Analysis of zz-www.sudokuoftheday.co.uk-20060827-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......98..5.92...974..5...8......3......4.5...7..19..68.....1..9.56..4...3.2... initial

Autosolve

position: .1......98..5.92...974..5...8......3......485...7..192.689..3.1..9.56..4...3.29.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # A1: 3,4 => SOL
* DIS # C1: 3,4 => CTR => C1: 2,5,6
* PRF # H2: 3,4 => SOL
* DIS # B6: 3,4 => CTR => B6: 5
* PRF # H2: 3,4 => SOL
* PRF # A1: 3,4 => SOL
* DIS # C1: 3,4 => CTR => C1: 2,5,6
* DIS # G1: 8 => CTR => G1: 6,7
* DIS # I9: 8 => CTR => I9: 6,7
* PRF # H2: 4 => SOL
* DIS # E3: 1,3 => CTR => E3: 2,6,8
* DIS # G1: 7 => CTR => G1: 6,8
* PRF # E3: 6,8 => SOL
* DIS # I9: 7 => CTR => I9: 6,8
* DIS # D5: 1,2 => CTR => D5: 6
* DIS # E5: 1,2 => CTR => E5: 3,6,9
* PRF # A4: 1,2 => SOL
* PRF # E5: 1,3 => SOL
* DIS # A5: 1,3 => CTR => A5: 2,6,7,9
* DIS # F3: 8 => CTR => F3: 1,3
* DIS # G1: 8 => CTR => G1: 6,7
* DIS # A4: 2,5 => CTR => A4: 1,4,9
* DIS # E3: 1,8 => CTR => E3: 2,3,6
* DIS # I9: 7,8 => CTR => I9: 6
* DIS # G1: 7,8 => CTR => G1: 6
* DIS # A8: 2,7 => CTR => A8: 1,3
* CNT  26 HDP CHAINS /  63 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 # A1: 3,4 => SOL
* STA A1: 3,4
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

.1......98..5.92...974..5...8......3......4.5...7..19..68.....1..9.56..4...3.2... initial
.1......98..5.92...974..5...8......3......485...7..192.689..3.1..9.56..4...3.29.. autosolve
415827639836519247297463518184295763972631485653748192568974321329156874741382956 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (17)
B2: 3,4
H1: 3,4
I2: 6,7
H3: 1,3
I3: 6,8
D4: 1,2
F5: 1,3
G4: 6,7
H4: 6,7
A7: 2,5
E7: 4,7
F7: 4,7
D8: 1,8
E9: 1,8
H7: 2,5
G8: 7,8
H8: 2,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H2,H3: 1.. / H2 = 1  => 17 pairs (_) / H3 = 1  =>  0 pairs (*)
D8,E9: 1.. / D8 = 1  => 14 pairs (_) / E9 = 1  =>  0 pairs (X)
E2,H2: 1.. / E2 = 1  =>  0 pairs (*) / H2 = 1  =>  0 pairs (X)
A8,D8: 1.. / A8 = 1  =>  0 pairs (X) / D8 = 1  => 14 pairs (_)
H7,H8: 2.. / H7 = 2  => 21 pairs (_) / H8 = 2  => 23 pairs (_)
A3,E3: 2.. / A3 = 2  =>  0 pairs (*) / E3 = 2  =>  0 pairs (X)
A7,H7: 2.. / A7 = 2  => 23 pairs (_) / H7 = 2  => 21 pairs (_)
B5,B8: 2.. / B5 = 2  => 23 pairs (_) / B8 = 2  => 21 pairs (_)
A8,B8: 3.. / A8 = 3  => 17 pairs (_) / B8 = 3  =>  0 pairs (X)
H1,H2: 4.. / H1 = 4  => 17 pairs (_) / H2 = 4  =>  0 pairs (*)
E7,F7: 4.. / E7 = 4  =>  0 pairs (X) / F7 = 4  => 17 pairs (_)
A1,C1: 5.. / A1 = 5  => 23 pairs (_) / C1 = 5  => 21 pairs (_)
F4,F6: 5.. / F4 = 5  => 17 pairs (_) / F6 = 5  =>  0 pairs (X)
H7,H9: 5.. / H7 = 5  => 23 pairs (_) / H9 = 5  => 21 pairs (_)
A7,H7: 5.. / A7 = 5  => 21 pairs (_) / H7 = 5  => 23 pairs (_)
B6,B9: 5.. / B6 = 5  => 18 pairs (_) / B9 = 5  =>  0 pairs (X)
G4,H4: 6.. / G4 = 6  =>  0 pairs (X) / H4 = 6  => 14 pairs (_)
H9,I9: 6.. / H9 = 6  =>  0 pairs (X) / I9 = 6  => 14 pairs (_)
D1,D5: 6.. / D1 = 6  =>  0 pairs (X) / D5 = 6  => 18 pairs (_)
G1,G4: 6.. / G1 = 6  => 14 pairs (_) / G4 = 6  =>  0 pairs (X)
H4,H9: 6.. / H4 = 6  => 14 pairs (_) / H9 = 6  =>  0 pairs (X)
G1,I2: 7.. / G1 = 7  =>  0 pairs (X) / I2 = 7  => 18 pairs (_)
A5,B5: 7.. / A5 = 7  => 19 pairs (_) / B5 = 7  =>  0 pairs (*)
G4,H4: 7.. / G4 = 7  => 14 pairs (_) / H4 = 7  =>  0 pairs (X)
E7,F7: 7.. / E7 = 7  => 17 pairs (_) / F7 = 7  =>  0 pairs (X)
E2,I2: 7.. / E2 = 7  =>  0 pairs (X) / I2 = 7  => 18 pairs (_)
F1,F7: 7.. / F1 = 7  => 17 pairs (_) / F7 = 7  =>  0 pairs (X)
I2,I9: 7.. / I2 = 7  => 18 pairs (_) / I9 = 7  =>  0 pairs (X)
G1,I3: 8.. / G1 = 8  =>  0 pairs (X) / I3 = 8  => 14 pairs (_)
E6,F6: 8.. / E6 = 8  =>  0 pairs (X) / F6 = 8  => 18 pairs (_)
D8,E9: 8.. / D8 = 8  =>  0 pairs (X) / E9 = 8  => 14 pairs (_)
G8,I9: 8.. / G8 = 8  => 14 pairs (_) / I9 = 8  =>  0 pairs (X)
D8,G8: 8.. / D8 = 8  =>  0 pairs (X) / G8 = 8  => 14 pairs (_)
E9,I9: 8.. / E9 = 8  => 14 pairs (_) / I9 = 8  =>  0 pairs (X)
D1,D8: 8.. / D1 = 8  => 14 pairs (_) / D8 = 8  =>  0 pairs (X)
G1,G8: 8.. / G1 = 8  =>  0 pairs (X) / G8 = 8  => 14 pairs (_)
I3,I9: 8.. / I3 = 8  => 14 pairs (_) / I9 = 8  =>  0 pairs (X)
A4,A5: 9.. / A4 = 9  => 17 pairs (_) / A5 = 9  =>  0 pairs (*)
E4,E5: 9.. / E4 = 9  =>  0 pairs (*) / E5 = 9  =>  0 pairs (X)
A4,E4: 9.. / A4 = 9  => 17 pairs (_) / E4 = 9  =>  0 pairs (*)
A5,E5: 9.. / A5 = 9  =>  0 pairs (*) / E5 = 9  =>  0 pairs (X)
* DURATION: 0:00:51.851884  START: 02:07:09.312854  END: 02:08:01.164738 2019-05-01
* CP COUNT: (41)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B2,D4,D8,E7,E9,F5,F7,G4,G8,H1,H3,H4,H7,H8,I2,I3)
* .1......98..5.92...974..5...8......3......485...7..192.689..3.1..9.56..4...3.29..
* PAIR B2: 3,4 BLK 1
A1: 3,4,2,5,6                            # reduction candidate for 3,4
A1: 3,4 => SOLVED
* 415827639836519247297463518184295763972631485653748192568974321329156874741382956
A1: 2,5,6                                # 17 pairs
C1: 3,4,2,5,6                            # reduction candidate for 3,4
C1: 3,4 => CTR
* 51......98..5.92..2974..5...8......3......485...7..192.689..3.1..9.56..4...3.29..
C1: 2,5,6                                # 17 pairs
C2: 3,4,6                                # reduction candidate for 3,4
C2: 3,4                                  # 19 pairs
* PAIR B2: 3,4 ROW 2
H2: 3,4,1                                # reduction candidate for 3,4
H2: 3,4 => SOLVED
* 415827639836519247297463518184295763972631485653748192568974321329156874741382956
H2: 1                                    # 17 pairs
* PAIR B2: 3,4 COL B
B6: 3,4,5                                # reduction candidate for 3,4
B6: 3,4 => CTR
* 5128...498..5.92..69742.5.898.2....372.69.485...7.81922689..351379156824.5.3829..
B6: 5                                    # 18 pairs
* PAIR H1: 3,4 BLK 3
H2: 3,4,1                                # reduction candidate for 3,4
H2: 3,4 => SOLVED
* 415827639836519247297463518184295763972631485653748192568974321329156874741382956
H2: 1                                    # 17 pairs
* PAIR H1: 3,4 ROW 1
A1: 3,4,2,5,6                            # reduction candidate for 3,4
A1: 3,4 => SOLVED
* 415827639836519247297463518184295763972631485653748192568974321329156874741382956
A1: 2,5,6                                # 17 pairs
C1: 3,4,2,5,6                            # reduction candidate for 3,4
C1: 3,4 => CTR
* 51......98..5.92..2974..5...8......3......485...7..192.689..3.1..9.56..4...3.29..
C1: 2,5,6                                # 17 pairs
* PAIR I2: 6,7 BLK 3
G1: 6,7,8                                # reduction candidate for 6,7
G1: 8 => CTR
* .1....8.98..5.9217.974.1536.8....673.2...3485...7.81922689..3.1..9856724...312968
G1: 6,7                                  # 14 pairs
* PAIR I2: 6,7 ROW 2
E2: 6,7,1,3                              # reduction candidate for 6,7
E2: 1,3                                  # 20 pairs
E2: 6,7                                  # 19 pairs
* PAIR I2: 6,7 COL I
I9: 6,7,8                                # reduction candidate for 6,7
I9: 8 => CTR
* .126..8.98465392173974..5.6.8....673.2....485...7..1922689..351.39856724.7.312968
I9: 6,7                                  # 14 pairs
* PAIR H3: 1,3 BLK 3
H2: 1,3,4                                # reduction candidate for 1,3
H2: 4 => SOLVED
* 415827639836519247297463518184295763972631485653748192568974321329156874741382956
H2: 1,3                                  # 17 pairs
* PAIR H3: 1,3 ROW 3
E3: 1,3,2,6,8                            # reduction candidate for 1,3
E3: 1,3 => CTR
* .1......98..5.92..2974..5.6.8....673......485...7..1925689..321..9.56..4...3.29..
E3: 2,6,8                                # 17 pairs
F3: 1,3,8                                # reduction candidate for 1,3
F3: 1,3                                  # 21 pairs
* PAIR I3: 6,8 BLK 3
G1: 6,8,7                                # reduction candidate for 6,8
G1: 7 => CTR
* .1.8.37498..579216.974.1538.8....673......485...7..192.689473.1..9.56824...382967
G1: 6,8                                  # 18 pairs
* PAIR I3: 6,8 ROW 3
E3: 6,8,1,2,3                            # reduction candidate for 6,8
E3: 6,8 => SOLVED
* 415827639836519247297463518184295763972631485653748192568974321329156874741382956
E3: 1,2,3                                # 17 pairs
* PAIR I3: 6,8 COL I
I9: 6,8,7                                # reduction candidate for 6,8
I9: 7 => CTR
* .1.8..7.98..579216.974..538.8....673...6..485...7.8192.689473.1..9.568.4...382967
I9: 6,8                                  # 18 pairs
* PAIR D4: 1,2 BLK 5
E4: 1,2,4,9                              # reduction candidate for 1,2
E4: 1,2                                  # 23 pairs
D5: 1,2,6                                # reduction candidate for 1,2
D5: 1,2 => CTR
* .1.6..8.98..5.9217.974.1536.8....673.2.1.3485...7.81922689..3.1..9856724...312968
D5: 6                                    # 18 pairs
E5: 1,2,3,6,9                            # reduction candidate for 1,2
E5: 1,2 => CTR
* 41582763983.5.92.7.974..5.818.295763972613485.53748192568974321329156874741382956
E5: 3,6,9                                # 17 pairs
* PAIR D4: 1,2 ROW 4
A4: 1,2,4,5,9                            # reduction candidate for 1,2
A4: 1,2 => SOLVED
* 415827639836519247297463518184295763972631485653748192568974321329156874741382956
A4: 4,5,9                                # 17 pairs
C4: 1,2,4,5                              # reduction candidate for 1,2
C4: 1,2                                  # 20 pairs
* PAIR F5: 1,3 BLK 5
E5: 1,3,2,6,9                            # reduction candidate for 1,3
E5: 1,3 => SOLVED
* 415827639836519247297463518184295763972631485653748192568974321329156874741382956
E5: 2,6,9                                # 17 pairs
* PAIR F5: 1,3 ROW 5
A5: 1,3,2,6,7,9                          # reduction candidate for 1,3
A5: 1,3 => CTR
* 4158276398365192.7.974..5.898.2.5763172693485.53748192568974321329156874741382956
A5: 2,6,7,9                              # 17 pairs
C5: 1,3,2,6                              # reduction candidate for 1,3
C5: 1,3                                  # 20 pairs
* PAIR F5: 1,3 COL F
F3: 1,3,8                                # reduction candidate for 1,3
F3: 8 => CTR
* .1......98..5.92...974.85.6.8....673......485...78.192.689..3.1..9856724...312968
F3: 1,3                                  # 21 pairs
* PAIR G4: 6,7 COL G
G1: 6,7,8                                # reduction candidate for 6,7
G1: 8 => CTR
* .1....8.98..5.9217.974.1536.8....673.2...3485...7.81922689..3.1..9856724...312968
G1: 6,7                                  # 14 pairs
* PAIR H4: 6,7 COL H
H9: 6,7,5                                # reduction candidate for 6,7
H9: 6,7                                  # 23 pairs
H9: 5                                    # 21 pairs
* PAIR A7: 2,5 COL A
A1: 2,5,3,4,6                            # reduction candidate for 2,5
A1: 2,5                                  # 22 pairs
A4: 2,5,1,4,9                            # reduction candidate for 2,5
A4: 2,5 => CTR
* .1......98..5.92...974..5...8..9...397....485...7..192.689..3.1.29.56.747..3.29..
A4: 1,4,9                                # 17 pairs
* PAIR E9: 1,8 COL E
E3: 1,8,2,3,6                            # reduction candidate for 1,8
E3: 1,8 => CTR
* .1......98..5.92..2974..5.6.8....673......485...7..1925689..321..9.56..4...3.29..
E3: 2,3,6                                # 17 pairs
* PAIR G8: 7,8 BLK 9
I9: 7,8,6                                # reduction candidate for 7,8
I9: 7,8 => CTR
* 5128637498..5792166974215..98.2..67372..9.485...7.81922689..351..9.56.24...382967
I9: 6                                    # 14 pairs
* PAIR G8: 7,8 COL G
G1: 7,8,6                                # reduction candidate for 7,8
G1: 7,8 => CTR
* 5128637498..5792166974215..98.2..67372..9.485...7.81922689..351..9.56.24...382967
G1: 6                                    # 14 pairs
* PAIR H8: 2,7 ROW 8
A8: 2,7,1,3                              # reduction candidate for 2,7
A8: 2,7 => CTR
* .128..64984.5.92.7.9742.5.8.8.2.576372.69.485.5.7.8192.689.43.1239156874.753829.6
A8: 1,3                                  # 18 pairs
B8: 2,7,3                                # reduction candidate for 2,7
B8: 2,7                                  # 17 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060827-absurd-base-pr-000.dot
* REASONING
* PRF # A1: 3,4 => SOL
* DIS # C1: 3,4 => CTR => C1: 2,5,6
* PRF # H2: 3,4 => SOL
* DIS # B6: 3,4 => CTR => B6: 5
* PRF # H2: 3,4 => SOL
* PRF # A1: 3,4 => SOL
* DIS # C1: 3,4 => CTR => C1: 2,5,6
* DIS # G1: 8 => CTR => G1: 6,7
* DIS # I9: 8 => CTR => I9: 6,7
* PRF # H2: 4 => SOL
* DIS # E3: 1,3 => CTR => E3: 2,6,8
* DIS # G1: 7 => CTR => G1: 6,8
* PRF # E3: 6,8 => SOL
* DIS # I9: 7 => CTR => I9: 6,8
* DIS # D5: 1,2 => CTR => D5: 6
* DIS # E5: 1,2 => CTR => E5: 3,6,9
* PRF # A4: 1,2 => SOL
* PRF # E5: 1,3 => SOL
* DIS # A5: 1,3 => CTR => A5: 2,6,7,9
* DIS # F3: 8 => CTR => F3: 1,3
* DIS # G1: 8 => CTR => G1: 6,7
* DIS # A4: 2,5 => CTR => A4: 1,4,9
* DIS # E3: 1,8 => CTR => E3: 2,3,6
* DIS # I9: 7,8 => CTR => I9: 6
* DIS # G1: 7,8 => CTR => G1: 6
* DIS # A8: 2,7 => CTR => A8: 1,3
* CNT  26 HDP CHAINS /  63 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B2,D4,D8,E7,E9,F5,F7,G4,G8,H1,H3,H4,H7,H8,I2,I3)
* .1......98..5.92...974..5...8......3......485...7..192.689..3.1..9.56..4...3.29..
* PAIR B2: 3,4 BLK 1
A1: 3,4,2,5,6                            # reduction candidate for 3,4
A1: 3,4 => SOLVED
* 415827639836519247297463518184295763972631485653748192568974321329156874741382956
* DURATION: 0:00:02.012626  START: 02:08:42.617932  END: 02:08:44.630558 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060827-absurd-base-pr-001.dot
* REASONING
* PRF # A1: 3,4 => SOL
* STA A1: 3,4
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060827, absurd

Solution

position: 415827639836519247297463518184295763972631485653748192568974321329156874741382956 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:

* PRF # A1: 3,4 => SOL
* INC # A1: 2,5,6 => UNS
* DIS # C1: 3,4 => CTR => C1: 2,5,6
* INC # C1: 2,5,6 => UNS
* INC # C2: 3,4 => UNS
* PRF # H2: 3,4 => SOL
* INC # H2: 1 => UNS
* DIS # B6: 3,4 => CTR => B6: 5
* INC # B6: 5 => UNS
* PRF # H2: 3,4 => SOL
* INC # H2: 1 => UNS
* PRF # A1: 3,4 => SOL
* INC # A1: 2,5,6 => UNS
* DIS # C1: 3,4 => CTR => C1: 2,5,6
* INC # C1: 2,5,6 => UNS
* INC # G1: 6,7 => UNS
* DIS # G1: 8 => CTR => G1: 6,7
* INC # E2: 6,7 => UNS
* INC # E2: 1,3 => UNS
* INC # I9: 6,7 => UNS
* DIS # I9: 8 => CTR => I9: 6,7
* INC # H2: 1,3 => UNS
* PRF # H2: 4 => SOL
* DIS # E3: 1,3 => CTR => E3: 2,6,8
* INC # E3: 2,6,8 => UNS
* INC # F3: 1,3 => UNS
* INC # G1: 6,8 => UNS
* DIS # G1: 7 => CTR => G1: 6,8
* PRF # E3: 6,8 => SOL
* INC # E3: 1,2,3 => UNS
* INC # I9: 6,8 => UNS
* DIS # I9: 7 => CTR => I9: 6,8
* INC # E4: 1,2 => UNS
* DIS # D5: 1,2 => CTR => D5: 6
* INC # D5: 6 => UNS
* DIS # E5: 1,2 => CTR => E5: 3,6,9
* INC # E5: 3,6,9 => UNS
* PRF # A4: 1,2 => SOL
* INC # A4: 4,5,9 => UNS
* INC # C4: 1,2 => UNS
* PRF # E5: 1,3 => SOL
* INC # E5: 2,6,9 => UNS
* DIS # A5: 1,3 => CTR => A5: 2,6,7,9
* INC # A5: 2,6,7,9 => UNS
* INC # C5: 1,3 => UNS
* INC # F3: 1,3 => UNS
* DIS # F3: 8 => CTR => F3: 1,3
* INC # G1: 6,7 => UNS
* DIS # G1: 8 => CTR => G1: 6,7
* INC # H9: 6,7 => UNS
* INC # H9: 5 => UNS
* INC # A1: 2,5 => UNS
* DIS # A4: 2,5 => CTR => A4: 1,4,9
* INC # A4: 1,4,9 => UNS
* DIS # E3: 1,8 => CTR => E3: 2,3,6
* INC # E3: 2,3,6 => UNS
* DIS # I9: 7,8 => CTR => I9: 6
* INC # I9: 6 => UNS
* DIS # G1: 7,8 => CTR => G1: 6
* INC # G1: 6 => UNS
* DIS # A8: 2,7 => CTR => A8: 1,3
* INC # A8: 1,3 => UNS
* INC # B8: 2,7 => UNS
* CNT  63 HDP CHAINS /  63 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # A1: 3,4 => SOL
* STA A1: 3,4
* CNT   1 HDP CHAINS /   1 HYP OPENED