Analysis of zz-www.sudokuoftheday.co.uk-20190405-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019

position: 7.6....8....972.4..2......1..9...5...634...1......52.64.21.6...........8..1..9... initial

Autosolve

position: 7.6....82...97264..2....7.12.9...5.4563427819....952.64.21.6.........1.8..1..94.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B2: 5,8 => CTR => B2: 1,3
* PRF # B1: 3,9 => SOL
* DIS # B1: 4,5 => CTR => B1: 3,9
* DIS # A8: 6 => CTR => A8: 3,9
* DIS # B1: 4,5 => CTR => B1: 3,9
* PRF # B1: 3,9 => SOL
* DIS # D3: 3,5 => CTR => D3: 6,8
* PRF # B1: 3,5 => SOL
* PRF # B1: 3,9 => SOL
* DIS # B1: 4,5 => CTR => B1: 3,9
* DIS # B2: 3,5 => CTR => B2: 1,8
* DIS # I7: 3,5 => CTR => I7: 7
* DIS # B6: 7,8 => CTR => B6: 1,4
* DIS # B6: 1,8 => CTR => B6: 4,7
* DIS # A2: 3 => CTR => A2: 1,8
* DIS # B8: 5,7 => CTR => B8: 3,9
* CNT  16 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:

* DIS # B2: 5,8 => CTR => B2: 1,3
* PRF B2: 1,3 # B1: 3,9 => SOL
* STA B2: 1,3 + B1: 3,9
* CNT   2 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

7.6....8....972.4..2......1..9...5...634...1......52.64.21.6...........8..1..9... initial
7.6....82...97264..2....7.12.9...5.4563427819....952.64.21.6.........1.8..1..94.. autosolve
736541982815972643924863751279618534563427819148395276452186397397254168681739425 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (20)
C2: 5,8
A3: 3,9
C3: 4,5
D1: 3,5
G1: 3,9
I2: 3,5
H3: 5,9
B4: 7,8
A6: 1,8
D6: 3,8
H4: 3,7
H6: 3,7
C8: 5,7
D8: 2,7
F8: 3,4
D9: 2,7
G7: 3,9
H7: 5,9
H8: 2,6
H9: 2,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A2,B2: 1.. / A2 = 1  =>  0 pairs (X) / B2 = 1  => 20 pairs (_)
E1,F1: 1.. / E1 = 1  => 22 pairs (_) / F1 = 1  => 22 pairs (_)
A6,B6: 1.. / A6 = 1  => 20 pairs (_) / B6 = 1  =>  0 pairs (X)
E4,F4: 1.. / E4 = 1  => 22 pairs (_) / F4 = 1  => 22 pairs (_)
A2,A6: 1.. / A2 = 1  =>  0 pairs (X) / A6 = 1  => 20 pairs (_)
B2,B6: 1.. / B2 = 1  => 20 pairs (_) / B6 = 1  =>  0 pairs (X)
E1,E4: 1.. / E1 = 1  => 22 pairs (_) / E4 = 1  => 22 pairs (_)
F1,F4: 1.. / F1 = 1  => 22 pairs (_) / F4 = 1  => 22 pairs (_)
D8,D9: 2.. / D8 = 2  => 20 pairs (_) / D9 = 2  =>  0 pairs (X)
H8,H9: 2.. / H8 = 2  =>  0 pairs (X) / H9 = 2  => 20 pairs (_)
D8,H8: 2.. / D8 = 2  => 20 pairs (_) / H8 = 2  =>  0 pairs (X)
D9,H9: 2.. / D9 = 2  =>  0 pairs (X) / H9 = 2  => 20 pairs (_)
G1,I2: 3.. / G1 = 3  =>  0 pairs (X) / I2 = 3  =>  0 pairs (_)
H4,H6: 3.. / H4 = 3  => 20 pairs (_) / H6 = 3  =>  0 pairs (X)
D6,H6: 3.. / D6 = 3  => 20 pairs (_) / H6 = 3  =>  0 pairs (X)
G1,G7: 3.. / G1 = 3  =>  0 pairs (X) / G7 = 3  =>  0 pairs (_)
B1,C3: 4.. / B1 = 4  =>  0 pairs (X) / C3 = 4  => 24 pairs (_)
B6,C6: 4.. / B6 = 4  => 24 pairs (_) / C6 = 4  =>  0 pairs (X)
E8,F8: 4.. / E8 = 4  => 31 pairs (_) / F8 = 4  => 25 pairs (_)
B1,B6: 4.. / B1 = 4  =>  0 pairs (X) / B6 = 4  => 24 pairs (_)
C3,C6: 4.. / C3 = 4  => 24 pairs (_) / C6 = 4  =>  0 pairs (X)
D1,D3: 5.. / D1 = 5  => 19 pairs (_) / D3 = 5  =>  0 pairs (X)
I2,H3: 5.. / I2 = 5  =>  0 pairs (X) / H3 = 5  =>  0 pairs (_)
B1,D1: 5.. / B1 = 5  =>  0 pairs (X) / D1 = 5  => 19 pairs (_)
H3,H7: 5.. / H3 = 5  =>  0 pairs (*) / H7 = 5  =>  0 pairs (X)
D3,E3: 6.. / D3 = 6  => 22 pairs (_) / E3 = 6  => 21 pairs (_)
D4,E4: 6.. / D4 = 6  => 21 pairs (_) / E4 = 6  => 22 pairs (_)
A8,A9: 6.. / A8 = 6  =>  0 pairs (X) / A9 = 6  => 20 pairs (_)
H8,H9: 6.. / H8 = 6  => 20 pairs (_) / H9 = 6  =>  0 pairs (X)
A8,H8: 6.. / A8 = 6  =>  0 pairs (X) / H8 = 6  => 20 pairs (_)
A9,H9: 6.. / A9 = 6  => 20 pairs (_) / H9 = 6  =>  0 pairs (X)
D3,D4: 6.. / D3 = 6  => 22 pairs (_) / D4 = 6  => 21 pairs (_)
E3,E4: 6.. / E3 = 6  => 21 pairs (_) / E4 = 6  => 22 pairs (_)
H4,H6: 7.. / H4 = 7  =>  0 pairs (X) / H6 = 7  => 20 pairs (_)
D8,D9: 7.. / D8 = 7  =>  0 pairs (X) / D9 = 7  => 20 pairs (_)
I7,I9: 7.. / I7 = 7  => 21 pairs (_) / I9 = 7  =>  0 pairs (X)
B4,H4: 7.. / B4 = 7  => 20 pairs (_) / H4 = 7  =>  0 pairs (X)
B7,I7: 7.. / B7 = 7  =>  0 pairs (X) / I7 = 7  => 21 pairs (_)
C6,C8: 7.. / C6 = 7  =>  0 pairs (X) / C8 = 7  => 20 pairs (_)
D3,F3: 8.. / D3 = 8  => 18 pairs (_) / F3 = 8  => 21 pairs (_)
E7,E9: 8.. / E7 = 8  => 21 pairs (_) / E9 = 8  => 22 pairs (_)
B7,E7: 8.. / B7 = 8  => 22 pairs (_) / E7 = 8  => 21 pairs (_)
C2,C6: 8.. / C2 = 8  => 21 pairs (_) / C6 = 8  =>  0 pairs (*)
F3,F4: 8.. / F3 = 8  => 21 pairs (_) / F4 = 8  => 18 pairs (_)
B1,A3: 9.. / B1 = 9  =>  0 pairs (X) / A3 = 9  =>  0 pairs (_)
G1,H3: 9.. / G1 = 9  =>  0 pairs (*) / H3 = 9  =>  0 pairs (X)
A8,B8: 9.. / A8 = 9  =>  0 pairs (X) / B8 = 9  =>  0 pairs (_)
G7,H7: 9.. / G7 = 9  =>  0 pairs (X) / H7 = 9  =>  0 pairs (_)
B1,G1: 9.. / B1 = 9  =>  0 pairs (X) / G1 = 9  =>  0 pairs (_)
A3,H3: 9.. / A3 = 9  =>  0 pairs (*) / H3 = 9  =>  0 pairs (X)
A3,A8: 9.. / A3 = 9  =>  0 pairs (*) / A8 = 9  =>  0 pairs (X)
B1,B8: 9.. / B1 = 9  =>  0 pairs (X) / B8 = 9  =>  0 pairs (_)
G1,G7: 9.. / G1 = 9  =>  0 pairs (*) / G7 = 9  =>  0 pairs (X)
H3,H7: 9.. / H3 = 9  =>  0 pairs (X) / H7 = 9  =>  0 pairs (_)
* DURATION: 0:01:12.552493  START: 05:04:32.570049  END: 05:05:45.122542 2019-05-01
* CP COUNT: (54)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A6,B4,C2,C3,C8,D1,D6,D8,D9,F8,G1,G7,H3,H4,H6,H7,H8,H9,I2)
* 7.6....82...97264..2....7.12.9...5.4563427819....952.64.21.6.........1.8..1..94..
* PAIR C2: 5,8 BLK 1
B2: 5,8,1,3                              # reduction candidate for 5,8
B2: 5,8 => CTR
* 7.6....821..972643.2....7512.9...5.4563427819814.952.64.21.6.........1.8..1..94..
B2: 1,3                                  # 21 pairs
* PAIR A3: 3,9 BLK 1
B1: 3,9,4,5                              # reduction candidate for 3,9
B1: 3,9 => SOLVED
* 736541982815972643924863751279618534563427819148395276452186397397254168681739425
B1: 4,5 => CTR
* 7.6...982...972643.2....7.12.9...5.4563427819....952.64.21.6.........1.8..1..94..
* PAIR A3: 3,9 COL A
A8: 3,9,6                                # reduction candidate for 3,9
A8: 6 => CTR
* 7365..982.15972643924...7512.9...5.4563427819.4..952.64.21.639.69.7..1283.12.946.
A8: 3,9                                  # 20 pairs
* PAIR C3: 4,5 BLK 1
B1: 4,5,3,9                              # reduction candidate for 4,5
B1: 4,5 => CTR
* 7.6...982...972643.2....7.12.9...5.4563427819....952.64.21.6.........1.8..1..94..
B1: 3,9 => SOLVED
* 736541982815972643924863751279618534563427819148395276452186397397254168681739425
* PAIR D1: 3,5 BLK 2
D3: 3,5,6,8                              # reduction candidate for 3,5
D3: 3,5 => CTR
* 7.6....82318972645924.687.12896..5745634278191478952364.2186.....5...1.88.1.5946.
D3: 6,8                                  # 22 pairs
* PAIR D1: 3,5 ROW 1
B1: 3,5,4,9                              # reduction candidate for 3,5
B1: 3,5 => SOLVED
* 736541982815972643924863751279618534563427819148395276452186397397254168681739425
B1: 4,9                                  # 20 pairs
* PAIR G1: 3,9 ROW 1
B1: 3,9,4,5                              # reduction candidate for 3,9
B1: 3,9 => SOLVED
* 736541982815972643924863751279618534563427819148395276452186397397254168681739425
B1: 4,5 => CTR
* 7.6...982...972643.2....7.12.9...5.4563427819....952.64.21.6.........1.8..1..94..
* PAIR I2: 3,5 ROW 2
B2: 3,5,1,8                              # reduction candidate for 3,5
B2: 3,5 => CTR
* 7465..9821.8972643.2....7.12.9...5.45634278198143952764.21.6.....72..1686.17.942.
B2: 1,8                                  # 21 pairs
* PAIR I2: 3,5 COL I
I7: 3,5,7                                # reduction candidate for 3,5
I7: 3,5 => CTR
* 7563..982..897264..24...7.1289...574563427819147895236472186...6957..128831259467
I7: 7                                    # 21 pairs
I9: 3,5,7                                # reduction candidate for 3,5
I9: 3,5                                  # 21 pairs
* PAIR B4: 7,8 BLK 4
B6: 7,8,1,4                              # reduction candidate for 7,8
B6: 7,8 => CTR
* 7465..982.1.972643.2....7.12.9...5.4563427819....952.64.21.6.........1.8..1..94..
B6: 1,4                                  # 21 pairs
C6: 7,8,4                                # reduction candidate for 7,8
C6: 7,8                                  # 24 pairs
* PAIR B4: 7,8 COL B
B7: 7,8,3,5                              # reduction candidate for 7,8
B7: 7,8                                  # 23 pairs
B9: 7,8,3,5                              # reduction candidate for 7,8
B9: 7,8                                  # 26 pairs
* PAIR A6: 1,8 BLK 4
B6: 1,8,4,7                              # reduction candidate for 1,8
B6: 1,8 => CTR
* 7465..982...972643.2....7.12.9...5.4563427819....952.64.21.6.........1.8..1..94..
B6: 4,7                                  # 21 pairs
* PAIR A6: 1,8 COL A
A2: 1,8,3                                # reduction candidate for 1,8
A2: 3 => CTR
* 7.6....8231897264592....7.12.9...5.4563427819....952.64.21.6.........1.8..1..94..
A2: 1,8                                  # 20 pairs
* PAIR D6: 3,8 BLK 5
D4: 3,8,6                                # reduction candidate for 3,8
D4: 3,8                                  # 22 pairs
F4: 3,8,1                                # reduction candidate for 3,8
F4: 3,8                                  # 22 pairs
* PAIR D6: 3,8 COL D
D3: 3,8,5,6                              # reduction candidate for 3,8
D3: 5,6                                  # 22 pairs
D3: 3,8                                  # 21 pairs
* PAIR C8: 5,7 BLK 7
B7: 5,7,3,8                              # reduction candidate for 5,7
B7: 5,7                                  # 25 pairs
B8: 5,7,3,9                              # reduction candidate for 5,7
B8: 5,7 => CTR
* 7965..382...97264532....7.12.9...5.4563427819....952.64.21.6.........1.8..1..94..
B8: 3,9                                  # 21 pairs
B9: 5,7,3,8                              # reduction candidate for 5,7
B9: 5,7                                  # 24 pairs
* PAIR F8: 3,4 BLK 8
E8: 3,4,5                                # reduction candidate for 3,4
E8: 5                                    # 28 pairs
E8: 3,4                                  # 28 pairs
* PAIR F8: 3,4 COL F
F1: 3,4,1                                # reduction candidate for 3,4
F1: 3,4                                  # 22 pairs
F3: 3,4,8                                # reduction candidate for 3,4
F3: 3,4                                  # 18 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190405-absurd-base-pr-000.dot
* REASONING
* DIS # B2: 5,8 => CTR => B2: 1,3
* PRF # B1: 3,9 => SOL
* DIS # B1: 4,5 => CTR => B1: 3,9
* DIS # A8: 6 => CTR => A8: 3,9
* DIS # B1: 4,5 => CTR => B1: 3,9
* PRF # B1: 3,9 => SOL
* DIS # D3: 3,5 => CTR => D3: 6,8
* PRF # B1: 3,5 => SOL
* PRF # B1: 3,9 => SOL
* DIS # B1: 4,5 => CTR => B1: 3,9
* DIS # B2: 3,5 => CTR => B2: 1,8
* DIS # I7: 3,5 => CTR => I7: 7
* DIS # B6: 7,8 => CTR => B6: 1,4
* DIS # B6: 1,8 => CTR => B6: 4,7
* DIS # A2: 3 => CTR => A2: 1,8
* DIS # B8: 5,7 => CTR => B8: 3,9
* CNT  16 HDP CHAINS /  40 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A6,B4,C2,C3,C8,D1,D6,D8,D9,F8,G1,G7,H3,H4,H6,H7,H8,H9,I2)
* 7.6....82...97264..2....7.12.9...5.4563427819....952.64.21.6.........1.8..1..94..
* PAIR C2: 5,8 BLK 1
B2: 5,8,1,3                              # reduction candidate for 5,8
B2: 5,8 => CTR
* 7.6....821..972643.2....7512.9...5.4563427819814.952.64.21.6.........1.8..1..94..
* PAIR A3: 3,9 BLK 1
B1: 3,9,4,5                              # reduction candidate for 3,9
B1: 3,9 => SOLVED
* 736541982815972643924863751279618534563427819148395276452186397397254168681739425
* DURATION: 0:00:03.246087  START: 05:06:14.877933  END: 05:06:18.124020 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190405-absurd-base-pr-001.dot
* REASONING
* DIS # B2: 5,8 => CTR => B2: 1,3
* PRF B2: 1,3 # B1: 3,9 => SOL
* STA B2: 1,3 + B1: 3,9
* CNT   2 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190405, absurd

Solution

position: 736541982815972643924863751279618534563427819148395276452186397397254168681739425 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:

* DIS # B2: 5,8 => CTR => B2: 1,3
* INC # B2: 1,3 => UNS
* PRF # B1: 3,9 => SOL
* DIS # B1: 4,5 => CTR => B1: 3,9
* INC # A8: 3,9 => UNS
* DIS # A8: 6 => CTR => A8: 3,9
* DIS # B1: 4,5 => CTR => B1: 3,9
* PRF # B1: 3,9 => SOL
* DIS # D3: 3,5 => CTR => D3: 6,8
* INC # D3: 6,8 => UNS
* PRF # B1: 3,5 => SOL
* INC # B1: 4,9 => UNS
* PRF # B1: 3,9 => SOL
* DIS # B1: 4,5 => CTR => B1: 3,9
* DIS # B2: 3,5 => CTR => B2: 1,8
* INC # B2: 1,8 => UNS
* DIS # I7: 3,5 => CTR => I7: 7
* INC # I7: 7 => UNS
* INC # I9: 3,5 => UNS
* DIS # B6: 7,8 => CTR => B6: 1,4
* INC # B6: 1,4 => UNS
* INC # C6: 7,8 => UNS
* INC # B7: 7,8 => UNS
* INC # B9: 7,8 => UNS
* DIS # B6: 1,8 => CTR => B6: 4,7
* INC # B6: 4,7 => UNS
* INC # A2: 1,8 => UNS
* DIS # A2: 3 => CTR => A2: 1,8
* INC # D4: 3,8 => UNS
* INC # F4: 3,8 => UNS
* INC # D3: 3,8 => UNS
* INC # D3: 5,6 => UNS
* INC # B7: 5,7 => UNS
* DIS # B8: 5,7 => CTR => B8: 3,9
* INC # B8: 3,9 => UNS
* INC # B9: 5,7 => UNS
* INC # E8: 3,4 => UNS
* INC # E8: 5 => UNS
* INC # F1: 3,4 => UNS
* INC # F3: 3,4 => UNS
* CNT  40 HDP CHAINS /  40 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B2: 5,8 => CTR => B2: 1,3
* PRF B2: 1,3 # B1: 3,9 => SOL
* STA B2: 1,3 + B1: 3,9
* CNT   2 HDP CHAINS /   2 HYP OPENED