Analysis of xx-top500-096-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 75.....2...86..........1....4..2........5.9........8.66.98............5.3........ initial

Autosolve

position: 75.....2...86.2.9....5.1....4..2........5.9.25.....8.66.98.5..........5.3.5...... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A8: 1,4 => CTR => A8: 2,8
* DIS # B5: 1,3 => CTR => B5: 6,7,8
* DIS # B6: 1,3 => CTR => B6: 2,7,9
* DIS # B5: 1,8 => CTR => B5: 3,6,7
* DIS # A8: 1,8 => CTR => A8: 2,4
* DIS # B5: 1,3,7 => CTR => B5: 6,8
* CNT   6 HDP CHAINS /  21 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 # A8: 1,4 => CTR => A8: 2,8
* DIS A8: 2,8 # B3: 6 => CTR => B3: 2,9
* DIS A8: 2,8 + B3: 2,9 # I3: 3,4 => CTR => I3: 7
* PRF A8: 2,8 + B3: 2,9 + I3: 7 # E6: 3,4 => SOL
* STA A8: 2,8 + B3: 2,9 + I3: 7 + E6: 3,4
* CNT   4 HDP CHAINS /  10 HYP OPENED

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

Details

Positions

75.....2...86..........1....4..2........5.9........8.66.98............5.3........ initial
75.....2...86.2.9....5.1....4..2........5.9.25.....8.66.98.5..........5.3.5...... autosolve
751489623438672591926531487847926315163758942592143876679815234284367159315294768 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
A2: 1,4
B2: 1,3
H3: 6,8
A5: 1,8
F4: 6,8
F5: 6,8
H9: 6,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B6,C6: 2.. / B6 = 2  =>  0 pairs (X) / C6 = 2  => 11 pairs (_)
D8,D9: 2.. / D8 = 2  =>  0 pairs (X) / D9 = 2  =>  7 pairs (_)
B7,G7: 2.. / B7 = 2  =>  0 pairs (X) / G7 = 2  =>  8 pairs (_)
A3,A8: 2.. / A3 = 2  =>  0 pairs (X) / A8 = 2  => 11 pairs (_)
H5,H6: 4.. / H5 = 4  =>  7 pairs (_) / H6 = 4  =>  8 pairs (_)
A8,C8: 4.. / A8 = 4  =>  0 pairs (X) / C8 = 4  =>  7 pairs (_)
D5,H5: 4.. / D5 = 4  =>  8 pairs (_) / H5 = 4  =>  7 pairs (_)
G2,I2: 5.. / G2 = 5  =>  7 pairs (_) / I2 = 5  =>  7 pairs (_)
G4,I4: 5.. / G4 = 5  =>  7 pairs (_) / I4 = 5  =>  7 pairs (_)
G2,G4: 5.. / G2 = 5  =>  7 pairs (_) / G4 = 5  =>  7 pairs (_)
I2,I4: 5.. / I2 = 5  =>  7 pairs (_) / I4 = 5  =>  7 pairs (_)
F4,F5: 6.. / F4 = 6  => 11 pairs (_) / F5 = 6  =>  0 pairs (X)
E8,E9: 6.. / E8 = 6  =>  7 pairs (_) / E9 = 6  =>  0 pairs (X)
C1,G1: 6.. / C1 = 6  =>  0 pairs (X) / G1 = 6  =>  9 pairs (_)
C4,F4: 6.. / C4 = 6  =>  0 pairs (X) / F4 = 6  => 11 pairs (_)
E8,G8: 6.. / E8 = 6  =>  7 pairs (_) / G8 = 6  =>  0 pairs (X)
B3,B5: 6.. / B3 = 6  =>  0 pairs (X) / B5 = 6  => 11 pairs (_)
H3,H9: 6.. / H3 = 6  =>  0 pairs (X) / H9 = 6  =>  7 pairs (_)
E2,E3: 7.. / E2 = 7  =>  7 pairs (_) / E3 = 7  => 10 pairs (_)
E1,E3: 8.. / E1 = 8  =>  7 pairs (_) / E3 = 8  =>  0 pairs (X)
F4,F5: 8.. / F4 = 8  =>  0 pairs (X) / F5 = 8  => 11 pairs (_)
E1,I1: 8.. / E1 = 8  =>  7 pairs (_) / I1 = 8  =>  0 pairs (X)
A4,F4: 8.. / A4 = 8  => 11 pairs (_) / F4 = 8  =>  0 pairs (X)
H3,H9: 8.. / H3 = 8  =>  7 pairs (_) / H9 = 8  =>  0 pairs (X)
A3,B3: 9.. / A3 = 9  => 11 pairs (_) / B3 = 9  =>  0 pairs (X)
A4,B6: 9.. / A4 = 9  =>  0 pairs (X) / B6 = 9  => 11 pairs (_)
I8,I9: 9.. / I8 = 9  =>  8 pairs (_) / I9 = 9  =>  8 pairs (_)
A4,D4: 9.. / A4 = 9  =>  0 pairs (X) / D4 = 9  => 11 pairs (_)
A3,A4: 9.. / A3 = 9  => 11 pairs (_) / A4 = 9  =>  0 pairs (X)
B3,B6: 9.. / B3 = 9  =>  0 pairs (X) / B6 = 9  => 11 pairs (_)
* DURATION: 0:00:47.039691  START: 06:03:26.238133  END: 06:04:13.277824 2017-05-04
* CP COUNT: (30)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B2,F4,F5,H3,H9)
* 75.....2...86.2.9....5.1....4..2........5.9.25.....8.66.98.5..........5.3.5......
* PAIR A2: 1,4 BLK 1
C1: 1,4,3,6                              # reduction candidate for 1,4
C1: 1,4                                  # 10 pairs
C1: 3,6                                  #  8 pairs
* PAIR A2: 1,4 ROW 2
G2: 1,4,3,5,7                            # reduction candidate for 1,4
G2: 1,4                                  #  7 pairs
I2: 1,4,3,5,7                            # reduction candidate for 1,4
I2: 1,4                                  #  7 pairs
* PAIR A2: 1,4 COL A
A8: 1,4,2,8                              # reduction candidate for 1,4
A8: 1,4 => CTR
* 75.....2...86.2.9.29.5.1...94..28...86..5.9.25.....8.66.98.5..........5.3.5......
A8: 2,8                                  # 15 pairs
* PAIR B2: 1,3 BLK 1
C1: 1,3,4,6                              # reduction candidate for 1,3
C1: 1,3                                  # 10 pairs
C1: 4,6                                  #  8 pairs
* PAIR B2: 1,3 ROW 2
G2: 1,3,4,5,7                            # reduction candidate for 1,3
G2: 1,3                                  #  8 pairs
I2: 1,3,4,5,7                            # reduction candidate for 1,3
I2: 1,3                                  #  8 pairs
* PAIR B2: 1,3 COL B
B5: 1,3,6,7,8                            # reduction candidate for 1,3
B5: 1,3 => CTR
* 75.....2...86.2.9..6.5.1.8..4..2........5.9.2592...8.66.98.5..........5.3.5....6.
B5: 6,7,8                                #  7 pairs
B6: 1,3,2,7,9                            # reduction candidate for 1,3
B6: 1,3 => CTR
* 75.....2...86.2.9..9.5.1...94..28....6..5.9.25.....8.66.98.5..........5.3.5......
B6: 2,7,9                                #  7 pairs
* PAIR A5: 1,8 BLK 4
A4: 1,8,9                                # reduction candidate for 1,8
A4: 1,8                                  # 11 pairs
B5: 1,8,3,6,7                            # reduction candidate for 1,8
B5: 1,8 => CTR
* 75.....2...86.2.9..6.5.1.8..4..2........5.9.2592...8.66.98.5..........5.3.5....6.
B5: 3,6,7                                #  7 pairs
* PAIR A5: 1,8 COL A
A8: 1,8,2,4                              # reduction candidate for 1,8
A8: 1,8 => CTR
* 75.....2...86.2.9.29.5.1...94..28....6..5.9.25.....8.66.98.5..........5.3.5......
A8: 2,4                                  #  8 pairs
* PAIR F5: 6,8 ROW 5
B5: 6,8,1,3,7                            # reduction candidate for 6,8
B5: 1,3,7 => CTR
* 75.....2...86.2.9..6.5.1.8..4..2........5.9.2592...8.66.98.5..........5.3.5....6.
B5: 6,8                                  # 15 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-096-base-pr-000.dot
* REASONING
* DIS # A8: 1,4 => CTR => A8: 2,8
* DIS # B5: 1,3 => CTR => B5: 6,7,8
* DIS # B6: 1,3 => CTR => B6: 2,7,9
* DIS # B5: 1,8 => CTR => B5: 3,6,7
* DIS # A8: 1,8 => CTR => A8: 2,4
* DIS # B5: 1,3,7 => CTR => B5: 6,8
* CNT   6 HDP CHAINS /  21 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B2,F4,F5,H3,H9)
* 75.....2...86.2.9....5.1....4..2........5.9.25.....8.66.98.5..........5.3.5......
* PAIR A2: 1,4 BLK 1
C1: 1,4,3,6                              # reduction candidate for 1,4
C1: 1,4                                  # 10 pairs
C1: 3,6                                  #  8 pairs
* PAIR A2: 1,4 ROW 2
G2: 1,4,3,5,7                            # reduction candidate for 1,4
G2: 1,4                                  #  7 pairs
I2: 1,4,3,5,7                            # reduction candidate for 1,4
I2: 1,4                                  #  7 pairs
* PAIR A2: 1,4 COL A
A8: 1,4,2,8                              # reduction candidate for 1,4
A8: 1,4 => CTR
* 75.....2...86.2.9.29.5.1...94..28...86..5.9.25.....8.66.98.5..........5.3.5......
* PAIR RESTART

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A3,A4,A8,B5,B6,C3,C5,E3,F4,F5,G2,I1,I2,I8,I9)
* 751.8.62.438672.9....5.1.8..4..2....1...5.9.25.....8.66.98.5.....4.6..5.3.5....6.
* PAIR A3: 2,9 BLK 1
B3: 2,9,6                                # reduction candidate for 2,9
B3: 6 => CTR
* 751.8.62.438672.9.9625.1.8.84..2....1...5.9.25.....8.66.98.5.....4.6..5.3.5....6.
* PAIR E3: 3,4 ROW 3
G3: 3,4,7                                # reduction candidate for 3,4
G3: 3,4                                  # 12 pairs
I3: 3,4,7                                # reduction candidate for 3,4
I3: 3,4 => CTR
* 751.8962.438672.9.9265.178.84.926...16..589.2592..48.66.98452..28416..593.529.468
* RESTART
* PAIR E3: 3,4 COL E
E6: 3,4,1                                # reduction candidate for 3,4
E6: 3,4 => SOLVED
* 751489623438672591926531487847926315163758942592143876679815234284367159315294768
* DURATION: 0:00:13.887004  START: 06:04:30.645313  END: 06:04:44.532317 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-096-base-pr-001.dot
* REASONING
* DIS # A8: 1,4 => CTR => A8: 2,8
* DIS A8: 2,8 # B3: 6 => CTR => B3: 2,9
* DIS A8: 2,8 + B3: 2,9 # I3: 3,4 => CTR => I3: 7
* PRF A8: 2,8 + B3: 2,9 + I3: 7 # E6: 3,4 => SOL
* STA A8: 2,8 + B3: 2,9 + I3: 7 + E6: 3,4
* CNT   4 HDP CHAINS /  10 HYP OPENED

Header Info

Top 500 Minimum 17 096

solution: 751489623438672591926531487847926315163758942592143876679815234284367159315294768
info: 1573     FNBHXY   S8.f     39272

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

Solution

position: 751489623438672591926531487847926315163758942592143876679815234284367159315294768 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 # C1: 1,4 => UNS
* INC # C1: 3,6 => UNS
* INC # G2: 1,4 => UNS
* INC # I2: 1,4 => UNS
* DIS # A8: 1,4 => CTR => A8: 2,8
* INC # A8: 2,8 => UNS
* INC # C1: 1,3 => UNS
* INC # C1: 4,6 => UNS
* INC # G2: 1,3 => UNS
* INC # I2: 1,3 => UNS
* DIS # B5: 1,3 => CTR => B5: 6,7,8
* INC # B5: 6,7,8 => UNS
* DIS # B6: 1,3 => CTR => B6: 2,7,9
* INC # B6: 2,7,9 => UNS
* INC # A4: 1,8 => UNS
* DIS # B5: 1,8 => CTR => B5: 3,6,7
* INC # B5: 3,6,7 => UNS
* DIS # A8: 1,8 => CTR => A8: 2,4
* INC # A8: 2,4 => UNS
* INC # B5: 6,8 => UNS
* DIS # B5: 1,3,7 => CTR => B5: 6,8
* CNT  21 HDP CHAINS /  21 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C1: 1,4 => UNS
* INC # C1: 3,6 => UNS
* INC # G2: 1,4 => UNS
* INC # I2: 1,4 => UNS
* DIS # A8: 1,4 => CTR => A8: 2,8
* INC A8: 2,8 # B3: 2,9 => UNS
* DIS A8: 2,8 # B3: 6 => CTR => B3: 2,9
* INC A8: 2,8 + B3: 2,9 # G3: 3,4 => UNS
* DIS A8: 2,8 + B3: 2,9 # I3: 3,4 => CTR => I3: 7
* PRF A8: 2,8 + B3: 2,9 + I3: 7 # E6: 3,4 => SOL
* STA A8: 2,8 + B3: 2,9 + I3: 7 + E6: 3,4
* CNT  10 HDP CHAINS /  10 HYP OPENED