Analysis of zz-www.sudokuoftheday.co.uk-20190106-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019

position: .1...42......1.7....69....4..48....2683.92..19........7...6........39.5...54..6.. initial

Autosolve

position: .1...42......1.7....69....41.48....2683.92..19...4....7...6.....6..39.5...54..6.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B6: 2 => CTR => B6: 5,7
* DIS # B6: 2,7 => CTR => B6: 5
* PRF # E3: 5,7 => SOL
* DIS # D1: 5,7 => CTR => D1: 3,6
* DIS # H9: 7,8 => CTR => H9: 1,2,3,9
* CNT   5 HDP CHAINS /  24 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 # B6: 2 => CTR => B6: 5,7
* PRF B6: 5,7 # E3: 5,7 => SOL
* STA B6: 5,7 + E3: 5,7
* CNT   2 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

.1...42......1.7....69....4..48....2683.92..19........7...6........39.5...54..6.. initial
.1...42......1.7....69....41.48....2683.92..19...4....7...6.....6..39.5...54..6.. autosolve
517384296439216785826975134174853962683792541952641873741568329268139457395427618 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
B4: 5,7
C6: 2,7
E4: 5,7
F4: 3,6
D5: 5,7
G4: 3,9
G5: 4,5
H5: 4,7
I8: 7,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G3,H3: 1.. / G3 = 1  => 14 pairs (_) / H3 = 1  => 27 pairs (_)
D6,F6: 1.. / D6 = 1  => 17 pairs (_) / F6 = 1  => 16 pairs (_)
C7,C8: 1.. / C7 = 1  => 12 pairs (_) / C8 = 1  => 11 pairs (_)
F9,H9: 1.. / F9 = 1  => 27 pairs (_) / H9 = 1  => 14 pairs (_)
D2,E3: 2.. / D2 = 2  =>  0 pairs (*) / E3 = 2  =>  0 pairs (X)
B6,C6: 2.. / B6 = 2  =>  0 pairs (X) / C6 = 2  => 13 pairs (_)
H7,H9: 2.. / H7 = 2  => 11 pairs (_) / H9 = 2  => 30 pairs (_)
E3,E9: 2.. / E3 = 2  => 11 pairs (_) / E9 = 2  =>  0 pairs (*)
A2,B2: 4.. / A2 = 4  => 14 pairs (_) / B2 = 4  => 10 pairs (_)
G5,H5: 4.. / G5 = 4  =>  0 pairs (X) / H5 = 4  => 10 pairs (_)
B7,A8: 4.. / B7 = 4  => 14 pairs (_) / A8 = 4  => 10 pairs (_)
A8,G8: 4.. / A8 = 4  => 10 pairs (_) / G8 = 4  => 14 pairs (_)
A2,A8: 4.. / A2 = 4  => 14 pairs (_) / A8 = 4  => 10 pairs (_)
B2,B7: 4.. / B2 = 4  => 10 pairs (_) / B7 = 4  => 14 pairs (_)
H5,H7: 4.. / H5 = 4  => 10 pairs (_) / H7 = 4  =>  0 pairs (X)
B4,B6: 5.. / B4 = 5  =>  0 pairs (X) / B6 = 5  => 10 pairs (_)
E4,D5: 5.. / E4 = 5  => 10 pairs (_) / D5 = 5  =>  0 pairs (X)
D7,F7: 5.. / D7 = 5  => 12 pairs (_) / F7 = 5  => 11 pairs (_)
B4,E4: 5.. / B4 = 5  =>  0 pairs (X) / E4 = 5  => 10 pairs (_)
D5,G5: 5.. / D5 = 5  =>  0 pairs (X) / G5 = 5  => 10 pairs (_)
F4,H4: 6.. / F4 = 6  => 12 pairs (_) / H4 = 6  =>  9 pairs (_)
C1,B3: 7.. / C1 = 7  => 13 pairs (_) / B3 = 7  =>  0 pairs (X)
E4,D5: 7.. / E4 = 7  =>  0 pairs (X) / D5 = 7  => 10 pairs (_)
B4,E4: 7.. / B4 = 7  => 10 pairs (_) / E4 = 7  =>  0 pairs (X)
D5,H5: 7.. / D5 = 7  => 10 pairs (_) / H5 = 7  =>  0 pairs (X)
D8,I8: 7.. / D8 = 7  =>  0 pairs (X) / I8 = 7  =>  9 pairs (_)
C1,C6: 7.. / C1 = 7  => 13 pairs (_) / C6 = 7  =>  0 pairs (X)
F3,F9: 7.. / F3 = 7  => 14 pairs (_) / F9 = 7  =>  0 pairs (*)
G4,H4: 9.. / G4 = 9  =>  9 pairs (_) / H4 = 9  => 14 pairs (_)
G4,G7: 9.. / G4 = 9  =>  9 pairs (_) / G7 = 9  => 14 pairs (_)
* DURATION: 0:00:31.402224  START: 02:45:16.091582  END: 02:45:47.493806 2019-05-01
* CP COUNT: (30)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,C6,D5,E4,F4,G4,G5,H5,I8)
* .1...42......1.7....69....41.48....2683.92..19...4....7...6.....6..39.5...54..6..
* PAIR B4: 5,7 BLK 4
B6: 5,7,2                                # reduction candidate for 5,7
B6: 2 => CTR
* .1.7.42...4..1.7...7692..1415487...2683592471927.4....7...65.4.46..39.57..548.62.
B6: 5,7                                  # 13 pairs
* PAIR C6: 2,7 BLK 4
B6: 2,7,5                                # reduction candidate for 2,7
B6: 2,7 => CTR
* .1..542..24..1.7.55.692781415487...268359247197214....7...65.4.46..39.5...5481627
B6: 5                                    # 10 pairs
* PAIR E4: 5,7 COL E
E1: 5,7,8                                # reduction candidate for 5,7
E1: 5,7                                  # 12 pairs
E3: 5,7,2,8                              # reduction candidate for 5,7
E3: 5,7 => SOLVED
* 517384296439216785826975134174853962683792541952641873741568329268139457395427618
E3: 2,8                                  # 10 pairs
* PAIR F4: 3,6 BLK 5
D6: 3,6,1                                # reduction candidate for 3,6
D6: 3,6                                  # 16 pairs
F6: 3,6,1                                # reduction candidate for 3,6
F6: 3,6                                  # 17 pairs
* PAIR F4: 3,6 ROW 4
H4: 3,6,9                                # reduction candidate for 3,6
H4: 9                                    # 14 pairs
H4: 3,6                                  #  9 pairs
* PAIR F4: 3,6 COL F
F2: 3,6,5,8                              # reduction candidate for 3,6
F2: 3,6                                  # 18 pairs
F2: 5,8                                  # 11 pairs
* PAIR D5: 5,7 COL D
D1: 5,7,3,6                              # reduction candidate for 5,7
D1: 5,7 => CTR
* .175842......1.7.553692.1.41.48....2683.92.419...41.7.7..165.2..61239.57..54..61.
D1: 3,6                                  # 10 pairs
* PAIR G4: 3,9 BLK 6
H4: 3,9,6                                # reduction candidate for 3,9
H4: 3,9                                  # 12 pairs
H4: 6                                    #  9 pairs
* PAIR G4: 3,9 COL G
G7: 3,9,1,4,8                            # reduction candidate for 3,9
G7: 3,9                                  # 13 pairs
G7: 1,4,8                                #  9 pairs
* PAIR I8: 7,8 BLK 9
H9: 7,8,1,2,3,9                          # reduction candidate for 7,8
H9: 7,8 => CTR
* .17.842.5....157..5.692781417485...268379254195214.3787..568.2..6.239.57..547168.
H9: 1,2,3,9                              #  9 pairs
I9: 7,8,3,9                              # reduction candidate for 7,8
I9: 7,8                                  # 12 pairs
* PAIR I8: 7,8 COL I
I6: 7,8,3,5,6                            # reduction candidate for 7,8
I6: 7,8                                  # 14 pairs
I6: 3,5,6                                #  9 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190106-absurd-base-pr-000.dot
* REASONING
* DIS # B6: 2 => CTR => B6: 5,7
* DIS # B6: 2,7 => CTR => B6: 5
* PRF # E3: 5,7 => SOL
* DIS # D1: 5,7 => CTR => D1: 3,6
* DIS # H9: 7,8 => CTR => H9: 1,2,3,9
* CNT   5 HDP CHAINS /  24 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,C6,D5,E4,F4,G4,G5,H5,I8)
* .1...42......1.7....69....41.48....2683.92..19...4....7...6.....6..39.5...54..6..
* PAIR B4: 5,7 BLK 4
B6: 5,7,2                                # reduction candidate for 5,7
B6: 2 => CTR
* .1.7.42...4..1.7...7692..1415487...2683592471927.4....7...65.4.46..39.57..548.62.
* PAIR E4: 5,7 COL E
E3: 5,7,2,8                              # reduction candidate for 5,7
E3: 5,7 => SOLVED
* 517384296439216785826975134174853962683792541952641873741568329268139457395427618
* DURATION: 0:00:02.998009  START: 02:46:00.831703  END: 02:46:03.829712 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190106-absurd-base-pr-001.dot
* REASONING
* DIS # B6: 2 => CTR => B6: 5,7
* PRF B6: 5,7 # E3: 5,7 => SOL
* STA B6: 5,7 + E3: 5,7
* CNT   2 HDP CHAINS /   3 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190106, absurd

Solution

position: 517384296439216785826975134174853962683792541952641873741568329268139457395427618 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 # B6: 5,7 => UNS
* DIS # B6: 2 => CTR => B6: 5,7
* DIS # B6: 2,7 => CTR => B6: 5
* INC # B6: 5 => UNS
* INC # E1: 5,7 => UNS
* PRF # E3: 5,7 => SOL
* INC # E3: 2,8 => UNS
* INC # D6: 3,6 => UNS
* INC # F6: 3,6 => UNS
* INC # H4: 3,6 => UNS
* INC # H4: 9 => UNS
* INC # F2: 3,6 => UNS
* INC # F2: 5,8 => UNS
* DIS # D1: 5,7 => CTR => D1: 3,6
* INC # D1: 3,6 => UNS
* INC # H4: 3,9 => UNS
* INC # H4: 6 => UNS
* INC # G7: 3,9 => UNS
* INC # G7: 1,4,8 => UNS
* DIS # H9: 7,8 => CTR => H9: 1,2,3,9
* INC # H9: 1,2,3,9 => UNS
* INC # I9: 7,8 => UNS
* INC # I6: 7,8 => UNS
* INC # I6: 3,5,6 => UNS
* CNT  24 HDP CHAINS /  24 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B6: 5,7 => UNS
* DIS # B6: 2 => CTR => B6: 5,7
* PRF B6: 5,7 # E3: 5,7 => SOL
* STA B6: 5,7 + E3: 5,7
* CNT   3 HDP CHAINS /   3 HYP OPENED