Analysis of zz-www.sudokuwiki.org-0151-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=151

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=151

position: ....4..3...28.....98......5.....8..3..1...7..5..6.....3...6..49..7..42...4..1.... initial

Autosolve

position: ....4..3...28.....98......5.....85.38.1...7..5..6.....3...6..49.9738425..4..1.3.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C6: 9 => CTR => C6: 3,4
* DIS # D4: 4,9 => CTR => D4: 1,2,7
* CNT   2 HDP CHAINS /  20 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 # C6: 9 => CTR => C6: 3,4
* DIS C6: 3,4 # A4: 2,6 => CTR => A4: 4,7
* PRF C6: 3,4 + A4: 4,7 # D4: 2,7 => SOL
* STA C6: 3,4 + A4: 4,7 + D4: 2,7
* CNT   3 HDP CHAINS /  22 HYP OPENED

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

Details

Positions

....4..3...28.....98......5.....8..3..1...7..5..6.....3...6..49..7..42...4..1.... initial
....4..3...28.....98......5.....85.38.1...7..5..6.....3...6..49.9738425..4..1.3.. autosolve
756942138132856974984173625469728513821435796573691482315267849697384251248519367 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
C1: 5,6
C3: 3,4
C4: 4,9
C7: 5,8
A8: 1,6
A9: 2,6
G7: 1,8
I8: 1,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D4,F6: 1.. / D4 = 1  => 13 pairs (_) / F6 = 1  => 11 pairs (_)
B7,A8: 1.. / B7 = 1  => 19 pairs (_) / A8 = 1  => 11 pairs (_)
G7,I8: 1.. / G7 = 1  => 11 pairs (_) / I8 = 1  => 19 pairs (_)
D4,H4: 1.. / D4 = 1  => 13 pairs (_) / H4 = 1  => 11 pairs (_)
B7,G7: 1.. / B7 = 1  => 19 pairs (_) / G7 = 1  => 11 pairs (_)
A8,I8: 1.. / A8 = 1  => 11 pairs (_) / I8 = 1  => 19 pairs (_)
I1,H3: 2.. / I1 = 2  =>  0 pairs (X) / H3 = 2  => 11 pairs (_)
B7,A9: 2.. / B7 = 2  => 19 pairs (_) / A9 = 2  => 13 pairs (_)
A4,A9: 2.. / A4 = 2  => 19 pairs (_) / A9 = 2  => 13 pairs (_)
B2,C3: 3.. / B2 = 3  => 19 pairs (_) / C3 = 3  => 10 pairs (_)
C3,C6: 3.. / C3 = 3  => 10 pairs (_) / C6 = 3  => 19 pairs (_)
A2,C3: 4.. / A2 = 4  => 10 pairs (_) / C3 = 4  => 19 pairs (_)
D4,D5: 4.. / D4 = 4  =>  0 pairs (X) / D5 = 4  => 10 pairs (_)
C3,G3: 4.. / C3 = 4  => 19 pairs (_) / G3 = 4  => 10 pairs (_)
D5,I5: 4.. / D5 = 4  => 10 pairs (_) / I5 = 4  =>  0 pairs (X)
A2,A4: 4.. / A2 = 4  => 10 pairs (_) / A4 = 4  => 19 pairs (_)
E2,E5: 5.. / E2 = 5  =>  8 pairs (_) / E5 = 5  =>  8 pairs (_)
F3,G3: 6.. / F3 = 6  =>  9 pairs (_) / G3 = 6  => 19 pairs (_)
A8,I8: 6.. / A8 = 6  => 19 pairs (_) / I8 = 6  => 11 pairs (_)
C1,C9: 6.. / C1 = 6  => 10 pairs (_) / C9 = 6  => 11 pairs (_)
D7,F7: 7.. / D7 = 7  => 10 pairs (_) / F7 = 7  =>  9 pairs (_)
H9,I9: 7.. / H9 = 7  => 12 pairs (_) / I9 = 7  => 10 pairs (_)
G1,I1: 8.. / G1 = 8  => 12 pairs (_) / I1 = 8  => 12 pairs (_)
C7,C9: 8.. / C7 = 8  => 11 pairs (_) / C9 = 8  => 19 pairs (_)
C7,G7: 8.. / C7 = 8  => 11 pairs (_) / G7 = 8  => 19 pairs (_)
H6,H9: 8.. / H6 = 8  =>  9 pairs (_) / H9 = 8  => 10 pairs (_)
C4,C6: 9.. / C4 = 9  =>  9 pairs (_) / C6 = 9  =>  0 pairs (X)
D9,F9: 9.. / D9 = 9  =>  9 pairs (_) / F9 = 9  =>  9 pairs (_)
* DURATION: 0:00:36.289688  START: 06:16:31.191443  END: 06:17:07.481131 2017-05-01
* CP COUNT: (28)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,C1,C3,C4,C7,G7,I8)
* ....4..3...28.....98......5.....85.38.1...7..5..6.....3...6..49.9738425..4..1.3..
* PAIR C1: 5,6 BLK 1
B1: 5,6,1,7                              # reduction candidate for 5,6
B1: 5,6                                  # 10 pairs
B2: 5,6,1,3,7                            # reduction candidate for 5,6
B2: 5,6                                  # 14 pairs
* PAIR C1: 5,6 ROW 1
F1: 5,6,1,2,7,9                          # reduction candidate for 5,6
F1: 5,6                                  # 15 pairs
F1: 1,2,7,9                              #  8 pairs
* PAIR C1: 5,6 COL C
C9: 5,6,8                                # reduction candidate for 5,6
C9: 8                                    # 19 pairs
C9: 5,6                                  # 11 pairs
* PAIR C3: 3,4 COL C
C6: 3,4,9                                # reduction candidate for 3,4
C6: 9 => CTR
* ....4..384.28.....983176425..4..85138.14..79.5.96....43...6..49.9738425..4..1.3..
C6: 3,4                                  #  9 pairs
* PAIR C4: 4,9 BLK 4
C6: 4,9,3                                # reduction candidate for 4,9
C6: 3                                    # 19 pairs
C6: 4,9                                  # 10 pairs
* PAIR C4: 4,9 ROW 4
D4: 4,9,1,2,7                            # reduction candidate for 4,9
D4: 4,9 => CTR
* ....4..3.4.28.....983.2.475....785138.1...7..57.631...3...6..49.9738425..4..1.3.7
D4: 1,2,7                                # 10 pairs
* PAIR C7: 5,8 BLK 7
C9: 5,8,6                                # reduction candidate for 5,8
C9: 6                                    # 11 pairs
C9: 5,8                                  # 10 pairs
* PAIR A8: 1,6 COL A
A1: 1,6,7                                # reduction candidate for 1,6
A1: 1,6                                  # 16 pairs
A2: 1,6,4,7                              # reduction candidate for 1,6
A2: 1,6                                  # 21 pairs
* PAIR A9: 2,6 COL A
A4: 2,6,4,7                              # reduction candidate for 2,6
A4: 4,7                                  # 14 pairs
A4: 2,6                                  # 14 pairs
* PAIR G7: 1,8 COL G
G1: 1,8,6,9                              # reduction candidate for 1,8
G1: 1,8                                  # 11 pairs
G6: 1,8,4,9                              # reduction candidate for 1,8
G6: 1,8                                  # 23 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0151-base-pr-000.dot
* REASONING
* DIS # C6: 9 => CTR => C6: 3,4
* DIS # D4: 4,9 => CTR => D4: 1,2,7
* CNT   2 HDP CHAINS /  20 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,C1,C3,C4,C7,G7,I8)
* ....4..3...28.....98......5.....85.38.1...7..5..6.....3...6..49.9738425..4..1.3..
* PAIR C1: 5,6 BLK 1
B1: 5,6,1,7                              # reduction candidate for 5,6
B1: 5,6                                  # 10 pairs
B2: 5,6,1,3,7                            # reduction candidate for 5,6
B2: 5,6                                  # 14 pairs
* PAIR C1: 5,6 ROW 1
F1: 5,6,1,2,7,9                          # reduction candidate for 5,6
F1: 5,6                                  # 15 pairs
F1: 1,2,7,9                              #  8 pairs
* PAIR C1: 5,6 COL C
C9: 5,6,8                                # reduction candidate for 5,6
C9: 8                                    # 19 pairs
C9: 5,6                                  # 11 pairs
* PAIR C3: 3,4 COL C
C6: 3,4,9                                # reduction candidate for 3,4
C6: 9 => CTR
* ....4..384.28.....983176425..4..85138.14..79.5.96....43...6..49.9738425..4..1.3..
* PAIR RESTART
* PAIR C7: 5,8 BLK 7
C9: 5,8,6                                # reduction candidate for 5,8
C9: 6                                    # 12 pairs
C9: 5,8                                  # 11 pairs
* PAIR A8: 1,6 COL A
A1: 1,6,7                                # reduction candidate for 1,6
A1: 1,6                                  # 17 pairs
A2: 1,6,4,7                              # reduction candidate for 1,6
A2: 1,6                                  # 21 pairs
* PAIR A9: 2,6 COL A
A4: 2,6,4,7                              # reduction candidate for 2,6
A4: 2,6 => CTR
* 7...4..3.4.28.7.91983126475..94785138.1..37645.46.1...3..76..49197384256.4..1.3..
* PAIR RESTART
* PAIR G7: 1,8 COL G
G1: 1,8,6,9                              # reduction candidate for 1,8
G1: 1,8                                  # 18 pairs
G6: 1,8,4,9                              # reduction candidate for 1,8
G6: 1,8                                  # 32 pairs

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A4,A8,B7,C1,C3,C6,C7,C9,D7,D9,E4,F7,F9,G7,I8)
* ....4..3...28.....98......5..9..85.38.1...7..5..6.....3...6..49.9738425.24..1.3..
* PAIR C1: 5,6 ROW 1
F1: 5,6,1,2,7,9                          # reduction candidate for 5,6
F1: 5,6                                  # 23 pairs
F1: 1,2,7,9                              # 15 pairs
* PAIR A4: 4,7 ROW 4
D4: 4,7,1,2                              # reduction candidate for 4,7
D4: 1,2                                  # 20 pairs
D4: 4,7                                  # 19 pairs
* PAIR A4: 4,7 COL A
A2: 4,7,1,6                              # reduction candidate for 4,7
A2: 1,6                                  # 21 pairs
A2: 4,7                                  # 17 pairs
* PAIR E4: 2,7 BLK 5
D4: 2,7,1,4                              # reduction candidate for 2,7
D4: 2,7 => SOLVED
* 756942138132856974984173625469728513821435796573691482315267849697384251248519367
* DURATION: 0:00:19.300806  START: 06:17:22.094042  END: 06:17:41.394848 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0151-base-pr-001.dot
* REASONING
* DIS # C6: 9 => CTR => C6: 3,4
* DIS C6: 3,4 # A4: 2,6 => CTR => A4: 4,7
* PRF C6: 3,4 + A4: 4,7 # D4: 2,7 => SOL
* STA C6: 3,4 + A4: 4,7 + D4: 2,7
* CNT   3 HDP CHAINS /  22 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=151

Solution

position: 756942138132856974984173625469728513821435796573691482315267849697384251248519367 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 # B1: 5,6 => UNS
* INC # B2: 5,6 => UNS
* INC # F1: 5,6 => UNS
* INC # F1: 1,2,7,9 => UNS
* INC # C9: 5,6 => UNS
* INC # C9: 8 => UNS
* INC # C6: 3,4 => UNS
* DIS # C6: 9 => CTR => C6: 3,4
* INC # C6: 4,9 => UNS
* INC # C6: 3 => UNS
* DIS # D4: 4,9 => CTR => D4: 1,2,7
* INC # D4: 1,2,7 => UNS
* INC # C9: 5,8 => UNS
* INC # C9: 6 => UNS
* INC # A1: 1,6 => UNS
* INC # A2: 1,6 => UNS
* INC # A4: 2,6 => UNS
* INC # A4: 4,7 => UNS
* INC # G1: 1,8 => UNS
* INC # G6: 1,8 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B1: 5,6 => UNS
* INC # B2: 5,6 => UNS
* INC # F1: 5,6 => UNS
* INC # F1: 1,2,7,9 => UNS
* INC # C9: 5,6 => UNS
* INC # C9: 8 => UNS
* INC # C6: 3,4 => UNS
* DIS # C6: 9 => CTR => C6: 3,4
* INC C6: 3,4 # C9: 5,8 => UNS
* INC C6: 3,4 # C9: 6 => UNS
* INC C6: 3,4 # A1: 1,6 => UNS
* INC C6: 3,4 # A2: 1,6 => UNS
* DIS C6: 3,4 # A4: 2,6 => CTR => A4: 4,7
* INC C6: 3,4 + A4: 4,7 # G1: 1,8 => UNS
* INC C6: 3,4 + A4: 4,7 # G6: 1,8 => UNS
* INC C6: 3,4 + A4: 4,7 # F1: 5,6 => UNS
* INC C6: 3,4 + A4: 4,7 # F1: 1,2,7,9 => UNS
* INC C6: 3,4 + A4: 4,7 # D4: 4,7 => UNS
* INC C6: 3,4 + A4: 4,7 # D4: 1,2 => UNS
* INC C6: 3,4 + A4: 4,7 # A2: 4,7 => UNS
* INC C6: 3,4 + A4: 4,7 # A2: 1,6 => UNS
* PRF C6: 3,4 + A4: 4,7 # D4: 2,7 => SOL
* STA C6: 3,4 + A4: 4,7 + D4: 2,7
* CNT  22 HDP CHAINS /  22 HYP OPENED