Analysis of zz-www.sudokuwiki.org-0277-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=277

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=277

position: 41.9.6..........7...5.4....6.....59.....5...18.4..3......3....29.8.......3....6.. initial

Autosolve

position: 41.9.6..........7...5.4....6.1...593...65...1854193......3....29.8.......3....6.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # G2: 2,3 => CTR => G2: 1,4,8,9
* DIS # C5: 2,7 => CTR => C5: 3,9
* DIS # C5: 2,7 => CTR => C5: 3,9
* DIS # H3: 1,3,8 => CTR => H3: 2,6
* DIS # C5: 2,7 => CTR => C5: 3,9
* CNT   5 HDP CHAINS /  56 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 # G2: 2,3 => CTR => G2: 1,4,8,9
* DIS G2: 1,4,8,9 # E2: 1,8 => CTR => E2: 2,3
* DIS G2: 1,4,8,9 + E2: 2,3 # A5: 7 => CTR => A5: 2,3
* DIS G2: 1,4,8,9 + E2: 2,3 + A5: 2,3 # B3: 6,9 => CTR => B3: 8
* PRF G2: 1,4,8,9 + E2: 2,3 + A5: 2,3 + B3: 8 # H1: 5,8 => SOL
* STA G2: 1,4,8,9 + E2: 2,3 + A5: 2,3 + B3: 8 + H1: 5,8
* CNT   5 HDP CHAINS /  11 HYP OPENED

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

Details

Positions

41.9.6..........7...5.4....6.....59.....5...18.4..3......3....29.8.......3....6.. initial
41.9.6..........7...5.4....6.1...593...65...1854193......3....29.8.......3....6.. autosolve
413976258296538174785241369671824593329657841854193726147365982968712435532489617 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
A2: 2,3
C2: 6,9
I1: 5,8
B4: 2,7
F5: 2,7
G5: 4,8
H5: 4,8
G6: 2,7
H6: 2,6
I6: 6,7
A7: 1,5
C7: 6,7
A9: 1,5
C9: 2,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A7,A9: 1.. / A7 = 1  => 12 pairs (_) / A9 = 1  => 12 pairs (_)
G6,H6: 2.. / G6 = 2  => 13 pairs (_) / H6 = 2  => 15 pairs (_)
B8,C9: 2.. / B8 = 2  =>  0 pairs (X) / C9 = 2  => 15 pairs (_)
E1,E2: 3.. / E1 = 3  =>  0 pairs (X) / E2 = 3  => 17 pairs (_)
A5,C5: 3.. / A5 = 3  => 18 pairs (_) / C5 = 3  => 17 pairs (_)
G8,H8: 3.. / G8 = 3  => 16 pairs (_) / H8 = 3  => 14 pairs (_)
C1,C5: 3.. / C1 = 3  => 18 pairs (_) / C5 = 3  => 17 pairs (_)
G2,I2: 4.. / G2 = 4  => 14 pairs (_) / I2 = 4  => 16 pairs (_)
D4,F4: 4.. / D4 = 4  => 14 pairs (_) / F4 = 4  => 14 pairs (_)
G5,H5: 4.. / G5 = 4  => 16 pairs (_) / H5 = 4  => 13 pairs (_)
B7,B8: 4.. / B7 = 4  => 14 pairs (_) / B8 = 4  => 18 pairs (_)
D2,F2: 5.. / D2 = 5  => 14 pairs (_) / F2 = 5  => 15 pairs (_)
H1,I1: 5.. / H1 = 5  => 17 pairs (_) / I1 = 5  => 14 pairs (_)
A7,A9: 5.. / A7 = 5  => 12 pairs (_) / A9 = 5  => 12 pairs (_)
H6,I6: 6.. / H6 = 6  => 13 pairs (_) / I6 = 6  => 15 pairs (_)
E7,E8: 6.. / E7 = 6  => 21 pairs (_) / E8 = 6  => 14 pairs (_)
B8,E8: 6.. / B8 = 6  => 21 pairs (_) / E8 = 6  => 14 pairs (_)
C2,C7: 6.. / C2 = 6  => 22 pairs (_) / C7 = 6  => 15 pairs (_)
H3,H6: 6.. / H3 = 6  => 15 pairs (_) / H6 = 6  => 13 pairs (_)
C1,A3: 7.. / C1 = 7  => 24 pairs (_) / A3 = 7  => 18 pairs (_)
G6,I6: 7.. / G6 = 7  => 15 pairs (_) / I6 = 7  => 13 pairs (_)
C1,E1: 7.. / C1 = 7  => 24 pairs (_) / E1 = 7  => 18 pairs (_)
A3,A5: 7.. / A3 = 7  => 18 pairs (_) / A5 = 7  => 24 pairs (_)
B2,B3: 8.. / B2 = 8  => 17 pairs (_) / B3 = 8  => 18 pairs (_)
G5,H5: 8.. / G5 = 8  => 13 pairs (_) / H5 = 8  => 16 pairs (_)
B5,C5: 9.. / B5 = 9  => 15 pairs (_) / C5 = 9  => 22 pairs (_)
F7,F9: 9.. / F7 = 9  => 16 pairs (_) / F9 = 9  => 14 pairs (_)
G7,I9: 9.. / G7 = 9  => 14 pairs (_) / I9 = 9  => 16 pairs (_)
F7,G7: 9.. / F7 = 9  => 16 pairs (_) / G7 = 9  => 14 pairs (_)
F9,I9: 9.. / F9 = 9  => 14 pairs (_) / I9 = 9  => 16 pairs (_)
C2,C5: 9.. / C2 = 9  => 15 pairs (_) / C5 = 9  => 22 pairs (_)
* DURATION: 0:00:28.116817  START: 14:41:15.140799  END: 14:41:43.257616 2019-04-28
* CP COUNT: (31)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,A9,B4,C2,C7,C9,F5,G5,G6,H5,H6,I1,I6)
* 41.9.6..........7...5.4....6.1...593...65...1854193......3....29.8.......3....6..
* PAIR A2: 2,3 BLK 1
C1: 2,3,7                                # reduction candidate for 2,3
C1: 2,3                                  # 18 pairs
A3: 2,3,7                                # reduction candidate for 2,3
A3: 2,3                                  # 24 pairs
* PAIR A2: 2,3 ROW 2
E2: 2,3,1,8                              # reduction candidate for 2,3
E2: 2,3                                  # 16 pairs
G2: 2,3,1,4,8,9                          # reduction candidate for 2,3
G2: 2,3 => CTR
* 417936...2.....374385.4....6.1...5937.3652..1854193.....63....29.8.6..3..32...6..
G2: 1,4,8,9                              # 14 pairs
* PAIR A2: 2,3 COL A
A5: 2,3,7                                # reduction candidate for 2,3
A5: 7                                    # 24 pairs
A5: 2,3                                  # 18 pairs
* PAIR C2: 6,9 BLK 1
B2: 6,9,8                                # reduction candidate for 6,9
B2: 6,9                                  # 18 pairs
B3: 6,9,8                                # reduction candidate for 6,9
B3: 6,9                                  # 17 pairs
* PAIR C2: 6,9 ROW 2
I2: 6,9,4,8                              # reduction candidate for 6,9
I2: 6,9                                  # 16 pairs
I2: 4,8                                  # 16 pairs
* PAIR I1: 5,8 BLK 3
H1: 5,8,2,3                              # reduction candidate for 5,8
H1: 5,8                                  # 19 pairs
H1: 2,3                                  # 15 pairs
* PAIR I1: 5,8 COL I
I9: 5,8,4,7,9                            # reduction candidate for 5,8
I9: 5,8                                  # 17 pairs
I9: 4,7,9                                # 15 pairs
* PAIR B4: 2,7 BLK 4
A5: 2,7,3                                # reduction candidate for 2,7
A5: 2,7                                  # 17 pairs
B5: 2,7,9                                # reduction candidate for 2,7
B5: 2,7                                  # 22 pairs
C5: 2,7,3,9                              # reduction candidate for 2,7
C5: 2,7 => CTR
* 413976.252.9.3..7.7.5.4....6.1...59339.65...1854193267..63..7.29.8.6...4.3....6..
C5: 3,9                                  # 15 pairs
* PAIR B4: 2,7 ROW 4
D4: 2,7,4,8                              # reduction candidate for 2,7
D4: 2,7                                  # 16 pairs
E4: 2,7,8                                # reduction candidate for 2,7
E4: 2,7                                  # 17 pairs
F4: 2,7,4,8                              # reduction candidate for 2,7
F4: 2,7                                  # 17 pairs
* PAIR B4: 2,7 COL B
B8: 2,7,4,6                              # reduction candidate for 2,7
B8: 4,6                                  # 16 pairs
B8: 2,7                                  # 15 pairs
* PAIR F5: 2,7 BLK 5
D4: 2,7,4,8                              # reduction candidate for 2,7
D4: 2,7                                  # 16 pairs
E4: 2,7,8                                # reduction candidate for 2,7
E4: 2,7                                  # 17 pairs
F4: 2,7,4,8                              # reduction candidate for 2,7
F4: 2,7                                  # 17 pairs
* PAIR F5: 2,7 ROW 5
A5: 2,7,3                                # reduction candidate for 2,7
A5: 2,7                                  # 17 pairs
B5: 2,7,9                                # reduction candidate for 2,7
B5: 2,7                                  # 22 pairs
C5: 2,7,3,9                              # reduction candidate for 2,7
C5: 2,7 => CTR
* 413976.252.9.3..7.7.5.4....6.1...59339.65...1854193267..63..7.29.8.6...4.3....6..
C5: 3,9                                  # 15 pairs
* PAIR F5: 2,7 COL F
F3: 2,7,1,8                              # reduction candidate for 2,7
F3: 2,7                                  # 16 pairs
F8: 2,7,1,4,5                            # reduction candidate for 2,7
F8: 2,7                                  # 17 pairs
F9: 2,7,1,4,5,8,9                        # reduction candidate for 2,7
F9: 2,7                                  # 20 pairs
* PAIR G5: 4,8 COL G
G2: 4,8,1,2,3,9                          # reduction candidate for 4,8
G2: 4,8                                  # 17 pairs
G7: 4,8,1,7,9                            # reduction candidate for 4,8
G7: 4,8                                  # 19 pairs
* PAIR H5: 4,8 COL H
H7: 4,8,1,5                              # reduction candidate for 4,8
H7: 4,8                                  # 16 pairs
H9: 4,8,1,5                              # reduction candidate for 4,8
H9: 4,8                                  # 16 pairs
* PAIR H6: 2,6 COL H
H3: 2,6,1,3,8                            # reduction candidate for 2,6
H3: 1,3,8 => CTR
* 41.986325....3147.3.5.4....6.1...5937.3652841854193267.4.3....2978.65134.32...6..
H3: 2,6                                  # 15 pairs
* PAIR A7: 1,5 ROW 7
F7: 1,5,4,7,8,9                          # reduction candidate for 1,5
F7: 1,5                                  # 17 pairs
H7: 1,5,4,8                              # reduction candidate for 1,5
H7: 1,5                                  # 15 pairs
* PAIR C7: 6,7 BLK 7
B7: 6,7,4                                # reduction candidate for 6,7
B7: 6,7                                  # 18 pairs
B8: 6,7,2,4                              # reduction candidate for 6,7
B8: 6,7                                  # 16 pairs
* PAIR C7: 6,7 ROW 7
E7: 6,7,1,8                              # reduction candidate for 6,7
E7: 6,7                                  # 15 pairs
E7: 1,8                                  # 15 pairs
* PAIR A9: 1,5 ROW 9
F9: 1,5,2,4,7,8,9                        # reduction candidate for 1,5
F9: 1,5                                  # 19 pairs
H9: 1,5,4,8                              # reduction candidate for 1,5
H9: 1,5                                  # 15 pairs
* PAIR C9: 2,7 BLK 7
B8: 2,7,4,6                              # reduction candidate for 2,7
B8: 4,6                                  # 16 pairs
B8: 2,7                                  # 15 pairs
* PAIR C9: 2,7 ROW 9
D9: 2,7,4,5,8                            # reduction candidate for 2,7
D9: 2,7                                  # 16 pairs
E9: 2,7,1,8                              # reduction candidate for 2,7
E9: 2,7                                  # 15 pairs
F9: 2,7,1,4,5,8,9                        # reduction candidate for 2,7
F9: 2,7                                  # 20 pairs
* PAIR C9: 2,7 COL C
C1: 2,7,3                                # reduction candidate for 2,7
C1: 2,7                                  # 17 pairs
C5: 2,7,3,9                              # reduction candidate for 2,7
C5: 2,7 => CTR
* 413976.252.9.3..7.7.5.4....6.1...59339.65...1854193267..63..7.29.8.6...4.3....6..
C5: 3,9                                  # 15 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0277-base-pr-000.dot
* REASONING
* DIS # G2: 2,3 => CTR => G2: 1,4,8,9
* DIS # C5: 2,7 => CTR => C5: 3,9
* DIS # C5: 2,7 => CTR => C5: 3,9
* DIS # H3: 1,3,8 => CTR => H3: 2,6
* DIS # C5: 2,7 => CTR => C5: 3,9
* CNT   5 HDP CHAINS /  56 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,A9,B4,C2,C7,C9,F5,G5,G6,H5,H6,I1,I6)
* 41.9.6..........7...5.4....6.1...593...65...1854193......3....29.8.......3....6..
* PAIR A2: 2,3 BLK 1
C1: 2,3,7                                # reduction candidate for 2,3
C1: 2,3                                  # 18 pairs
A3: 2,3,7                                # reduction candidate for 2,3
A3: 2,3                                  # 24 pairs
* PAIR A2: 2,3 ROW 2
E2: 2,3,1,8                              # reduction candidate for 2,3
E2: 2,3                                  # 16 pairs
G2: 2,3,1,4,8,9                          # reduction candidate for 2,3
G2: 2,3 => CTR
* 417936...2.....374385.4....6.1...5937.3652..1854193.....63....29.8.6..3..32...6..
* RESTART
* PAIR A2: 2,3 ROW 2
E2: 2,3,1,8                              # reduction candidate for 2,3
E2: 1,8 => CTR
* 417936...3.9....7.2.5.4....6.1...593793652..1854193.....63....29.8.6.....32...6..
* PAIR A2: 2,3 COL A
A5: 2,3,7                                # reduction candidate for 2,3
A5: 7 => CTR
* 4179.68.5.695.8174.85741269621874593793652481854193726.763..9.2948265317.32..96.8
* PAIR RESTART
* PAIR C2: 6,9 BLK 1
B2: 6,9,8                                # reduction candidate for 6,9
B2: 6,9                                  # 22 pairs
B3: 6,9,8                                # reduction candidate for 6,9
B3: 6,9 => CTR
* 413976.2528.531.7.7.5.4....6.1...5933..65...1854193267...3....29.8.....4.3....6.8
* RESTART
* PAIR I1: 5,8 BLK 3
H1: 5,8,2                                # reduction candidate for 5,8
H1: 5,8 => SOLVED
* 413976258296538174785241369671824593329657841854193726147365982968712435532489617
* DURATION: 0:00:08.181824  START: 14:42:11.314733  END: 14:42:19.496557 2019-04-28
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0277-base-pr-001.dot
* REASONING
* DIS # G2: 2,3 => CTR => G2: 1,4,8,9
* DIS G2: 1,4,8,9 # E2: 1,8 => CTR => E2: 2,3
* DIS G2: 1,4,8,9 + E2: 2,3 # A5: 7 => CTR => A5: 2,3
* DIS G2: 1,4,8,9 + E2: 2,3 + A5: 2,3 # B3: 6,9 => CTR => B3: 8
* PRF G2: 1,4,8,9 + E2: 2,3 + A5: 2,3 + B3: 8 # H1: 5,8 => SOL
* STA G2: 1,4,8,9 + E2: 2,3 + A5: 2,3 + B3: 8 + H1: 5,8
* CNT   5 HDP CHAINS /  11 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=277

Solution

position: 413976258296538174785241369671824593329657841854193726147365982968712435532489617 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: 2,3 => UNS
* INC # A3: 2,3 => UNS
* INC # E2: 2,3 => UNS
* DIS # G2: 2,3 => CTR => G2: 1,4,8,9
* INC # G2: 1,4,8,9 => UNS
* INC # A5: 2,3 => UNS
* INC # A5: 7 => UNS
* INC # B2: 6,9 => UNS
* INC # B3: 6,9 => UNS
* INC # I2: 6,9 => UNS
* INC # I2: 4,8 => UNS
* INC # H1: 5,8 => UNS
* INC # H1: 2,3 => UNS
* INC # I9: 5,8 => UNS
* INC # I9: 4,7,9 => UNS
* INC # A5: 2,7 => UNS
* INC # B5: 2,7 => UNS
* DIS # C5: 2,7 => CTR => C5: 3,9
* INC # C5: 3,9 => UNS
* INC # D4: 2,7 => UNS
* INC # E4: 2,7 => UNS
* INC # F4: 2,7 => UNS
* INC # B8: 2,7 => UNS
* INC # B8: 4,6 => UNS
* INC # D4: 2,7 => UNS
* INC # E4: 2,7 => UNS
* INC # F4: 2,7 => UNS
* INC # A5: 2,7 => UNS
* INC # B5: 2,7 => UNS
* DIS # C5: 2,7 => CTR => C5: 3,9
* INC # C5: 3,9 => UNS
* INC # F3: 2,7 => UNS
* INC # F8: 2,7 => UNS
* INC # F9: 2,7 => UNS
* INC # G2: 4,8 => UNS
* INC # G7: 4,8 => UNS
* INC # H7: 4,8 => UNS
* INC # H9: 4,8 => UNS
* INC # H3: 2,6 => UNS
* DIS # H3: 1,3,8 => CTR => H3: 2,6
* INC # F7: 1,5 => UNS
* INC # H7: 1,5 => UNS
* INC # B7: 6,7 => UNS
* INC # B8: 6,7 => UNS
* INC # E7: 6,7 => UNS
* INC # E7: 1,8 => UNS
* INC # F9: 1,5 => UNS
* INC # H9: 1,5 => UNS
* INC # B8: 2,7 => UNS
* INC # B8: 4,6 => UNS
* INC # D9: 2,7 => UNS
* INC # E9: 2,7 => UNS
* INC # F9: 2,7 => UNS
* INC # C1: 2,7 => UNS
* DIS # C5: 2,7 => CTR => C5: 3,9
* INC # C5: 3,9 => UNS
* CNT  56 HDP CHAINS /  56 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C1: 2,3 => UNS
* INC # A3: 2,3 => UNS
* INC # E2: 2,3 => UNS
* DIS # G2: 2,3 => CTR => G2: 1,4,8,9
* INC G2: 1,4,8,9 # E2: 2,3 => UNS
* DIS G2: 1,4,8,9 # E2: 1,8 => CTR => E2: 2,3
* INC G2: 1,4,8,9 + E2: 2,3 # A5: 2,3 => UNS
* DIS G2: 1,4,8,9 + E2: 2,3 # A5: 7 => CTR => A5: 2,3
* INC G2: 1,4,8,9 + E2: 2,3 + A5: 2,3 # B2: 6,9 => UNS
* DIS G2: 1,4,8,9 + E2: 2,3 + A5: 2,3 # B3: 6,9 => CTR => B3: 8
* PRF G2: 1,4,8,9 + E2: 2,3 + A5: 2,3 + B3: 8 # H1: 5,8 => SOL
* STA G2: 1,4,8,9 + E2: 2,3 + A5: 2,3 + B3: 8 + H1: 5,8
* CNT  11 HDP CHAINS /  11 HYP OPENED