Analysis of xx-top500-333-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ..8..1.......2..3.5.....4....76..5...1..3..............2.....1....5..7..6..4..... initial

Autosolve

position: 2.8..1.......2.13.5.1...4.23.76..521.1.23......21......2.....1.1..5.27..6..41.2.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # E6: 4,5 => CTR => E6: 7,8,9
* DIS # F6: 4,5 => CTR => F6: 7,8,9
* DIS # I2: 6,9 => CTR => I2: 5,7,8
* DIS # B1: 6,9 => CTR => B1: 3,4,7
* DIS # G6: 6,9 => CTR => G6: 3,8
* CNT   5 HDP CHAINS /  15 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 # E6: 4,5 => CTR => E6: 7,8,9
* PRF E6: 7,8,9 # G7: 6,9 => SOL
* STA E6: 7,8,9 + G7: 6,9
* CNT   2 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

..8..1.......2..3.5.....4....76..5...1..3..............2.....1....5..7..6..4..... initial
2.8..1.......2.13.5.1...4.23.76..521.1.23......21......2.....1.1..5.27..6..41.2.. autosolve
248351967769824135531976482397648521416235879852197346925783614184562793673419258 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
E1: 4,5
F2: 4,5
G1: 6,9
C5: 5,6
B6: 5,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B1,B3: 3.. / B1 = 3  =>  0 pairs (X) / B3 = 3  =>  5 pairs (_)
G6,I6: 3.. / G6 = 3  =>  5 pairs (_) / I6 = 3  =>  0 pairs (X)
B1,D1: 3.. / B1 = 3  =>  0 pairs (X) / D1 = 3  =>  5 pairs (_)
C8,I8: 3.. / C8 = 3  =>  6 pairs (_) / I8 = 3  =>  6 pairs (_)
G6,G7: 3.. / G6 = 3  =>  5 pairs (_) / G7 = 3  =>  0 pairs (X)
E1,F2: 4.. / E1 = 4  =>  0 pairs (X) / F2 = 4  => 13 pairs (_)
B1,E1: 4.. / B1 = 4  => 13 pairs (_) / E1 = 4  =>  0 pairs (X)
E1,F2: 5.. / E1 = 5  => 13 pairs (_) / F2 = 5  =>  0 pairs (X)
C5,B6: 5.. / C5 = 5  =>  0 pairs (X) / B6 = 5  => 13 pairs (_)
F2,I2: 5.. / F2 = 5  =>  0 pairs (X) / I2 = 5  => 13 pairs (_)
C5,F5: 5.. / C5 = 5  =>  0 pairs (X) / F5 = 5  => 13 pairs (_)
C7,I7: 5.. / C7 = 5  => 13 pairs (_) / I7 = 5  =>  0 pairs (X)
B6,B9: 5.. / B6 = 5  => 13 pairs (_) / B9 = 5  =>  0 pairs (X)
E1,E6: 5.. / E1 = 5  => 13 pairs (_) / E6 = 5  =>  0 pairs (X)
H1,H9: 5.. / H1 = 5  =>  0 pairs (X) / H9 = 5  => 13 pairs (_)
E3,F3: 6.. / E3 = 6  =>  6 pairs (_) / F3 = 6  =>  5 pairs (_)
C5,B6: 6.. / C5 = 6  => 13 pairs (_) / B6 = 6  =>  0 pairs (X)
C2,C5: 6.. / C2 = 6  =>  0 pairs (X) / C5 = 6  => 13 pairs (_)
F3,F7: 6.. / F3 = 6  =>  5 pairs (_) / F7 = 6  =>  6 pairs (_)
A7,B9: 7.. / A7 = 7  =>  0 pairs (X) / B9 = 7  => 13 pairs (_)
B9,F9: 7.. / B9 = 7  => 13 pairs (_) / F9 = 7  =>  0 pairs (X)
A2,A7: 7.. / A2 = 7  => 13 pairs (_) / A7 = 7  =>  0 pairs (X)
I2,H3: 8.. / I2 = 8  =>  0 pairs (X) / H3 = 8  =>  6 pairs (_)
D2,I2: 8.. / D2 = 8  =>  6 pairs (_) / I2 = 8  =>  0 pairs (X)
* DURATION: 0:00:38.763102  START: 14:09:45.712764  END: 14:10:24.475866 2017-05-04
* CP COUNT: (24)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,C5,E1,F2,G1)
* 2.8..1.......2.13.5.1...4.23.76..521.1.23......21......2.....1.1..5.27..6..41.2..
* PAIR E1: 4,5 COL E
E6: 4,5,7,8,9                            # reduction candidate for 4,5
E6: 4,5 => CTR
* 248351...769824135531...4823.76..521416235....52147....25....141.45.27.367341.25.
E6: 7,8,9                                # 13 pairs
* PAIR F2: 4,5 COL F
F5: 4,5,7,8,9                            # reduction candidate for 4,5
F5: 4,5                                  #  7 pairs
F6: 4,5,7,8,9                            # reduction candidate for 4,5
F6: 4,5 => CTR
* 2.8..1.5...6.2513.5.1...4.23.76..521.1523.....621......2.....151..5.27..65.4172..
F6: 7,8,9                                #  5 pairs
* PAIR G1: 6,9 BLK 3
H1: 6,9,5,7                              # reduction candidate for 6,9
H1: 6,9                                  # 16 pairs
I1: 6,9,5,7                              # reduction candidate for 6,9
I1: 6,9                                  #  9 pairs
I2: 6,9,5,7,8                            # reduction candidate for 6,9
I2: 6,9 => CTR
* 2.8..1......82513.5.1...4823.76..521.1523.....6215.....2.....151..5.27..65.417298
I2: 5,7,8                                #  5 pairs
* PAIR G1: 6,9 ROW 1
B1: 6,9,3,4,7                            # reduction candidate for 6,9
B1: 6,9 => CTR
* 2.8341.......2513.531...4.23.76..521.1523.....6215.....2.....151..5.27..65.4172..
B1: 3,4,7                                #  5 pairs
* PAIR G1: 6,9 COL G
G5: 6,9,8                                # reduction candidate for 6,9
G5: 6,9                                  #  8 pairs
G6: 6,9,3,8                              # reduction candidate for 6,9
G6: 6,9 => CTR
* 2.8.51...7...241355.1...4823.76..521.1623.8...521....3.2....31.1.35.27..67.4132..
G6: 3,8                                  #  6 pairs
G7: 6,9,3,8                              # reduction candidate for 6,9
G7: 6,9                                  #  7 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-333-base-pr-000.dot
* REASONING
* DIS # E6: 4,5 => CTR => E6: 7,8,9
* DIS # F6: 4,5 => CTR => F6: 7,8,9
* DIS # I2: 6,9 => CTR => I2: 5,7,8
* DIS # B1: 6,9 => CTR => B1: 3,4,7
* DIS # G6: 6,9 => CTR => G6: 3,8
* CNT   5 HDP CHAINS /  15 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,C5,E1,F2,G1)
* 2.8..1.......2.13.5.1...4.23.76..521.1.23......21......2.....1.1..5.27..6..41.2..
* PAIR E1: 4,5 COL E
E6: 4,5,7,8,9                            # reduction candidate for 4,5
E6: 4,5 => CTR
* 248351...769824135531...4823.76..521416235....52147....25....141.45.27.367341.25.
* PAIR RESTART
* PAIR G1: 6,9 BLK 3
H1: 6,9,7                                # reduction candidate for 6,9
H1: 6,9                                  # 16 pairs
I1: 6,9,7                                # reduction candidate for 6,9
I1: 6,9                                  # 15 pairs
* PAIR G1: 6,9 COL G
G7: 6,9,8                                # reduction candidate for 6,9
G7: 6,9 => SOLVED
* 248351967769824135531976482397648521416235879852197346925783614184562793673419258
* DURATION: 0:00:07.150971  START: 14:10:37.455215  END: 14:10:44.606186 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-333-base-pr-001.dot
* REASONING
* DIS # E6: 4,5 => CTR => E6: 7,8,9
* PRF E6: 7,8,9 # G7: 6,9 => SOL
* STA E6: 7,8,9 + G7: 6,9
* CNT   2 HDP CHAINS /   4 HYP OPENED

Header Info

Top 500 Minimum 17 333

solution: 248351967769824135531976482397648521416235879852197346925783614184562793673419258
info: 3044     FNBHWXY  S8.f     14526

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

Solution

position: 248351967769824135531976482397648521416235879852197346925783614184562793673419258 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 # E6: 4,5 => CTR => E6: 7,8,9
* INC # E6: 7,8,9 => UNS
* INC # F5: 4,5 => UNS
* DIS # F6: 4,5 => CTR => F6: 7,8,9
* INC # F6: 7,8,9 => UNS
* INC # H1: 6,9 => UNS
* INC # I1: 6,9 => UNS
* DIS # I2: 6,9 => CTR => I2: 5,7,8
* INC # I2: 5,7,8 => UNS
* DIS # B1: 6,9 => CTR => B1: 3,4,7
* INC # B1: 3,4,7 => UNS
* INC # G5: 6,9 => UNS
* DIS # G6: 6,9 => CTR => G6: 3,8
* INC # G6: 3,8 => UNS
* INC # G7: 6,9 => UNS
* CNT  15 HDP CHAINS /  15 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # E6: 4,5 => CTR => E6: 7,8,9
* INC E6: 7,8,9 # H1: 6,9 => UNS
* INC E6: 7,8,9 # I1: 6,9 => UNS
* PRF E6: 7,8,9 # G7: 6,9 => SOL
* STA E6: 7,8,9 + G7: 6,9
* CNT   4 HDP CHAINS /   4 HYP OPENED