Analysis of zz-www.sudokuoftheday.co.uk-20060330-absurd-base.sdk

Contents

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

level: medium

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

position: ...6........8..7.14...12..58....62.7..4..7.5..3....9...6......2.734.1..99.1.6.... initial

Autosolve

position: ...6........8..7.14...12..58....62.7..4..7.5..3....9..568.....22734.1..994126..7. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D4: 3,9 => CTR => D4: 1,5
* DIS # E6: 4,8 => CTR => E6: 2
* DIS # I6: 4,8 => CTR => I6: 6
* DIS # G8: 6 => CTR => G8: 5,8
* DIS # G9: 3 => CTR => G9: 5,8
* DIS # H4: 1,4 => CTR => H4: 3
* PRF # H4: 3 => SOL
* PRF # H6: 1,4 => SOL
* DIS # H6: 8 => CTR => H6: 1,4
* DIS # G8: 6,8 => CTR => G8: 5
* PRF # G8: 5 => SOL
* DIS # H3: 6,8 => CTR => H3: 3,9
* PRF # G9: 3,8 => SOL
* DIS # G9: 5 => CTR => G9: 3,8
* DIS # I1: 3,8 => CTR => I1: 4
* CNT  15 HDP CHAINS /  42 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 # D4: 3,9 => CTR => D4: 1,5
* DIS D4: 1,5 # E6: 4,8 => CTR => E6: 2
* DIS D4: 1,5 + E6: 2 # I6: 4,8 => CTR => I6: 6
* DIS D4: 1,5 + E6: 2 + I6: 6 # F1: 5 => CTR => F1: 3,9
* DIS D4: 1,5 + E6: 2 + I6: 6 + F1: 3,9 # G8: 6 => CTR => G8: 5,8
* PRF D4: 1,5 + E6: 2 + I6: 6 + F1: 3,9 + G8: 5,8 # G9: 5,8 => SOL
* STA D4: 1,5 + E6: 2 + I6: 6 + F1: 3,9 + G8: 5,8 + G9: 5,8
* CNT   6 HDP CHAINS /  28 HYP OPENED

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

Details

Positions

...6........8..7.14...12..58....62.7..4..7.5..3....9...6......2.734.1..99.1.6.... initial
...6........8..7.14...12..58....62.7..4..7.5..3....9..568.....22734.1..994126..7. autosolve
152679384396854721487312695819546237624937158735128946568793412273481569941265873 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
A2: 3,6
B3: 8,9
C4: 5,9
A5: 1,6
D6: 1,5
F6: 4,8
F7: 3,9
E8: 5,8
F9: 5,8
G7: 1,4
H7: 1,4
H8: 6,8
I9: 3,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,B1: 1.. / A1 = 1  => 18 pairs (_) / B1 = 1  => 18 pairs (_)
G7,H7: 1.. / G7 = 1  =>  0 pairs (X) / H7 = 1  => 22 pairs (_)
G5,G7: 1.. / G5 = 1  => 22 pairs (_) / G7 = 1  =>  0 pairs (X)
H1,H2: 2.. / H1 = 2  => 13 pairs (_) / H2 = 2  => 15 pairs (_)
B5,C6: 2.. / B5 = 2  => 15 pairs (_) / C6 = 2  =>  0 pairs (X)
E5,E6: 2.. / E5 = 2  =>  0 pairs (X) / E6 = 2  => 15 pairs (_)
B5,E5: 2.. / B5 = 2  => 15 pairs (_) / E5 = 2  =>  0 pairs (X)
C6,E6: 2.. / C6 = 2  =>  0 pairs (X) / E6 = 2  => 15 pairs (_)
A1,A2: 3.. / A1 = 3  =>  0 pairs (X) / A2 = 3  => 13 pairs (_)
G9,I9: 3.. / G9 = 3  =>  0 pairs (X) / I9 = 3  => 15 pairs (_)
G7,H7: 4.. / G7 = 4  => 22 pairs (_) / H7 = 4  =>  0 pairs (X)
E4,H4: 4.. / E4 = 4  =>  0 pairs (*) / H4 = 4  =>  0 pairs (X)
G1,G7: 4.. / G1 = 4  =>  0 pairs (X) / G7 = 4  => 22 pairs (_)
I1,I6: 4.. / I1 = 4  => 22 pairs (_) / I6 = 4  =>  0 pairs (X)
D4,D6: 5.. / D4 = 5  => 18 pairs (_) / D6 = 5  => 12 pairs (_)
E8,F9: 5.. / E8 = 5  =>  0 pairs (X) / F9 = 5  =>  0 pairs (_)
G8,G9: 5.. / G8 = 5  =>  0 pairs (*) / G9 = 5  =>  0 pairs (X)
C6,D6: 5.. / C6 = 5  => 18 pairs (_) / D6 = 5  => 12 pairs (_)
E8,G8: 5.. / E8 = 5  =>  0 pairs (X) / G8 = 5  =>  0 pairs (_)
F9,G9: 5.. / F9 = 5  =>  0 pairs (*) / G9 = 5  =>  0 pairs (X)
I5,I6: 6.. / I5 = 6  =>  0 pairs (X) / I6 = 6  => 22 pairs (_)
G8,H8: 6.. / G8 = 6  =>  0 pairs (X) / H8 = 6  => 14 pairs (_)
A5,I5: 6.. / A5 = 6  => 22 pairs (_) / I5 = 6  =>  0 pairs (X)
G3,G8: 6.. / G3 = 6  => 14 pairs (_) / G8 = 6  =>  0 pairs (X)
E1,D3: 7.. / E1 = 7  => 16 pairs (_) / D3 = 7  => 18 pairs (_)
A6,C6: 7.. / A6 = 7  => 14 pairs (_) / C6 = 7  => 23 pairs (_)
D7,E7: 7.. / D7 = 7  => 16 pairs (_) / E7 = 7  => 18 pairs (_)
C3,D3: 7.. / C3 = 7  => 16 pairs (_) / D3 = 7  => 18 pairs (_)
A1,A6: 7.. / A1 = 7  => 23 pairs (_) / A6 = 7  => 14 pairs (_)
D3,D7: 7.. / D3 = 7  => 18 pairs (_) / D7 = 7  => 16 pairs (_)
E1,E7: 7.. / E1 = 7  => 16 pairs (_) / E7 = 7  => 18 pairs (_)
B1,B3: 8.. / B1 = 8  =>  0 pairs (X) / B3 = 8  => 13 pairs (_)
E8,F9: 8.. / E8 = 8  =>  0 pairs (*) / F9 = 8  =>  0 pairs (X)
F6,F9: 8.. / F6 = 8  =>  0 pairs (*) / F9 = 8  =>  0 pairs (X)
* DURATION: 0:00:36.184592  START: 22:00:51.097376  END: 22:01:27.281968 2019-04-30
* CP COUNT: (34)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B3,C4,D6,E8,F6,F7,F9,G7,H7,H8,I9)
* ...6........8..7.14...12..58....62.7..4..7.5..3....9..568.....22734.1..994126..7.
* PAIR A2: 3,6 ROW 2
H2: 3,6,2,4,9                            # reduction candidate for 3,6
H2: 3,6                                  # 18 pairs
H2: 2,4,9                                # 14 pairs
* PAIR B3: 8,9 BLK 1
B1: 8,9,1,2,5                            # reduction candidate for 8,9
B1: 8,9                                  # 22 pairs
B1: 1,2,5                                # 13 pairs
* PAIR B3: 8,9 ROW 3
H3: 8,9,3,6                              # reduction candidate for 8,9
H3: 8,9                                  # 17 pairs
H3: 3,6                                  # 17 pairs
* PAIR C4: 5,9 BLK 4
B4: 5,9,1                                # reduction candidate for 5,9
B4: 1                                    # 18 pairs
B4: 5,9                                  # 16 pairs
* PAIR C4: 5,9 ROW 4
D4: 5,9,1,3                              # reduction candidate for 5,9
D4: 5,9                                  # 18 pairs
D4: 1,3                                  # 13 pairs
* PAIR C4: 5,9 COL C
C1: 5,9,2,7                              # reduction candidate for 5,9
C1: 5,9                                  # 15 pairs
C2: 5,9,2,6                              # reduction candidate for 5,9
C2: 5,9                                  # 15 pairs
* PAIR A5: 1,6 BLK 4
A6: 1,6,7                                # reduction candidate for 1,6
A6: 1,6                                  # 23 pairs
A6: 7                                    # 14 pairs
* PAIR D6: 1,5 BLK 5
D4: 1,5,3,9                              # reduction candidate for 1,5
D4: 3,9 => CTR
* ...6..4.....8..7.14...12..58...462.76.41.7.5..3.5.89..568...1422734.1..994126..7.
D4: 1,5                                  # 18 pairs
* PAIR F6: 4,8 BLK 5
E6: 4,8,2                                # reduction candidate for 4,8
E6: 4,8 => CTR
* ...6........8..7.14...12..58....62.7..4.27.5.7325..916568...1422734.1..994126..7.
E6: 2                                    # 15 pairs
* PAIR F6: 4,8 ROW 6
H6: 4,8,1                                # reduction candidate for 4,8
H6: 4,8                                  # 22 pairs
I6: 4,8,6                                # reduction candidate for 4,8
I6: 4,8 => CTR
* .1.6..4833.68.472148.3126958..146237124937856637..8914568...142273481569941265.7.
I6: 6                                    # 22 pairs
* PAIR F7: 3,9 BLK 8
D7: 3,9,7                                # reduction candidate for 3,9
D7: 3,9                                  # 18 pairs
E7: 3,9,7                                # reduction candidate for 3,9
E7: 3,9                                  # 16 pairs
* PAIR F7: 3,9 COL F
F1: 3,9,4,5                              # reduction candidate for 3,9
F1: 3,9                                  # 15 pairs
F2: 3,9,4,5                              # reduction candidate for 3,9
F2: 3,9                                  # 15 pairs
* PAIR E8: 5,8 ROW 8
G8: 5,8,6                                # reduction candidate for 5,8
G8: 6 => CTR
* ...6........8..7.14...12..58....62.7..4..7.5..3...491.568...142273451689941268573
G8: 5,8                                  # 14 pairs
* PAIR F9: 5,8 ROW 9
G9: 5,8,3                                # reduction candidate for 5,8
G9: 3 => CTR
* ...6..4.33.68.47.14..3126.58...46237..4.37856637528914568793142273481569941265378
G9: 5,8                                  # 15 pairs
* PAIR H7: 1,4 COL H
H4: 1,4,3                                # reduction candidate for 1,4
H4: 1,4 => CTR
* ...6....8...8..7.148..126.58....62.7..4.87356.3..2498.568.....22734.1.69941268573
H4: 3 => SOLVED
* 152679384396854721487312695819546237624937158735128946568793412273481569941265873
H6: 1,4,8                                # reduction candidate for 1,4
H6: 1,4 => SOLVED
* 152679384396854721487312695819546237624937158735128946568793412273481569941265873
H6: 8 => CTR
* ...6....8...8..7.148..126.58....62.7..4.87.56.3..2498.568.....22734.1.69941268573
* PAIR H8: 6,8 BLK 9
G8: 6,8,5                                # reduction candidate for 6,8
G8: 6,8 => CTR
* ...6....4...84.7.14...12..58....6247..4..735..3...491.568.....2273451..9941268573
G8: 5 => SOLVED
* 152679384396854721487312695819546237624937158735128946568793412273481569941265873
* PAIR H8: 6,8 COL H
H3: 6,8,3,9                              # reduction candidate for 6,8
H3: 6,8 => CTR
* .8.6........8.47.14973126858.9.46237.24.37.5.73..289..568793..2273481569941265.7.
H3: 3,9                                  # 14 pairs
* PAIR I9: 3,8 BLK 9
G9: 3,8,5                                # reduction candidate for 3,8
G9: 3,8 => SOLVED
* 152679384396854721487312695819546237624937158735128946568793412273481569941265873
G9: 5 => CTR
* ...6....4...84.7.14...12..58....6247..4..735..3...491.568.....2273451..9941268573
* PAIR I9: 3,8 COL I
I1: 3,8,4                                # reduction candidate for 3,8
I1: 3,8 => CTR
* .1.6..4833.68.472148.3126958..146237124937856637528914568...142273481569941265378
I1: 4                                    # 22 pairs
I5: 3,8,6                                # reduction candidate for 3,8
I5: 3,8                                  # 22 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060330-absurd-base-pr-000.dot
* REASONING
* DIS # D4: 3,9 => CTR => D4: 1,5
* DIS # E6: 4,8 => CTR => E6: 2
* DIS # I6: 4,8 => CTR => I6: 6
* DIS # G8: 6 => CTR => G8: 5,8
* DIS # G9: 3 => CTR => G9: 5,8
* DIS # H4: 1,4 => CTR => H4: 3
* PRF # H4: 3 => SOL
* PRF # H6: 1,4 => SOL
* DIS # H6: 8 => CTR => H6: 1,4
* DIS # G8: 6,8 => CTR => G8: 5
* PRF # G8: 5 => SOL
* DIS # H3: 6,8 => CTR => H3: 3,9
* PRF # G9: 3,8 => SOL
* DIS # G9: 5 => CTR => G9: 3,8
* DIS # I1: 3,8 => CTR => I1: 4
* CNT  15 HDP CHAINS /  42 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B3,C4,D6,E8,F6,F7,F9,G7,H7,H8,I9)
* ...6........8..7.14...12..58....62.7..4..7.5..3....9..568.....22734.1..994126..7.
* PAIR A2: 3,6 ROW 2
H2: 3,6,2,4,9                            # reduction candidate for 3,6
H2: 3,6                                  # 18 pairs
H2: 2,4,9                                # 14 pairs
* PAIR B3: 8,9 BLK 1
B1: 8,9,1,2,5                            # reduction candidate for 8,9
B1: 8,9                                  # 22 pairs
B1: 1,2,5                                # 13 pairs
* PAIR B3: 8,9 ROW 3
H3: 8,9,3,6                              # reduction candidate for 8,9
H3: 8,9                                  # 17 pairs
H3: 3,6                                  # 17 pairs
* PAIR C4: 5,9 BLK 4
B4: 5,9,1                                # reduction candidate for 5,9
B4: 1                                    # 18 pairs
B4: 5,9                                  # 16 pairs
* PAIR C4: 5,9 ROW 4
D4: 5,9,1,3                              # reduction candidate for 5,9
D4: 5,9                                  # 18 pairs
D4: 1,3                                  # 13 pairs
* PAIR C4: 5,9 COL C
C1: 5,9,2,7                              # reduction candidate for 5,9
C1: 5,9                                  # 15 pairs
C2: 5,9,2,6                              # reduction candidate for 5,9
C2: 5,9                                  # 15 pairs
* PAIR A5: 1,6 BLK 4
A6: 1,6,7                                # reduction candidate for 1,6
A6: 1,6                                  # 23 pairs
A6: 7                                    # 14 pairs
* PAIR D6: 1,5 BLK 5
D4: 1,5,3,9                              # reduction candidate for 1,5
D4: 3,9 => CTR
* ...6..4.....8..7.14...12..58...462.76.41.7.5..3.5.89..568...1422734.1..994126..7.
* PAIR F6: 4,8 BLK 5
E6: 4,8,2                                # reduction candidate for 4,8
E6: 4,8 => CTR
* ...6........8..7.14...12..58..1.62.7.14927.5.7325..916568...1422734.1..994126..7.
* PAIR F6: 4,8 ROW 6
H6: 4,8,1                                # reduction candidate for 4,8
H6: 4,8                                  # 22 pairs
I6: 4,8,6                                # reduction candidate for 4,8
I6: 4,8 => CTR
* .1.6..4833.68.472148.3126958..146237124937856637528914568...142273481569941265378
* RESTART
* PAIR RESTART
* PAIR F7: 3,9 BLK 8
D7: 3,9,7                                # reduction candidate for 3,9
D7: 3,9                                  # 26 pairs
E7: 3,9,7                                # reduction candidate for 3,9
E7: 3,9                                  # 16 pairs
* PAIR F7: 3,9 COL F
F1: 3,9,5                                # reduction candidate for 3,9
F1: 5 => CTR
* ...6.5..435.8.97.14...12..58....6237624.8715..3..2.9.6568..3412273451..9941268573
* PAIR RESTART
* PAIR F7: 3,9 BLK 8
D7: 3,9,7                                # reduction candidate for 3,9
D7: 3,9                                  # 28 pairs
E7: 3,9,7                                # reduction candidate for 3,9
E7: 3,9                                  # 18 pairs
* PAIR E8: 5,8 ROW 8
G8: 5,8,6                                # reduction candidate for 5,8
G8: 6 => CTR
* ...6....43..8..7.14...12..58....62.7624..715..3..2.9.6568...412273451689941268573
* PAIR RESTART
* PAIR F9: 5,8 ROW 9
G9: 5,8,3                                # reduction candidate for 5,8
G9: 5,8 => SOLVED
* 152679384396854721487312695819546237624937158735128946568793412273481569941265873
* DURATION: 0:00:18.843075  START: 22:01:52.481927  END: 22:02:11.325002 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060330-absurd-base-pr-001.dot
* REASONING
* DIS # D4: 3,9 => CTR => D4: 1,5
* DIS D4: 1,5 # E6: 4,8 => CTR => E6: 2
* DIS D4: 1,5 + E6: 2 # I6: 4,8 => CTR => I6: 6
* DIS D4: 1,5 + E6: 2 + I6: 6 # F1: 5 => CTR => F1: 3,9
* DIS D4: 1,5 + E6: 2 + I6: 6 + F1: 3,9 # G8: 6 => CTR => G8: 5,8
* PRF D4: 1,5 + E6: 2 + I6: 6 + F1: 3,9 + G8: 5,8 # G9: 5,8 => SOL
* STA D4: 1,5 + E6: 2 + I6: 6 + F1: 3,9 + G8: 5,8 + G9: 5,8
* CNT   6 HDP CHAINS /  28 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060330, absurd

Solution

position: 152679384396854721487312695819546237624937158735128946568793412273481569941265873 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 # H2: 3,6 => UNS
* INC # H2: 2,4,9 => UNS
* INC # B1: 8,9 => UNS
* INC # B1: 1,2,5 => UNS
* INC # H3: 8,9 => UNS
* INC # H3: 3,6 => UNS
* INC # B4: 5,9 => UNS
* INC # B4: 1 => UNS
* INC # D4: 5,9 => UNS
* INC # D4: 1,3 => UNS
* INC # C1: 5,9 => UNS
* INC # C2: 5,9 => UNS
* INC # A6: 1,6 => UNS
* INC # A6: 7 => UNS
* INC # D4: 1,5 => UNS
* DIS # D4: 3,9 => CTR => D4: 1,5
* DIS # E6: 4,8 => CTR => E6: 2
* INC # E6: 2 => UNS
* INC # H6: 4,8 => UNS
* DIS # I6: 4,8 => CTR => I6: 6
* INC # I6: 6 => UNS
* INC # D7: 3,9 => UNS
* INC # E7: 3,9 => UNS
* INC # F1: 3,9 => UNS
* INC # F2: 3,9 => UNS
* INC # G8: 5,8 => UNS
* DIS # G8: 6 => CTR => G8: 5,8
* INC # G9: 5,8 => UNS
* DIS # G9: 3 => CTR => G9: 5,8
* DIS # H4: 1,4 => CTR => H4: 3
* PRF # H4: 3 => SOL
* PRF # H6: 1,4 => SOL
* DIS # H6: 8 => CTR => H6: 1,4
* DIS # G8: 6,8 => CTR => G8: 5
* PRF # G8: 5 => SOL
* DIS # H3: 6,8 => CTR => H3: 3,9
* INC # H3: 3,9 => UNS
* PRF # G9: 3,8 => SOL
* DIS # G9: 5 => CTR => G9: 3,8
* DIS # I1: 3,8 => CTR => I1: 4
* INC # I1: 4 => UNS
* INC # I5: 3,8 => UNS
* CNT  42 HDP CHAINS /  42 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # H2: 3,6 => UNS
* INC # H2: 2,4,9 => UNS
* INC # B1: 8,9 => UNS
* INC # B1: 1,2,5 => UNS
* INC # H3: 8,9 => UNS
* INC # H3: 3,6 => UNS
* INC # B4: 5,9 => UNS
* INC # B4: 1 => UNS
* INC # D4: 5,9 => UNS
* INC # D4: 1,3 => UNS
* INC # C1: 5,9 => UNS
* INC # C2: 5,9 => UNS
* INC # A6: 1,6 => UNS
* INC # A6: 7 => UNS
* INC # D4: 1,5 => UNS
* DIS # D4: 3,9 => CTR => D4: 1,5
* DIS D4: 1,5 # E6: 4,8 => CTR => E6: 2
* INC D4: 1,5 + E6: 2 # H6: 4,8 => UNS
* DIS D4: 1,5 + E6: 2 # I6: 4,8 => CTR => I6: 6
* INC D4: 1,5 + E6: 2 + I6: 6 # D7: 3,9 => UNS
* INC D4: 1,5 + E6: 2 + I6: 6 # E7: 3,9 => UNS
* INC D4: 1,5 + E6: 2 + I6: 6 # F1: 3,9 => UNS
* DIS D4: 1,5 + E6: 2 + I6: 6 # F1: 5 => CTR => F1: 3,9
* INC D4: 1,5 + E6: 2 + I6: 6 + F1: 3,9 # D7: 3,9 => UNS
* INC D4: 1,5 + E6: 2 + I6: 6 + F1: 3,9 # E7: 3,9 => UNS
* INC D4: 1,5 + E6: 2 + I6: 6 + F1: 3,9 # G8: 5,8 => UNS
* DIS D4: 1,5 + E6: 2 + I6: 6 + F1: 3,9 # G8: 6 => CTR => G8: 5,8
* PRF D4: 1,5 + E6: 2 + I6: 6 + F1: 3,9 + G8: 5,8 # G9: 5,8 => SOL
* STA D4: 1,5 + E6: 2 + I6: 6 + F1: 3,9 + G8: 5,8 + G9: 5,8
* CNT  28 HDP CHAINS /  28 HYP OPENED