Analysis of zz-www.sudokuoftheday.co.uk-20060321-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: .4.....8.1...........2...7...27...39....938..5..8.276.729.5164......8.....1.4..9. initial

Autosolve

position: 24.1...8.1........9..2...7...276..39....938..593812764729351648...928..7..1647.9. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # E2: 8 => CTR => E2: 3,7
* DIS # E2: 7 => CTR => E2: 3,8
* DIS # G2: 2,5 => CTR => G2: 3,4,9
* DIS # I2: 2,5 => CTR => I2: 3,6
* DIS # H5: 1 => CTR => H5: 2,5
* DIS # C5: 4,6 => CTR => C5: 7
* DIS # A8: 4,6 => CTR => A8: 3
* PRF # A8: 3 => SOL
* DIS # I5: 1,5 => CTR => I5: 2
* DIS # G3: 1,5 => CTR => G3: 3,4
* PRF # G8: 1,5 => SOL
* DIS # G8: 3 => CTR => G8: 1,5
* DIS # C8: 5,6 => CTR => C8: 4
* DIS # B2: 5,6 => CTR => B2: 3,7
* DIS # B3: 5,6 => CTR => B3: 3
* PRF # G8: 1,5 => SOL
* DIS # G8: 3 => CTR => G8: 1,5
* DIS # H5: 2 => CTR => H5: 1,5
* CNT  18 HDP CHAINS /  37 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 # E2: 8 => CTR => E2: 3,7
* DIS E2: 3,7 # G2: 2,5 => CTR => G2: 3,4,9
* DIS E2: 3,7 + G2: 3,4,9 # I2: 2,5 => CTR => I2: 3,6
* DIS E2: 3,7 + G2: 3,4,9 + I2: 3,6 # C5: 4,6 => CTR => C5: 7
* DIS E2: 3,7 + G2: 3,4,9 + I2: 3,6 + C5: 7 # F2: 9 => CTR => F2: 4,5
* PRF E2: 3,7 + G2: 3,4,9 + I2: 3,6 + C5: 7 + F2: 4,5 # G8: 1,5 => SOL
* STA E2: 3,7 + G2: 3,4,9 + I2: 3,6 + C5: 7 + F2: 4,5 + G8: 1,5
* CNT   6 HDP CHAINS /  12 HYP OPENED

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

Details

Positions

.4.....8.1...........2...7...27...39....938..5..8.276.729.5164......8.....1.4..9. initial
24.1...8.1........9..2...7...276..39....938..593812764729351648...928..7..1647.9. autosolve
246179385178534926935286471482765139617493852593812764729351648364928517851647293 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
E1: 3,7
D2: 4,5
E3: 3,8
H2: 2,5
A4: 4,8
B4: 1,8
A5: 4,6
F4: 4,5
D5: 4,5
G4: 1,5
B8: 5,6
A9: 3,8
B9: 5,8
H8: 1,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G3,I3: 1.. / G3 = 1  =>  0 pairs (X) / I3 = 1  => 15 pairs (_)
B4,B5: 1.. / B4 = 1  =>  0 pairs (X) / B5 = 1  =>  0 pairs (_)
G8,H8: 1.. / G8 = 1  =>  0 pairs (X) / H8 = 1  => 15 pairs (_)
B4,G4: 1.. / B4 = 1  =>  0 pairs (X) / G4 = 1  =>  0 pairs (_)
H5,H8: 1.. / H5 = 1  =>  0 pairs (X) / H8 = 1  => 15 pairs (_)
I3,I5: 1.. / I3 = 1  => 15 pairs (_) / I5 = 1  =>  0 pairs (X)
H5,I5: 2.. / H5 = 2  =>  0 pairs (X) / I5 = 2  => 15 pairs (_)
G9,I9: 2.. / G9 = 2  => 15 pairs (_) / I9 = 2  =>  0 pairs (X)
G2,G9: 2.. / G2 = 2  =>  0 pairs (X) / G9 = 2  => 15 pairs (_)
H2,H5: 2.. / H2 = 2  => 15 pairs (_) / H5 = 2  =>  0 pairs (X)
B2,B3: 3.. / B2 = 3  =>  0 pairs (X) / B3 = 3  => 15 pairs (_)
A8,A9: 3.. / A8 = 3  =>  0 pairs (*) / A9 = 3  =>  0 pairs (X)
A8,G8: 3.. / A8 = 3  =>  0 pairs (*) / G8 = 3  =>  0 pairs (X)
G2,G3: 4.. / G2 = 4  =>  0 pairs (X) / G3 = 4  => 16 pairs (_)
F4,D5: 4.. / F4 = 4  =>  0 pairs (X) / D5 = 4  =>  0 pairs (_)
A8,C8: 4.. / A8 = 4  =>  0 pairs (X) / C8 = 4  => 17 pairs (_)
F3,G3: 4.. / F3 = 4  =>  0 pairs (X) / G3 = 4  => 16 pairs (_)
A4,F4: 4.. / A4 = 4  =>  0 pairs (*) / F4 = 4  =>  0 pairs (X)
C5,C8: 4.. / C5 = 4  =>  0 pairs (X) / C8 = 4  => 17 pairs (_)
D2,D5: 4.. / D2 = 4  =>  0 pairs (X) / D5 = 4  =>  0 pairs (_)
F4,D5: 5.. / F4 = 5  =>  0 pairs (*) / D5 = 5  =>  0 pairs (X)
F4,G4: 5.. / F4 = 5  =>  0 pairs (*) / G4 = 5  =>  0 pairs (X)
D2,D5: 5.. / D2 = 5  =>  0 pairs (*) / D5 = 5  =>  0 pairs (X)
A5,A8: 6.. / A5 = 6  => 16 pairs (_) / A8 = 6  =>  0 pairs (X)
E1,E2: 7.. / E1 = 7  => 17 pairs (_) / E2 = 7  =>  0 pairs (X)
B5,C5: 7.. / B5 = 7  =>  0 pairs (X) / C5 = 7  => 16 pairs (_)
C1,E1: 7.. / C1 = 7  =>  0 pairs (X) / E1 = 7  => 17 pairs (_)
B2,B5: 7.. / B2 = 7  => 16 pairs (_) / B5 = 7  =>  0 pairs (X)
C2,C3: 8.. / C2 = 8  => 15 pairs (_) / C3 = 8  =>  0 pairs (X)
E2,E3: 8.. / E2 = 8  =>  0 pairs (X) / E3 = 8  => 15 pairs (_)
A4,B4: 8.. / A4 = 8  =>  0 pairs (X) / B4 = 8  =>  0 pairs (_)
A9,B9: 8.. / A9 = 8  =>  0 pairs (*) / B9 = 8  =>  0 pairs (X)
C2,E2: 8.. / C2 = 8  => 15 pairs (_) / E2 = 8  =>  0 pairs (X)
C3,E3: 8.. / C3 = 8  =>  0 pairs (X) / E3 = 8  => 15 pairs (_)
A4,A9: 8.. / A4 = 8  =>  0 pairs (X) / A9 = 8  =>  0 pairs (_)
B4,B9: 8.. / B4 = 8  =>  0 pairs (*) / B9 = 8  =>  0 pairs (X)
F1,F2: 9.. / F1 = 9  => 18 pairs (_) / F2 = 9  => 15 pairs (_)
G1,G2: 9.. / G1 = 9  => 15 pairs (_) / G2 = 9  => 18 pairs (_)
F1,G1: 9.. / F1 = 9  => 18 pairs (_) / G1 = 9  => 15 pairs (_)
F2,G2: 9.. / F2 = 9  => 15 pairs (_) / G2 = 9  => 18 pairs (_)
* DURATION: 0:00:43.333080  START: 20:14:47.792622  END: 20:15:31.125702 2019-04-30
* CP COUNT: (40)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,A9,B4,B8,B9,D2,D5,E1,E3,F4,G4,H2,H8)
* 24.1...8.1........9..2...7...276..39....938..593812764729351648...928..7..1647.9.
* PAIR E1: 3,7 BLK 2
E2: 3,7,8                                # reduction candidate for 3,7
E2: 8 => CTR
* 24.17..8313748..5.9.823.471812764539.7.5938..593812764729351648...928..7.81647.95
E2: 3,7                                  # 15 pairs
* PAIR D2: 4,5 BLK 2
F2: 4,5,6,9                              # reduction candidate for 4,5
F2: 4,5                                  # 21 pairs
F3: 4,5,6                                # reduction candidate for 4,5
F3: 4,5                                  # 17 pairs
* PAIR D2: 4,5 ROW 2
G2: 4,5,2,3,9                            # reduction candidate for 4,5
G2: 4,5                                  # 18 pairs
G2: 2,3,9                                # 16 pairs
* PAIR E3: 3,8 BLK 2
E2: 3,8,7                                # reduction candidate for 3,8
E2: 7 => CTR
* 2471359861.8479.5.9..286471812764539.7.5938..593812764729351648...928..7.81647.95
E2: 3,8                                  # 17 pairs
* PAIR H2: 2,5 BLK 3
G2: 2,5,3,4,9                            # reduction candidate for 2,5
G2: 2,5 => CTR
* 24.1..98.1....9...9..2..471..2764539...593812593812764729351648...928157..1647.9.
G2: 3,4,9                                # 15 pairs
I2: 2,5,3,6                              # reduction candidate for 2,5
I2: 2,5 => CTR
* 24.1...8.1..4.....9..2..471..2764539...593812593812764729351648...928157.51647293
I2: 3,6                                  # 15 pairs
* PAIR H2: 2,5 COL H
H5: 2,5,1                                # reduction candidate for 2,5
H5: 1 => CTR
* 24.1...8.1......2.9..2...7...276..39....93812593812764729351648...928157.51647293
H5: 2,5                                  # 15 pairs
* PAIR A5: 4,6 BLK 4
C5: 4,6,7                                # reduction candidate for 4,6
C5: 4,6 => CTR
* 24.1...8.1..4...5.9..2..471812764539.7.5938..593812764729351648...928..7.81647.95
C5: 7                                    # 16 pairs
* PAIR A5: 4,6 COL A
A8: 4,6,3                                # reduction candidate for 4,6
A8: 4,6 => CTR
* 24.1...8.1........9..2...7.812764539....938..593812764729351648...928317381647.9.
A8: 3 => SOLVED
* 246179385178534926935286471482765139617493852593812764729351648364928517851647293
* PAIR F4: 4,5 COL F
F2: 4,5,6,9                              # reduction candidate for 4,5
F2: 4,5                                  # 21 pairs
F3: 4,5,6                                # reduction candidate for 4,5
F3: 4,5                                  # 17 pairs
* PAIR G4: 1,5 BLK 6
H5: 1,5,2                                # reduction candidate for 1,5
H5: 1,5                                  # 15 pairs
I5: 1,5,2                                # reduction candidate for 1,5
I5: 1,5 => CTR
* 24.1...8.1..4...529..2...7...276..39...593821593812764729351648...928.17..1647.95
I5: 2                                    # 15 pairs
* PAIR G4: 1,5 COL G
G3: 1,5,3,4                              # reduction candidate for 1,5
G3: 1,5 => CTR
* 24.1...8.1.....4..9..2.4.7.4827651396174938..5938127647293516483.49285.7..1647.9.
G3: 3,4                                  # 16 pairs
G8: 1,5,3                                # reduction candidate for 1,5
G8: 1,5 => SOLVED
* 246179385178534926935286471482765139617493852593812764729351648364928517851647293
G8: 3 => CTR
* 24.1...8.1........9..2...7.812764539....938..593812764729351648...928317381647.9.
* PAIR B8: 5,6 BLK 7
C8: 5,6,4                                # reduction candidate for 5,6
C8: 5,6 => CTR
* 24.1...8.1..4...5.9..2..4718.276..39..45938..5938127647293516484..928317381647.9.
C8: 4                                    # 17 pairs
* PAIR B8: 5,6 COL B
B2: 5,6,3,7                              # reduction candidate for 5,6
B2: 5,6 => CTR
* 2471359861.8479.53935286471812764539.7.5938..593812764729351648...928..7.81647.95
B2: 3,7                                  # 15 pairs
B3: 5,6,3                                # reduction candidate for 5,6
B3: 5,6 => CTR
* 24.1...8.13.4...5.9..2..471812764539.7.5938..593812764729351648...928..7.81647.95
B3: 3                                    # 15 pairs
* PAIR H8: 1,5 BLK 9
G8: 1,5,3                                # reduction candidate for 1,5
G8: 1,5 => SOLVED
* 246179385178534926935286471482765139617493852593812764729351648364928517851647293
G8: 3 => CTR
* 24.1...8.1........9..2...7.812764539....938..593812764729351648...928317381647.9.
* PAIR H8: 1,5 COL H
H5: 1,5,2                                # reduction candidate for 1,5
H5: 2 => CTR
* 24.1...8.1..4...529..2...7...276..39...593821593812764729351648...928.17..1647.95
H5: 1,5                                  # 15 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060321-absurd-base-pr-000.dot
* REASONING
* DIS # E2: 8 => CTR => E2: 3,7
* DIS # E2: 7 => CTR => E2: 3,8
* DIS # G2: 2,5 => CTR => G2: 3,4,9
* DIS # I2: 2,5 => CTR => I2: 3,6
* DIS # H5: 1 => CTR => H5: 2,5
* DIS # C5: 4,6 => CTR => C5: 7
* DIS # A8: 4,6 => CTR => A8: 3
* PRF # A8: 3 => SOL
* DIS # I5: 1,5 => CTR => I5: 2
* DIS # G3: 1,5 => CTR => G3: 3,4
* PRF # G8: 1,5 => SOL
* DIS # G8: 3 => CTR => G8: 1,5
* DIS # C8: 5,6 => CTR => C8: 4
* DIS # B2: 5,6 => CTR => B2: 3,7
* DIS # B3: 5,6 => CTR => B3: 3
* PRF # G8: 1,5 => SOL
* DIS # G8: 3 => CTR => G8: 1,5
* DIS # H5: 2 => CTR => H5: 1,5
* CNT  18 HDP CHAINS /  37 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,A9,B4,B8,B9,D2,D5,E1,E3,F4,G4,H2,H8)
* 24.1...8.1........9..2...7...276..39....938..593812764729351648...928..7..1647.9.
* PAIR E1: 3,7 BLK 2
E2: 3,7,8                                # reduction candidate for 3,7
E2: 8 => CTR
* 24.17..8313748..5.9.823.471812764539.7.5938..593812764729351648...928..7.81647.95
* PAIR D2: 4,5 BLK 2
F2: 4,5,6,9                              # reduction candidate for 4,5
F2: 4,5                                  # 21 pairs
F3: 4,5,6                                # reduction candidate for 4,5
F3: 4,5                                  # 18 pairs
* PAIR D2: 4,5 ROW 2
G2: 4,5,2,3,9                            # reduction candidate for 4,5
G2: 4,5                                  # 19 pairs
G2: 2,3,9                                # 17 pairs
* PAIR H2: 2,5 BLK 3
G2: 2,5,3,4,9                            # reduction candidate for 2,5
G2: 2,5 => CTR
* 24.1..98.1.8..9...9..28.471..2764539...593812593812764729351648...928157..1647.9.
I2: 2,5,3,6                              # reduction candidate for 2,5
I2: 2,5 => CTR
* 24.1...8.1.84.....9..28.471..2764539...5938125938127647293516483.49281578.164729.
* PAIR A5: 4,6 BLK 4
C5: 4,6,7                                # reduction candidate for 4,6
C5: 4,6 => CTR
* 24713..8.1.8.7..2.9..28..71..276..39.7..93812593812764729351648...928157.51647293
* PAIR F4: 4,5 COL F
F2: 4,5,9                                # reduction candidate for 4,5
F2: 9 => CTR
* 24.17..8.17853942693.2845714827651396174938525938127647293516483.4928..7..164729.
* PAIR RESTART
* PAIR G4: 1,5 COL G
G8: 1,5,3                                # reduction candidate for 1,5
G8: 1,5 => SOLVED
* 246179385178534926935286471482765139617493852593812764729351648364928517851647293
* DURATION: 0:00:10.033224  START: 20:15:53.758990  END: 20:16:03.792214 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060321-absurd-base-pr-001.dot
* REASONING
* DIS # E2: 8 => CTR => E2: 3,7
* DIS E2: 3,7 # G2: 2,5 => CTR => G2: 3,4,9
* DIS E2: 3,7 + G2: 3,4,9 # I2: 2,5 => CTR => I2: 3,6
* DIS E2: 3,7 + G2: 3,4,9 + I2: 3,6 # C5: 4,6 => CTR => C5: 7
* DIS E2: 3,7 + G2: 3,4,9 + I2: 3,6 + C5: 7 # F2: 9 => CTR => F2: 4,5
* PRF E2: 3,7 + G2: 3,4,9 + I2: 3,6 + C5: 7 + F2: 4,5 # G8: 1,5 => SOL
* STA E2: 3,7 + G2: 3,4,9 + I2: 3,6 + C5: 7 + F2: 4,5 + G8: 1,5
* CNT   6 HDP CHAINS /  12 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060321, absurd

Solution

position: 246179385178534926935286471482765139617493852593812764729351648364928517851647293 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 # E2: 3,7 => UNS
* DIS # E2: 8 => CTR => E2: 3,7
* INC # F2: 4,5 => UNS
* INC # F3: 4,5 => UNS
* INC # G2: 4,5 => UNS
* INC # G2: 2,3,9 => UNS
* INC # E2: 3,8 => UNS
* DIS # E2: 7 => CTR => E2: 3,8
* DIS # G2: 2,5 => CTR => G2: 3,4,9
* INC # G2: 3,4,9 => UNS
* DIS # I2: 2,5 => CTR => I2: 3,6
* INC # I2: 3,6 => UNS
* INC # H5: 2,5 => UNS
* DIS # H5: 1 => CTR => H5: 2,5
* DIS # C5: 4,6 => CTR => C5: 7
* INC # C5: 7 => UNS
* DIS # A8: 4,6 => CTR => A8: 3
* PRF # A8: 3 => SOL
* INC # F2: 4,5 => UNS
* INC # F3: 4,5 => UNS
* INC # H5: 1,5 => UNS
* DIS # I5: 1,5 => CTR => I5: 2
* INC # I5: 2 => UNS
* DIS # G3: 1,5 => CTR => G3: 3,4
* INC # G3: 3,4 => UNS
* PRF # G8: 1,5 => SOL
* DIS # G8: 3 => CTR => G8: 1,5
* DIS # C8: 5,6 => CTR => C8: 4
* INC # C8: 4 => UNS
* DIS # B2: 5,6 => CTR => B2: 3,7
* INC # B2: 3,7 => UNS
* DIS # B3: 5,6 => CTR => B3: 3
* INC # B3: 3 => UNS
* PRF # G8: 1,5 => SOL
* DIS # G8: 3 => CTR => G8: 1,5
* INC # H5: 1,5 => UNS
* DIS # H5: 2 => CTR => H5: 1,5
* CNT  37 HDP CHAINS /  37 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E2: 3,7 => UNS
* DIS # E2: 8 => CTR => E2: 3,7
* INC E2: 3,7 # F2: 4,5 => UNS
* INC E2: 3,7 # F3: 4,5 => UNS
* INC E2: 3,7 # G2: 4,5 => UNS
* INC E2: 3,7 # G2: 2,3,9 => UNS
* DIS E2: 3,7 # G2: 2,5 => CTR => G2: 3,4,9
* DIS E2: 3,7 + G2: 3,4,9 # I2: 2,5 => CTR => I2: 3,6
* DIS E2: 3,7 + G2: 3,4,9 + I2: 3,6 # C5: 4,6 => CTR => C5: 7
* INC E2: 3,7 + G2: 3,4,9 + I2: 3,6 + C5: 7 # F2: 4,5 => UNS
* DIS E2: 3,7 + G2: 3,4,9 + I2: 3,6 + C5: 7 # F2: 9 => CTR => F2: 4,5
* PRF E2: 3,7 + G2: 3,4,9 + I2: 3,6 + C5: 7 + F2: 4,5 # G8: 1,5 => SOL
* STA E2: 3,7 + G2: 3,4,9 + I2: 3,6 + C5: 7 + F2: 4,5 + G8: 1,5
* CNT  12 HDP CHAINS /  12 HYP OPENED