Analysis of zz-www.sudokuwiki.org-0088-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=88

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=88

position: ....35....81.....6......2..6..9..1...49.1.65...5..2..8..4......9.....73....76.... initial

Autosolve

position: ....35....81.....6.....62..6..95.1...49.1.65...56.2..8..4....6.9.....73....76.... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B3: 3,5 => CTR => B3: 7,9
* DIS # B3: 3,7 => CTR => B3: 5,9
* DIS # B3: 3,5 => CTR => B3: 7,9
* CNT   3 HDP CHAINS /  29 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 # B3: 3,5 => CTR => B3: 7,9
* DIS B3: 7,9 # B1: 7,9 => CTR => B1: 2,6
* DIS B3: 7,9 + B1: 2,6 # C4: 3,7 => CTR => C4: 2,8
* DIS B3: 7,9 + B1: 2,6 + C4: 2,8 # E2: 2,4 => CTR => E2: 7,9
* DIS B3: 7,9 + B1: 2,6 + C4: 2,8 + E2: 7,9 # A3: 4 => CTR => A3: 3,5
* DIS B3: 7,9 + B1: 2,6 + C4: 2,8 + E2: 7,9 + A3: 3,5 # C8: 8 => CTR => C8: 2,6
* PRF B3: 7,9 + B1: 2,6 + C4: 2,8 + E2: 7,9 + A3: 3,5 + C8: 2,6 # D3: 1,8 => SOL
* STA B3: 7,9 + B1: 2,6 + C4: 2,8 + E2: 7,9 + A3: 3,5 + C8: 2,6 + D3: 1,8
* CNT   7 HDP CHAINS /  46 HYP OPENED

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

Details

Positions

....35....81.....6......2..6..9..1...49.1.65...5..2..8..4......9.....73....76.... initial
....35....81.....6.....62..6..95.1...49.1.65...56.2..8..4....6.9.....73....76.... autosolve
462835971581297346397146285678954123249318657135672498714523869956481732823769514 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
A2: 3,5
C3: 3,7
D2: 2,4
G2: 3,5
I3: 3,5
D5: 3,8
E6: 4,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D1,D3: 1.. / D1 = 1  =>  8 pairs (_) / D3 = 1  =>  8 pairs (_)
A6,B6: 1.. / A6 = 1  =>  8 pairs (_) / B6 = 1  =>  8 pairs (_)
D3,H3: 1.. / D3 = 1  =>  8 pairs (_) / H3 = 1  =>  8 pairs (_)
D2,E2: 2.. / D2 = 2  =>  6 pairs (_) / E2 = 2  => 19 pairs (_)
A5,I5: 2.. / A5 = 2  => 23 pairs (_) / I5 = 2  => 13 pairs (_)
H4,H9: 2.. / H4 = 2  => 22 pairs (_) / H9 = 2  => 13 pairs (_)
G2,I3: 3.. / G2 = 3  =>  8 pairs (_) / I3 = 3  =>  0 pairs (X)
A2,G2: 3.. / A2 = 3  =>  0 pairs (X) / G2 = 3  =>  8 pairs (_)
D5,D7: 3.. / D5 = 3  =>  9 pairs (_) / D7 = 3  => 19 pairs (_)
G2,G6: 3.. / G2 = 3  =>  8 pairs (_) / G6 = 3  =>  0 pairs (X)
A1,A3: 4.. / A1 = 4  => 16 pairs (_) / A3 = 4  =>  9 pairs (_)
F4,E6: 4.. / F4 = 4  => 23 pairs (_) / E6 = 4  => 10 pairs (_)
G2,I3: 5.. / G2 = 5  =>  0 pairs (X) / I3 = 5  =>  8 pairs (_)
D7,D8: 5.. / D7 = 5  => 10 pairs (_) / D8 = 5  =>  8 pairs (_)
A2,G2: 5.. / A2 = 5  =>  8 pairs (_) / G2 = 5  =>  0 pairs (X)
B1,C1: 6.. / B1 = 6  => 10 pairs (_) / C1 = 6  =>  8 pairs (_)
B8,C8: 6.. / B8 = 6  =>  8 pairs (_) / C8 = 6  => 10 pairs (_)
B1,B8: 6.. / B1 = 6  => 10 pairs (_) / B8 = 6  =>  8 pairs (_)
C1,C8: 6.. / C1 = 6  =>  8 pairs (_) / C8 = 6  => 10 pairs (_)
A7,B7: 7.. / A7 = 7  =>  9 pairs (_) / B7 = 7  =>  9 pairs (_)
C4,A5: 8.. / C4 = 8  => 11 pairs (_) / A5 = 8  => 16 pairs (_)
C4,F4: 8.. / C4 = 8  => 11 pairs (_) / F4 = 8  => 16 pairs (_)
B1,B3: 9.. / B1 = 9  =>  0 pairs (X) / B3 = 9  =>  8 pairs (_)
G6,H6: 9.. / G6 = 9  => 10 pairs (_) / H6 = 9  =>  9 pairs (_)
* DURATION: 0:00:32.591360  START: 05:01:41.256861  END: 05:02:13.848221 2017-05-01
* CP COUNT: (24)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,C3,D2,D5,E6,G2,I3)
* ....35....81.....6.....62..6..95.1...49.1.65...56.2..8..4....6.9.....73....76....
* PAIR A2: 3,5 BLK 1
A3: 3,5,4,7                              # reduction candidate for 3,5
A3: 3,5                                  # 17 pairs
B3: 3,5,7,9                              # reduction candidate for 3,5
B3: 3,5 => CTR
* 296.354.7581427396437.962.56..95.1.3749.1.6523156729488.4....6.96.5..73..5376.82.
B3: 7,9                                  #  8 pairs
* PAIR A2: 3,5 COL A
A7: 3,5,1,2,7,8                          # reduction candidate for 3,5
A7: 3,5                                  # 12 pairs
A9: 3,5,1,2,8                            # reduction candidate for 3,5
A9: 3,5                                  # 10 pairs
* PAIR C3: 3,7 BLK 1
A3: 3,7,4,5                              # reduction candidate for 3,7
A3: 3,7                                  # 21 pairs
B3: 3,7,5,9                              # reduction candidate for 3,7
B3: 3,7 => CTR
* 296.354.75814273964...962.56..95.1.3749.1.652..5672948.7428.56.96.5..73....76..2.
B3: 5,9                                  #  8 pairs
* PAIR C3: 3,7 COL C
C4: 3,7,2,8                              # reduction candidate for 3,7
C4: 3,7                                  # 20 pairs
C4: 2,8                                  #  9 pairs
* PAIR D2: 2,4 BLK 2
E2: 2,4,7,9                              # reduction candidate for 2,4
E2: 2,4                                  # 18 pairs
E2: 7,9                                  #  7 pairs
* PAIR D2: 2,4 COL D
D8: 2,4,5,8                              # reduction candidate for 2,4
D8: 2,4                                  # 14 pairs
D8: 5,8                                  #  9 pairs
* PAIR I3: 3,5 ROW 3
A3: 3,5,4,7                              # reduction candidate for 3,5
A3: 3,5                                  # 17 pairs
B3: 3,5,7,9                              # reduction candidate for 3,5
B3: 3,5 => CTR
* 296.354.7581427396437.962.56..95.1.3749.1.6523156729488.4....6.96.5..73..5376.82.
B3: 7,9                                  #  8 pairs
* PAIR D5: 3,8 BLK 5
F4: 3,8,4,7                              # reduction candidate for 3,8
F4: 3,8                                  # 12 pairs
F5: 3,8,7                                # reduction candidate for 3,8
F5: 3,8                                  # 15 pairs
* PAIR D5: 3,8 ROW 5
A5: 3,8,2,7                              # reduction candidate for 3,8
A5: 3,8                                  # 18 pairs
A5: 2,7                                  # 12 pairs
* PAIR D5: 3,8 COL D
D7: 3,8,2,5                              # reduction candidate for 3,8
D7: 3,8                                  # 16 pairs
D7: 2,5                                  # 10 pairs
* PAIR E6: 4,7 BLK 5
F4: 4,7,3,8                              # reduction candidate for 4,7
F4: 4,7                                  # 15 pairs
F4: 3,8                                  # 12 pairs
* PAIR E6: 4,7 ROW 6
H6: 4,7,9                                # reduction candidate for 4,7
H6: 4,7                                  # 10 pairs
H6: 9                                    #  9 pairs
* PAIR E6: 4,7 COL E
E2: 4,7,2,9                              # reduction candidate for 4,7
E2: 4,7                                  # 10 pairs
E3: 4,7,8,9                              # reduction candidate for 4,7
E3: 4,7                                  # 17 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0088-base-pr-000.dot
* REASONING
* DIS # B3: 3,5 => CTR => B3: 7,9
* DIS # B3: 3,7 => CTR => B3: 5,9
* DIS # B3: 3,5 => CTR => B3: 7,9
* CNT   3 HDP CHAINS /  29 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,C3,D2,D5,E6,G2,I3)
* ....35....81.....6.....62..6..95.1...49.1.65...56.2..8..4....6.9.....73....76....
* PAIR A2: 3,5 BLK 1
A3: 3,5,4,7                              # reduction candidate for 3,5
A3: 3,5                                  # 17 pairs
B3: 3,5,7,9                              # reduction candidate for 3,5
B3: 3,5 => CTR
* 296.354.7581427396437.962.56..95.1.3749.1.6523156729488.4....6.96.5..73..5376.82.
* RESTART
* PAIR A2: 3,5 BLK 1
A3: 3,5,4,7                              # reduction candidate for 3,5
A3: 3,5                                  # 17 pairs
A3: 4,7                                  # 10 pairs
* PAIR C3: 3,7 BLK 1
A3: 3,7,4,5                              # reduction candidate for 3,7
A3: 3,7                                  # 21 pairs
A3: 4,5                                  #  9 pairs
* PAIR C3: 3,7 COL C
C4: 3,7,2,8                              # reduction candidate for 3,7
C4: 3,7                                  # 22 pairs
C4: 2,8                                  # 11 pairs
* PAIR D2: 2,4 BLK 2
E2: 2,4,7,9                              # reduction candidate for 2,4
E2: 2,4                                  # 20 pairs
E2: 7,9                                  #  8 pairs
* PAIR D2: 2,4 COL D
D8: 2,4,5,8                              # reduction candidate for 2,4
D8: 2,4                                  # 15 pairs
D8: 5,8                                  # 10 pairs
* PAIR I3: 3,5 ROW 3
A3: 3,5,4,7                              # reduction candidate for 3,5
A3: 3,5                                  # 17 pairs
A3: 4,7                                  # 10 pairs
* PAIR D5: 3,8 BLK 5
F4: 3,8,4,7                              # reduction candidate for 3,8
F4: 3,8                                  # 13 pairs
F5: 3,8,7                                # reduction candidate for 3,8
F5: 3,8                                  # 17 pairs
* PAIR D5: 3,8 ROW 5
A5: 3,8,2,7                              # reduction candidate for 3,8
A5: 3,8                                  # 19 pairs
A5: 2,7                                  # 14 pairs
* PAIR D5: 3,8 COL D
D7: 3,8,2,5                              # reduction candidate for 3,8
D7: 3,8                                  # 17 pairs
D7: 2,5                                  # 11 pairs
* PAIR E6: 4,7 BLK 5
F4: 4,7,3,8                              # reduction candidate for 4,7
F4: 4,7                                  # 17 pairs
F4: 3,8                                  # 13 pairs
* PAIR E6: 4,7 ROW 6
H6: 4,7,9                                # reduction candidate for 4,7
H6: 4,7                                  # 11 pairs
H6: 9                                    #  9 pairs
* PAIR E6: 4,7 COL E
E2: 4,7,2,9                              # reduction candidate for 4,7
E2: 4,7                                  # 11 pairs
E3: 4,7,8,9                              # reduction candidate for 4,7
E3: 4,7                                  # 17 pairs

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A2,B3,C3,D2,D5,E6,G2,I3)
* ....35....81.....6.....62..6..95.1...49.1.65...56.2..8..4....6.9.....73....76....
* PAIR A2: 3,5 BLK 1
A3: 3,5,4,7                              # reduction candidate for 3,5
A3: 3,5                                  # 17 pairs
A3: 4,7                                  # 10 pairs
* PAIR B3: 7,9 BLK 1
B1: 7,9,2,6                              # reduction candidate for 7,9
B1: 7,9 => CTR
* 2.6.35..7581.7.396473.962.5627958143849317652..56429787.42...6.96258.73...876..2.
* PAIR C3: 3,7 BLK 1
A3: 3,7,4,5                              # reduction candidate for 3,7
A3: 3,7                                  # 21 pairs
A3: 4,5                                  # 10 pairs
* PAIR C3: 3,7 COL C
C4: 3,7,2,8                              # reduction candidate for 3,7
C4: 3,7 => CTR
* 462.359.7.81..9..6.9...62..62.9581..849317652715642398274593861956..1734138764.2.
* PAIR RESTART
* PAIR D2: 2,4 BLK 2
E2: 2,4,7,9                              # reduction candidate for 2,4
E2: 2,4 => CTR
* ..7.35....81429.76.93.762.56..95.1...49.1.65...5642398..4.9..6.9...8.73....76....
* PAIR I3: 3,5 ROW 3
A3: 3,5,4                                # reduction candidate for 3,5
A3: 4 => CTR
* 267.35...5812..3.6493..62.56..95.1...49.1.652..56.2..8..4....6.9.6...73....76..2.
* PAIR RESTART
* PAIR D5: 3,8 BLK 5
F4: 3,8,4,7                              # reduction candidate for 3,8
F4: 3,8                                  # 25 pairs
F5: 3,8,7                                # reduction candidate for 3,8
F5: 3,8                                  # 25 pairs
* PAIR D5: 3,8 COL D
D7: 3,8,5                                # reduction candidate for 3,8
D7: 5                                    # 24 pairs
D7: 3,8                                  # 19 pairs
* PAIR E6: 4,7 BLK 5
F4: 4,7,3,8                              # reduction candidate for 4,7
F4: 4,7                                  # 25 pairs
F4: 3,8                                  # 25 pairs

* LEVEL 0 PASS 1 ROUND 3 (AUTO SOLVE) (A2,A3,A6,B1,C1,C4,D1,D5,E2,E3,E6,F2,G1,G2,H3,H4,H6,I3)
* 4...35....812...46.97..62..6..95.1...49.1.65...56.2..8..4....6.9.....73...376....
* PAIR B1: 2,6 COL B
B8: 2,6,1,5                              # reduction candidate for 2,6
B8: 2,6                                  # 22 pairs
B8: 1,5                                  # 19 pairs
* PAIR C1: 2,6 COL C
C8: 2,6,8                                # reduction candidate for 2,6
C8: 8 => CTR
* 4.6.35....812...46.97..62..6.2958174849317652..5642398..4..3.6.968.2.73...376.4..
* PAIR RESTART
* PAIR D1: 1,8 BLK 2
D3: 1,8,4                                # reduction candidate for 1,8
D3: 1,8 => SOLVED
* 462835971581297346397146285678954123249318657135672498714523869956481732823769514
* DURATION: 0:00:43.289730  START: 05:02:35.379603  END: 05:03:18.669333 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0088-base-pr-001.dot
* REASONING
* DIS # B3: 3,5 => CTR => B3: 7,9
* DIS B3: 7,9 # B1: 7,9 => CTR => B1: 2,6
* DIS B3: 7,9 + B1: 2,6 # C4: 3,7 => CTR => C4: 2,8
* DIS B3: 7,9 + B1: 2,6 + C4: 2,8 # E2: 2,4 => CTR => E2: 7,9
* DIS B3: 7,9 + B1: 2,6 + C4: 2,8 + E2: 7,9 # A3: 4 => CTR => A3: 3,5
* DIS B3: 7,9 + B1: 2,6 + C4: 2,8 + E2: 7,9 + A3: 3,5 # C8: 8 => CTR => C8: 2,6
* PRF B3: 7,9 + B1: 2,6 + C4: 2,8 + E2: 7,9 + A3: 3,5 + C8: 2,6 # D3: 1,8 => SOL
* STA B3: 7,9 + B1: 2,6 + C4: 2,8 + E2: 7,9 + A3: 3,5 + C8: 2,6 + D3: 1,8
* CNT   7 HDP CHAINS /  46 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=88

Solution

position: 462835971581297346397146285678954123249318657135672498714523869956481732823769514 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 # A3: 3,5 => UNS
* DIS # B3: 3,5 => CTR => B3: 7,9
* INC # B3: 7,9 => UNS
* INC # A7: 3,5 => UNS
* INC # A9: 3,5 => UNS
* INC # A3: 3,7 => UNS
* DIS # B3: 3,7 => CTR => B3: 5,9
* INC # B3: 5,9 => UNS
* INC # C4: 3,7 => UNS
* INC # C4: 2,8 => UNS
* INC # E2: 2,4 => UNS
* INC # E2: 7,9 => UNS
* INC # D8: 2,4 => UNS
* INC # D8: 5,8 => UNS
* INC # A3: 3,5 => UNS
* DIS # B3: 3,5 => CTR => B3: 7,9
* INC # B3: 7,9 => UNS
* INC # F4: 3,8 => UNS
* INC # F5: 3,8 => UNS
* INC # A5: 3,8 => UNS
* INC # A5: 2,7 => UNS
* INC # D7: 3,8 => UNS
* INC # D7: 2,5 => UNS
* INC # F4: 4,7 => UNS
* INC # F4: 3,8 => UNS
* INC # H6: 4,7 => UNS
* INC # H6: 9 => UNS
* INC # E2: 4,7 => UNS
* INC # E3: 4,7 => UNS
* CNT  29 HDP CHAINS /  29 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A3: 3,5 => UNS
* DIS # B3: 3,5 => CTR => B3: 7,9
* INC B3: 7,9 # A3: 3,5 => UNS
* INC B3: 7,9 # A3: 4,7 => UNS
* INC B3: 7,9 # A3: 3,7 => UNS
* INC B3: 7,9 # A3: 4,5 => UNS
* INC B3: 7,9 # C4: 3,7 => UNS
* INC B3: 7,9 # C4: 2,8 => UNS
* INC B3: 7,9 # E2: 2,4 => UNS
* INC B3: 7,9 # E2: 7,9 => UNS
* INC B3: 7,9 # D8: 2,4 => UNS
* INC B3: 7,9 # D8: 5,8 => UNS
* INC B3: 7,9 # A3: 3,5 => UNS
* INC B3: 7,9 # A3: 4,7 => UNS
* INC B3: 7,9 # F4: 3,8 => UNS
* INC B3: 7,9 # F5: 3,8 => UNS
* INC B3: 7,9 # A5: 3,8 => UNS
* INC B3: 7,9 # A5: 2,7 => UNS
* INC B3: 7,9 # D7: 3,8 => UNS
* INC B3: 7,9 # D7: 2,5 => UNS
* INC B3: 7,9 # F4: 4,7 => UNS
* INC B3: 7,9 # F4: 3,8 => UNS
* INC B3: 7,9 # H6: 4,7 => UNS
* INC B3: 7,9 # H6: 9 => UNS
* INC B3: 7,9 # E2: 4,7 => UNS
* INC B3: 7,9 # E3: 4,7 => UNS
* INC B3: 7,9 # A3: 3,5 => UNS
* INC B3: 7,9 # A3: 4,7 => UNS
* DIS B3: 7,9 # B1: 7,9 => CTR => B1: 2,6
* INC B3: 7,9 + B1: 2,6 # A3: 3,7 => UNS
* INC B3: 7,9 + B1: 2,6 # A3: 4,5 => UNS
* DIS B3: 7,9 + B1: 2,6 # C4: 3,7 => CTR => C4: 2,8
* DIS B3: 7,9 + B1: 2,6 + C4: 2,8 # E2: 2,4 => CTR => E2: 7,9
* INC B3: 7,9 + B1: 2,6 + C4: 2,8 + E2: 7,9 # A3: 3,5 => UNS
* DIS B3: 7,9 + B1: 2,6 + C4: 2,8 + E2: 7,9 # A3: 4 => CTR => A3: 3,5
* INC B3: 7,9 + B1: 2,6 + C4: 2,8 + E2: 7,9 + A3: 3,5 # F4: 3,8 => UNS
* INC B3: 7,9 + B1: 2,6 + C4: 2,8 + E2: 7,9 + A3: 3,5 # F5: 3,8 => UNS
* INC B3: 7,9 + B1: 2,6 + C4: 2,8 + E2: 7,9 + A3: 3,5 # D7: 3,8 => UNS
* INC B3: 7,9 + B1: 2,6 + C4: 2,8 + E2: 7,9 + A3: 3,5 # D7: 5 => UNS
* INC B3: 7,9 + B1: 2,6 + C4: 2,8 + E2: 7,9 + A3: 3,5 # F4: 4,7 => UNS
* INC B3: 7,9 + B1: 2,6 + C4: 2,8 + E2: 7,9 + A3: 3,5 # F4: 3,8 => UNS
* INC B3: 7,9 + B1: 2,6 + C4: 2,8 + E2: 7,9 + A3: 3,5 # B8: 2,6 => UNS
* INC B3: 7,9 + B1: 2,6 + C4: 2,8 + E2: 7,9 + A3: 3,5 # B8: 1,5 => UNS
* INC B3: 7,9 + B1: 2,6 + C4: 2,8 + E2: 7,9 + A3: 3,5 # C8: 2,6 => UNS
* DIS B3: 7,9 + B1: 2,6 + C4: 2,8 + E2: 7,9 + A3: 3,5 # C8: 8 => CTR => C8: 2,6
* PRF B3: 7,9 + B1: 2,6 + C4: 2,8 + E2: 7,9 + A3: 3,5 + C8: 2,6 # D3: 1,8 => SOL
* STA B3: 7,9 + B1: 2,6 + C4: 2,8 + E2: 7,9 + A3: 3,5 + C8: 2,6 + D3: 1,8
* CNT  46 HDP CHAINS /  46 HYP OPENED