Analysis of zz-www.sudokuoftheday.co.uk-20060328-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: ..57...8.9.3.2.....1..56............54...2..6.79...5....76.32..........7..24..83. initial

Autosolve

position: ..57...8.9.3.2....71..56.....65.....54...2..6.79.6.5....76.32.....2....7..24..83. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 4 => CTR => A1: 2,6
* PRF # C8: 1 => SOL
* DIS # F2: 1,8 => CTR => F2: 4
* DIS # D5: 1,8 => CTR => D5: 3,9
* DIS # D6: 1,8 => CTR => D6: 3
* DIS # D5: 1,8 => CTR => D5: 3,9
* DIS # C8: 4 => CTR => C8: 1,8
* CNT   7 HDP CHAINS /  17 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: 4 => CTR => A1: 2,6
* DIS A1: 2,6 # A4: 1,8 => CTR => A4: 2,3
* DIS A1: 2,6 + A4: 2,3 # E5: 1,8 => CTR => E5: 7
* PRF A1: 2,6 + A4: 2,3 + E5: 7 => SOL
* STA A1: 2,6 + A4: 2,3 + E5: 7
* CNT   4 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

..57...8.9.3.2.....1..56............54...2..6.79...5....76.32..........7..24..83. initial
..57...8.9.3.2....71..56.....65.....54...2..6.79.6.5....76.32.....2....7..24..83. autosolve
265739184983124675714856923326541798548972316179368542497683251831295467652417839 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (6)
B1: 2,6
B2: 6,8
C3: 4,8
D2: 1,8
C5: 1,8
A9: 1,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C5,C8: 1.. / C5 = 1  =>  9 pairs (_) / C8 = 1  =>  0 pairs (*)
A1,B1: 2.. / A1 = 2  => 17 pairs (_) / B1 = 2  =>  7 pairs (_)
H3,I3: 2.. / H3 = 2  => 10 pairs (_) / I3 = 2  =>  7 pairs (_)
B1,B4: 2.. / B1 = 2  =>  7 pairs (_) / B4 = 2  => 17 pairs (_)
E1,D3: 3.. / E1 = 3  => 10 pairs (_) / D3 = 3  =>  0 pairs (X)
A8,B8: 3.. / A8 = 3  =>  6 pairs (_) / B8 = 3  =>  9 pairs (_)
B4,B8: 3.. / B4 = 3  =>  6 pairs (_) / B8 = 3  =>  9 pairs (_)
A1,C3: 4.. / A1 = 4  =>  0 pairs (X) / C3 = 4  => 18 pairs (_)
C3,C8: 4.. / C3 = 4  => 18 pairs (_) / C8 = 4  =>  0 pairs (X)
E1,E4: 4.. / E1 = 4  =>  0 pairs (X) / E4 = 4  =>  7 pairs (_)
H2,I2: 5.. / H2 = 5  =>  0 pairs (X) / I2 = 5  =>  7 pairs (_)
F8,F9: 5.. / F8 = 5  =>  6 pairs (_) / F9 = 5  =>  8 pairs (_)
A9,B9: 6.. / A9 = 6  =>  7 pairs (_) / B9 = 6  =>  0 pairs (X)
G8,H8: 6.. / G8 = 6  =>  0 pairs (X) / H8 = 6  =>  6 pairs (_)
A1,A9: 6.. / A1 = 6  =>  0 pairs (X) / A9 = 6  =>  7 pairs (_)
H2,H8: 6.. / H2 = 6  =>  0 pairs (X) / H8 = 6  =>  6 pairs (_)
G2,H2: 7.. / G2 = 7  =>  6 pairs (_) / H2 = 7  =>  9 pairs (_)
E9,F9: 7.. / E9 = 7  =>  6 pairs (_) / F9 = 7  =>  9 pairs (_)
F4,F9: 7.. / F4 = 7  =>  6 pairs (_) / F9 = 7  =>  9 pairs (_)
B2,C3: 8.. / B2 = 8  => 18 pairs (_) / C3 = 8  =>  0 pairs (X)
I4,I6: 8.. / I4 = 8  =>  7 pairs (_) / I6 = 8  =>  8 pairs (_)
C3,D3: 8.. / C3 = 8  =>  0 pairs (X) / D3 = 8  => 18 pairs (_)
D3,D5: 9.. / D3 = 9  =>  0 pairs (X) / D5 = 9  =>  8 pairs (_)
* DURATION: 0:00:22.023382  START: 21:58:49.765319  END: 21:59:11.788701 2019-04-30
* CP COUNT: (23)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B1,B2,C3,C5,D2)
* ..57...8.9.3.2....71..56.....65.....54...2..6.79.6.5....76.32.....2....7..24..83.
* PAIR B1: 2,6 BLK 1
A1: 2,6,4                                # reduction candidate for 2,6
A1: 4 => CTR
* 4257..68.963824...718.564....654....541.82..6.7916.5....76.32....42...676.24..83.
A1: 2,6                                  # 18 pairs
* PAIR C3: 4,8 COL C
C8: 4,8,1                                # reduction candidate for 4,8
C8: 1 => SOLVED
* 265739184983124675714856923326541798548972316179368542497683251831295467652417839
C8: 4,8                                  #  9 pairs
* PAIR D2: 1,8 BLK 2
F2: 1,8,4                                # reduction candidate for 1,8
F2: 1,8 => CTR
* ..57...8.9.3.2....714856.....65.....54.9.2..6.7936.5....76.32.....2....7..24..83.
F2: 4                                    # 10 pairs
* PAIR D2: 1,8 COL D
D5: 1,8,3,9                              # reduction candidate for 1,8
D5: 1,8 => CTR
* 4.573..8.9.3.2....718956.....654....5418.23.6.793615....76.32....42....7..24..83.
D5: 3,9                                  #  7 pairs
D6: 1,8,3                                # reduction candidate for 1,8
D6: 1,8 => CTR
* 4257..68.963821...718.56..22.65.7...541.82..6.7916452...76.32....42.8.67692475831
D6: 3                                    # 11 pairs
* PAIR C5: 1,8 BLK 4
A4: 1,8,2,3                              # reduction candidate for 1,8
A4: 1,8                                  #  9 pairs
A6: 1,8,2,3                              # reduction candidate for 1,8
A6: 1,8                                  #  9 pairs
* PAIR C5: 1,8 ROW 5
D5: 1,8,3,9                              # reduction candidate for 1,8
D5: 1,8 => CTR
* 4.573..8.9.3.2....718956.....654....5418.23.6.793615....76.32....42....7..24..83.
D5: 3,9                                  #  7 pairs
E5: 1,8,3,7,9                            # reduction candidate for 1,8
E5: 1,8                                  # 13 pairs
* PAIR C5: 1,8 COL C
C8: 1,8,4                                # reduction candidate for 1,8
C8: 4 => CTR
* 4257..68.963824...718.564....654....541.82..6.7916.5....76.32....42...676.24..83.
C8: 1,8                                  # 18 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060328-absurd-base-pr-000.dot
* REASONING
* DIS # A1: 4 => CTR => A1: 2,6
* PRF # C8: 1 => SOL
* DIS # F2: 1,8 => CTR => F2: 4
* DIS # D5: 1,8 => CTR => D5: 3,9
* DIS # D6: 1,8 => CTR => D6: 3
* DIS # D5: 1,8 => CTR => D5: 3,9
* DIS # C8: 4 => CTR => C8: 1,8
* CNT   7 HDP CHAINS /  17 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B1,B2,C3,C5,D2)
* ..57...8.9.3.2....71..56.....65.....54...2..6.79.6.5....76.32.....2....7..24..83.
* PAIR B1: 2,6 BLK 1
A1: 2,6,4                                # reduction candidate for 2,6
A1: 4 => CTR
* 4257..68.963824...718.564....654....541.82..6.7916.5....76.32....42...676.24..83.
* PAIR C5: 1,8 BLK 4
A4: 1,8,2,3                              # reduction candidate for 1,8
A4: 1,8 => CTR
* 62573918498312467571485692313654..9254.9.23.6279361548..76.32..3..2..467..24..83.
* RESTART
* PAIR C5: 1,8 ROW 5
E5: 1,8,7                                # reduction candidate for 1,8
E5: 1,8 => CTR
* 265739481983124765714856923326547198541982376.7936.542.976.325443.295617.52471839
E5: 7 => SOLVED
* 265739184983124675714856923326541798548972316179368542497683251831295467652417839
* DURATION: 0:00:05.039909  START: 21:59:21.487581  END: 21:59:26.527490 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060328-absurd-base-pr-001.dot
* REASONING
* DIS # A1: 4 => CTR => A1: 2,6
* DIS A1: 2,6 # A4: 1,8 => CTR => A4: 2,3
* DIS A1: 2,6 + A4: 2,3 # E5: 1,8 => CTR => E5: 7
* PRF A1: 2,6 + A4: 2,3 + E5: 7 => SOL
* STA A1: 2,6 + A4: 2,3 + E5: 7
* CNT   4 HDP CHAINS /   4 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060328, absurd

Solution

position: 265739184983124675714856923326541798548972316179368542497683251831295467652417839 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 # A1: 2,6 => UNS
* DIS # A1: 4 => CTR => A1: 2,6
* INC # C8: 4,8 => UNS
* PRF # C8: 1 => SOL
* DIS # F2: 1,8 => CTR => F2: 4
* INC # F2: 4 => UNS
* DIS # D5: 1,8 => CTR => D5: 3,9
* INC # D5: 3,9 => UNS
* DIS # D6: 1,8 => CTR => D6: 3
* INC # D6: 3 => UNS
* INC # A4: 1,8 => UNS
* INC # A6: 1,8 => UNS
* DIS # D5: 1,8 => CTR => D5: 3,9
* INC # D5: 3,9 => UNS
* INC # E5: 1,8 => UNS
* INC # C8: 1,8 => UNS
* DIS # C8: 4 => CTR => C8: 1,8
* CNT  17 HDP CHAINS /  17 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A1: 2,6 => UNS
* DIS # A1: 4 => CTR => A1: 2,6
* DIS A1: 2,6 # A4: 1,8 => CTR => A4: 2,3
* DIS A1: 2,6 + A4: 2,3 # E5: 1,8 => CTR => E5: 7
* PRF A1: 2,6 + A4: 2,3 + E5: 7 => SOL
* STA A1: 2,6 + A4: 2,3 + E5: 7
* CNT   5 HDP CHAINS /   4 HYP OPENED