Analysis of zz-www.sudokuwiki.org-0086-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=86

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=86

position: .......78.3.8..2..48...71....7..5...9...2...3...9..6....52...81..4..1.5.12....... initial

Autosolve

position: .....2.7873.8..2..482..71....7..58..9..72.5.3...9..6.7..52...81..4..1.5212....... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B5: 6 => CTR => B5: 1,4
* PRF # A8: 3,6 => SOL
* DIS # E7: 3,6 => CTR => E7: 4,7,9
* DIS # E7: 3,6 => CTR => E7: 4,7,9
* DIS # E8: 3,6 => CTR => E8: 7,8,9
* PRF # A8: 3,6 => SOL
* DIS # D1: 3,6 => CTR => D1: 1,4
* PRF # D4: 3,6 => SOL
* CNT   8 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 # B5: 6 => CTR => B5: 1,4
* PRF B5: 1,4 # A8: 3,6 => SOL
* STA B5: 1,4 + A8: 3,6
* CNT   2 HDP CHAINS /  13 HYP OPENED

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

Details

Positions

.......78.3.8..2..48...71....7..5...9...2...3...9..6....52...81..4..1.5.12....... initial
.....2.7873.8..2..482..71....7..58..9..72.5.3...9..6.7..52...81..4..1.5212....... autosolve
569142378731896245482537169217365894946728513853914627695273481374681952128459736 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
A1: 5,6
I4: 4,9
H5: 1,4
A7: 3,6
D8: 3,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C2,E2: 1.. / C2 = 1  => 10 pairs (_) / E2 = 1  =>  8 pairs (_)
D1,D4: 1.. / D1 = 1  => 11 pairs (_) / D4 = 1  =>  6 pairs (_)
A4,A6: 2.. / A4 = 2  =>  9 pairs (_) / A6 = 2  =>  9 pairs (_)
H4,H6: 2.. / H4 = 2  =>  9 pairs (_) / H6 = 2  =>  9 pairs (_)
A4,H4: 2.. / A4 = 2  =>  9 pairs (_) / H4 = 2  =>  9 pairs (_)
A6,H6: 2.. / A6 = 2  =>  9 pairs (_) / H6 = 2  =>  9 pairs (_)
G1,H3: 3.. / G1 = 3  =>  0 pairs (*) / H3 = 3  =>  0 pairs (X)
C6,C9: 3.. / C6 = 3  => 11 pairs (_) / C9 = 3  => 12 pairs (_)
H3,H9: 3.. / H3 = 3  =>  7 pairs (_) / H9 = 3  =>  0 pairs (*)
A1,B1: 5.. / A1 = 5  =>  4 pairs (_) / B1 = 5  =>  0 pairs (X)
I2,I3: 5.. / I2 = 5  =>  6 pairs (_) / I3 = 5  => 13 pairs (_)
A6,B6: 5.. / A6 = 5  =>  0 pairs (X) / B6 = 5  =>  4 pairs (_)
D9,E9: 5.. / D9 = 5  =>  8 pairs (_) / E9 = 5  =>  8 pairs (_)
E2,I2: 5.. / E2 = 5  => 13 pairs (_) / I2 = 5  =>  6 pairs (_)
A1,A6: 5.. / A1 = 5  =>  4 pairs (_) / A6 = 5  =>  0 pairs (X)
B1,B6: 5.. / B1 = 5  =>  0 pairs (X) / B6 = 5  =>  4 pairs (_)
D3,D9: 5.. / D3 = 5  =>  8 pairs (_) / D9 = 5  =>  8 pairs (_)
H9,I9: 6.. / H9 = 6  => 12 pairs (_) / I9 = 6  =>  6 pairs (_)
B7,B8: 7.. / B7 = 7  =>  6 pairs (_) / B8 = 7  =>  7 pairs (_)
E9,G9: 7.. / E9 = 7  =>  8 pairs (_) / G9 = 7  =>  6 pairs (_)
A8,C9: 8.. / A8 = 8  =>  6 pairs (_) / C9 = 8  =>  0 pairs (*)
C5,F5: 8.. / C5 = 8  =>  9 pairs (_) / F5 = 8  => 13 pairs (_)
A8,E8: 8.. / A8 = 8  =>  6 pairs (_) / E8 = 8  =>  0 pairs (*)
A6,A8: 8.. / A6 = 8  =>  0 pairs (*) / A8 = 8  =>  0 pairs (X)
H4,I4: 9.. / H4 = 9  => 14 pairs (_) / I4 = 9  =>  7 pairs (_)
* DURATION: 0:00:34.936317  START: 04:58:20.308242  END: 04:58:55.244559 2017-05-01
* CP COUNT: (25)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A7,D8,H5,I4)
* .....2.7873.8..2..482..71....7..58..9..72.5.3...9..6.7..52...81..4..1.5212.......
* PAIR A1: 5,6 BLK 1
B1: 5,6,1,9                              # reduction candidate for 5,6
B1: 5,6                                  # 14 pairs
B1: 1,9                                  #  6 pairs
* PAIR I4: 4,9 BLK 6
H4: 4,9,1,2                              # reduction candidate for 4,9
H4: 4,9                                  # 13 pairs
H4: 1,2                                  #  8 pairs
* PAIR I4: 4,9 COL I
I2: 4,9,5,6                              # reduction candidate for 4,9
I2: 4,9                                  # 14 pairs
I9: 4,9,6                                # reduction candidate for 4,9
I9: 4,9                                  # 12 pairs
* PAIR H5: 1,4 BLK 6
H4: 1,4,2,9                              # reduction candidate for 1,4
H4: 1,4                                  # 12 pairs
H6: 1,4,2                                # reduction candidate for 1,4
H6: 1,4                                  #  9 pairs
* PAIR H5: 1,4 ROW 5
B5: 1,4,6                                # reduction candidate for 1,4
B5: 6 => CTR
* 5164.2.78739816245482..71.6.4716582996.72.5.325.9..6.7..52...818.46.1.5212.....64
B5: 1,4                                  #  8 pairs
* PAIR A7: 3,6 BLK 7
A8: 3,6,8                                # reduction candidate for 3,6
A8: 3,6 => SOLVED
* 569142378731896245482537169217365894946728513853914627695273481374681952128459736
A8: 8                                    #  6 pairs
* PAIR A7: 3,6 ROW 7
E7: 3,6,4,7,9                            # reduction candidate for 3,6
E7: 3,6 => CTR
* 5..3.2.7873.8..2..4825971363.71.58299..72.5.325.9.36.76.523..818946713521234.....
E7: 4,7,9                                #  5 pairs
F7: 3,6,4,9                              # reduction candidate for 3,6
F7: 3,6                                  #  8 pairs
* PAIR A7: 3,6 COL A
A4: 3,6,2                                # reduction candidate for 3,6
A4: 3,6                                  #  9 pairs
A4: 2                                    #  9 pairs
* PAIR D8: 3,6 BLK 8
E7: 3,6,4,7,9                            # reduction candidate for 3,6
E7: 3,6 => CTR
* 5..3.2.7873.8..2..4825971363.71.58299..72.5.325.9.36.76.523..818946713521234.....
E7: 4,7,9                                #  5 pairs
F7: 3,6,4,9                              # reduction candidate for 3,6
F7: 3,6                                  #  8 pairs
E8: 3,6,7,8,9                            # reduction candidate for 3,6
E8: 3,6 => CTR
* 5...32.7873185.2..4826971353.7..58299..7265.325.9836476.52..3818.4361.52123578...
E8: 7,8,9                                #  5 pairs
* PAIR D8: 3,6 ROW 8
A8: 3,6,8                                # reduction candidate for 3,6
A8: 3,6 => SOLVED
* 569142378731896245482537169217365894946728513853914627695273481374681952128459736
A8: 8                                    #  6 pairs
* PAIR D8: 3,6 COL D
D1: 3,6,1,4                              # reduction candidate for 3,6
D1: 3,6 => CTR
* ...34297873.81.2454825.71..267135894948726513...984627..52..4818.4..1.5212.4587..
D1: 1,4                                  #  6 pairs
D3: 3,6,5                                # reduction candidate for 3,6
D3: 3,6                                  #  8 pairs
D4: 3,6,1,4                              # reduction candidate for 3,6
D4: 3,6 => SOLVED
* 569142378731896245482537169217365894946728513853914627695273481374681952128459736
D4: 1,4                                  #  6 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0086-base-pr-000.dot
* REASONING
* DIS # B5: 6 => CTR => B5: 1,4
* PRF # A8: 3,6 => SOL
* DIS # E7: 3,6 => CTR => E7: 4,7,9
* DIS # E7: 3,6 => CTR => E7: 4,7,9
* DIS # E8: 3,6 => CTR => E8: 7,8,9
* PRF # A8: 3,6 => SOL
* DIS # D1: 3,6 => CTR => D1: 1,4
* PRF # D4: 3,6 => SOL
* CNT   8 HDP CHAINS /  29 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A7,D8,H5,I4)
* .....2.7873.8..2..482..71....7..58..9..72.5.3...9..6.7..52...81..4..1.5212.......
* PAIR A1: 5,6 BLK 1
B1: 5,6,1,9                              # reduction candidate for 5,6
B1: 5,6                                  # 14 pairs
B1: 1,9                                  #  6 pairs
* PAIR I4: 4,9 BLK 6
H4: 4,9,1,2                              # reduction candidate for 4,9
H4: 4,9                                  # 13 pairs
H4: 1,2                                  #  8 pairs
* PAIR I4: 4,9 COL I
I2: 4,9,5,6                              # reduction candidate for 4,9
I2: 4,9                                  # 14 pairs
I9: 4,9,6                                # reduction candidate for 4,9
I9: 4,9                                  # 12 pairs
* PAIR H5: 1,4 BLK 6
H4: 1,4,2,9                              # reduction candidate for 1,4
H4: 1,4                                  # 12 pairs
H6: 1,4,2                                # reduction candidate for 1,4
H6: 1,4                                  #  9 pairs
* PAIR H5: 1,4 ROW 5
B5: 1,4,6                                # reduction candidate for 1,4
B5: 6 => CTR
* 5164.2.78739816245482..71.6.4716582996.72.5.325.9..6.7..52...818.46.1.5212.....64
* PAIR RESTART
* PAIR H5: 1,4 BLK 6
H4: 1,4,2,9                              # reduction candidate for 1,4
H4: 1,4                                  # 15 pairs
H6: 1,4,2                                # reduction candidate for 1,4
H6: 1,4                                  # 12 pairs
* PAIR A7: 3,6 BLK 7
A8: 3,6,8                                # reduction candidate for 3,6
A8: 3,6 => SOLVED
* 569142378731896245482537169217365894946728513853914627695273481374681952128459736
* DURATION: 0:00:11.979601  START: 04:59:19.501337  END: 04:59:31.480938 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0086-base-pr-001.dot
* REASONING
* DIS # B5: 6 => CTR => B5: 1,4
* PRF B5: 1,4 # A8: 3,6 => SOL
* STA B5: 1,4 + A8: 3,6
* CNT   2 HDP CHAINS /  13 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=86

Solution

position: 569142378731896245482537169217365894946728513853914627695273481374681952128459736 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 # B1: 1,9 => UNS
* INC # H4: 4,9 => UNS
* INC # H4: 1,2 => UNS
* INC # I2: 4,9 => UNS
* INC # I9: 4,9 => UNS
* INC # H4: 1,4 => UNS
* INC # H6: 1,4 => UNS
* INC # B5: 1,4 => UNS
* DIS # B5: 6 => CTR => B5: 1,4
* PRF # A8: 3,6 => SOL
* INC # A8: 8 => UNS
* DIS # E7: 3,6 => CTR => E7: 4,7,9
* INC # E7: 4,7,9 => UNS
* INC # F7: 3,6 => UNS
* INC # A4: 3,6 => UNS
* INC # A4: 2 => UNS
* DIS # E7: 3,6 => CTR => E7: 4,7,9
* INC # E7: 4,7,9 => UNS
* INC # F7: 3,6 => UNS
* DIS # E8: 3,6 => CTR => E8: 7,8,9
* INC # E8: 7,8,9 => UNS
* PRF # A8: 3,6 => SOL
* INC # A8: 8 => UNS
* DIS # D1: 3,6 => CTR => D1: 1,4
* INC # D1: 1,4 => UNS
* INC # D3: 3,6 => UNS
* PRF # D4: 3,6 => SOL
* INC # D4: 1,4 => UNS
* CNT  29 HDP CHAINS /  29 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B1: 5,6 => UNS
* INC # B1: 1,9 => UNS
* INC # H4: 4,9 => UNS
* INC # H4: 1,2 => UNS
* INC # I2: 4,9 => UNS
* INC # I9: 4,9 => UNS
* INC # H4: 1,4 => UNS
* INC # H6: 1,4 => UNS
* INC # B5: 1,4 => UNS
* DIS # B5: 6 => CTR => B5: 1,4
* INC B5: 1,4 # H4: 1,4 => UNS
* INC B5: 1,4 # H6: 1,4 => UNS
* PRF B5: 1,4 # A8: 3,6 => SOL
* STA B5: 1,4 + A8: 3,6
* CNT  13 HDP CHAINS /  13 HYP OPENED