Analysis of zz-www.sudokuoftheday.co.uk-20190126-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: ..76.......3.1..89....84..6.6....3..1..7458..5......91...12.....92.....3..1...... initial

Autosolve

position: ..76.....6.3.17.89..5.84..6.6..913..1397458625......91..612.....92.....3..1...... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 2,4 => CTR => A1: 8,9
* PRF # B1: 2,4 => SOL
* PRF # G2: 2,4 => SOL
* DIS # G2: 5 => CTR => G2: 2,4
* DIS # A1: 2,9 => CTR => A1: 4,8
* PRF # A1: 4,8 => SOL
* PRF # D3: 2,9 => SOL
* DIS # D3: 3 => CTR => D3: 2,9
* PRF # B1: 1,2 => SOL
* DIS # G3: 1,2 => CTR => G3: 7
* PRF # G3: 7 => SOL
* DIS # H3: 1,2 => CTR => H3: 3,7
* PRF # H1: 1,2,4 => SOL
* DIS # G2: 4 => CTR => G2: 2,5
* DIS # G1: 4,5 => CTR => G1: 1,2
* PRF # H1: 4,5 => SOL
* DIS # I7: 4,5 => CTR => I7: 7,8
* PRF # I9: 4,5 => SOL
* DIS # D6: 2,8 => CTR => D6: 3
* PRF # D6: 3 => SOL
* PRF # F6: 2,8 => SOL
* DIS # F6: 3,6 => CTR => F6: 2,8
* DIS # F6: 3,6 => CTR => F6: 2,8
* PRF # F6: 2,8 => SOL
* DIS # E9: 3,6 => CTR => E9: 5,7
* DIS # G7: 4,7 => CTR => G7: 5,9
* DIS # G8: 4,7 => CTR => G8: 1,5,6
* DIS # G9: 4,7 => CTR => G9: 2,5,6,9
* DIS # F6: 6,8 => CTR => F6: 2,3
* CNT  29 HDP CHAINS /  52 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: 2,4 => CTR => A1: 8,9
* PRF A1: 8,9 # B1: 2,4 => SOL
* STA A1: 8,9 + B1: 2,4
* CNT   2 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

..76.......3.1..89....84..6.6....3..1..7458..5......91...12.....92.....3..1...... initial
..76.....6.3.17.89..5.84..6.6..913..1397458625......91..612.....92.....3..1...... autosolve
827639145643517289915284736264891357139745862578362491456123978792458613381976524 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
B2: 2,4
A3: 2,9
B3: 1,2
E1: 3,5
D2: 2,5
I1: 4,5
A4: 2,7
C4: 4,8
B6: 2,7
C6: 4,8
D4: 2,8
E6: 3,6
G6: 4,7
F8: 6,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B1,B3: 1.. / B1 = 1  =>  0 pairs (X) / B3 = 1  => 14 pairs (_)
G8,H8: 1.. / G8 = 1  =>  0 pairs (X) / H8 = 1  => 14 pairs (_)
A4,B6: 2.. / A4 = 2  =>  0 pairs (*) / B6 = 2  =>  0 pairs (X)
G9,H9: 2.. / G9 = 2  =>  0 pairs (X) / H9 = 2  => 14 pairs (_)
A4,D4: 2.. / A4 = 2  =>  0 pairs (*) / D4 = 2  =>  0 pairs (X)
F1,F6: 2.. / F1 = 2  =>  0 pairs (X) / F6 = 2  =>  0 pairs (_)
H1,H3: 3.. / H1 = 3  =>  0 pairs (X) / H3 = 3  =>  0 pairs (_)
A7,A9: 3.. / A7 = 3  => 15 pairs (_) / A9 = 3  => 15 pairs (_)
D3,H3: 3.. / D3 = 3  =>  0 pairs (X) / H3 = 3  =>  0 pairs (_)
A7,F7: 3.. / A7 = 3  => 15 pairs (_) / F7 = 3  => 15 pairs (_)
C4,C6: 4.. / C4 = 4  =>  0 pairs (*) / C6 = 4  =>  0 pairs (X)
D8,D9: 4.. / D8 = 4  => 15 pairs (_) / D9 = 4  =>  0 pairs (X)
B2,G2: 4.. / B2 = 4  => 14 pairs (_) / G2 = 4  =>  0 pairs (X)
C6,G6: 4.. / C6 = 4  =>  0 pairs (X) / G6 = 4  =>  0 pairs (_)
E1,D2: 5.. / E1 = 5  =>  0 pairs (X) / D2 = 5  =>  0 pairs (_)
H4,I4: 5.. / H4 = 5  => 16 pairs (_) / I4 = 5  => 17 pairs (_)
B7,B9: 5.. / B7 = 5  => 15 pairs (_) / B9 = 5  => 14 pairs (_)
D2,G2: 5.. / D2 = 5  =>  0 pairs (*) / G2 = 5  =>  0 pairs (X)
E6,F6: 6.. / E6 = 6  => 14 pairs (_) / F6 = 6  =>  0 pairs (X)
G8,G9: 6.. / G8 = 6  => 17 pairs (_) / G9 = 6  => 15 pairs (_)
G3,H3: 7.. / G3 = 7  =>  0 pairs (*) / H3 = 7  =>  0 pairs (X)
A4,B6: 7.. / A4 = 7  =>  0 pairs (X) / B6 = 7  =>  0 pairs (_)
E8,E9: 7.. / E8 = 7  => 15 pairs (_) / E9 = 7  => 15 pairs (_)
B6,G6: 7.. / B6 = 7  =>  0 pairs (*) / G6 = 7  =>  0 pairs (X)
A1,B1: 8.. / A1 = 8  =>  0 pairs (*) / B1 = 8  =>  0 pairs (X)
C4,C6: 8.. / C4 = 8  =>  0 pairs (X) / C6 = 8  =>  0 pairs (_)
I7,I9: 8.. / I7 = 8  => 15 pairs (_) / I9 = 8  => 14 pairs (_)
C4,D4: 8.. / C4 = 8  =>  0 pairs (X) / D4 = 8  =>  0 pairs (_)
A1,A3: 9.. / A1 = 9  =>  0 pairs (X) / A3 = 9  =>  0 pairs (_)
F1,D3: 9.. / F1 = 9  =>  0 pairs (*) / D3 = 9  =>  0 pairs (X)
G7,G9: 9.. / G7 = 9  => 15 pairs (_) / G9 = 9  =>  0 pairs (X)
A1,F1: 9.. / A1 = 9  =>  0 pairs (X) / F1 = 9  =>  0 pairs (_)
A3,D3: 9.. / A3 = 9  =>  0 pairs (*) / D3 = 9  =>  0 pairs (X)
F7,G7: 9.. / F7 = 9  =>  0 pairs (X) / G7 = 9  => 15 pairs (_)
D3,D9: 9.. / D3 = 9  =>  0 pairs (X) / D9 = 9  =>  0 pairs (_)
* DURATION: 0:00:36.371403  START: 03:13:40.823291  END: 03:14:17.194694 2019-05-01
* CP COUNT: (35)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B2,B3,B6,C4,C6,D2,D4,E1,E6,F8,G6,I1)
* ..76.....6.3.17.89..5.84..6.6..913..1397458625......91..612.....92.....3..1......
* PAIR B2: 2,4 BLK 1
A1: 2,4,8,9                              # reduction candidate for 2,4
A1: 2,4 => CTR
* .876.9...6235174899152847.6.6..913..1397458625....2.91..612.9...92.....3..19.....
A1: 8,9                                  # 15 pairs
B1: 2,4,1,8                              # reduction candidate for 2,4
B1: 2,4 => SOLVED
* 827639145643517289915284736264891357139745862578362491456123978792458613381976524
B1: 1,8                                  # 15 pairs
* PAIR B2: 2,4 ROW 2
G2: 2,4,5                                # reduction candidate for 2,4
G2: 2,4 => SOLVED
* 827639145643517289915284736264891357139745862578362491456123978792458613381976524
G2: 5 => CTR
* ..76.....643217589..5.84..626.8913..139745862578362491..612.....92.....3..1......
* PAIR A3: 2,9 BLK 1
A1: 2,9,4,8                              # reduction candidate for 2,9
A1: 2,9 => CTR
* .876.2...643517289.15.84..6.6..913..13974586252....791..612.....92.....3..1......
A1: 4,8 => SOLVED
* 827639145643517289915284736264891357139745862578362491456123978792458613381976524
* PAIR A3: 2,9 ROW 3
D3: 2,9,3                                # reduction candidate for 2,9
D3: 2,9 => SOLVED
* 827639145643517289915284736264891357139745862578362491456123978792458613381976524
D3: 3 => CTR
* ..76.9...6.32175899.5384..626.8913..1397458625......91..612.....92.....3..1......
* PAIR B3: 1,2 BLK 1
B1: 1,2,4,8                              # reduction candidate for 1,2
B1: 1,2 => SOLVED
* 827639145643517289915284736264891357139745862578362491456123978792458613381976524
B1: 4,8                                  # 15 pairs
* PAIR B3: 1,2 ROW 3
G3: 1,2,7                                # reduction candidate for 1,2
G3: 1,2 => CTR
* ..7659.34643217.89..5384.76.6..913..1397458625......91..612.....92....13..19...2.
G3: 7 => SOLVED
* 827639145643517289915284736264891357139745862578362491456123978792458613381976524
H3: 1,2,3,7                              # reduction candidate for 1,2
H3: 1,2 => CTR
* ..7659.34643217.89..53847.6.6..913..13974586257....491..612.....92.....3..19.....
H3: 3,7                                  # 15 pairs
* PAIR E1: 3,5 ROW 1
H1: 3,5,1,2,4                            # reduction candidate for 3,5
H1: 1,2,4 => SOLVED
* 827639145643517289915284736264891357139745862578362491456123978792458613381976524
H1: 3,5                                  # 17 pairs
* PAIR E1: 3,5 COL E
E9: 3,5,6,7                              # reduction candidate for 3,5
E9: 6,7                                  # 15 pairs
E9: 3,5                                  # 15 pairs
* PAIR D2: 2,5 ROW 2
G2: 2,5,4                                # reduction candidate for 2,5
G2: 4 => CTR
* ..76.....6.3517489..5.84..6.6..913..1397458625.4...791..612.....92.....3..1......
G2: 2,5                                  # 14 pairs
* PAIR I1: 4,5 BLK 3
G1: 4,5,1,2                              # reduction candidate for 4,5
G1: 4,5 => CTR
* 8276395146435172899152847362648913..1397458625783624913.61289477924561.34.19.362.
G1: 1,2                                  # 15 pairs
H1: 4,5,1,2,3                            # reduction candidate for 4,5
H1: 4,5 => SOLVED
* 827639145643517289915284736264891357139745862578362491456123978792458613381976524
H1: 1,2,3                                # 14 pairs
G2: 4,5,2                                # reduction candidate for 4,5
G2: 4,5                                  # 16 pairs
* PAIR I1: 4,5 COL I
I4: 4,5,7                                # reduction candidate for 4,5
I4: 4,5                                  # 18 pairs
I7: 4,5,7,8                              # reduction candidate for 4,5
I7: 4,5 => CTR
* 8.76.9...643.17.899.5.84..6264891357139745862578..2491.861239.5.92458613351976248
I7: 7,8                                  # 15 pairs
I9: 4,5,7,8                              # reduction candidate for 4,5
I9: 4,5 => SOLVED
* 827639145643517289915284736264891357139745862578362491456123978792458613381976524
I9: 7,8                                  # 15 pairs
* PAIR D4: 2,8 BLK 5
D6: 2,8,3                                # reduction candidate for 2,8
D6: 2,8 => CTR
* 987632...64351728921598473676..913..1397458625......91..612.....924....3..13...2.
D6: 3 => SOLVED
* 827639145643517289915284736264891357139745862578362491456123978792458613381976524
F6: 2,8,3,6                              # reduction candidate for 2,8
F6: 2,8 => SOLVED
* 827639145643517289915284736264891357139745862578362491456123978792458613381976524
F6: 3,6 => CTR
* 987632...64351728921598473676..913..1397458625......91..612.....92.....3..1....2.
* PAIR E6: 3,6 BLK 5
F6: 3,6,2,8                              # reduction candidate for 3,6
F6: 3,6 => CTR
* 987632...64351728921598473676..913..1397458625......91..612.....92.....3..1....2.
F6: 2,8 => SOLVED
* 827639145643517289915284736264891357139745862578362491456123978792458613381976524
* PAIR E6: 3,6 COL E
E9: 3,6,5,7                              # reduction candidate for 3,6
E9: 3,6 => CTR
* ..765...4643217589..5.84..626.8913..139745862578362491..612.....92.7...3..1.3....
E9: 5,7                                  # 15 pairs
* PAIR G6: 4,7 BLK 6
H4: 4,7,5                                # reduction candidate for 4,7
H4: 4,7                                  # 17 pairs
I4: 4,7,5                                # reduction candidate for 4,7
I4: 4,7                                  # 16 pairs
* PAIR G6: 4,7 COL G
G7: 4,7,5,9                              # reduction candidate for 4,7
G7: 4,7 => CTR
* 9876.....643.17.8921598473676..913..1397458625......91..6129....92.....3..1...92.
G7: 5,9                                  # 15 pairs
G8: 4,7,1,5,6                            # reduction candidate for 4,7
G8: 4,7 => CTR
* ..7659.34643217.89..5384.76.6..913..1397458625......91..612.9...92....13..19..62.
G8: 1,5,6                                # 14 pairs
G9: 4,7,2,5,6,9                          # reduction candidate for 4,7
G9: 4,7 => CTR
* ..76...34643.17.89..5384.76.6..913..1397458625...36.91..61239...92..86133.19...2.
G9: 2,5,6,9                              # 14 pairs
* PAIR F8: 6,8 BLK 8
F9: 6,8,3,9                              # reduction candidate for 6,8
F9: 6,8                                  # 18 pairs
F9: 3,9                                  # 15 pairs
* PAIR F8: 6,8 COL F
F6: 6,8,2,3                              # reduction candidate for 6,8
F6: 6,8 => CTR
* 987632...64351728921598473676..913..1397458625......91..612.....92.....3..1....2.
F6: 2,3                                  # 16 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190126-absurd-base-pr-000.dot
* REASONING
* DIS # A1: 2,4 => CTR => A1: 8,9
* PRF # B1: 2,4 => SOL
* PRF # G2: 2,4 => SOL
* DIS # G2: 5 => CTR => G2: 2,4
* DIS # A1: 2,9 => CTR => A1: 4,8
* PRF # A1: 4,8 => SOL
* PRF # D3: 2,9 => SOL
* DIS # D3: 3 => CTR => D3: 2,9
* PRF # B1: 1,2 => SOL
* DIS # G3: 1,2 => CTR => G3: 7
* PRF # G3: 7 => SOL
* DIS # H3: 1,2 => CTR => H3: 3,7
* PRF # H1: 1,2,4 => SOL
* DIS # G2: 4 => CTR => G2: 2,5
* DIS # G1: 4,5 => CTR => G1: 1,2
* PRF # H1: 4,5 => SOL
* DIS # I7: 4,5 => CTR => I7: 7,8
* PRF # I9: 4,5 => SOL
* DIS # D6: 2,8 => CTR => D6: 3
* PRF # D6: 3 => SOL
* PRF # F6: 2,8 => SOL
* DIS # F6: 3,6 => CTR => F6: 2,8
* DIS # F6: 3,6 => CTR => F6: 2,8
* PRF # F6: 2,8 => SOL
* DIS # E9: 3,6 => CTR => E9: 5,7
* DIS # G7: 4,7 => CTR => G7: 5,9
* DIS # G8: 4,7 => CTR => G8: 1,5,6
* DIS # G9: 4,7 => CTR => G9: 2,5,6,9
* DIS # F6: 6,8 => CTR => F6: 2,3
* CNT  29 HDP CHAINS /  52 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B2,B3,B6,C4,C6,D2,D4,E1,E6,F8,G6,I1)
* ..76.....6.3.17.89..5.84..6.6..913..1397458625......91..612.....92.....3..1......
* PAIR B2: 2,4 BLK 1
A1: 2,4,8,9                              # reduction candidate for 2,4
A1: 2,4 => CTR
* .876.9...6235174899152847.6.6..913..1397458625....2.91..612.9...92.....3..19.....
B1: 2,4,1,8                              # reduction candidate for 2,4
B1: 2,4 => SOLVED
* 827639145643517289915284736264891357139745862578362491456123978792458613381976524
* DURATION: 0:00:02.356243  START: 03:14:49.061092  END: 03:14:51.417335 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190126-absurd-base-pr-001.dot
* REASONING
* DIS # A1: 2,4 => CTR => A1: 8,9
* PRF A1: 8,9 # B1: 2,4 => SOL
* STA A1: 8,9 + B1: 2,4
* CNT   2 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190126, absurd

Solution

position: 827639145643517289915284736264891357139745862578362491456123978792458613381976524 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: 2,4 => CTR => A1: 8,9
* INC # A1: 8,9 => UNS
* PRF # B1: 2,4 => SOL
* INC # B1: 1,8 => UNS
* PRF # G2: 2,4 => SOL
* DIS # G2: 5 => CTR => G2: 2,4
* DIS # A1: 2,9 => CTR => A1: 4,8
* PRF # A1: 4,8 => SOL
* PRF # D3: 2,9 => SOL
* DIS # D3: 3 => CTR => D3: 2,9
* PRF # B1: 1,2 => SOL
* INC # B1: 4,8 => UNS
* DIS # G3: 1,2 => CTR => G3: 7
* PRF # G3: 7 => SOL
* DIS # H3: 1,2 => CTR => H3: 3,7
* INC # H3: 3,7 => UNS
* INC # H1: 3,5 => UNS
* PRF # H1: 1,2,4 => SOL
* INC # E9: 3,5 => UNS
* INC # E9: 6,7 => UNS
* INC # G2: 2,5 => UNS
* DIS # G2: 4 => CTR => G2: 2,5
* DIS # G1: 4,5 => CTR => G1: 1,2
* INC # G1: 1,2 => UNS
* PRF # H1: 4,5 => SOL
* INC # H1: 1,2,3 => UNS
* INC # G2: 4,5 => UNS
* INC # I4: 4,5 => UNS
* DIS # I7: 4,5 => CTR => I7: 7,8
* INC # I7: 7,8 => UNS
* PRF # I9: 4,5 => SOL
* INC # I9: 7,8 => UNS
* DIS # D6: 2,8 => CTR => D6: 3
* PRF # D6: 3 => SOL
* PRF # F6: 2,8 => SOL
* DIS # F6: 3,6 => CTR => F6: 2,8
* DIS # F6: 3,6 => CTR => F6: 2,8
* PRF # F6: 2,8 => SOL
* DIS # E9: 3,6 => CTR => E9: 5,7
* INC # E9: 5,7 => UNS
* INC # H4: 4,7 => UNS
* INC # I4: 4,7 => UNS
* DIS # G7: 4,7 => CTR => G7: 5,9
* INC # G7: 5,9 => UNS
* DIS # G8: 4,7 => CTR => G8: 1,5,6
* INC # G8: 1,5,6 => UNS
* DIS # G9: 4,7 => CTR => G9: 2,5,6,9
* INC # G9: 2,5,6,9 => UNS
* INC # F9: 6,8 => UNS
* INC # F9: 3,9 => UNS
* DIS # F6: 6,8 => CTR => F6: 2,3
* INC # F6: 2,3 => UNS
* CNT  52 HDP CHAINS /  52 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A1: 2,4 => CTR => A1: 8,9
* PRF A1: 8,9 # B1: 2,4 => SOL
* STA A1: 8,9 + B1: 2,4
* CNT   2 HDP CHAINS /   2 HYP OPENED