Analysis of zz-www.sudokuoftheday.co.uk-20060525-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006
Autosolve
Pair Reduction Variants
- Pair Reduction Analysis
- Pair Reduction
Details
Solution
Appendix: Full HDP Chains
- A1. Pair Reduction Analysis
- A2. Pair Reduction

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

level: medium

position: 4....1.3..5.6.....7.38..4......68.95....1...492.......81....9.35.....84...7..91.. initial

Autosolve

position: 4....153..5.6.....7.38..4......68.95...91...492.......81....9.35..1..84...7.891.. autosolve

Pair Reduction Variants

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C2: 8,9 => CTR => C2: 1,2
* PRF # C1: 6,9 => SOL
* DIS # I3: 6,9 => CTR => I3: 1,2
* DIS # E1: 2,7 => CTR => E1: 9
* DIS # D7: 2,7 => CTR => D7: 4,5
* DIS # E3: 9 => CTR => E3: 2,5
* DIS # H2: 2,7 => CTR => H2: 8
* DIS # I2: 2,7 => CTR => I2: 8,9
* PRF # G5: 2,7 => SOL
* PRF # B5: 3,6 => SOL
* PRF # G5: 2,7 => SOL
* DIS # I8: 2,6 => CTR => I8: 7
* PRF # H9: 2,6 => SOL
* PRF # A9: 3 => SOL
* DIS # I3: 2,6 => CTR => I3: 1,9
* CNT  15 HDP CHAINS /  45 HYP OPENED

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

Pair Reduction

The following important HDP chains were detected:

* DIS # C2: 8,9 => CTR => C2: 1,2
* PRF C2: 1,2 # C1: 6,9 => SOL
* STA C2: 1,2 + C1: 6,9
* CNT   2 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

`4....1.3..5.6.....7.38..4......68.95....1...492.......81....9.35.....84...7..91..`	initial
`4....153..5.6.....7.38..4......68.95...91...492.......81....9.35..1..84...7.891..`	autosolve
`486791532251634789793852461174268395638915274925347618812476953569123847347589126`	solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (11)
A2: 1,2
B3: 6,9
D1: 2,7
E2: 3,4
F2: 3,4
F3: 2,5
G2: 2,7
A4: 1,3
C4: 1,4
A5: 3,6
I9: 2,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A2,C2: 1.. / A2 = 1  => 20 pairs (_) / C2 = 1  => 19 pairs (_)
H3,I3: 1.. / H3 = 1  =>  0 pairs (X) / I3 = 1  => 13 pairs (_)
A4,C4: 1.. / A4 = 1  => 19 pairs (_) / C4 = 1  => 20 pairs (_)
H6,I6: 1.. / H6 = 1  => 13 pairs (_) / I6 = 1  =>  0 pairs (X)
A2,A4: 1.. / A2 = 1  => 20 pairs (_) / A4 = 1  => 19 pairs (_)
C2,C4: 1.. / C2 = 1  => 19 pairs (_) / C4 = 1  => 20 pairs (_)
H3,H6: 1.. / H3 = 1  =>  0 pairs (X) / H6 = 1  => 13 pairs (_)
I3,I6: 1.. / I3 = 1  => 13 pairs (_) / I6 = 1  =>  0 pairs (X)
D4,F5: 2.. / D4 = 2  => 13 pairs (_) / F5 = 2  => 15 pairs (_)
D4,G4: 2.. / D4 = 2  => 13 pairs (_) / G4 = 2  => 15 pairs (_)
A2,A9: 2.. / A2 = 2  => 19 pairs (_) / A9 = 2  => 20 pairs (_)
E2,F2: 3.. / E2 = 3  => 10 pairs (_) / F2 = 3  =>  9 pairs (_)
E2,F2: 4.. / E2 = 4  =>  9 pairs (_) / F2 = 4  => 10 pairs (_)
C7,B9: 4.. / C7 = 4  =>  0 pairs (X) / B9 = 4  => 13 pairs (_)
B9,D9: 4.. / B9 = 4  => 13 pairs (_) / D9 = 4  =>  0 pairs (X)
B4,B9: 4.. / B4 = 4  =>  0 pairs (X) / B9 = 4  => 13 pairs (_)
E3,F3: 5.. / E3 = 5  => 13 pairs (_) / F3 = 5  => 11 pairs (_)
C5,C6: 5.. / C5 = 5  => 11 pairs (_) / C6 = 5  => 18 pairs (_)
H7,H9: 5.. / H7 = 5  =>  0 pairs (*) / H9 = 5  =>  0 pairs (X)
C5,F5: 5.. / C5 = 5  => 11 pairs (_) / F5 = 5  => 18 pairs (_)
D9,H9: 5.. / D9 = 5  =>  0 pairs (*) / H9 = 5  =>  0 pairs (X)
G5,G6: 6.. / G5 = 6  =>  0 pairs (X) / G6 = 6  => 11 pairs (_)
F7,F8: 6.. / F7 = 6  => 12 pairs (_) / F8 = 6  => 14 pairs (_)
C6,G6: 6.. / C6 = 6  =>  0 pairs (X) / G6 = 6  => 11 pairs (_)
A5,A9: 6.. / A5 = 6  => 12 pairs (_) / A9 = 6  =>  0 pairs (X)
D1,E1: 7.. / D1 = 7  => 11 pairs (_) / E1 = 7  =>  0 pairs (X)
B4,B5: 7.. / B4 = 7  => 13 pairs (_) / B5 = 7  => 21 pairs (_)
H7,I8: 7.. / H7 = 7  =>  0 pairs (X) / I8 = 7  => 13 pairs (_)
B1,B5: 8.. / B1 = 8  => 15 pairs (_) / B5 = 8  => 24 pairs (_)
E1,E3: 9.. / E1 = 9  => 13 pairs (_) / E3 = 9  =>  0 pairs (X)
B8,C8: 9.. / B8 = 9  =>  0 pairs (X) / C8 = 9  => 12 pairs (_)
C2,I2: 9.. / C2 = 9  =>  0 pairs (X) / I2 = 9  => 11 pairs (_)
* DURATION: 0:00:32.655745  START: 23:24:19.095212  END: 23:24:51.750957 2019-04-30
* CP COUNT: (32)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,A5,B3,C4,D1,E2,F2,F3,G2,I9)
* 4....153..5.6.....7.38..4......68.95...91...492.......81....9.35..1..84...7.891..
* PAIR A2: 1,2 BLK 1
C2: 1,2,8,9                              # reduction candidate for 1,2
C2: 8,9 => CTR
* 4.27915381586....97938..4613.1.68.9568591.3.492....6..81....9.35..1..84.2.7.891.6
C2: 1,2                                  # 17 pairs
* PAIR B3: 6,9 BLK 1
B1: 6,9,8                                # reduction candidate for 6,9
B1: 6,9                                  # 24 pairs
C1: 6,9,2,8                              # reduction candidate for 6,9
C1: 6,9 => SOLVED
* 486791532251634789793852461174268395638915274925347618812476953569123847347589126
C1: 2,8                                  # 14 pairs
* PAIR B3: 6,9 ROW 3
I3: 6,9,1,2                              # reduction candidate for 6,9
I3: 6,9 => CTR
* 4.279153.15.6.....7.38..41.3.1.68.956..91...492......181....9.35..1..84...7.891.2
I3: 1,2                                  # 12 pairs
* PAIR B3: 6,9 COL B
B8: 6,9,3                                # reduction candidate for 6,9
B8: 6,9                                  # 21 pairs
B8: 3                                    # 17 pairs
* PAIR D1: 2,7 BLK 2
E1: 2,7,9                                # reduction candidate for 2,7
E1: 2,7 => CTR
* 4....15362516..7897638954211.4.68.95.8591..74926...318812...9.35.91.6847647389152
E1: 9                                    # 13 pairs
* PAIR D1: 2,7 COL D
D4: 2,7,3,4                              # reduction candidate for 2,7
D4: 2,7                                  # 13 pairs
D7: 2,7,4,5                              # reduction candidate for 2,7
D7: 2,7 => CTR
* 4..27153..5.6..7.97.38954..3714682956859123749245376..816754923539126847247389156
D7: 4,5                                  # 12 pairs
* PAIR E2: 3,4 COL E
E6: 3,4,5,7                              # reduction candidate for 3,4
E6: 3,4                                  # 13 pairs
E6: 5,7                                  # 12 pairs
* PAIR F2: 3,4 COL F
F6: 3,4,5,7                              # reduction candidate for 3,4
F6: 5,7                                  # 12 pairs
F6: 3,4                                  # 12 pairs
* PAIR F3: 2,5 BLK 2
E3: 2,5,9                                # reduction candidate for 2,5
E3: 9 => CTR
* 4....15362516..7897638954211.4.68.95.8591..74926...318812...9.35.91.6847647389152
E3: 2,5                                  # 13 pairs
* PAIR F3: 2,5 COL F
F5: 2,5,3,7                              # reduction candidate for 2,5
F5: 2,5                                  # 12 pairs
F7: 2,5,4,6,7                            # reduction candidate for 2,5
F7: 2,5                                  # 19 pairs
* PAIR G2: 2,7 BLK 3
H2: 2,7,8                                # reduction candidate for 2,7
H2: 2,7 => CTR
* 4627915381586....97938..4613.1.68.9568591.3.492....6..81....9.35..1..84.2.7.891.6
H2: 8                                    # 13 pairs
I2: 2,7,8,9                              # reduction candidate for 2,7
I2: 2,7 => CTR
* 482791536.596...8.7638..4....1.68.95...91...492......881....9.359.1..84...7.891..
I2: 8,9                                  # 12 pairs
* PAIR G2: 2,7 COL G
G4: 2,7,3                                # reduction candidate for 2,7
G4: 2,7                                  # 16 pairs
G5: 2,7,3,6                              # reduction candidate for 2,7
G5: 2,7 => SOLVED
* 486791532251634789793852461174268395638915274925347618812476953569123847347589126
G5: 3,6                                  # 14 pairs
* PAIR A5: 3,6 BLK 4
B5: 3,6,7,8                              # reduction candidate for 3,6
B5: 3,6 => SOLVED
* 486791532251634789793852461174268395638915274925347618812476953569123847347589126
B5: 7,8                                  # 12 pairs
* PAIR A5: 3,6 ROW 5
G5: 3,6,2,7                              # reduction candidate for 3,6
G5: 2,7 => SOLVED
* 486791532251634789793852461174268395638915274925347618812476953569123847347589126
G5: 3,6                                  # 14 pairs
* PAIR A5: 3,6 COL A
A9: 3,6,2                                # reduction candidate for 3,6
A9: 2                                    # 20 pairs
A9: 3,6                                  # 19 pairs
* PAIR I9: 2,6 BLK 9
H7: 2,6,5,7                              # reduction candidate for 2,6
H7: 2,6                                  # 14 pairs
I8: 2,6,7                                # reduction candidate for 2,6
I8: 2,6 => CTR
* 4..791538.586..7297938..461.71468295.8.91...492.....1781....9735.917.84...7.8915.
I8: 7                                    # 13 pairs
H9: 2,6,5                                # reduction candidate for 2,6
H9: 2,6 => SOLVED
* 486791532251634789793852461174268395638915274925347618812476953569123847347589126
H9: 5                                    # 11 pairs
* PAIR I9: 2,6 ROW 9
A9: 2,6,3                                # reduction candidate for 2,6
A9: 3 => SOLVED
* 486791532251634789793852461174268395638915274925347618812476953569123847347589126
A9: 2,6                                  # 15 pairs
* PAIR I9: 2,6 COL I
I1: 2,6,8,9                              # reduction candidate for 2,6
I1: 2,6                                  # 16 pairs
I3: 2,6,1,9                              # reduction candidate for 2,6
I3: 2,6 => CTR
* 4....153.2516..7..7.38..41.....68.95...91...492......181....9.35..1..84...7.891.2
I3: 1,9                                  # 12 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060525-absurd-base-pr-000.dot
* REASONING
* DIS # C2: 8,9 => CTR => C2: 1,2
* PRF # C1: 6,9 => SOL
* DIS # I3: 6,9 => CTR => I3: 1,2
* DIS # E1: 2,7 => CTR => E1: 9
* DIS # D7: 2,7 => CTR => D7: 4,5
* DIS # E3: 9 => CTR => E3: 2,5
* DIS # H2: 2,7 => CTR => H2: 8
* DIS # I2: 2,7 => CTR => I2: 8,9
* PRF # G5: 2,7 => SOL
* PRF # B5: 3,6 => SOL
* PRF # G5: 2,7 => SOL
* DIS # I8: 2,6 => CTR => I8: 7
* PRF # H9: 2,6 => SOL
* PRF # A9: 3 => SOL
* DIS # I3: 2,6 => CTR => I3: 1,9
* CNT  15 HDP CHAINS /  45 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,A5,B3,C4,D1,E2,F2,F3,G2,I9)
* 4....153..5.6.....7.38..4......68.95...91...492.......81....9.35..1..84...7.891..
* PAIR A2: 1,2 BLK 1
C2: 1,2,8,9                              # reduction candidate for 1,2
C2: 8,9 => CTR
* 4.27915381586....97938..4613.1.68.9568591.3.492....6..81....9.35..1..84.2.7.891.6
* PAIR B3: 6,9 BLK 1
B1: 6,9,8                                # reduction candidate for 6,9
B1: 6,9                                  # 23 pairs
C1: 6,9,8                                # reduction candidate for 6,9
C1: 6,9 => SOLVED
* 486791532251634789793852461174268395638915274925347618812476953569123847347589126
* DURATION: 0:00:03.653333  START: 23:25:19.072306  END: 23:25:22.725639 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060525-absurd-base-pr-001.dot
* REASONING
* DIS # C2: 8,9 => CTR => C2: 1,2
* PRF C2: 1,2 # C1: 6,9 => SOL
* STA C2: 1,2 + C1: 6,9
* CNT   2 HDP CHAINS /   4 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060525, absurd

Solution

position: 486791532251634789793852461174268395638915274925347618812476953569123847347589126 solved

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 # C2: 1,2 => UNS
* DIS # C2: 8,9 => CTR => C2: 1,2
* INC # B1: 6,9 => UNS
* PRF # C1: 6,9 => SOL
* INC # C1: 2,8 => UNS
* DIS # I3: 6,9 => CTR => I3: 1,2
* INC # I3: 1,2 => UNS
* INC # B8: 6,9 => UNS
* INC # B8: 3 => UNS
* DIS # E1: 2,7 => CTR => E1: 9
* INC # E1: 9 => UNS
* INC # D4: 2,7 => UNS
* DIS # D7: 2,7 => CTR => D7: 4,5
* INC # D7: 4,5 => UNS
* INC # E6: 3,4 => UNS
* INC # E6: 5,7 => UNS
* INC # F6: 3,4 => UNS
* INC # F6: 5,7 => UNS
* INC # E3: 2,5 => UNS
* DIS # E3: 9 => CTR => E3: 2,5
* INC # F5: 2,5 => UNS
* INC # F7: 2,5 => UNS
* DIS # H2: 2,7 => CTR => H2: 8
* INC # H2: 8 => UNS
* DIS # I2: 2,7 => CTR => I2: 8,9
* INC # I2: 8,9 => UNS
* INC # G4: 2,7 => UNS
* PRF # G5: 2,7 => SOL
* INC # G5: 3,6 => UNS
* PRF # B5: 3,6 => SOL
* INC # B5: 7,8 => UNS
* INC # G5: 3,6 => UNS
* PRF # G5: 2,7 => SOL
* INC # A9: 3,6 => UNS
* INC # A9: 2 => UNS
* INC # H7: 2,6 => UNS
* DIS # I8: 2,6 => CTR => I8: 7
* INC # I8: 7 => UNS
* PRF # H9: 2,6 => SOL
* INC # H9: 5 => UNS
* INC # A9: 2,6 => UNS
* PRF # A9: 3 => SOL
* INC # I1: 2,6 => UNS
* DIS # I3: 2,6 => CTR => I3: 1,9
* INC # I3: 1,9 => UNS
* CNT  45 HDP CHAINS /  45 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C2: 1,2 => UNS
* DIS # C2: 8,9 => CTR => C2: 1,2
* INC C2: 1,2 # B1: 6,9 => UNS
* PRF C2: 1,2 # C1: 6,9 => SOL
* STA C2: 1,2 + C1: 6,9
* CNT   4 HDP CHAINS /   4 HYP OPENED