Analysis of zz-www.sudokuoftheday.co.uk-20060530-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: 8...5...9..5.89.3176..........8.4....7...3.....8175...5.7..21.439.....27.......5. initial

Autosolve

position: 8...5...9..5.89.31769..1....5.8.4....7...3.....8175...587..21.439.5...27.......5. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # G1: 6,7 => SOL
* PRF # G1: 6,7 => SOL
* PRF # G1: 6,7 => SOL
* DIS # H5: 4,8 => CTR => H5: 1,9
* DIS # G5: 4,9 => CTR => G5: 2,5,8
* DIS # H5: 4,9 => CTR => H5: 1,8
* DIS # C9: 1,4 => CTR => C9: 2,6
* DIS # E9: 9 => CTR => E9: 1,4
* DIS # G9: 3,8 => CTR => G9: 9
* PRF # G9: 9 => SOL
* CNT  10 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:

* PRF # G1: 6,7 => SOL
* STA G1: 6,7
* CNT   1 HDP CHAINS /  11 HYP OPENED

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

Details

Positions

8...5...9..5.89.3176..........8.4....7...3.....8175...5.7..21.439.....27.......5. initial
8...5...9..5.89.31769..1....5.8.4....7...3.....8175...587..21.439.5...27.......5. autosolve
813257649245689731769431285951824376472963518638175492587392164394516827126748953 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (17)
B1: 1,3
C1: 1,3
A2: 2,4
B2: 2,4
D1: 2,4
F1: 6,7
D2: 6,7
G2: 6,7
H3: 4,8
H6: 4,9
C8: 1,4
E8: 1,4
F8: 6,8
F9: 7,8
H7: 6,9
G8: 6,8
I9: 3,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B1,C1: 1.. / B1 = 1  => 17 pairs (_) / C1 = 1  => 25 pairs (_)
H4,H5: 1.. / H4 = 1  =>  0 pairs (X) / H5 = 1  => 21 pairs (_)
E8,E9: 1.. / E8 = 1  => 17 pairs (_) / E9 = 1  => 18 pairs (_)
C8,E8: 1.. / C8 = 1  => 18 pairs (_) / E8 = 1  => 17 pairs (_)
B1,B9: 1.. / B1 = 1  => 17 pairs (_) / B9 = 1  => 25 pairs (_)
A2,B2: 2.. / A2 = 2  => 17 pairs (_) / B2 = 2  => 19 pairs (_)
D1,G1: 2.. / D1 = 2  => 22 pairs (_) / G1 = 2  => 22 pairs (_)
B1,C1: 3.. / B1 = 3  => 25 pairs (_) / C1 = 3  => 17 pairs (_)
D3,E3: 3.. / D3 = 3  => 20 pairs (_) / E3 = 3  => 22 pairs (_)
C4,B6: 3.. / C4 = 3  => 25 pairs (_) / B6 = 3  => 17 pairs (_)
D7,E7: 3.. / D7 = 3  => 22 pairs (_) / E7 = 3  => 20 pairs (_)
G9,I9: 3.. / G9 = 3  =>  0 pairs (X) / I9 = 3  => 21 pairs (_)
B1,B6: 3.. / B1 = 3  => 25 pairs (_) / B6 = 3  => 17 pairs (_)
C1,C4: 3.. / C1 = 3  => 17 pairs (_) / C4 = 3  => 25 pairs (_)
D3,D7: 3.. / D3 = 3  => 20 pairs (_) / D7 = 3  => 22 pairs (_)
E3,E7: 3.. / E3 = 3  => 22 pairs (_) / E7 = 3  => 20 pairs (_)
A2,B2: 4.. / A2 = 4  => 19 pairs (_) / B2 = 4  => 17 pairs (_)
C8,E8: 4.. / C8 = 4  => 17 pairs (_) / E8 = 4  => 18 pairs (_)
G3,I3: 5.. / G3 = 5  => 18 pairs (_) / I3 = 5  => 17 pairs (_)
G5,I5: 5.. / G5 = 5  => 17 pairs (_) / I5 = 5  => 18 pairs (_)
G3,G5: 5.. / G3 = 5  => 18 pairs (_) / G5 = 5  => 17 pairs (_)
I3,I5: 5.. / I3 = 5  => 17 pairs (_) / I5 = 5  => 18 pairs (_)
F1,D2: 6.. / F1 = 6  =>  0 pairs (X) / D2 = 6  =>  0 pairs (_)
A9,C9: 6.. / A9 = 6  => 18 pairs (_) / C9 = 6  => 19 pairs (_)
H7,G8: 6.. / H7 = 6  =>  0 pairs (*) / G8 = 6  =>  0 pairs (X)
D2,G2: 6.. / D2 = 6  =>  0 pairs (*) / G2 = 6  =>  0 pairs (X)
A6,I6: 6.. / A6 = 6  => 23 pairs (_) / I6 = 6  => 18 pairs (_)
F8,G8: 6.. / F8 = 6  =>  0 pairs (*) / G8 = 6  =>  0 pairs (X)
F1,F8: 6.. / F1 = 6  =>  0 pairs (X) / F8 = 6  =>  0 pairs (_)
H1,H7: 6.. / H1 = 6  =>  0 pairs (X) / H7 = 6  =>  0 pairs (_)
F1,D2: 7.. / F1 = 7  =>  0 pairs (*) / D2 = 7  =>  0 pairs (X)
G4,H4: 7.. / G4 = 7  =>  0 pairs (X) / H4 = 7  => 21 pairs (_)
D9,F9: 7.. / D9 = 7  =>  0 pairs (*) / F9 = 7  =>  0 pairs (X)
D2,G2: 7.. / D2 = 7  =>  0 pairs (X) / G2 = 7  =>  0 pairs (_)
D2,D9: 7.. / D2 = 7  =>  0 pairs (X) / D9 = 7  =>  0 pairs (_)
F1,F9: 7.. / F1 = 7  =>  0 pairs (*) / F9 = 7  =>  0 pairs (X)
H1,H4: 7.. / H1 = 7  =>  0 pairs (X) / H4 = 7  => 21 pairs (_)
F8,F9: 8.. / F8 = 8  =>  0 pairs (X) / F9 = 8  =>  0 pairs (_)
F8,G8: 8.. / F8 = 8  =>  0 pairs (X) / G8 = 8  =>  0 pairs (_)
H3,H5: 8.. / H3 = 8  => 19 pairs (_) / H5 = 8  =>  0 pairs (X)
H7,G9: 9.. / H7 = 9  =>  0 pairs (X) / G9 = 9  =>  0 pairs (_)
* DURATION: 0:00:50.892980  START: 23:30:13.832289  END: 23:31:04.725269 2019-04-30
* CP COUNT: (41)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B1,B2,C1,C8,D1,D2,E8,F1,F8,F9,G2,G8,H3,H6,H7,I9)
* 8...5...9..5.89.31769..1....5.8.4....7...3.....8175...587..21.439.5...27.......5.
* PAIR C1: 1,3 COL C
C4: 1,3,2,6                              # reduction candidate for 1,3
C4: 1,3                                  # 23 pairs
C4: 2,6                                  # 18 pairs
* PAIR A2: 2,4 COL A
A5: 2,4,1,6,9                            # reduction candidate for 2,4
A5: 2,4                                  # 20 pairs
A6: 2,4,6,9                              # reduction candidate for 2,4
A6: 2,4                                  # 21 pairs
A9: 2,4,1,6                              # reduction candidate for 2,4
A9: 2,4                                  # 23 pairs
* PAIR B2: 2,4 COL B
B6: 2,4,3                                # reduction candidate for 2,4
B6: 2,4                                  # 25 pairs
B9: 2,4,1                                # reduction candidate for 2,4
B9: 2,4                                  # 17 pairs
* PAIR D1: 2,4 BLK 2
D3: 2,4,3                                # reduction candidate for 2,4
D3: 2,4                                  # 22 pairs
E3: 2,4,3                                # reduction candidate for 2,4
E3: 2,4                                  # 20 pairs
* PAIR D1: 2,4 ROW 1
G1: 2,4,6,7                              # reduction candidate for 2,4
G1: 6,7 => SOLVED
* 813257649245689731769431285951824376472963518638175492587392164394516827126748953
G1: 2,4                                  # 19 pairs
* PAIR F1: 6,7 ROW 1
G1: 6,7,2,4                              # reduction candidate for 6,7
G1: 6,7 => SOLVED
* 813257649245689731769431285951824376472963518638175492587392164394516827126748953
G1: 2,4                                  # 19 pairs
H1: 6,7,4                                # reduction candidate for 6,7
H1: 6,7                                  # 19 pairs
* PAIR G2: 6,7 BLK 3
G1: 6,7,2,4                              # reduction candidate for 6,7
G1: 6,7 => SOLVED
* 813257649245689731769431285951824376472963518638175492587392164394516827126748953
G1: 2,4                                  # 19 pairs
H1: 6,7,4                                # reduction candidate for 6,7
H1: 6,7                                  # 19 pairs
* PAIR H3: 4,8 BLK 3
G3: 4,8,2,5                              # reduction candidate for 4,8
G3: 4,8                                  # 22 pairs
G3: 2,5                                  # 18 pairs
* PAIR H3: 4,8 COL H
H5: 4,8,1,9                              # reduction candidate for 4,8
H5: 4,8 => CTR
* 8...5..79..5789631769..1....5.8.471..7...3.....8175...587..216439.5.6.27.......5.
H5: 1,9                                  # 21 pairs
* PAIR H6: 4,9 BLK 6
G5: 4,9,2,5,8                            # reduction candidate for 4,9
G5: 4,9 => CTR
* 8...5...9..5.89.31769..1548.5.8.4.1..7...3.85..8175.9.587..216439.5.6827.......5.
G5: 2,5,8                                # 17 pairs
H5: 4,9,1,8                              # reduction candidate for 4,9
H5: 4,9 => CTR
* 8...5..79..5789631769..1.8..5.8.471..7...3.....8175...587..216439.5.6.27.......5.
H5: 1,8                                  # 18 pairs
G6: 4,9,2,3                              # reduction candidate for 4,9
G6: 4,9                                  # 22 pairs
* PAIR H6: 4,9 ROW 6
A6: 4,9,2,6                              # reduction candidate for 4,9
A6: 4,9                                  # 23 pairs
A6: 2,6                                  # 19 pairs
* PAIR C8: 1,4 BLK 7
A9: 1,4,2,6                              # reduction candidate for 1,4
A9: 1,4                                  # 17 pairs
B9: 1,4,2                                # reduction candidate for 1,4
B9: 1,4                                  # 20 pairs
C9: 1,4,2,6                              # reduction candidate for 1,4
C9: 1,4 => CTR
* 81325...9245.89.31769..1582.5.8.4..3.7...38.5.381752.6587..219439.5.862762...7358
C9: 2,6                                  # 18 pairs
* PAIR C8: 1,4 COL C
C5: 1,4,2,6                              # reduction candidate for 1,4
C5: 2,6                                  # 22 pairs
C5: 1,4                                  # 20 pairs
* PAIR E8: 1,4 BLK 8
E9: 1,4,9                                # reduction candidate for 1,4
E9: 9 => CTR
* 8..256..9..5789631769341.8..5.8.4....7...3.....8175...587..21.439.51..27...497.5.
E9: 1,4                                  # 20 pairs
* PAIR H7: 6,9 ROW 7
D7: 6,9,3                                # reduction candidate for 6,9
D7: 6,9                                  # 20 pairs
E7: 6,9,3                                # reduction candidate for 6,9
E7: 6,9                                  # 22 pairs
* PAIR I9: 3,8 BLK 9
G9: 3,8,9                                # reduction candidate for 3,8
G9: 3,8 => CTR
* 8...56..9..5789.31769..1....5.8.4....7...3.....8175...587..219439.5..627.......5.
G9: 9 => SOLVED
* 813257649245689731769431285951824376472963518638175492587392164394516827126748953
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060530-absurd-base-pr-000.dot
* REASONING
* PRF # G1: 6,7 => SOL
* PRF # G1: 6,7 => SOL
* PRF # G1: 6,7 => SOL
* DIS # H5: 4,8 => CTR => H5: 1,9
* DIS # G5: 4,9 => CTR => G5: 2,5,8
* DIS # H5: 4,9 => CTR => H5: 1,8
* DIS # C9: 1,4 => CTR => C9: 2,6
* DIS # E9: 9 => CTR => E9: 1,4
* DIS # G9: 3,8 => CTR => G9: 9
* PRF # G9: 9 => SOL
* CNT  10 HDP CHAINS /  40 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B1,B2,C1,C8,D1,D2,E8,F1,F8,F9,G2,G8,H3,H6,H7,I9)
* 8...5...9..5.89.31769..1....5.8.4....7...3.....8175...587..21.439.5...27.......5.
* PAIR C1: 1,3 COL C
C4: 1,3,2,6                              # reduction candidate for 1,3
C4: 1,3                                  # 23 pairs
C4: 2,6                                  # 18 pairs
* PAIR A2: 2,4 COL A
A5: 2,4,1,6,9                            # reduction candidate for 2,4
A5: 2,4                                  # 20 pairs
A6: 2,4,6,9                              # reduction candidate for 2,4
A6: 2,4                                  # 21 pairs
A9: 2,4,1,6                              # reduction candidate for 2,4
A9: 2,4                                  # 23 pairs
* PAIR B2: 2,4 COL B
B6: 2,4,3                                # reduction candidate for 2,4
B6: 2,4                                  # 25 pairs
B9: 2,4,1                                # reduction candidate for 2,4
B9: 2,4                                  # 17 pairs
* PAIR D1: 2,4 BLK 2
D3: 2,4,3                                # reduction candidate for 2,4
D3: 2,4                                  # 22 pairs
E3: 2,4,3                                # reduction candidate for 2,4
E3: 2,4                                  # 20 pairs
* PAIR D1: 2,4 ROW 1
G1: 2,4,6,7                              # reduction candidate for 2,4
G1: 6,7 => SOLVED
* 813257649245689731769431285951824376472963518638175492587392164394516827126748953
* DURATION: 0:00:08.141050  START: 23:31:31.807905  END: 23:31:39.948955 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060530-absurd-base-pr-001.dot
* REASONING
* PRF # G1: 6,7 => SOL
* STA G1: 6,7
* CNT   1 HDP CHAINS /  11 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060530, absurd

Solution

position: 813257649245689731769431285951824376472963518638175492587392164394516827126748953 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 # C4: 1,3 => UNS
* INC # C4: 2,6 => UNS
* INC # A5: 2,4 => UNS
* INC # A6: 2,4 => UNS
* INC # A9: 2,4 => UNS
* INC # B6: 2,4 => UNS
* INC # B9: 2,4 => UNS
* INC # D3: 2,4 => UNS
* INC # E3: 2,4 => UNS
* INC # G1: 2,4 => UNS
* PRF # G1: 6,7 => SOL
* PRF # G1: 6,7 => SOL
* INC # G1: 2,4 => UNS
* INC # H1: 6,7 => UNS
* PRF # G1: 6,7 => SOL
* INC # G1: 2,4 => UNS
* INC # H1: 6,7 => UNS
* INC # G3: 4,8 => UNS
* INC # G3: 2,5 => UNS
* DIS # H5: 4,8 => CTR => H5: 1,9
* INC # H5: 1,9 => UNS
* DIS # G5: 4,9 => CTR => G5: 2,5,8
* INC # G5: 2,5,8 => UNS
* DIS # H5: 4,9 => CTR => H5: 1,8
* INC # H5: 1,8 => UNS
* INC # G6: 4,9 => UNS
* INC # A6: 4,9 => UNS
* INC # A6: 2,6 => UNS
* INC # A9: 1,4 => UNS
* INC # B9: 1,4 => UNS
* DIS # C9: 1,4 => CTR => C9: 2,6
* INC # C9: 2,6 => UNS
* INC # C5: 1,4 => UNS
* INC # C5: 2,6 => UNS
* INC # E9: 1,4 => UNS
* DIS # E9: 9 => CTR => E9: 1,4
* INC # D7: 6,9 => UNS
* INC # E7: 6,9 => UNS
* DIS # G9: 3,8 => CTR => G9: 9
* PRF # G9: 9 => SOL
* CNT  40 HDP CHAINS /  40 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C4: 1,3 => UNS
* INC # C4: 2,6 => UNS
* INC # A5: 2,4 => UNS
* INC # A6: 2,4 => UNS
* INC # A9: 2,4 => UNS
* INC # B6: 2,4 => UNS
* INC # B9: 2,4 => UNS
* INC # D3: 2,4 => UNS
* INC # E3: 2,4 => UNS
* INC # G1: 2,4 => UNS
* PRF # G1: 6,7 => SOL
* STA G1: 6,7
* CNT  11 HDP CHAINS /  11 HYP OPENED