Analysis of zz-www.sudokuoftheday.co.uk-20060429-absurd-base.sdk

Contents

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

level: medium

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

position: 9.6.7..3..4...3...83.....9..8.5..2....2..4..87........6.438.9.....7.26.33...4..81 initial

Autosolve

position: 9.6.7..3.24...3...83.....9.48.5.72....2..4.787........674381925..87.264332..4.781 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B5: 1,5 => CTR => B5: 6,9
* DIS # B6: 1,5 => CTR => B6: 6,9
* PRF # B8: 1,5 => SOL
* DIS # B8: 9 => CTR => B8: 1,5
* PRF # G1: 5,8 => SOL
* PRF # F9: 5,6 => SOL
* DIS # F9: 9 => CTR => F9: 5,6
* DIS # D1: 1,8 => CTR => D1: 2,4
* DIS # B5: 1,5 => CTR => B5: 6,9
* DIS # B6: 1,5 => CTR => B6: 6,9
* DIS # C6: 1,5 => CTR => C6: 3,9
* DIS # G5: 1,5 => CTR => G5: 3
* PRF # B8: 1,5 => SOL
* DIS # B8: 9 => CTR => B8: 1,5
* DIS # B8: 1 => CTR => B8: 5,9
* DIS # F9: 6 => CTR => F9: 5,9
* DIS # C6: 5,9 => CTR => C6: 1,3
* DIS # F9: 6 => CTR => F9: 5,9
* DIS # B8: 1 => CTR => B8: 5,9
* DIS # F9: 6,9 => CTR => F9: 5
* PRF # F9: 5 => SOL
* DIS # D5: 6,9 => CTR => D5: 1
* DIS # D6: 6,9 => CTR => D6: 1,2,8
* CNT  23 HDP CHAINS /  61 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 # B5: 1,5 => CTR => B5: 6,9
* DIS B5: 6,9 # B6: 1,5 => CTR => B6: 6,9
* PRF B5: 6,9 + B6: 6,9 => SOL
* STA B5: 6,9 + B6: 6,9
* CNT   3 HDP CHAINS /   6 HYP OPENED

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

Details

Positions

9.6.7..3..4...3...83.....9..8.5..2....2..4..87........6.438.9.....7.26.33...4..81 initial
9.6.7..3.24...3...83.....9.48.5.72....2..4.787........674381925..87.264332..4.781 autosolve
916478532247953816835216497481537269592164378763829154674381925158792643329645781 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (12)
B1: 1,5
F1: 5,8
F3: 5,6
I1: 2,4
I2: 6,7
A5: 1,5
H4: 1,6
I4: 6,9
A8: 1,5
C9: 5,9
E8: 5,9
D9: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A8,B8: 1.. / A8 = 1  => 12 pairs (_) / B8 = 1  =>  0 pairs (X)
A5,A8: 1.. / A5 = 1  =>  0 pairs (X) / A8 = 1  => 12 pairs (_)
I1,I3: 2.. / I1 = 2  => 11 pairs (_) / I3 = 2  =>  0 pairs (X)
D6,E6: 2.. / D6 = 2  =>  0 pairs (X) / E6 = 2  => 14 pairs (_)
D1,I1: 2.. / D1 = 2  =>  0 pairs (X) / I1 = 2  => 11 pairs (_)
E3,E6: 2.. / E3 = 2  =>  0 pairs (X) / E6 = 2  => 14 pairs (_)
C4,C6: 3.. / C4 = 3  => 12 pairs (_) / C6 = 3  => 15 pairs (_)
G5,G6: 3.. / G5 = 3  => 12 pairs (_) / G6 = 3  =>  0 pairs (X)
C4,E4: 3.. / C4 = 3  => 12 pairs (_) / E4 = 3  => 15 pairs (_)
E5,G5: 3.. / E5 = 3  =>  0 pairs (X) / G5 = 3  => 12 pairs (_)
D1,D3: 4.. / D1 = 4  => 11 pairs (_) / D3 = 4  => 13 pairs (_)
G6,I6: 4.. / G6 = 4  => 16 pairs (_) / I6 = 4  => 13 pairs (_)
E8,F9: 5.. / E8 = 5  =>  0 pairs (X) / F9 = 5  =>  0 pairs (_)
C9,F9: 5.. / C9 = 5  =>  0 pairs (X) / F9 = 5  =>  0 pairs (_)
A5,A8: 5.. / A5 = 5  => 12 pairs (_) / A8 = 5  =>  0 pairs (X)
H2,H6: 5.. / H2 = 5  => 18 pairs (_) / H6 = 5  => 14 pairs (_)
B5,B6: 6.. / B5 = 6  =>  0 pairs (X) / B6 = 6  => 15 pairs (_)
D9,F9: 6.. / D9 = 6  => 13 pairs (_) / F9 = 6  =>  0 pairs (X)
C2,C3: 7.. / C2 = 7  => 12 pairs (_) / C3 = 7  => 12 pairs (_)
I2,I3: 7.. / I2 = 7  => 12 pairs (_) / I3 = 7  => 12 pairs (_)
C2,I2: 7.. / C2 = 7  => 12 pairs (_) / I2 = 7  => 12 pairs (_)
C3,I3: 7.. / C3 = 7  => 12 pairs (_) / I3 = 7  => 12 pairs (_)
G1,G2: 8.. / G1 = 8  =>  0 pairs (X) / G2 = 8  => 14 pairs (_)
D6,F6: 8.. / D6 = 8  => 15 pairs (_) / F6 = 8  =>  0 pairs (X)
D2,G2: 8.. / D2 = 8  =>  0 pairs (X) / G2 = 8  => 14 pairs (_)
F1,F6: 8.. / F1 = 8  => 15 pairs (_) / F6 = 8  =>  0 pairs (X)
D2,E2: 9.. / D2 = 9  => 15 pairs (_) / E2 = 9  =>  0 pairs (X)
I4,I6: 9.. / I4 = 9  => 13 pairs (_) / I6 = 9  =>  0 pairs (X)
B8,C9: 9.. / B8 = 9  =>  0 pairs (X) / C9 = 9  =>  0 pairs (_)
B8,E8: 9.. / B8 = 9  =>  0 pairs (X) / E8 = 9  =>  0 pairs (_)
F6,F9: 9.. / F6 = 9  =>  0 pairs (*) / F9 = 9  =>  0 pairs (X)
* DURATION: 0:00:31.814941  START: 22:45:03.184824  END: 22:45:34.999765 2019-04-30
* CP COUNT: (31)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,B1,C9,D9,E8,F1,F3,H4,I1,I2,I4)
* 9.6.7..3.24...3...83.....9.48.5.72....2..4.787........674381925..87.264332..4.781
* PAIR B1: 1,5 BLK 1
C2: 1,5,7                                # reduction candidate for 1,5
C2: 1,5                                  # 12 pairs
C3: 1,5,7                                # reduction candidate for 1,5
C3: 1,5                                  # 12 pairs
* PAIR B1: 1,5 ROW 1
G1: 1,5,4,8                              # reduction candidate for 1,5
G1: 1,5                                  # 15 pairs
G1: 4,8                                  # 13 pairs
* PAIR B1: 1,5 COL B
B5: 1,5,6,9                              # reduction candidate for 1,5
B5: 1,5 => CTR
* 956.78.3.24...385.83...5.9.48.5.7269512..4378769......674381925.98752643325.4.781
B5: 6,9                                  # 13 pairs
B6: 1,5,6,9                              # reduction candidate for 1,5
B6: 1,5 => CTR
* 956.78.3224...385.83.2.549.48.567219562.34.7871.82.564674381925198752643325.46781
B6: 6,9                                  # 13 pairs
B8: 1,5,9                                # reduction candidate for 1,5
B8: 1,5 => SOLVED
* 916478532247953816835216497481537269592164378763829154674381925158792643329645781
B8: 9 => CTR
* 956.78.3224...385.83.2.549.48.5.72.95.2..43787..82.5.4674381925198752643325.4.781
* PAIR F1: 5,8 ROW 1
G1: 5,8,1,4                              # reduction candidate for 5,8
G1: 5,8 => SOLVED
* 916478532247953816835216497481537269592164378763829154674381925158792643329645781
G1: 1,4                                  # 15 pairs
* PAIR F3: 5,6 BLK 2
E2: 5,6,1,9                              # reduction candidate for 5,6
E2: 5,6                                  # 22 pairs
E3: 5,6,1,2                              # reduction candidate for 5,6
E3: 5,6                                  # 23 pairs
* PAIR F3: 5,6 COL F
F9: 5,6,9                                # reduction candidate for 5,6
F9: 5,6 => SOLVED
* 916478532247953816835216497481537269592164378763829154674381925158792643329645781
F9: 9 => CTR
* 956.78.3.24...385.83...5.9.48.5.72..5.2..4.787..826514674381925198752643325649781
* PAIR I1: 2,4 BLK 3
I3: 2,4,6,7                              # reduction candidate for 2,4
I3: 2,4                                  # 16 pairs
I3: 6,7                                  # 13 pairs
* PAIR I1: 2,4 ROW 1
D1: 2,4,1,8                              # reduction candidate for 2,4
D1: 1,8 => CTR
* 9.6.7543224...38..83.426.9748.5.72.9..2..4.787.92.8..4674381925.98752643325649781
D1: 2,4                                  # 13 pairs
* PAIR I2: 6,7 BLK 3
I3: 6,7,2,4                              # reduction candidate for 6,7
I3: 2,4                                  # 16 pairs
I3: 6,7                                  # 13 pairs
* PAIR A5: 1,5 BLK 4
B5: 1,5,6,9                              # reduction candidate for 1,5
B5: 1,5 => CTR
* 956.78.3.24...385.83...5.9.48.5.7269512..4378769......674381925.98752643325.4.781
B5: 6,9                                  # 13 pairs
B6: 1,5,6,9                              # reduction candidate for 1,5
B6: 1,5 => CTR
* 956.78.3224...385.83.2.549.48.567219562.34.7871.82.564674381925198752643325.46781
B6: 6,9                                  # 13 pairs
C6: 1,5,3,9                              # reduction candidate for 1,5
C6: 1,5 => CTR
* 9.6.78.3224.9.38..83.2.64974835.72.9.921.4.787..8293.4674381925..8792643329645781
C6: 3,9                                  # 13 pairs
* PAIR A5: 1,5 ROW 5
G5: 1,5,3                                # reduction candidate for 1,5
G5: 1,5 => CTR
* 956.78.32247193856831..54974835.72.95629341787.....3.4674381925.98752643325.4.781
G5: 3                                    # 12 pairs
* PAIR H4: 1,6 BLK 6
H6: 1,6,5                                # reduction candidate for 1,6
H6: 1,6                                  # 18 pairs
H6: 5                                    # 14 pairs
* PAIR H4: 1,6 ROW 4
E4: 1,6,3,9                              # reduction candidate for 1,6
E4: 3,9                                  # 15 pairs
E4: 1,6                                  # 13 pairs
* PAIR H4: 1,6 COL H
H2: 1,6,5                                # reduction candidate for 1,6
H2: 5                                    # 18 pairs
H2: 1,6                                  # 14 pairs
* PAIR I4: 6,9 BLK 6
I6: 6,9,4                                # reduction candidate for 6,9
I6: 6,9                                  # 16 pairs
I6: 4                                    # 13 pairs
* PAIR I4: 6,9 ROW 4
E4: 6,9,1,3                              # reduction candidate for 6,9
E4: 6,9                                  # 15 pairs
E4: 1,3                                  # 15 pairs
* PAIR A8: 1,5 BLK 7
B8: 1,5,9                                # reduction candidate for 1,5
B8: 1,5 => SOLVED
* 916478532247953816835216497481537269592164378763829154674381925158792643329645781
B8: 9 => CTR
* 956.78.3224...385.83.2.549.48.5.72.95.2..43787..82.5.4674381925198752643325.4.781
* PAIR C9: 5,9 BLK 7
B8: 5,9,1                                # reduction candidate for 5,9
B8: 1 => CTR
* 956.78.3.24.9.38..83...6.9.48.5.72.91.2..4.787........674381925.18792643329645781
B8: 5,9                                  # 12 pairs
* PAIR C9: 5,9 ROW 9
F9: 5,9,6                                # reduction candidate for 5,9
F9: 6 => CTR
* 956.78.3.24..9385.83...5.9.489537216..2..4.787....9...674381925..8752643325946781
F9: 5,9                                  # 13 pairs
* PAIR C9: 5,9 COL C
C6: 5,9,1,3                              # reduction candidate for 5,9
C6: 5,9 => CTR
* 95647813224.9.385.83.256497483567219..2.345787.582.3.4674381925518792643329645781
C6: 1,3                                  # 13 pairs
* PAIR E8: 5,9 BLK 8
F9: 5,9,6                                # reduction candidate for 5,9
F9: 6 => CTR
* 956.78.3.24..9385.83...5.9.489537216..2..4.787....9...674381925..8752643325946781
F9: 5,9                                  # 13 pairs
* PAIR E8: 5,9 ROW 8
B8: 5,9,1                                # reduction candidate for 5,9
B8: 1 => CTR
* 956.78.3.24.9.38..83...6.9.48.5.72.91.2..4.787........674381925.18792643329645781
B8: 5,9                                  # 12 pairs
* PAIR E8: 5,9 COL E
E2: 5,9,1,6                              # reduction candidate for 5,9
E2: 1,6                                  # 16 pairs
E2: 5,9                                  # 13 pairs
* PAIR D9: 6,9 BLK 8
F9: 6,9,5                                # reduction candidate for 6,9
F9: 6,9 => CTR
* 956.78.3224...385.83.2.549.48.5.72.95.2..43787..82.5.4674381925198752643325.4.781
F9: 5 => SOLVED
* 916478532247953816835216497481537269592164378763829154674381925158792643329645781
* PAIR D9: 6,9 COL D
D2: 6,9,1,8                              # reduction candidate for 6,9
D2: 6,9                                  # 16 pairs
D5: 6,9,1                                # reduction candidate for 6,9
D5: 6,9 => CTR
* 956.78.3.24.193856831..549748.5.72.95.29.4.787.9826...674381925.98752643325.4.781
D5: 1                                    # 13 pairs
D6: 6,9,1,2,8                            # reduction candidate for 6,9
D6: 6,9 => CTR
* 9.6.75.3.24...3...83...6.9.48.5.72....2..4.787...28...674381925.98752643325649781
D6: 1,2,8                                # 12 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060429-absurd-base-pr-000.dot
* REASONING
* DIS # B5: 1,5 => CTR => B5: 6,9
* DIS # B6: 1,5 => CTR => B6: 6,9
* PRF # B8: 1,5 => SOL
* DIS # B8: 9 => CTR => B8: 1,5
* PRF # G1: 5,8 => SOL
* PRF # F9: 5,6 => SOL
* DIS # F9: 9 => CTR => F9: 5,6
* DIS # D1: 1,8 => CTR => D1: 2,4
* DIS # B5: 1,5 => CTR => B5: 6,9
* DIS # B6: 1,5 => CTR => B6: 6,9
* DIS # C6: 1,5 => CTR => C6: 3,9
* DIS # G5: 1,5 => CTR => G5: 3
* PRF # B8: 1,5 => SOL
* DIS # B8: 9 => CTR => B8: 1,5
* DIS # B8: 1 => CTR => B8: 5,9
* DIS # F9: 6 => CTR => F9: 5,9
* DIS # C6: 5,9 => CTR => C6: 1,3
* DIS # F9: 6 => CTR => F9: 5,9
* DIS # B8: 1 => CTR => B8: 5,9
* DIS # F9: 6,9 => CTR => F9: 5
* PRF # F9: 5 => SOL
* DIS # D5: 6,9 => CTR => D5: 1
* DIS # D6: 6,9 => CTR => D6: 1,2,8
* CNT  23 HDP CHAINS /  61 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,B1,C9,D9,E8,F1,F3,H4,I1,I2,I4)
* 9.6.7..3.24...3...83.....9.48.5.72....2..4.787........674381925..87.264332..4.781
* PAIR B1: 1,5 BLK 1
C2: 1,5,7                                # reduction candidate for 1,5
C2: 1,5                                  # 12 pairs
C3: 1,5,7                                # reduction candidate for 1,5
C3: 1,5                                  # 12 pairs
* PAIR B1: 1,5 ROW 1
G1: 1,5,4,8                              # reduction candidate for 1,5
G1: 1,5                                  # 15 pairs
G1: 4,8                                  # 13 pairs
* PAIR B1: 1,5 COL B
B5: 1,5,6,9                              # reduction candidate for 1,5
B5: 1,5 => CTR
* 956.78.3.24...385.83...5.9.48.5.7269512..4378769......674381925.98752643325.4.781
B6: 1,5,6,9                              # reduction candidate for 1,5
B6: 1,5 => CTR
* 956.78.3224...385.83.2.549.48.567219562.34.7871.82.564674381925198752643325.46781
B6: 6,9 => SOLVED
* 916478532247953816835216497481537269592164378763829154674381925158792643329645781
* DURATION: 0:00:03.919539  START: 22:46:09.623771  END: 22:46:13.543310 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060429-absurd-base-pr-001.dot
* REASONING
* DIS # B5: 1,5 => CTR => B5: 6,9
* DIS B5: 6,9 # B6: 1,5 => CTR => B6: 6,9
* PRF B5: 6,9 + B6: 6,9 => SOL
* STA B5: 6,9 + B6: 6,9
* CNT   3 HDP CHAINS /   6 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060429, absurd

Solution

position: 916478532247953816835216497481537269592164378763829154674381925158792643329645781 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 # C2: 1,5 => UNS
* INC # C3: 1,5 => UNS
* INC # G1: 1,5 => UNS
* INC # G1: 4,8 => UNS
* DIS # B5: 1,5 => CTR => B5: 6,9
* INC # B5: 6,9 => UNS
* DIS # B6: 1,5 => CTR => B6: 6,9
* INC # B6: 6,9 => UNS
* PRF # B8: 1,5 => SOL
* DIS # B8: 9 => CTR => B8: 1,5
* PRF # G1: 5,8 => SOL
* INC # G1: 1,4 => UNS
* INC # E2: 5,6 => UNS
* INC # E3: 5,6 => UNS
* PRF # F9: 5,6 => SOL
* DIS # F9: 9 => CTR => F9: 5,6
* INC # I3: 2,4 => UNS
* INC # I3: 6,7 => UNS
* INC # D1: 2,4 => UNS
* DIS # D1: 1,8 => CTR => D1: 2,4
* INC # I3: 6,7 => UNS
* INC # I3: 2,4 => UNS
* DIS # B5: 1,5 => CTR => B5: 6,9
* INC # B5: 6,9 => UNS
* DIS # B6: 1,5 => CTR => B6: 6,9
* INC # B6: 6,9 => UNS
* DIS # C6: 1,5 => CTR => C6: 3,9
* INC # C6: 3,9 => UNS
* DIS # G5: 1,5 => CTR => G5: 3
* INC # G5: 3 => UNS
* INC # H6: 1,6 => UNS
* INC # H6: 5 => UNS
* INC # E4: 1,6 => UNS
* INC # E4: 3,9 => UNS
* INC # H2: 1,6 => UNS
* INC # H2: 5 => UNS
* INC # I6: 6,9 => UNS
* INC # I6: 4 => UNS
* INC # E4: 6,9 => UNS
* INC # E4: 1,3 => UNS
* PRF # B8: 1,5 => SOL
* DIS # B8: 9 => CTR => B8: 1,5
* INC # B8: 5,9 => UNS
* DIS # B8: 1 => CTR => B8: 5,9
* INC # F9: 5,9 => UNS
* DIS # F9: 6 => CTR => F9: 5,9
* DIS # C6: 5,9 => CTR => C6: 1,3
* INC # C6: 1,3 => UNS
* INC # F9: 5,9 => UNS
* DIS # F9: 6 => CTR => F9: 5,9
* INC # B8: 5,9 => UNS
* DIS # B8: 1 => CTR => B8: 5,9
* INC # E2: 5,9 => UNS
* INC # E2: 1,6 => UNS
* DIS # F9: 6,9 => CTR => F9: 5
* PRF # F9: 5 => SOL
* INC # D2: 6,9 => UNS
* DIS # D5: 6,9 => CTR => D5: 1
* INC # D5: 1 => UNS
* DIS # D6: 6,9 => CTR => D6: 1,2,8
* INC # D6: 1,2,8 => UNS
* CNT  61 HDP CHAINS /  61 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C2: 1,5 => UNS
* INC # C3: 1,5 => UNS
* INC # G1: 1,5 => UNS
* INC # G1: 4,8 => UNS
* DIS # B5: 1,5 => CTR => B5: 6,9
* DIS B5: 6,9 # B6: 1,5 => CTR => B6: 6,9
* PRF B5: 6,9 + B6: 6,9 => SOL
* STA B5: 6,9 + B6: 6,9
* CNT   7 HDP CHAINS /   6 HYP OPENED