Analysis of zz-www.sudokuoftheday.co.uk-20060810-absurd-base.sdk

Contents

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

level: medium

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

position: .1..3..89.27...........2......34.1.64...2.89..8..6....8..65.73.6.1..........8.4.. initial

Autosolve

position: 51..3.289.278.......8..2......3481.64...2.89.18..6....8..65.73.6.1.7.9.8....8.46. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # F1: 7 => SOL
* PRF # F1: 4,7 => SOL
* PRF # F2: 6 => SOL
* DIS # I3: 4,5 => CTR => I3: 3,7
* DIS # H4: 5 => CTR => H4: 2,7
* PRF # I6: 3,5 => SOL
* PRF # C6: 2 => SOL
* PRF # G2: 3,5 => SOL
* DIS # B8: 5 => CTR => B8: 3,4
* DIS # I9: 5 => CTR => I9: 1,2
* DIS # H6: 2,5 => CTR => H6: 4,7
* CNT  11 HDP CHAINS /  32 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* PRF # F1: 7 => SOL
* STA F1: 7
* CNT   1 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

.1..3..89.27...........2......34.1.64...2.89..8..6....8..65.73.6.1..........8.4.. initial
51..3.289.278.......8..2......3481.64...2.89.18..6....8..65.73.6.1.7.9.8....8.46. autosolve
516437289327896514948512673759348126463125897182769345894651732631274958275983461 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (16)
C1: 4,6
A2: 3,9
A3: 3,9
B3: 4,6
D1: 4,7
E2: 1,9
D3: 4,5
E3: 1,9
A4: 2,7
G6: 3,5
B7: 4,9
A9: 2,7
D8: 2,4
F8: 3,4
I7: 1,2
H8: 2,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E2,E3: 1.. / E2 = 1  => 22 pairs (_) / E3 = 1  => 14 pairs (_)
H2,H3: 1.. / H2 = 1  => 14 pairs (_) / H3 = 1  => 22 pairs (_)
D5,F5: 1.. / D5 = 1  => 18 pairs (_) / F5 = 1  =>  0 pairs (X)
I7,I9: 1.. / I7 = 1  => 24 pairs (_) / I9 = 1  => 27 pairs (_)
E2,H2: 1.. / E2 = 1  => 22 pairs (_) / H2 = 1  => 14 pairs (_)
E3,H3: 1.. / E3 = 1  => 14 pairs (_) / H3 = 1  => 22 pairs (_)
F7,I7: 1.. / F7 = 1  => 27 pairs (_) / I7 = 1  => 24 pairs (_)
D5,D9: 1.. / D5 = 1  => 18 pairs (_) / D9 = 1  =>  0 pairs (X)
D8,D9: 2.. / D8 = 2  => 26 pairs (_) / D9 = 2  =>  0 pairs (X)
C7,I7: 2.. / C7 = 2  => 24 pairs (_) / I7 = 2  => 27 pairs (_)
D8,H8: 2.. / D8 = 2  => 26 pairs (_) / H8 = 2  =>  0 pairs (X)
A4,A9: 2.. / A4 = 2  => 25 pairs (_) / A9 = 2  =>  0 pairs (*)
A2,A3: 3.. / A2 = 3  => 14 pairs (_) / A3 = 3  => 22 pairs (_)
F8,F9: 3.. / F8 = 3  => 17 pairs (_) / F9 = 3  => 26 pairs (_)
B8,F8: 3.. / B8 = 3  => 26 pairs (_) / F8 = 3  => 17 pairs (_)
C1,B3: 4.. / C1 = 4  => 18 pairs (_) / B3 = 4  =>  0 pairs (*)
H6,I6: 4.. / H6 = 4  => 17 pairs (_) / I6 = 4  => 24 pairs (_)
C1,C7: 4.. / C1 = 4  => 18 pairs (_) / C7 = 4  =>  0 pairs (*)
F2,D3: 5.. / F2 = 5  => 27 pairs (_) / D3 = 5  => 19 pairs (_)
H8,I9: 5.. / H8 = 5  => 26 pairs (_) / I9 = 5  =>  0 pairs (X)
B8,H8: 5.. / B8 = 5  =>  0 pairs (X) / H8 = 5  => 26 pairs (_)
C1,B3: 6.. / C1 = 6  =>  0 pairs (*) / B3 = 6  =>  0 pairs (X)
F1,F2: 6.. / F1 = 6  => 18 pairs (_) / F2 = 6  =>  0 pairs (*)
G2,G3: 6.. / G2 = 6  => 18 pairs (_) / G3 = 6  =>  0 pairs (*)
B5,C5: 6.. / B5 = 6  =>  0 pairs (*) / C5 = 6  =>  0 pairs (X)
C1,F1: 6.. / C1 = 6  =>  0 pairs (*) / F1 = 6  =>  0 pairs (X)
F2,G2: 6.. / F2 = 6  =>  0 pairs (*) / G2 = 6  =>  0 pairs (X)
B3,G3: 6.. / B3 = 6  => 18 pairs (_) / G3 = 6  =>  0 pairs (*)
B3,B5: 6.. / B3 = 6  => 18 pairs (_) / B5 = 6  =>  0 pairs (*)
C1,C5: 6.. / C1 = 6  =>  0 pairs (*) / C5 = 6  =>  0 pairs (X)
D1,F1: 7.. / D1 = 7  => 18 pairs (_) / F1 = 7  =>  0 pairs (*)
H3,I3: 7.. / H3 = 7  => 15 pairs (_) / I3 = 7  => 23 pairs (_)
A9,B9: 7.. / A9 = 7  => 25 pairs (_) / B9 = 7  =>  0 pairs (*)
A4,A9: 7.. / A4 = 7  =>  0 pairs (*) / A9 = 7  =>  0 pairs (X)
A2,A3: 9.. / A2 = 9  => 22 pairs (_) / A3 = 9  => 14 pairs (_)
E2,E3: 9.. / E2 = 9  => 14 pairs (_) / E3 = 9  => 22 pairs (_)
B4,C4: 9.. / B4 = 9  => 20 pairs (_) / C4 = 9  => 18 pairs (_)
D6,F6: 9.. / D6 = 9  => 18 pairs (_) / F6 = 9  => 29 pairs (_)
A2,E2: 9.. / A2 = 9  => 22 pairs (_) / E2 = 9  => 14 pairs (_)
A3,E3: 9.. / A3 = 9  => 14 pairs (_) / E3 = 9  => 22 pairs (_)
D6,D9: 9.. / D6 = 9  => 18 pairs (_) / D9 = 9  => 29 pairs (_)
* DURATION: 0:00:50.688021  START: 01:41:28.984809  END: 01:42:19.672830 2019-05-01
* CP COUNT: (41)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A4,A9,B3,B7,C1,D1,D3,D8,E2,E3,F8,G6,H8,I7)
* 51..3.289.278.......8..2......3481.64...2.89.18..6....8..65.73.6.1.7.9.8....8.46.
* PAIR C1: 4,6 ROW 1
F1: 4,6,7                                # reduction candidate for 4,6
F1: 7 => SOLVED
* 516437289327896514948512673759348126463125897182769345894651732631274958275983461
F1: 4,6                                  # 18 pairs
* PAIR D1: 4,7 BLK 2
F1: 4,7,6                                # reduction candidate for 4,7
F1: 4,7 => SOLVED
* 516437289327896514948512673759348126463125897182769345894651732631274958275983461
F1: 6                                    # 18 pairs
* PAIR D3: 4,5 BLK 2
F2: 4,5,6                                # reduction candidate for 4,5
F2: 6 => SOLVED
* 516437289327896514948512673759348126463125897182769345894651732631274958275983461
F2: 4,5                                  # 18 pairs
* PAIR D3: 4,5 ROW 3
H3: 4,5,1,7                              # reduction candidate for 4,5
H3: 4,5                                  # 17 pairs
I3: 4,5,3,7                              # reduction candidate for 4,5
I3: 4,5 => CTR
* 51..3.28932789.61.968.1237....3481264.6.2.89.182.6.5438..65.7326.127.95827..8.46.
I3: 3,7                                  # 17 pairs
* PAIR A4: 2,7 ROW 4
H4: 2,7,5                                # reduction candidate for 2,7
H4: 5 => CTR
* 514736289.278.4.....8..2...2793481564..12.8971859673428.265.7316514739287.3281465
H4: 2,7                                  # 21 pairs
* PAIR G6: 3,5 BLK 6
I5: 3,5,7                                # reduction candidate for 3,5
I5: 3,5                                  # 22 pairs
I6: 3,5,2,4,7                            # reduction candidate for 3,5
I6: 3,5 => SOLVED
* 516437289327896514948512673759348126463125897182769345894651732631274958275983461
I6: 2,4,7                                # 16 pairs
* PAIR G6: 3,5 ROW 6
C6: 3,5,2                                # reduction candidate for 3,5
C6: 2 => SOLVED
* 516437289327896514948512673759348126463125897182769345894651732631274958275983461
C6: 3,5                                  # 26 pairs
* PAIR G6: 3,5 COL G
G2: 3,5,6                                # reduction candidate for 3,5
G2: 3,5 => SOLVED
* 516437289327896514948512673759348126463125897182769345894651732631274958275983461
G2: 6                                    # 18 pairs
G3: 3,5,6                                # reduction candidate for 3,5
G3: 3,5                                  # 18 pairs
* PAIR B7: 4,9 BLK 7
C7: 4,9,2                                # reduction candidate for 4,9
C7: 4,9                                  # 27 pairs
C7: 2                                    # 24 pairs
* PAIR B7: 4,9 ROW 7
F7: 4,9,1                                # reduction candidate for 4,9
F7: 1                                    # 27 pairs
F7: 4,9                                  # 24 pairs
* PAIR F8: 3,4 ROW 8
B8: 3,4,5                                # reduction candidate for 3,4
B8: 5 => CTR
* 514736289.278.4653..8..2...2..3481.64..12.89.18.96...28.265.7316514739287..281465
B8: 3,4                                  # 26 pairs
* PAIR I7: 1,2 BLK 9
I9: 1,2,5                                # reduction candidate for 1,2
I9: 5 => CTR
* 514736289.278.4653..8..2...2..3481.64..12.89.18.96...28.26597316514739287..281465
I9: 1,2                                  # 26 pairs
* PAIR H8: 2,5 BLK 9
I9: 2,5,1                                # reduction candidate for 2,5
I9: 1                                    # 27 pairs
I9: 2,5                                  # 24 pairs
* PAIR H8: 2,5 COL H
H4: 2,5,7                                # reduction candidate for 2,5
H4: 2,5                                  # 19 pairs
H6: 2,5,4,7                              # reduction candidate for 2,5
H6: 2,5 => CTR
* 514736289.278..6.5.68..2......348176476.2.893183.6.5248..65.73.6.127.9587...8.46.
H6: 4,7                                  # 17 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060810-absurd-base-pr-000.dot
* REASONING
* PRF # F1: 7 => SOL
* PRF # F1: 4,7 => SOL
* PRF # F2: 6 => SOL
* DIS # I3: 4,5 => CTR => I3: 3,7
* DIS # H4: 5 => CTR => H4: 2,7
* PRF # I6: 3,5 => SOL
* PRF # C6: 2 => SOL
* PRF # G2: 3,5 => SOL
* DIS # B8: 5 => CTR => B8: 3,4
* DIS # I9: 5 => CTR => I9: 1,2
* DIS # H6: 2,5 => CTR => H6: 4,7
* CNT  11 HDP CHAINS /  32 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A4,A9,B3,B7,C1,D1,D3,D8,E2,E3,F8,G6,H8,I7)
* 51..3.289.278.......8..2......3481.64...2.89.18..6....8..65.73.6.1.7.9.8....8.46.
* PAIR C1: 4,6 ROW 1
F1: 4,6,7                                # reduction candidate for 4,6
F1: 7 => SOLVED
* 516437289327896514948512673759348126463125897182769345894651732631274958275983461
* DURATION: 0:00:02.303733  START: 01:42:43.724169  END: 01:42:46.027902 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060810-absurd-base-pr-001.dot
* REASONING
* PRF # F1: 7 => SOL
* STA F1: 7
* CNT   1 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060810, absurd

Solution

position: 516437289327896514948512673759348126463125897182769345894651732631274958275983461 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 # F1: 4,6 => UNS
* PRF # F1: 7 => SOL
* PRF # F1: 4,7 => SOL
* INC # F1: 6 => UNS
* INC # F2: 4,5 => UNS
* PRF # F2: 6 => SOL
* INC # H3: 4,5 => UNS
* DIS # I3: 4,5 => CTR => I3: 3,7
* INC # I3: 3,7 => UNS
* INC # H4: 2,7 => UNS
* DIS # H4: 5 => CTR => H4: 2,7
* INC # I5: 3,5 => UNS
* PRF # I6: 3,5 => SOL
* INC # I6: 2,4,7 => UNS
* INC # C6: 3,5 => UNS
* PRF # C6: 2 => SOL
* PRF # G2: 3,5 => SOL
* INC # G2: 6 => UNS
* INC # G3: 3,5 => UNS
* INC # C7: 4,9 => UNS
* INC # C7: 2 => UNS
* INC # F7: 4,9 => UNS
* INC # F7: 1 => UNS
* INC # B8: 3,4 => UNS
* DIS # B8: 5 => CTR => B8: 3,4
* INC # I9: 1,2 => UNS
* DIS # I9: 5 => CTR => I9: 1,2
* INC # I9: 2,5 => UNS
* INC # I9: 1 => UNS
* INC # H4: 2,5 => UNS
* DIS # H6: 2,5 => CTR => H6: 4,7
* INC # H6: 4,7 => UNS
* CNT  32 HDP CHAINS /  32 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F1: 4,6 => UNS
* PRF # F1: 7 => SOL
* STA F1: 7
* CNT   2 HDP CHAINS /   2 HYP OPENED