Analysis of zz-www.sudokuoftheday.co.uk-20060516-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006

position: ..78.......815.....5..43..8.92....5......1.6....4..2...34...1..1..3.452..2.6...7. initial

Autosolve

position: .178...45.481576.2.5..43718.927...51..3..1.6..614..2...34...18.1..3.452..2561..7. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # A1: 3,9 => SOL
* DIS # A1: 2 => CTR => A1: 3,9
* DIS # A3: 6,9 => CTR => A3: 2
* PRF # A3: 2 => SOL
* DIS # E1: 2,9 => CTR => E1: 6
* PRF # A3: 2,9 => SOL
* DIS # A3: 6 => CTR => A3: 2,9
* PRF # D7: 2,9 => SOL
* PRF # A1: 3,9 => SOL
* DIS # A1: 2 => CTR => A1: 3,9
* DIS # A5: 4,8 => CTR => A5: 5,7
* DIS # G4: 3 => CTR => G4: 4,8
* PRF # A5: 7,8 => SOL
* DIS # E4: 6,8 => CTR => E4: 3
* PRF # A5: 4,7 => SOL
* DIS # E6: 8 => CTR => E6: 3,9
* PRF # A7: 6,9 => SOL
* DIS # A7: 7 => CTR => A7: 6,9
* PRF # F6: 8,9 => SOL
* PRF # A7: 6,9 => SOL
* DIS # A7: 7 => CTR => A7: 6,9
* DIS # G4: 3,4 => CTR => G4: 8
* CNT  22 HDP CHAINS /  35 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* PRF # A1: 3,9 => SOL
* STA A1: 3,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

..78.......815.....5..43..8.92....5......1.6....4..2...34...1..1..3.452..2.6...7. initial
.178...45.481576.2.5..43718.927...51..3..1.6..614..2...34...18.1..3.452..2561..7. autosolve
917862345348157692256943718492736851783521964561498237634275189179384526825619473 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (20)
A2: 3,9
C3: 6,9
D3: 2,9
G1: 3,9
H2: 3,9
A4: 4,8
B5: 7,8
F4: 6,8
I5: 4,7
H6: 3,9
I6: 3,7
B8: 7,8
C8: 6,9
A9: 8,9
E8: 7,8
F9: 8,9
I7: 6,9
I8: 6,9
G9: 3,4
I9: 3,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,A3: 2.. / A1 = 2  =>  0 pairs (X) / A3 = 2  =>  0 pairs (_)
D5,E5: 2.. / D5 = 2  =>  0 pairs (X) / E5 = 2  => 25 pairs (_)
A3,D3: 2.. / A3 = 2  =>  0 pairs (*) / D3 = 2  =>  0 pairs (X)
F1,F7: 2.. / F1 = 2  =>  0 pairs (*) / F7 = 2  =>  0 pairs (X)
A1,A2: 3.. / A1 = 3  =>  0 pairs (X) / A2 = 3  => 16 pairs (_)
G1,H2: 3.. / G1 = 3  => 16 pairs (_) / H2 = 3  =>  0 pairs (X)
E4,E6: 3.. / E4 = 3  => 22 pairs (_) / E6 = 3  =>  0 pairs (X)
G9,I9: 3.. / G9 = 3  =>  0 pairs (X) / I9 = 3  => 18 pairs (_)
A1,G1: 3.. / A1 = 3  =>  0 pairs (X) / G1 = 3  => 16 pairs (_)
A2,H2: 3.. / A2 = 3  => 16 pairs (_) / H2 = 3  =>  0 pairs (X)
E4,G4: 3.. / E4 = 3  => 22 pairs (_) / G4 = 3  =>  0 pairs (X)
H2,H6: 3.. / H2 = 3  =>  0 pairs (X) / H6 = 3  => 16 pairs (_)
I6,I9: 3.. / I6 = 3  =>  0 pairs (X) / I9 = 3  => 18 pairs (_)
A4,A5: 4.. / A4 = 4  => 20 pairs (_) / A5 = 4  =>  0 pairs (X)
G9,I9: 4.. / G9 = 4  => 18 pairs (_) / I9 = 4  =>  0 pairs (X)
A4,G4: 4.. / A4 = 4  => 20 pairs (_) / G4 = 4  =>  0 pairs (X)
I5,I9: 4.. / I5 = 4  => 18 pairs (_) / I9 = 4  =>  0 pairs (X)
A5,A6: 5.. / A5 = 5  => 23 pairs (_) / A6 = 5  =>  0 pairs (*)
D5,F6: 5.. / D5 = 5  =>  0 pairs (*) / F6 = 5  =>  0 pairs (X)
D7,F7: 5.. / D7 = 5  => 23 pairs (_) / F7 = 5  =>  0 pairs (*)
A5,D5: 5.. / A5 = 5  => 23 pairs (_) / D5 = 5  =>  0 pairs (*)
A6,F6: 5.. / A6 = 5  =>  0 pairs (*) / F6 = 5  =>  0 pairs (X)
D5,D7: 5.. / D5 = 5  =>  0 pairs (*) / D7 = 5  =>  0 pairs (X)
F6,F7: 5.. / F6 = 5  => 23 pairs (_) / F7 = 5  =>  0 pairs (*)
A3,C3: 6.. / A3 = 6  =>  0 pairs (X) / C3 = 6  =>  0 pairs (_)
E1,F1: 6.. / E1 = 6  => 21 pairs (_) / F1 = 6  =>  0 pairs (X)
E4,F4: 6.. / E4 = 6  =>  0 pairs (X) / F4 = 6  => 21 pairs (_)
A7,C8: 6.. / A7 = 6  =>  0 pairs (*) / C8 = 6  =>  0 pairs (X)
I7,I8: 6.. / I7 = 6  =>  0 pairs (X) / I8 = 6  =>  0 pairs (_)
A7,I7: 6.. / A7 = 6  =>  0 pairs (*) / I7 = 6  =>  0 pairs (X)
C8,I8: 6.. / C8 = 6  =>  0 pairs (X) / I8 = 6  =>  0 pairs (_)
A3,A7: 6.. / A3 = 6  =>  0 pairs (X) / A7 = 6  =>  0 pairs (_)
C3,C8: 6.. / C3 = 6  =>  0 pairs (*) / C8 = 6  =>  0 pairs (X)
E1,E4: 6.. / E1 = 6  => 21 pairs (_) / E4 = 6  =>  0 pairs (X)
F1,F4: 6.. / F1 = 6  =>  0 pairs (X) / F4 = 6  => 21 pairs (_)
I5,I6: 7.. / I5 = 7  =>  0 pairs (X) / I6 = 7  => 18 pairs (_)
A7,B8: 7.. / A7 = 7  =>  0 pairs (X) / B8 = 7  =>  0 pairs (_)
E7,E8: 7.. / E7 = 7  =>  0 pairs (*) / E8 = 7  =>  0 pairs (X)
A6,I6: 7.. / A6 = 7  =>  0 pairs (X) / I6 = 7  => 18 pairs (_)
A7,E7: 7.. / A7 = 7  =>  0 pairs (X) / E7 = 7  =>  0 pairs (_)
B8,E8: 7.. / B8 = 7  =>  0 pairs (*) / E8 = 7  =>  0 pairs (X)
B5,B8: 7.. / B5 = 7  =>  0 pairs (X) / B8 = 7  =>  0 pairs (_)
G4,G5: 8.. / G4 = 8  => 21 pairs (_) / G5 = 8  =>  0 pairs (X)
B8,A9: 8.. / B8 = 8  =>  0 pairs (X) / A9 = 8  =>  0 pairs (_)
E8,F9: 8.. / E8 = 8  =>  0 pairs (*) / F9 = 8  =>  0 pairs (X)
B8,E8: 8.. / B8 = 8  =>  0 pairs (X) / E8 = 8  =>  0 pairs (_)
A9,F9: 8.. / A9 = 8  =>  0 pairs (*) / F9 = 8  =>  0 pairs (X)
B5,B8: 8.. / B5 = 8  =>  0 pairs (*) / B8 = 8  =>  0 pairs (X)
G1,H2: 9.. / G1 = 9  =>  0 pairs (X) / H2 = 9  => 16 pairs (_)
G5,H6: 9.. / G5 = 9  => 16 pairs (_) / H6 = 9  =>  0 pairs (X)
I7,I8: 9.. / I7 = 9  =>  0 pairs (*) / I8 = 9  =>  0 pairs (X)
A2,H2: 9.. / A2 = 9  =>  0 pairs (X) / H2 = 9  => 16 pairs (_)
C8,I8: 9.. / C8 = 9  =>  0 pairs (*) / I8 = 9  =>  0 pairs (X)
A9,F9: 9.. / A9 = 9  =>  0 pairs (X) / F9 = 9  =>  0 pairs (_)
C3,C8: 9.. / C3 = 9  =>  0 pairs (X) / C8 = 9  =>  0 pairs (_)
G1,G5: 9.. / G1 = 9  =>  0 pairs (X) / G5 = 9  => 16 pairs (_)
H2,H6: 9.. / H2 = 9  => 16 pairs (_) / H6 = 9  =>  0 pairs (X)
* DURATION: 0:01:19.114540  START: 23:11:03.218896  END: 23:12:22.333436 2019-04-30
* CP COUNT: (57)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,A9,B5,B8,C3,C8,D3,E8,F4,F9,G1,G9,H2,H6,I5,I6,I7,I8,I9)
* .178...45.481576.2.5..43718.927...51..3..1.6..614..2...34...18.1..3.452..2561..7.
* PAIR A2: 3,9 BLK 1
A1: 3,9,2                                # reduction candidate for 3,9
A1: 3,9 => SOLVED
* 917862345348157692256943718492736851783521964561498237634275189179384526825619473
A1: 2 => CTR
* 2178..345348157692.5.243718.92736.51..3.2196..614..237.3497.18.1..3.452..2561..7.
* PAIR C3: 6,9 BLK 1
A3: 6,9,2                                # reduction candidate for 6,9
A3: 6,9 => CTR
* 2178..345348157692.5.243718.92736.51..3.2196..614..237.3497.18.1..3.452..2561..7.
A3: 2 => SOLVED
* 917862345348157692256943718492736851783521964561498237634275189179384526825619473
* PAIR D3: 2,9 BLK 2
E1: 2,9,6                                # reduction candidate for 2,9
E1: 2,9 => CTR
* .178.6.45.481576.2.5..43718.92768351..3..1864861435297.345.218.18.37452.92561..7.
E1: 6                                    # 21 pairs
F1: 2,9,6                                # reduction candidate for 2,9
F1: 2,9                                  # 21 pairs
* PAIR D3: 2,9 ROW 3
A3: 2,9,6                                # reduction candidate for 2,9
A3: 2,9 => SOLVED
* 917862345348157692256943718492736851783521964561498237634275189179384526825619473
A3: 6 => CTR
* 2178..345348157692659243718.92736.51..3.2196..614..237.3497.18.1..3.452..2561..7.
* PAIR D3: 2,9 COL D
D5: 2,9,5                                # reduction candidate for 2,9
D5: 2,9                                  # 23 pairs
D7: 2,9,5                                # reduction candidate for 2,9
D7: 2,9 => SOLVED
* 917862345348157692256943718492736851783521964561498237634275189179384526825619473
D7: 5                                    # 23 pairs
* PAIR G1: 3,9 ROW 1
A1: 3,9,2                                # reduction candidate for 3,9
A1: 3,9 => SOLVED
* 917862345348157692256943718492736851783521964561498237634275189179384526825619473
A1: 2 => CTR
* 2178..345348157692.5.243718.92736.51..3.2196..614..237.3497.18.1..3.452..2561..7.
* PAIR A4: 4,8 BLK 4
A5: 4,8,5,7                              # reduction candidate for 4,8
A5: 4,8 => CTR
* .178...45.481576.2.5..43718.927...51..352196.5614..237734.95186186374529925618.7.
A5: 5,7                                  # 21 pairs
* PAIR A4: 4,8 ROW 4
G4: 4,8,3                                # reduction candidate for 4,8
G4: 3 => CTR
* .178...45.481576.2.5..437184927..351..3..1864861435297.345..18.18.37452.925618473
G4: 4,8                                  # 22 pairs
* PAIR B5: 7,8 BLK 4
A5: 7,8,4,5                              # reduction candidate for 7,8
A5: 7,8 => SOLVED
* 917862345348157692256943718492736851783521964561498237634275189179384526825619473
A5: 4,5                                  # 21 pairs
A6: 7,8,5                                # reduction candidate for 7,8
A6: 7,8                                  # 23 pairs
* PAIR F4: 6,8 BLK 5
E4: 6,8,3                                # reduction candidate for 6,8
E4: 6,8 => CTR
* .178...45.481576.2.5..43718.927..351..3..1864.6143.297.34...18.18.37452.925618473
E4: 3                                    # 22 pairs
* PAIR I5: 4,7 ROW 5
A5: 4,7,5,8                              # reduction candidate for 4,7
A5: 4,7 => SOLVED
* 917862345348157692256943718492736851783521964561498237634275189179384526825619473
A5: 5,8                                  # 21 pairs
* PAIR H6: 3,9 ROW 6
E6: 3,9,8                                # reduction candidate for 3,9
E6: 8 => CTR
* .1786..45348157692.59243718.92736.51.73.219645614892...34...18.18.37452.925618.7.
E6: 3,9                                  # 20 pairs
* PAIR C8: 6,9 BLK 7
A7: 6,9,7                                # reduction candidate for 6,9
A7: 6,9 => SOLVED
* 917862345348157692256943718492736851783521964561498237634275189179384526825619473
A7: 7 => CTR
* 217869345348157692659243718.927...51..3.21.6..614..2..734.92186186374529925618.7.
* PAIR F9: 8,9 COL F
F6: 8,9,5                                # reduction candidate for 8,9
F6: 8,9 => SOLVED
* 917862345348157692256943718492736851783521964561498237634275189179384526825619473
F6: 5                                    # 23 pairs
* PAIR I7: 6,9 ROW 7
A7: 6,9,7                                # reduction candidate for 6,9
A7: 6,9 => SOLVED
* 917862345348157692256943718492736851783521964561498237634275189179384526825619473
A7: 7 => CTR
* 217869345348157692659243718.927...51..3.21.6..614..2..734.92186186374529925618.7.
* PAIR G9: 3,4 COL G
G4: 3,4,8                                # reduction candidate for 3,4
G4: 3,4 => CTR
* .178...45.481576.2.5..43718.927...51..3..186..614..29..34...18.18.37452.925618.7.
G4: 8                                    # 21 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060516-absurd-base-pr-000.dot
* REASONING
* PRF # A1: 3,9 => SOL
* DIS # A1: 2 => CTR => A1: 3,9
* DIS # A3: 6,9 => CTR => A3: 2
* PRF # A3: 2 => SOL
* DIS # E1: 2,9 => CTR => E1: 6
* PRF # A3: 2,9 => SOL
* DIS # A3: 6 => CTR => A3: 2,9
* PRF # D7: 2,9 => SOL
* PRF # A1: 3,9 => SOL
* DIS # A1: 2 => CTR => A1: 3,9
* DIS # A5: 4,8 => CTR => A5: 5,7
* DIS # G4: 3 => CTR => G4: 4,8
* PRF # A5: 7,8 => SOL
* DIS # E4: 6,8 => CTR => E4: 3
* PRF # A5: 4,7 => SOL
* DIS # E6: 8 => CTR => E6: 3,9
* PRF # A7: 6,9 => SOL
* DIS # A7: 7 => CTR => A7: 6,9
* PRF # F6: 8,9 => SOL
* PRF # A7: 6,9 => SOL
* DIS # A7: 7 => CTR => A7: 6,9
* DIS # G4: 3,4 => CTR => G4: 8
* CNT  22 HDP CHAINS /  35 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,A9,B5,B8,C3,C8,D3,E8,F4,F9,G1,G9,H2,H6,I5,I6,I7,I8,I9)
* .178...45.481576.2.5..43718.927...51..3..1.6..614..2...34...18.1..3.452..2561..7.
* PAIR A2: 3,9 BLK 1
A1: 3,9,2                                # reduction candidate for 3,9
A1: 3,9 => SOLVED
* 917862345348157692256943718492736851783521964561498237634275189179384526825619473
* DURATION: 0:00:01.717816  START: 23:12:51.660102  END: 23:12:53.377918 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060516-absurd-base-pr-001.dot
* REASONING
* PRF # A1: 3,9 => SOL
* STA A1: 3,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060516, absurd

Solution

position: 917862345348157692256943718492736851783521964561498237634275189179384526825619473 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:

* PRF # A1: 3,9 => SOL
* DIS # A1: 2 => CTR => A1: 3,9
* DIS # A3: 6,9 => CTR => A3: 2
* PRF # A3: 2 => SOL
* DIS # E1: 2,9 => CTR => E1: 6
* INC # E1: 6 => UNS
* INC # F1: 2,9 => UNS
* PRF # A3: 2,9 => SOL
* DIS # A3: 6 => CTR => A3: 2,9
* INC # D5: 2,9 => UNS
* PRF # D7: 2,9 => SOL
* INC # D7: 5 => UNS
* PRF # A1: 3,9 => SOL
* DIS # A1: 2 => CTR => A1: 3,9
* DIS # A5: 4,8 => CTR => A5: 5,7
* INC # A5: 5,7 => UNS
* INC # G4: 4,8 => UNS
* DIS # G4: 3 => CTR => G4: 4,8
* PRF # A5: 7,8 => SOL
* INC # A5: 4,5 => UNS
* INC # A6: 7,8 => UNS
* DIS # E4: 6,8 => CTR => E4: 3
* INC # E4: 3 => UNS
* PRF # A5: 4,7 => SOL
* INC # A5: 5,8 => UNS
* INC # E6: 3,9 => UNS
* DIS # E6: 8 => CTR => E6: 3,9
* PRF # A7: 6,9 => SOL
* DIS # A7: 7 => CTR => A7: 6,9
* PRF # F6: 8,9 => SOL
* INC # F6: 5 => UNS
* PRF # A7: 6,9 => SOL
* DIS # A7: 7 => CTR => A7: 6,9
* DIS # G4: 3,4 => CTR => G4: 8
* INC # G4: 8 => UNS
* CNT  35 HDP CHAINS /  35 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # A1: 3,9 => SOL
* STA A1: 3,9
* CNT   1 HDP CHAINS /   1 HYP OPENED