Analysis of zz-www.sudokuoftheday.co.uk-20190216-absurd-base.sdk

Contents

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

level: medium

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

position: .1....5......9..7.8......46.9..51..3.539...1.....2...5.417.......2..6.97....35... initial

Autosolve

position: .1.8.2539..5.9..7.8.95...46.9..51.232539...1.1...2.9.5.41789.525.2..6.979..235... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D2: 3,4 => CTR => D2: 1,6
* DIS # A2: 6 => CTR => A2: 3,4
* DIS # F6: 3,4 => CTR => F6: 7,8
* DIS # B3: 2 => CTR => B3: 3,7
* DIS # G2: 2 => CTR => G2: 1,8
* DIS # G2: 8 => CTR => G2: 1,2
* PRF # E5: 4,6 => SOL
* DIS # E5: 7 => CTR => E5: 4,6
* DIS # D6: 4,6 => CTR => D6: 3
* DIS # C4: 4,6 => CTR => C4: 7,8
* PRF # G4: 4,6 => SOL
* DIS # D2: 1,3 => CTR => D2: 4,6
* DIS # G4: 4,8 => CTR => G4: 6,7
* DIS # G5: 4,8 => CTR => G5: 6,7
* DIS # F5: 7 => CTR => F5: 4,8
* PRF # G4: 6,8 => SOL
* DIS # C6: 6,8 => CTR => C6: 4,7
* DIS # A2: 4 => CTR => A2: 3,6
* DIS # D2: 1,4 => CTR => D2: 3,6
* CNT  19 HDP CHAINS /  43 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 # D2: 3,4 => CTR => D2: 1,6
* DIS D2: 1,6 # A2: 6 => CTR => A2: 3,4
* PRF D2: 1,6 + A2: 3,4 # B3: 3,7 => SOL
* STA D2: 1,6 + A2: 3,4 + B3: 3,7
* CNT   3 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

.1....5......9..7.8......46.9..51..3.539...1.....2...5.417.......2..6.97....35... initial
.1.8.2539..5.9..7.8.95...46.9..51.232539...1.1...2.9.5.41789.525.2..6.979..235... autosolve
416872539325694178879513246798451623253968714164327985641789352532146897987235461 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (17)
F2: 3,4
E3: 1,7
F3: 3,7
I2: 1,8
G3: 1,2
D4: 4,6
I5: 4,8
H6: 6,8
A7: 3,6
B8: 3,8
D8: 1,4
E8: 1,4
G7: 3,6
G8: 3,8
G9: 1,4
H9: 6,8
I9: 1,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D2,E3: 1.. / D2 = 1  =>  0 pairs (X) / E3 = 1  => 20 pairs (_)
D8,E8: 1.. / D8 = 1  => 20 pairs (_) / E8 = 1  =>  0 pairs (X)
G9,I9: 1.. / G9 = 1  =>  0 pairs (X) / I9 = 1  => 16 pairs (_)
E3,G3: 1.. / E3 = 1  => 20 pairs (_) / G3 = 1  =>  0 pairs (X)
D2,D8: 1.. / D2 = 1  =>  0 pairs (X) / D8 = 1  => 20 pairs (_)
E3,E8: 1.. / E3 = 1  => 20 pairs (_) / E8 = 1  =>  0 pairs (X)
I2,I9: 1.. / I2 = 1  =>  0 pairs (X) / I9 = 1  => 16 pairs (_)
B2,B3: 2.. / B2 = 2  => 20 pairs (_) / B3 = 2  =>  0 pairs (X)
G2,G3: 2.. / G2 = 2  =>  0 pairs (X) / G3 = 2  => 20 pairs (_)
B2,G2: 2.. / B2 = 2  => 20 pairs (_) / G2 = 2  =>  0 pairs (X)
B3,G3: 2.. / B3 = 2  =>  0 pairs (X) / G3 = 2  => 20 pairs (_)
D6,F6: 3.. / D6 = 3  => 17 pairs (_) / F6 = 3  =>  0 pairs (X)
A7,B8: 3.. / A7 = 3  =>  0 pairs (X) / B8 = 3  =>  0 pairs (_)
G7,G8: 3.. / G7 = 3  =>  0 pairs (*) / G8 = 3  =>  0 pairs (X)
B3,F3: 3.. / B3 = 3  =>  0 pairs (X) / F3 = 3  =>  0 pairs (_)
A7,G7: 3.. / A7 = 3  =>  0 pairs (X) / G7 = 3  =>  0 pairs (_)
B8,G8: 3.. / B8 = 3  =>  0 pairs (*) / G8 = 3  =>  0 pairs (X)
A2,A7: 3.. / A2 = 3  =>  0 pairs (*) / A7 = 3  =>  0 pairs (X)
D2,D6: 3.. / D2 = 3  =>  0 pairs (X) / D6 = 3  => 17 pairs (_)
D8,E8: 4.. / D8 = 4  =>  0 pairs (X) / E8 = 4  => 20 pairs (_)
G9,I9: 4.. / G9 = 4  => 16 pairs (_) / I9 = 4  =>  0 pairs (X)
I5,I9: 4.. / I5 = 4  => 16 pairs (_) / I9 = 4  =>  0 pairs (X)
E1,D2: 6.. / E1 = 6  =>  0 pairs (X) / D2 = 6  =>  0 pairs (_)
G7,H9: 6.. / G7 = 6  =>  0 pairs (X) / H9 = 6  =>  0 pairs (_)
E5,G5: 6.. / E5 = 6  =>  0 pairs (*) / G5 = 6  =>  0 pairs (X)
A7,G7: 6.. / A7 = 6  =>  0 pairs (*) / G7 = 6  =>  0 pairs (X)
E1,E5: 6.. / E1 = 6  =>  0 pairs (X) / E5 = 6  =>  0 pairs (_)
H6,H9: 6.. / H6 = 6  =>  0 pairs (X) / H9 = 6  =>  0 pairs (_)
G4,G5: 7.. / G4 = 7  => 25 pairs (_) / G5 = 7  =>  0 pairs (*)
B9,C9: 7.. / B9 = 7  => 22 pairs (_) / C9 = 7  => 20 pairs (_)
A1,A4: 7.. / A1 = 7  => 25 pairs (_) / A4 = 7  =>  0 pairs (*)
G2,I2: 8.. / G2 = 8  =>  0 pairs (X) / I2 = 8  => 16 pairs (_)
F5,F6: 8.. / F5 = 8  => 16 pairs (_) / F6 = 8  =>  0 pairs (X)
G8,H9: 8.. / G8 = 8  =>  0 pairs (*) / H9 = 8  =>  0 pairs (X)
C4,G4: 8.. / C4 = 8  => 19 pairs (_) / G4 = 8  =>  0 pairs (X)
B8,G8: 8.. / B8 = 8  =>  0 pairs (X) / G8 = 8  =>  0 pairs (_)
H6,H9: 8.. / H6 = 8  =>  0 pairs (*) / H9 = 8  =>  0 pairs (X)
I2,I5: 8.. / I2 = 8  => 16 pairs (_) / I5 = 8  =>  0 pairs (X)
* DURATION: 0:00:50.873662  START: 03:46:20.261135  END: 03:47:11.134797 2019-05-01
* CP COUNT: (38)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B8,D4,D8,E3,E8,F2,F3,G3,G7,G8,G9,H6,H9,I2,I5,I9)
* .1.8.2539..5.9..7.8.95...46.9..51.232539...1.1...2.9.5.41789.525.2..6.979..235...
* PAIR F2: 3,4 BLK 2
D2: 3,4,1,6                              # reduction candidate for 3,4
D2: 3,4 => CTR
* .1.862539..5.9..7.8.9517246.9..51.2325397.61.1...2.985641789352532..6.979..235...
D2: 1,6                                  # 18 pairs
* PAIR F2: 3,4 ROW 2
A2: 3,4,6                                # reduction candidate for 3,4
A2: 6 => CTR
* .1.8625396.5.9..7.8.95...46.9..51.232539...1.1...2.965341789652582..6397967235.8.
A2: 3,4                                  # 20 pairs
* PAIR F2: 3,4 COL F
F6: 3,4,7,8                              # reduction candidate for 3,4
F6: 3,4 => CTR
* .1.8.2539..5.9..788.95.7.46.9..51.232539786141...2.985641789352532..6897987235461
F6: 7,8                                  # 20 pairs
* PAIR F3: 3,7 ROW 3
B3: 3,7,2                                # reduction candidate for 3,7
B3: 2 => CTR
* .1.8.2539..5194278829573146.9.651.2325394..1.1..32.9.5.41789.525.2.16.979..2354.1
B3: 3,7                                  # 20 pairs
* PAIR F3: 3,7 COL F
F6: 3,7,4,8                              # reduction candidate for 3,7
F6: 4,8                                  # 26 pairs
F6: 3,7                                  # 17 pairs
* PAIR I2: 1,8 BLK 3
G2: 1,8,2                                # reduction candidate for 1,8
G2: 2 => CTR
* .1.842539..5.9.2788295.3146.9..51.232539...141..32.9.5.41789.525.2.16.979..2354.1
G2: 1,8                                  # 20 pairs
* PAIR G3: 1,2 BLK 3
G2: 1,2,8                                # reduction candidate for 1,2
G2: 8 => CTR
* .16872539.256948718.951.246.98.51.232539...181...28965.41789652582146397967235184
G2: 1,2                                  # 16 pairs
* PAIR D4: 4,6 BLK 5
E5: 4,6,7                                # reduction candidate for 4,6
E5: 4,6 => SOLVED
* 416872539325694178879513246798451623253968714164327985641789352532146897987235461
E5: 7 => CTR
* .1.862539..5.9..7.8.95...46.9..51.2325397.61.1...2.985641789352532.46897987235.6.
D6: 4,6,3                                # reduction candidate for 4,6
D6: 4,6 => CTR
* .1.8.2539..5394.7.839517246.9..51.232539786141...23985.41789.525.2..6.979..235...
D6: 3                                    # 17 pairs
* PAIR D4: 4,6 ROW 4
A4: 4,6,7                                # reduction candidate for 4,6
A4: 4,6                                  # 25 pairs
C4: 4,6,7,8                              # reduction candidate for 4,6
C4: 4,6 => CTR
* .1.8.2539..5.9..7.8.95...46.9..518232539.87141...27965.41789652582..6.979..235...
C4: 7,8                                  # 18 pairs
G4: 4,6,7,8                              # reduction candidate for 4,6
G4: 4,6 => SOLVED
* 416872539325694178879513246798451623253968714164327985641789352532146897987235461
G4: 7,8                                  # 20 pairs
* PAIR D4: 4,6 COL D
D2: 4,6,1,3                              # reduction candidate for 4,6
D2: 1,3 => CTR
* 714862539365194.7.8.95...46.9..51.232539..61.1...2.985641789352532..6897987235.6.
D2: 4,6                                  # 21 pairs
* PAIR I5: 4,8 BLK 6
G4: 4,8,6,7                              # reduction candidate for 4,8
G4: 4,8 => CTR
* .1.8.2539..5.9..7.8.95...46.9..51.232539..71.1...27965.417896525.2..63979..235.8.
G4: 6,7                                  # 22 pairs
G5: 4,8,6,7                              # reduction candidate for 4,8
G5: 4,8 => CTR
* 7168425394.5693.7.8.95...46.9..51723253967.1.1...28965.417896525.2..63979..235.8.
G5: 6,7                                  # 18 pairs
* PAIR I5: 4,8 ROW 5
F5: 4,8,7                                # reduction candidate for 4,8
F5: 7 => CTR
* .1.8.2539..5.94.7.8.95.3.46.98.51723253967.1.1743289653417896525.2..63979..235.8.
F5: 4,8                                  # 20 pairs
* PAIR H6: 6,8 BLK 6
G4: 6,8,4,7                              # reduction candidate for 6,8
G4: 6,8 => SOLVED
* 416872539325694178879513246798451623253968714164327985641789352532146897987235461
G4: 4,7                                  # 20 pairs
G5: 6,8,4,7                              # reduction candidate for 6,8
G5: 6,8                                  # 23 pairs
* PAIR H6: 6,8 ROW 6
B6: 6,8,7                                # reduction candidate for 6,8
B6: 6,8                                  # 19 pairs
C6: 6,8,4,7                              # reduction candidate for 6,8
C6: 6,8 => CTR
* .1.862539365.942788295.3146.9865172325397.6141...2.985641789352532..6897987235461
C6: 4,7                                  # 18 pairs
* PAIR A7: 3,6 COL A
A2: 3,6,4                                # reduction candidate for 3,6
A2: 4 => CTR
* .1.8.25394.5.93.7.8395.7246.9..51.2325397.61.1..32.985.41789.525.2..6.979..235...
A2: 3,6                                  # 21 pairs
* PAIR D8: 1,4 COL D
D2: 1,4,3,6                              # reduction candidate for 1,4
D2: 1,4 => CTR
* 714862539365.942788295.314649865172325394.61.1..32.985641789352532..6897987235.6.
D2: 3,6                                  # 21 pairs
* PAIR H9: 6,8 ROW 9
B9: 6,8,7                                # reduction candidate for 6,8
B9: 6,8                                  # 20 pairs
C9: 6,8,7                                # reduction candidate for 6,8
C9: 6,8                                  # 22 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190216-absurd-base-pr-000.dot
* REASONING
* DIS # D2: 3,4 => CTR => D2: 1,6
* DIS # A2: 6 => CTR => A2: 3,4
* DIS # F6: 3,4 => CTR => F6: 7,8
* DIS # B3: 2 => CTR => B3: 3,7
* DIS # G2: 2 => CTR => G2: 1,8
* DIS # G2: 8 => CTR => G2: 1,2
* PRF # E5: 4,6 => SOL
* DIS # E5: 7 => CTR => E5: 4,6
* DIS # D6: 4,6 => CTR => D6: 3
* DIS # C4: 4,6 => CTR => C4: 7,8
* PRF # G4: 4,6 => SOL
* DIS # D2: 1,3 => CTR => D2: 4,6
* DIS # G4: 4,8 => CTR => G4: 6,7
* DIS # G5: 4,8 => CTR => G5: 6,7
* DIS # F5: 7 => CTR => F5: 4,8
* PRF # G4: 6,8 => SOL
* DIS # C6: 6,8 => CTR => C6: 4,7
* DIS # A2: 4 => CTR => A2: 3,6
* DIS # D2: 1,4 => CTR => D2: 3,6
* CNT  19 HDP CHAINS /  43 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B8,D4,D8,E3,E8,F2,F3,G3,G7,G8,G9,H6,H9,I2,I5,I9)
* .1.8.2539..5.9..7.8.95...46.9..51.232539...1.1...2.9.5.41789.525.2..6.979..235...
* PAIR F2: 3,4 BLK 2
D2: 3,4,1,6                              # reduction candidate for 3,4
D2: 3,4 => CTR
* .1.862539..5.9..7.8.9517246.9..51.2325397.61.1...2.985641789352532..6.979..235...
* PAIR F2: 3,4 ROW 2
A2: 3,4,6                                # reduction candidate for 3,4
A2: 6 => CTR
* .1.8.25396.5194.788.9573146.9.651.2325394..1.1..32.9.5.41789.525.2..6.979..235...
* PAIR RESTART
* PAIR F3: 3,7 ROW 3
B3: 3,7,2                                # reduction candidate for 3,7
B3: 3,7 => SOLVED
* 416872539325694178879513246798451623253968714164327985641789352532146897987235461
* DURATION: 0:00:04.014327  START: 03:47:38.621332  END: 03:47:42.635659 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190216-absurd-base-pr-001.dot
* REASONING
* DIS # D2: 3,4 => CTR => D2: 1,6
* DIS D2: 1,6 # A2: 6 => CTR => A2: 3,4
* PRF D2: 1,6 + A2: 3,4 # B3: 3,7 => SOL
* STA D2: 1,6 + A2: 3,4 + B3: 3,7
* CNT   3 HDP CHAINS /   4 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190216, absurd

Solution

position: 416872539325694178879513246798451623253968714164327985641789352532146897987235461 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 # D2: 3,4 => CTR => D2: 1,6
* INC # D2: 1,6 => UNS
* INC # A2: 3,4 => UNS
* DIS # A2: 6 => CTR => A2: 3,4
* DIS # F6: 3,4 => CTR => F6: 7,8
* INC # F6: 7,8 => UNS
* INC # B3: 3,7 => UNS
* DIS # B3: 2 => CTR => B3: 3,7
* INC # F6: 3,7 => UNS
* INC # F6: 4,8 => UNS
* INC # G2: 1,8 => UNS
* DIS # G2: 2 => CTR => G2: 1,8
* INC # G2: 1,2 => UNS
* DIS # G2: 8 => CTR => G2: 1,2
* PRF # E5: 4,6 => SOL
* DIS # E5: 7 => CTR => E5: 4,6
* DIS # D6: 4,6 => CTR => D6: 3
* INC # D6: 3 => UNS
* INC # A4: 4,6 => UNS
* DIS # C4: 4,6 => CTR => C4: 7,8
* INC # C4: 7,8 => UNS
* PRF # G4: 4,6 => SOL
* INC # G4: 7,8 => UNS
* INC # D2: 4,6 => UNS
* DIS # D2: 1,3 => CTR => D2: 4,6
* DIS # G4: 4,8 => CTR => G4: 6,7
* INC # G4: 6,7 => UNS
* DIS # G5: 4,8 => CTR => G5: 6,7
* INC # G5: 6,7 => UNS
* INC # F5: 4,8 => UNS
* DIS # F5: 7 => CTR => F5: 4,8
* PRF # G4: 6,8 => SOL
* INC # G4: 4,7 => UNS
* INC # G5: 6,8 => UNS
* INC # B6: 6,8 => UNS
* DIS # C6: 6,8 => CTR => C6: 4,7
* INC # C6: 4,7 => UNS
* INC # A2: 3,6 => UNS
* DIS # A2: 4 => CTR => A2: 3,6
* DIS # D2: 1,4 => CTR => D2: 3,6
* INC # D2: 3,6 => UNS
* INC # B9: 6,8 => UNS
* INC # C9: 6,8 => UNS
* CNT  43 HDP CHAINS /  43 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # D2: 3,4 => CTR => D2: 1,6
* INC D2: 1,6 # A2: 3,4 => UNS
* DIS D2: 1,6 # A2: 6 => CTR => A2: 3,4
* PRF D2: 1,6 + A2: 3,4 # B3: 3,7 => SOL
* STA D2: 1,6 + A2: 3,4 + B3: 3,7
* CNT   4 HDP CHAINS /   4 HYP OPENED