Analysis of zz-www.sudokuoftheday.co.uk-20190321-absurd-base.sdk

Contents

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

level: medium

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

position: .....9..51.9...........3...7.64.21.9.4.8.6..7...3...6.9..1.8524......9....5.6..8. initial

Autosolve

position: .....9..51.9...........3.9.786452139341896257592371468967138524......9.6..596..8. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 4,8 => CTR => A1: 2,6
* PRF # C1: 4,8 => SOL
* DIS # C1: 3 => CTR => C1: 4,8
* DIS # A3: 4,8 => CTR => A3: 2,6
* DIS # E3: 4,8 => CTR => E3: 1,2
* DIS # C8: 4,8 => CTR => C8: 3
* PRF # C8: 3 => SOL
* DIS # H1: 4,7 => CTR => H1: 1
* PRF # H1: 1 => SOL
* DIS # E3: 4,8 => CTR => E3: 1,2
* DIS # C8: 4,8 => CTR => C8: 3
* PRF # C8: 3 => SOL
* DIS # A1: 4,8 => CTR => A1: 2,6
* DIS # A3: 4,8 => CTR => A3: 2,6
* PRF # E1: 2,4 => SOL
* DIS # E2: 2,4 => CTR => E2: 8
* DIS # E3: 2,4 => CTR => E3: 1,8
* DIS # H1: 4 => CTR => H1: 1,7
* CNT  18 HDP CHAINS /  40 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 # A1: 4,8 => CTR => A1: 2,6
* PRF A1: 2,6 # C1: 4,8 => SOL
* STA A1: 2,6 + C1: 4,8
* CNT   2 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

.....9..51.9...........3...7.64.21.9.4.8.6..7...3...6.9..1.8524......9....5.6..8. initial
.....9..51.9...........3.9.786452139341896257592371468967138524......9.6..596..8. autosolve
238649715179285643654713892786452139341896257592371468967138524813524976425967381 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
C3: 4,8
H2: 4,7
I2: 2,3
I3: 1,2
A8: 4,8
B8: 1,3
A9: 2,4
B9: 1,2
E8: 2,4
F9: 4,7
H8: 1,7
G9: 3,7
I9: 1,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E1,E3: 1.. / E1 = 1  =>  0 pairs (X) / E3 = 1  =>  0 pairs (_)
H1,I3: 1.. / H1 = 1  =>  0 pairs (*) / I3 = 1  =>  0 pairs (X)
B8,B9: 1.. / B8 = 1  =>  0 pairs (*) / B9 = 1  =>  0 pairs (X)
H8,I9: 1.. / H8 = 1  =>  0 pairs (X) / I9 = 1  =>  0 pairs (_)
E1,H1: 1.. / E1 = 1  =>  0 pairs (X) / H1 = 1  =>  0 pairs (_)
E3,I3: 1.. / E3 = 1  =>  0 pairs (*) / I3 = 1  =>  0 pairs (X)
B8,H8: 1.. / B8 = 1  =>  0 pairs (*) / H8 = 1  =>  0 pairs (X)
B9,I9: 1.. / B9 = 1  =>  0 pairs (X) / I9 = 1  =>  0 pairs (_)
H1,H8: 1.. / H1 = 1  =>  0 pairs (*) / H8 = 1  =>  0 pairs (X)
I3,I9: 1.. / I3 = 1  =>  0 pairs (X) / I9 = 1  =>  0 pairs (_)
I2,I3: 2.. / I2 = 2  =>  0 pairs (X) / I3 = 2  =>  0 pairs (_)
A9,B9: 2.. / A9 = 2  =>  0 pairs (X) / B9 = 2  =>  0 pairs (_)
D8,E8: 2.. / D8 = 2  =>  0 pairs (X) / E8 = 2  => 15 pairs (_)
B8,C8: 3.. / B8 = 3  =>  0 pairs (X) / C8 = 3  =>  0 pairs (_)
G9,I9: 3.. / G9 = 3  =>  0 pairs (*) / I9 = 3  =>  0 pairs (X)
C1,C8: 3.. / C1 = 3  =>  0 pairs (X) / C8 = 3  =>  0 pairs (_)
I2,I9: 3.. / I2 = 3  =>  0 pairs (*) / I9 = 3  =>  0 pairs (X)
H1,H2: 4.. / H1 = 4  =>  0 pairs (X) / H2 = 4  => 16 pairs (_)
A9,F9: 4.. / A9 = 4  =>  0 pairs (*) / F9 = 4  =>  0 pairs (X)
B2,B3: 5.. / B2 = 5  => 18 pairs (_) / B3 = 5  => 13 pairs (_)
D8,F8: 5.. / D8 = 5  => 14 pairs (_) / F8 = 5  => 16 pairs (_)
B3,D3: 5.. / B3 = 5  => 13 pairs (_) / D3 = 5  => 18 pairs (_)
F2,F8: 5.. / F2 = 5  => 14 pairs (_) / F8 = 5  => 16 pairs (_)
A1,A3: 6.. / A1 = 6  => 16 pairs (_) / A3 = 6  => 14 pairs (_)
D2,G2: 6.. / D2 = 6  => 14 pairs (_) / G2 = 6  => 14 pairs (_)
H8,G9: 7.. / H8 = 7  =>  0 pairs (*) / G9 = 7  =>  0 pairs (X)
F9,G9: 7.. / F9 = 7  =>  0 pairs (*) / G9 = 7  =>  0 pairs (X)
A8,C8: 8.. / A8 = 8  => 13 pairs (_) / C8 = 8  =>  0 pairs (X)
E2,G2: 8.. / E2 = 8  => 13 pairs (_) / G2 = 8  =>  0 pairs (X)
* DURATION: 0:00:33.642473  START: 04:41:17.753143  END: 04:41:51.395616 2019-05-01
* CP COUNT: (29)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,B8,B9,C3,E8,F9,G9,H2,H8,I2,I3,I9)
* .....9..51.9...........3.9.786452139341896257592371468967138524......9.6..596..8.
* PAIR C3: 4,8 BLK 1
A1: 4,8,2,6                              # reduction candidate for 4,8
A1: 4,8 => CTR
* .....9..51.9.....26....3891786452139341896257592371468967138524.3..2.916215964783
A1: 2,6                                  # 14 pairs
C1: 4,8,3                                # reduction candidate for 4,8
C1: 4,8 => SOLVED
* 238649715179285643654713892786452139341896257592371468967138524813524976425967381
C1: 3 => CTR
* 4.3.19..51.968.342....43.91786452139341896257592371468967138524.34.2.916215964783
A3: 4,8,2,6                              # reduction candidate for 4,8
A3: 4,8 => CTR
* 6.3.198451.9.....2.....3.91786452139341896257592371468967138524.3..2.916215964783
A3: 2,6                                  # 14 pairs
* PAIR C3: 4,8 ROW 3
E3: 4,8,1,2                              # reduction candidate for 4,8
E3: 4,8 => CTR
* 4.3.19..51.968.342....43.91786452139341896257592371468967138524.34.2.916215964783
E3: 1,2                                  # 18 pairs
* PAIR C3: 4,8 COL C
C8: 4,8,3                                # reduction candidate for 4,8
C8: 4,8 => CTR
* 4.3.19..51.968.342....43.91786452139341896257592371468967138524.34.2.916215964783
C8: 3 => SOLVED
* 238649715179285643654713892786452139341896257592371468967138524813524976425967381
* PAIR H2: 4,7 BLK 3
H1: 4,7,1                                # reduction candidate for 4,7
H1: 4,7 => CTR
* 4.3.19..51.968.342....43.91786452139341896257592371468967138524.34.2.916215964783
H1: 1 => SOLVED
* 238649715179285643654713892786452139341896257592371468967138524813524976425967381
* PAIR H2: 4,7 ROW 2
F2: 4,7,5                                # reduction candidate for 4,7
F2: 4,7                                  # 16 pairs
F2: 5                                    # 14 pairs
* PAIR I2: 2,3 ROW 2
B2: 2,3,5,7                              # reduction candidate for 2,3
B2: 2,3                                  # 17 pairs
B2: 5,7                                  # 16 pairs
* PAIR I3: 1,2 ROW 3
E3: 1,2,4,8                              # reduction candidate for 1,2
E3: 4,8 => CTR
* 4.3.19..51.968.342....43.91786452139341896257592371468967138524.34.2.916215964783
E3: 1,2                                  # 18 pairs
* PAIR A8: 4,8 BLK 7
C8: 4,8,3                                # reduction candidate for 4,8
C8: 4,8 => CTR
* 4.3.19..51.968.342....43.91786452139341896257592371468967138524.34.2.916215964783
C8: 3 => SOLVED
* 238649715179285643654713892786452139341896257592371468967138524813524976425967381
* PAIR A8: 4,8 COL A
A1: 4,8,2,6                              # reduction candidate for 4,8
A1: 4,8 => CTR
* .....9..51.9.....26....3891786452139341896257592371468967138524.3..2.916215964783
A1: 2,6                                  # 14 pairs
A3: 4,8,2,6                              # reduction candidate for 4,8
A3: 4,8 => CTR
* 6.3.198451.9.....2.....3.91786452139341896257592371468967138524.3..2.916215964783
A3: 2,6                                  # 14 pairs
* PAIR A9: 2,4 COL A
A1: 2,4,6,8                              # reduction candidate for 2,4
A1: 2,4                                  # 15 pairs
A3: 2,4,6,8                              # reduction candidate for 2,4
A3: 2,4                                  # 17 pairs
* PAIR E8: 2,4 COL E
E1: 2,4,1,8                              # reduction candidate for 2,4
E1: 2,4 => SOLVED
* 238649715179285643654713892786452139341896257592371468967138524813524976425967381
E1: 1,8                                  # 14 pairs
E2: 2,4,8                                # reduction candidate for 2,4
E2: 2,4 => CTR
* 6...193451396..87......3691786452139341896257592371468967138524......916.1596.783
E2: 8                                    # 13 pairs
E3: 2,4,1,8                              # reduction candidate for 2,4
E3: 2,4 => CTR
* 4.3.198751.968.3426...43.91786452139341896257592371468967138524.34.2.916215964783
E3: 1,8                                  # 17 pairs
* PAIR F9: 4,7 BLK 8
F8: 4,7,5                                # reduction candidate for 4,7
F8: 5                                    # 16 pairs
F8: 4,7                                  # 14 pairs
* PAIR F9: 4,7 COL F
F2: 4,7,5                                # reduction candidate for 4,7
F2: 4,7                                  # 16 pairs
F2: 5                                    # 14 pairs
* PAIR H8: 1,7 COL H
H1: 1,7,4                                # reduction candidate for 1,7
H1: 4 => CTR
* ....19.451.9....72.....3.91786452139341896257592371468967138524.3...7916215964783
H1: 1,7                                  # 16 pairs
* PAIR G9: 3,7 COL G
G1: 3,7,6,8                              # reduction candidate for 3,7
G1: 3,7                                  # 18 pairs
G2: 3,7,6,8                              # reduction candidate for 3,7
G2: 3,7                                  # 19 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190321-absurd-base-pr-000.dot
* REASONING
* DIS # A1: 4,8 => CTR => A1: 2,6
* PRF # C1: 4,8 => SOL
* DIS # C1: 3 => CTR => C1: 4,8
* DIS # A3: 4,8 => CTR => A3: 2,6
* DIS # E3: 4,8 => CTR => E3: 1,2
* DIS # C8: 4,8 => CTR => C8: 3
* PRF # C8: 3 => SOL
* DIS # H1: 4,7 => CTR => H1: 1
* PRF # H1: 1 => SOL
* DIS # E3: 4,8 => CTR => E3: 1,2
* DIS # C8: 4,8 => CTR => C8: 3
* PRF # C8: 3 => SOL
* DIS # A1: 4,8 => CTR => A1: 2,6
* DIS # A3: 4,8 => CTR => A3: 2,6
* PRF # E1: 2,4 => SOL
* DIS # E2: 2,4 => CTR => E2: 8
* DIS # E3: 2,4 => CTR => E3: 1,8
* DIS # H1: 4 => CTR => H1: 1,7
* CNT  18 HDP CHAINS /  40 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,B8,B9,C3,E8,F9,G9,H2,H8,I2,I3,I9)
* .....9..51.9...........3.9.786452139341896257592371468967138524......9.6..596..8.
* PAIR C3: 4,8 BLK 1
A1: 4,8,2,6                              # reduction candidate for 4,8
A1: 4,8 => CTR
* .....9..51.9.....26....3891786452139341896257592371468967138524.3..2.916215964783
C1: 4,8,3                                # reduction candidate for 4,8
C1: 4,8 => SOLVED
* 238649715179285643654713892786452139341896257592371468967138524813524976425967381
* DURATION: 0:00:02.240167  START: 04:42:17.795733  END: 04:42:20.035900 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190321-absurd-base-pr-001.dot
* REASONING
* DIS # A1: 4,8 => CTR => A1: 2,6
* PRF A1: 2,6 # C1: 4,8 => SOL
* STA A1: 2,6 + C1: 4,8
* CNT   2 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190321, absurd

Solution

position: 238649715179285643654713892786452139341896257592371468967138524813524976425967381 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:

* DIS # A1: 4,8 => CTR => A1: 2,6
* INC # A1: 2,6 => UNS
* PRF # C1: 4,8 => SOL
* DIS # C1: 3 => CTR => C1: 4,8
* DIS # A3: 4,8 => CTR => A3: 2,6
* INC # A3: 2,6 => UNS
* DIS # E3: 4,8 => CTR => E3: 1,2
* INC # E3: 1,2 => UNS
* DIS # C8: 4,8 => CTR => C8: 3
* PRF # C8: 3 => SOL
* DIS # H1: 4,7 => CTR => H1: 1
* PRF # H1: 1 => SOL
* INC # F2: 4,7 => UNS
* INC # F2: 5 => UNS
* INC # B2: 2,3 => UNS
* INC # B2: 5,7 => UNS
* INC # E3: 1,2 => UNS
* DIS # E3: 4,8 => CTR => E3: 1,2
* DIS # C8: 4,8 => CTR => C8: 3
* PRF # C8: 3 => SOL
* DIS # A1: 4,8 => CTR => A1: 2,6
* INC # A1: 2,6 => UNS
* DIS # A3: 4,8 => CTR => A3: 2,6
* INC # A3: 2,6 => UNS
* INC # A1: 2,4 => UNS
* INC # A3: 2,4 => UNS
* PRF # E1: 2,4 => SOL
* INC # E1: 1,8 => UNS
* DIS # E2: 2,4 => CTR => E2: 8
* INC # E2: 8 => UNS
* DIS # E3: 2,4 => CTR => E3: 1,8
* INC # E3: 1,8 => UNS
* INC # F8: 4,7 => UNS
* INC # F8: 5 => UNS
* INC # F2: 4,7 => UNS
* INC # F2: 5 => UNS
* INC # H1: 1,7 => UNS
* DIS # H1: 4 => CTR => H1: 1,7
* INC # G1: 3,7 => UNS
* INC # G2: 3,7 => UNS
* CNT  40 HDP CHAINS /  40 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A1: 4,8 => CTR => A1: 2,6
* PRF A1: 2,6 # C1: 4,8 => SOL
* STA A1: 2,6 + C1: 4,8
* CNT   2 HDP CHAINS /   2 HYP OPENED