A2 = 7  => 18 pairs (_) / C3 = 7  =>  0 pairs (X)
C3,C9: 7.. / C3 = 7  =>  0 pairs (X) / C9 = 7  => 18 pairs (_)
E2,E3: 8.. / E2 = 8  => 17 pairs (_) / E3 = 8  => 16 pairs (_)
C1,I1: 8.. / C1 = 8  =>  0 pairs (X) / I1 = 8  => 11 pairs (_)
C4,I4: 8.. / C4 = 8  => 11 pairs (_) / I4 = 8  =>  0 pairs (X)
A6,A9: 8.. / A6 = 8  =>  0 pairs (X) / A9 = 8  => 11 pairs (_)
H2,H6: 8.. / H2 = 8  =>  0 pairs (X) / H6 = 8  => 11 pairs (_)
D4,F4: 9.. / D4 = 9  => 13 pairs (_) / F4 = 9  =>  0 pairs (X)
* DURATION: 0:00:37.502342  START: 10:20:32.575954  END: 10:21:10.078296 2017-05-04
* CP COUNT: (22)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,C3,D4,F2,G9,H9,I9)
* 45..73.2...3...5..6......3.17....34.34.8.7....6.3.4...524791863.36248......536...
* PAIR F2: 2,9 BLK 2
F3: 2,9,5                                # reduction candidate for 2,9
F3: 2,9                                  # 19 pairs
F3: 5                                    # 10 pairs
* PAIR F2: 2,9 COL F
F4: 2,9,5                                # reduction candidate for 2,9
F4: 5                                    # 19 pairs
F4: 2,9                                  # 10 pairs
* PAIR D4: 6,9 COL D
D1: 6,9,1                                # reduction candidate for 6,9
D1: 6,9                                  # 11 pairs
D2: 6,9,1,4                              # reduction candidate for 6,9
D2: 6,9 => CTR
* 45.173.2.2.3..95746.74...3.17.9..34.34.8.7....6.3.4.8.524791863.36248.....15364.2
D2: 1,4                                  #  9 pairs
* PAIR A8: 7,9 BLK 7
A9: 7,9,8                                # reduction candidate for 7,9
A9: 7,9 => CTR
* 45..73.2.2.3..95876.7.8..3.17....34.34.8.7...86.3.4...524791863.36248......536...
A9: 8                                    # 11 pairs
C9: 7,9,1,8                              # reduction candidate for 7,9
C9: 7,9                                  # 16 pairs
* PAIR A8: 7,9 ROW 8
G8: 7,9,1                                # reduction candidate for 7,9
G8: 7,9                                  # 11 pairs
H8: 7,9,1,5                              # reduction candidate for 7,9
H8: 7,9                                  # 12 pairs
I8: 7,9,1,5                              # reduction candidate for 7,9
I8: 7,9                                  # 11 pairs
* PAIR H9: 7,9 BLK 9
G8: 7,9,1                                # reduction candidate for 7,9
G8: 7,9                                  # 11 pairs
H8: 7,9,1,5                              # reduction candidate for 7,9
H8: 7,9                                  # 12 pairs
I8: 7,9,1,5                              # reduction candidate for 7,9
I8: 7,9                                  # 11 pairs
* PAIR H9: 7,9 ROW 9
A9: 7,9,8                                # reduction candidate for 7,9
A9: 7,9 => CTR
* 45..73.2.2.3..95876.7.8..3.17....34.34.8.7...86.3.4...524791863.36248......536...
A9: 8                                    # 11 pairs
C9: 7,9,1,8                              # reduction candidate for 7,9
C9: 7,9                                  # 16 pairs
* PAIR H9: 7,9 COL H
H2: 7,9,1,8                              # reduction candidate for 7,9
H2: 7,9                                  # 16 pairs
H6: 7,9,1,5,8                            # reduction candidate for 7,9
H6: 7,9 => CTR
* 45..73.2...3...58.6...85.3.17....34.34.8.7....6.3.4...524791863.36248....81536...
H6: 1,5,8                                #  8 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-221-base-pr-000.dot
* REASONING
* DIS # D2: 6,9 => CTR => D2: 1,4
* DIS # A9: 7,9 => CTR => A9: 8
* DIS # A9: 7,9 => CTR => A9: 8
* DIS # H6: 7,9 => CTR => H6: 1,5,8
* CNT   4 HDP CHAINS /  22 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,C3,D4,F2,G9,H9,I9)
* 45..73.2...3...5..6......3.17....34.34.8.7....6.3.4...524791863.36248......536...
* PAIR F2: 2,9 BLK 2
F3: 2,9,5                                # reduction candidate for 2,9
F3: 2,9                                  # 19 pairs
F3: 5                                    # 10 pairs
* PAIR F2: 2,9 COL F
F4: 2,9,5                                # reduction candidate for 2,9
F4: 5                                    # 19 pairs
F4: 2,9                                  # 10 pairs
* PAIR D4: 6,9 COL D
D1: 6,9,1                                # reduction candidate for 6,9
D1: 6,9                                  # 11 pairs
D2: 6,9,1,4                              # reduction candidate for 6,9
D2: 6,9 => CTR
* 45.173.2.2.3..95746.74...3.17.9..34.34.8.7....6.3.4.8.524791863.36248.....15364.2
* RESTART
* PAIR D4: 6,9 COL D
D1: 6,9,1                                # reduction candidate for 6,9
D1: 1 => CTR
* 45.173.2...346.5..6..985.3.17.6.934.34.8.7....6.3.4...524791863.36248.....1536...
* PAIR RESTART
* PAIR A8: 7,9 BLK 7
A9: 7,9,8                                # reduction candidate for 7,9
A9: 7,9 => CTR
* 45..73.2.2.3..95876.7.8..3.17....34.34.8.7...86.3.4...524791863.36248......536...
C9: 7,9,1                                # reduction candidate for 7,9
C9: 7,9                                  # 16 pairs
* RESTART
* PAIR A8: 7,9 BLK 7
C9: 7,9,1                                # reduction candidate for 7,9
C9: 1 => CTR
* 459673128..3...5..6.7....3.178...34.34.8.7....6.3.4.8.524791863736248...891536.7.
* PAIR A8: 7,9 ROW 8
G8: 7,9,1                                # reduction candidate for 7,9
G8: 7,9                                  # 19 pairs
H8: 7,9,1,5                              # reduction candidate for 7,9
H8: 7,9                                  # 18 pairs
I8: 7,9,1,5                              # reduction candidate for 7,9
I8: 7,9                                  # 18 pairs
* PAIR H9: 7,9 BLK 9
G8: 7,9,1                                # reduction candidate for 7,9
G8: 7,9                                  # 19 pairs
H8: 7,9,1,5                              # reduction candidate for 7,9
H8: 7,9                                  # 18 pairs
I8: 7,9,1,5                              # reduction candidate for 7,9
I8: 7,9                                  # 18 pairs
* PAIR H9: 7,9 COL H
H2: 7,9,1                                # reduction candidate for 7,9
H2: 7,9 => CTR
* 451973628.83.6259.692.85.3.1786.934.34.8.7..626.3.4.8.524791863936248...81.536...
* PAIR RESTART
* PAIR H9: 7,9 BLK 9
H8: 7,9,5                                # reduction candidate for 7,9
H8: 5 => CTR
* 451.73.282.34.951769718..3.178...34.34.8.7....6.3.4.8.524791863736248.5.819536.7.

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A2,A6,A8,B2,B3,C3,C5,C9,D1,D4,E6,F2,G1,G9,H8,H9,I4,I9)
* 451.73.28..34..51.6..1...3.178...34.34.8.7.5..653.4.8.524791863.362481.581.536...
* PAIR F2: 2,9 BLK 2
F3: 2,9,5                                # reduction candidate for 2,9
F3: 2,9 => SOLVED
* 451673928793482516682159437178965342349827651265314789524791863936248175817536294
* DURATION: 0:00:24.629928  START: 10:21:29.885178  END: 10:21:54.515106 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-221-base-pr-001.dot
* REASONING
* DIS # D2: 6,9 => CTR => D2: 1,4
* DIS D2: 1,4 # D1: 1 => CTR => D1: 6,9
* DIS D2: 1,4 + D1: 6,9 # A9: 7,9 => CTR => A9: 8
* DIS D2: 1,4 + D1: 6,9 + A9: 8 # C9: 1 => CTR => C9: 7,9
* DIS D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 # H2: 7,9 => CTR => H2: 1
* DIS D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 + H2: 1 # H8: 5 => CTR => H8: 7,9
* PRF D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 + H2: 1 + H8: 7,9 # F3: 2,9 => SOL
* STA D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 + H2: 1 + H8: 7,9 + F3: 2,9
* CNT   7 HDP CHAINS /  22 HYP OPENED

Header Info

Top 500 Minimum 17 221

solution: 451673928793482516682159437178965342349827651265314789524791863936248175817536294
info: 1962     FNBTHWXY S8.f     5607

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

Solution

position: 451673928793482516682159437178965342349827651265314789524791863936248175817536294 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 # F3: 2,9 => UNS
* INC # F3: 5 => UNS
* INC # F4: 2,9 => UNS
* INC # F4: 5 => UNS
* INC # D1: 6,9 => UNS
* DIS # D2: 6,9 => CTR => D2: 1,4
* INC # D2: 1,4 => UNS
* DIS # A9: 7,9 => CTR => A9: 8
* INC # A9: 8 => UNS
* INC # C9: 7,9 => UNS
* INC # G8: 7,9 => UNS
* INC # H8: 7,9 => UNS
* INC # I8: 7,9 => UNS
* INC # G8: 7,9 => UNS
* INC # H8: 7,9 => UNS
* INC # I8: 7,9 => UNS
* DIS # A9: 7,9 => CTR => A9: 8
* INC # A9: 8 => UNS
* INC # C9: 7,9 => UNS
* INC # H2: 7,9 => UNS
* DIS # H6: 7,9 => CTR => H6: 1,5,8
* INC # H6: 1,5,8 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F3: 2,9 => UNS
* INC # F3: 5 => UNS
* INC # F4: 2,9 => UNS
* INC # F4: 5 => UNS
* INC # D1: 6,9 => UNS
* DIS # D2: 6,9 => CTR => D2: 1,4
* INC D2: 1,4 # D1: 6,9 => UNS
* DIS D2: 1,4 # D1: 1 => CTR => D1: 6,9
* DIS D2: 1,4 + D1: 6,9 # A9: 7,9 => CTR => A9: 8
* INC D2: 1,4 + D1: 6,9 + A9: 8 # C9: 7,9 => UNS
* INC D2: 1,4 + D1: 6,9 + A9: 8 # C9: 7,9 => UNS
* DIS D2: 1,4 + D1: 6,9 + A9: 8 # C9: 1 => CTR => C9: 7,9
* INC D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 # G8: 7,9 => UNS
* INC D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 # H8: 7,9 => UNS
* INC D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 # I8: 7,9 => UNS
* INC D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 # G8: 7,9 => UNS
* INC D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 # H8: 7,9 => UNS
* INC D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 # I8: 7,9 => UNS
* DIS D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 # H2: 7,9 => CTR => H2: 1
* INC D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 + H2: 1 # H8: 7,9 => UNS
* DIS D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 + H2: 1 # H8: 5 => CTR => H8: 7,9
* PRF D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 + H2: 1 + H8: 7,9 # F3: 2,9 => SOL
* STA D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 + H2: 1 + H8: 7,9 + F3: 2,9
* CNT  22 HDP CHAINS /  22 HYP OPENED