Analysis of zz-www.sudokuwiki.org-0023-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=23

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=23

position: .....8.1.3......85...6..9.4.1.5..2......6......5..2.697.6..1...19.4....7.8.2..... initial

Autosolve

position: .....8.1.3......85...6..9.461.5..2......6......5..2.697.6..1...19.4....7.8.2..... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A5: 4,8 => CTR => A5: 2,9
* DIS # H9: 4,5 => CTR => H9: 3,9
* PRF # G9: 3,4 => SOL
* CNT   3 HDP CHAINS /  37 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 # A5: 4,8 => CTR => A5: 2,9
* DIS A5: 2,9 # H9: 4,5 => CTR => H9: 3,9
* PRF A5: 2,9 + H9: 3,9 # G9: 3,4 => SOL
* STA A5: 2,9 + H9: 3,9 + G9: 3,4
* CNT   3 HDP CHAINS /  43 HYP OPENED

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

Details

Positions

.....8.1.3......85...6..9.4.1.5..2......6......5..2.697.6..1...19.4....7.8.2..... initial
.....8.1.3......85...6..9.461.5..2......6......5..2.697.6..1...19.4....7.8.2..... autosolve
924758316361924785857613924618549273239167548475832169746391852192485637583276491 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (6)
G2: 6,7
A6: 4,8
I4: 3,8
C8: 2,3
A9: 4,5
C9: 3,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C2,C3: 1.. / C2 = 1  =>  8 pairs (_) / C3 = 1  =>  7 pairs (_)
G9,I9: 1.. / G9 = 1  =>  7 pairs (_) / I9 = 1  => 15 pairs (_)
C3,E3: 1.. / C3 = 1  =>  7 pairs (_) / E3 = 1  =>  8 pairs (_)
I5,I9: 1.. / I5 = 1  =>  7 pairs (_) / I9 = 1  => 15 pairs (_)
I1,H3: 2.. / I1 = 2  =>  8 pairs (_) / H3 = 2  => 12 pairs (_)
B7,C8: 2.. / B7 = 2  =>  0 pairs (X) / C8 = 2  =>  6 pairs (_)
C8,H8: 2.. / C8 = 2  =>  6 pairs (_) / H8 = 2  =>  0 pairs (X)
I1,I7: 2.. / I1 = 2  =>  8 pairs (_) / I7 = 2  => 12 pairs (_)
G5,H5: 5.. / G5 = 5  =>  6 pairs (_) / H5 = 5  =>  9 pairs (_)
B7,A9: 5.. / B7 = 5  => 10 pairs (_) / A9 = 5  =>  6 pairs (_)
B1,B2: 6.. / B1 = 6  =>  7 pairs (_) / B2 = 6  =>  9 pairs (_)
F8,F9: 6.. / F8 = 6  =>  8 pairs (_) / F9 = 6  => 16 pairs (_)
B2,G2: 6.. / B2 = 6  =>  9 pairs (_) / G2 = 6  =>  7 pairs (_)
F8,G8: 6.. / F8 = 6  =>  8 pairs (_) / G8 = 6  => 16 pairs (_)
I1,I9: 6.. / I1 = 6  => 14 pairs (_) / I9 = 6  =>  7 pairs (_)
E9,F9: 7.. / E9 = 7  =>  6 pairs (_) / F9 = 7  => 11 pairs (_)
A3,C3: 8.. / A3 = 8  =>  7 pairs (_) / C3 = 8  =>  9 pairs (_)
E8,G8: 8.. / E8 = 8  =>  7 pairs (_) / G8 = 8  => 10 pairs (_)
H7,H9: 9.. / H7 = 9  => 13 pairs (_) / H9 = 9  =>  6 pairs (_)
A1,A5: 9.. / A1 = 9  =>  7 pairs (_) / A5 = 9  =>  7 pairs (_)
* DURATION: 0:00:20.822054  START: 03:50:34.355599  END: 03:50:55.177653 2017-05-01
* CP COUNT: (20)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A9,C8,C9,G2,I4)
* .....8.1.3......85...6..9.461.5..2......6......5..2.697.6..1...19.4....7.8.2.....
* PAIR G2: 6,7 BLK 3
G1: 6,7,3                                # reduction candidate for 6,7
G1: 6,7                                  #  9 pairs
G1: 3                                    #  9 pairs
* PAIR G2: 6,7 ROW 2
B2: 6,7,2,4                              # reduction candidate for 6,7
B2: 6,7                                  #  9 pairs
B2: 2,4                                  #  8 pairs
* PAIR A6: 4,8 BLK 4
C4: 4,8,3,7,9                            # reduction candidate for 4,8
C4: 4,8                                  #  9 pairs
A5: 4,8,2,9                              # reduction candidate for 4,8
A5: 4,8 => CTR
* 95473861236192478527861593461.54.278..7869..18.5172.697463.1...19.4.6..758.2.71.6
A5: 2,9                                  #  7 pairs
C5: 4,8,2,3,7,9                          # reduction candidate for 4,8
C5: 4,8                                  #  9 pairs
* PAIR A6: 4,8 ROW 6
E6: 4,8,1,3,7                            # reduction candidate for 4,8
E6: 4,8                                  #  9 pairs
G6: 4,8,1,3,7                            # reduction candidate for 4,8
G6: 4,8                                  #  8 pairs
* PAIR I4: 3,8 BLK 6
G5: 3,8,1,4,5,7                          # reduction candidate for 3,8
G5: 3,8                                  # 13 pairs
I5: 3,8,1                                # reduction candidate for 3,8
I5: 3,8                                  # 15 pairs
G6: 3,8,1,4,7                            # reduction candidate for 3,8
G6: 3,8                                  #  9 pairs
* PAIR I4: 3,8 ROW 4
C4: 3,8,4,7,9                            # reduction candidate for 3,8
C4: 3,8                                  #  8 pairs
E4: 3,8,4,7,9                            # reduction candidate for 3,8
E4: 3,8                                  #  8 pairs
* PAIR I4: 3,8 COL I
I7: 3,8,2                                # reduction candidate for 3,8
I7: 2                                    # 12 pairs
I7: 3,8                                  #  8 pairs
* PAIR C8: 2,3 BLK 7
B7: 2,3,4,5                              # reduction candidate for 2,3
B7: 4,5                                  #  7 pairs
B7: 2,3                                  #  7 pairs
* PAIR C8: 2,3 ROW 8
H8: 2,3,5                                # reduction candidate for 2,3
H8: 2,3                                  #  9 pairs
H8: 5                                    #  7 pairs
* PAIR C8: 2,3 COL C
C5: 2,3,4,7,8,9                          # reduction candidate for 2,3
C5: 2,3                                  #  9 pairs
C5: 4,7,8,9                              #  6 pairs
* PAIR A9: 4,5 BLK 7
B7: 4,5,2,3                              # reduction candidate for 4,5
B7: 4,5                                  #  7 pairs
B7: 2,3                                  #  7 pairs
* PAIR A9: 4,5 ROW 9
G9: 4,5,1,3,6                            # reduction candidate for 4,5
G9: 4,5                                  # 18 pairs
H9: 4,5,3,9                              # reduction candidate for 4,5
H9: 4,5 => CTR
* .5...8.1.36..2.78587163592461.5..2...2..6.45.435.128697463815921924563.75832...4.
H9: 3,9                                  #  7 pairs
* PAIR A9: 4,5 COL A
A1: 4,5,2,9                              # reduction candidate for 4,5
A1: 4,5                                  # 12 pairs
A1: 2,9                                  #  7 pairs
* PAIR C9: 3,4 BLK 7
B7: 3,4,2,5                              # reduction candidate for 3,4
B7: 3,4                                  #  7 pairs
B7: 2,5                                  #  7 pairs
* PAIR C9: 3,4 ROW 9
G9: 3,4,1,5,6                            # reduction candidate for 3,4
G9: 3,4 => SOLVED
* 924758316361924785857613924618549273239167548475832169746391852192485637583276491
G9: 1,5,6                                #  6 pairs
H9: 3,4,5,9                              # reduction candidate for 3,4
H9: 3,4                                  # 16 pairs
* PAIR C9: 3,4 COL C
C4: 3,4,7,8,9                            # reduction candidate for 3,4
C4: 3,4                                  #  8 pairs
C5: 3,4,2,7,8,9                          # reduction candidate for 3,4
C5: 3,4                                  #  8 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0023-base-pr-000.dot
* REASONING
* DIS # A5: 4,8 => CTR => A5: 2,9
* DIS # H9: 4,5 => CTR => H9: 3,9
* PRF # G9: 3,4 => SOL
* CNT   3 HDP CHAINS /  37 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A9,C8,C9,G2,I4)
* .....8.1.3......85...6..9.461.5..2......6......5..2.697.6..1...19.4....7.8.2.....
* PAIR G2: 6,7 BLK 3
G1: 6,7,3                                # reduction candidate for 6,7
G1: 6,7                                  #  9 pairs
G1: 3                                    #  9 pairs
* PAIR G2: 6,7 ROW 2
B2: 6,7,2,4                              # reduction candidate for 6,7
B2: 6,7                                  #  9 pairs
B2: 2,4                                  #  8 pairs
* PAIR A6: 4,8 BLK 4
C4: 4,8,3,7,9                            # reduction candidate for 4,8
C4: 4,8                                  #  9 pairs
A5: 4,8,2,9                              # reduction candidate for 4,8
A5: 4,8 => CTR
* 95473861236192478527861593461.54.278..7869..18.5172.697463.1...19.4.6..758.2.71.6
C5: 4,8,2,3,7,9                          # reduction candidate for 4,8
C5: 4,8                                  #  9 pairs
* PAIR A6: 4,8 ROW 6
E6: 4,8,1,3,7                            # reduction candidate for 4,8
E6: 4,8                                  # 10 pairs
G6: 4,8,1,3,7                            # reduction candidate for 4,8
G6: 4,8                                  #  9 pairs
* PAIR RESTART
* PAIR A6: 4,8 BLK 4
C4: 4,8,3,7,9                            # reduction candidate for 4,8
C4: 4,8                                  #  9 pairs
C5: 4,8,2,3,7,9                          # reduction candidate for 4,8
C5: 4,8                                  #  9 pairs
* PAIR A6: 4,8 ROW 6
E6: 4,8,1,3,7                            # reduction candidate for 4,8
E6: 4,8                                  # 10 pairs
G6: 4,8,1,3,7                            # reduction candidate for 4,8
G6: 4,8                                  #  9 pairs
* PAIR I4: 3,8 BLK 6
G5: 3,8,1,4,5,7                          # reduction candidate for 3,8
G5: 3,8                                  # 14 pairs
I5: 3,8,1                                # reduction candidate for 3,8
I5: 3,8                                  # 15 pairs
G6: 3,8,1,4,7                            # reduction candidate for 3,8
G6: 3,8                                  # 10 pairs
* PAIR I4: 3,8 ROW 4
C4: 3,8,4,7,9                            # reduction candidate for 3,8
C4: 3,8                                  #  9 pairs
E4: 3,8,4,7,9                            # reduction candidate for 3,8
E4: 3,8                                  #  9 pairs
* PAIR I4: 3,8 COL I
I7: 3,8,2                                # reduction candidate for 3,8
I7: 2                                    # 12 pairs
I7: 3,8                                  #  9 pairs
* PAIR C8: 2,3 BLK 7
B7: 2,3,4,5                              # reduction candidate for 2,3
B7: 4,5                                  #  8 pairs
B7: 2,3                                  #  8 pairs
* PAIR C8: 2,3 ROW 8
H8: 2,3,5                                # reduction candidate for 2,3
H8: 2,3                                  # 10 pairs
H8: 5                                    #  8 pairs
* PAIR C8: 2,3 COL C
C5: 2,3,4,7,8,9                          # reduction candidate for 2,3
C5: 2,3                                  # 10 pairs
C5: 4,7,8,9                              #  7 pairs
* PAIR A9: 4,5 BLK 7
B7: 4,5,2,3                              # reduction candidate for 4,5
B7: 4,5                                  #  8 pairs
B7: 2,3                                  #  8 pairs
* PAIR A9: 4,5 ROW 9
G9: 4,5,1,3,6                            # reduction candidate for 4,5
G9: 4,5                                  # 18 pairs
H9: 4,5,3,9                              # reduction candidate for 4,5
H9: 4,5 => CTR
* .5...8.1.36..2.78587163592461.5..2...2..6.45.435.128697463815921924563.75832...4.
* RESTART
* PAIR A9: 4,5 ROW 9
G9: 4,5,1,3,6                            # reduction candidate for 4,5
G9: 4,5                                  # 18 pairs
G9: 1,3,6                                #  8 pairs
* PAIR A9: 4,5 COL A
A1: 4,5,2,9                              # reduction candidate for 4,5
A1: 4,5                                  # 13 pairs
A1: 2,9                                  # 10 pairs
* PAIR RESTART
* PAIR A9: 4,5 BLK 7
B7: 4,5,2,3                              # reduction candidate for 4,5
B7: 4,5                                  #  9 pairs
B7: 2,3                                  #  8 pairs
* PAIR A9: 4,5 ROW 9
G9: 4,5,1,3,6                            # reduction candidate for 4,5
G9: 4,5                                  # 18 pairs
G9: 1,3,6                                #  8 pairs
* PAIR A9: 4,5 COL A
A1: 4,5,2,9                              # reduction candidate for 4,5
A1: 4,5                                  # 13 pairs
A1: 2,9                                  # 10 pairs
* PAIR C9: 3,4 BLK 7
B7: 3,4,2,5                              # reduction candidate for 3,4
B7: 3,4                                  #  9 pairs
B7: 2,5                                  #  9 pairs
* PAIR C9: 3,4 ROW 9
G9: 3,4,1,5,6                            # reduction candidate for 3,4
G9: 3,4 => SOLVED
* 924758316361924785857613924618549273239167548475832169746391852192485637583276491
* DURATION: 0:00:27.585014  START: 03:51:17.579723  END: 03:51:45.164737 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0023-base-pr-001.dot
* REASONING
* DIS # A5: 4,8 => CTR => A5: 2,9
* DIS A5: 2,9 # H9: 4,5 => CTR => H9: 3,9
* PRF A5: 2,9 + H9: 3,9 # G9: 3,4 => SOL
* STA A5: 2,9 + H9: 3,9 + G9: 3,4
* CNT   3 HDP CHAINS /  43 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=23

Solution

position: 924758316361924785857613924618549273239167548475832169746391852192485637583276491 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 # G1: 6,7 => UNS
* INC # G1: 3 => UNS
* INC # B2: 6,7 => UNS
* INC # B2: 2,4 => UNS
* INC # C4: 4,8 => UNS
* DIS # A5: 4,8 => CTR => A5: 2,9
* INC # A5: 2,9 => UNS
* INC # C5: 4,8 => UNS
* INC # E6: 4,8 => UNS
* INC # G6: 4,8 => UNS
* INC # G5: 3,8 => UNS
* INC # I5: 3,8 => UNS
* INC # G6: 3,8 => UNS
* INC # C4: 3,8 => UNS
* INC # E4: 3,8 => UNS
* INC # I7: 3,8 => UNS
* INC # I7: 2 => UNS
* INC # B7: 2,3 => UNS
* INC # B7: 4,5 => UNS
* INC # H8: 2,3 => UNS
* INC # H8: 5 => UNS
* INC # C5: 2,3 => UNS
* INC # C5: 4,7,8,9 => UNS
* INC # B7: 4,5 => UNS
* INC # B7: 2,3 => UNS
* INC # G9: 4,5 => UNS
* DIS # H9: 4,5 => CTR => H9: 3,9
* INC # H9: 3,9 => UNS
* INC # A1: 4,5 => UNS
* INC # A1: 2,9 => UNS
* INC # B7: 3,4 => UNS
* INC # B7: 2,5 => UNS
* PRF # G9: 3,4 => SOL
* INC # G9: 1,5,6 => UNS
* INC # H9: 3,4 => UNS
* INC # C4: 3,4 => UNS
* INC # C5: 3,4 => UNS
* CNT  37 HDP CHAINS /  37 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G1: 6,7 => UNS
* INC # G1: 3 => UNS
* INC # B2: 6,7 => UNS
* INC # B2: 2,4 => UNS
* INC # C4: 4,8 => UNS
* DIS # A5: 4,8 => CTR => A5: 2,9
* INC A5: 2,9 # C5: 4,8 => UNS
* INC A5: 2,9 # E6: 4,8 => UNS
* INC A5: 2,9 # G6: 4,8 => UNS
* INC A5: 2,9 # C4: 4,8 => UNS
* INC A5: 2,9 # C5: 4,8 => UNS
* INC A5: 2,9 # E6: 4,8 => UNS
* INC A5: 2,9 # G6: 4,8 => UNS
* INC A5: 2,9 # G5: 3,8 => UNS
* INC A5: 2,9 # I5: 3,8 => UNS
* INC A5: 2,9 # G6: 3,8 => UNS
* INC A5: 2,9 # C4: 3,8 => UNS
* INC A5: 2,9 # E4: 3,8 => UNS
* INC A5: 2,9 # I7: 3,8 => UNS
* INC A5: 2,9 # I7: 2 => UNS
* INC A5: 2,9 # B7: 2,3 => UNS
* INC A5: 2,9 # B7: 4,5 => UNS
* INC A5: 2,9 # H8: 2,3 => UNS
* INC A5: 2,9 # H8: 5 => UNS
* INC A5: 2,9 # C5: 2,3 => UNS
* INC A5: 2,9 # C5: 4,7,8,9 => UNS
* INC A5: 2,9 # B7: 4,5 => UNS
* INC A5: 2,9 # B7: 2,3 => UNS
* INC A5: 2,9 # G9: 4,5 => UNS
* DIS A5: 2,9 # H9: 4,5 => CTR => H9: 3,9
* INC A5: 2,9 + H9: 3,9 # G9: 4,5 => UNS
* INC A5: 2,9 + H9: 3,9 # G9: 1,3,6 => UNS
* INC A5: 2,9 + H9: 3,9 # A1: 4,5 => UNS
* INC A5: 2,9 + H9: 3,9 # A1: 2,9 => UNS
* INC A5: 2,9 + H9: 3,9 # B7: 4,5 => UNS
* INC A5: 2,9 + H9: 3,9 # B7: 2,3 => UNS
* INC A5: 2,9 + H9: 3,9 # G9: 4,5 => UNS
* INC A5: 2,9 + H9: 3,9 # G9: 1,3,6 => UNS
* INC A5: 2,9 + H9: 3,9 # A1: 4,5 => UNS
* INC A5: 2,9 + H9: 3,9 # A1: 2,9 => UNS
* INC A5: 2,9 + H9: 3,9 # B7: 3,4 => UNS
* INC A5: 2,9 + H9: 3,9 # B7: 2,5 => UNS
* PRF A5: 2,9 + H9: 3,9 # G9: 3,4 => SOL
* STA A5: 2,9 + H9: 3,9 + G9: 3,4
* CNT  43 HDP CHAINS /  43 HYP OPENED