Analysis of zz-www.sudokuoftheday.co.uk-20190411-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: 2.9....4...7..68......1..9....18.46.42.6.............7............435..63...6.5.1 initial

Autosolve

position: 219...64.5.7..681.....1.79.7..1824694216..358......127.....1.341..435..63...6.5.1 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B3: 3,4 => CTR => B3: 6,8
* DIS # C3: 6,8 => CTR => C3: 3,4
* DIS # A6: 6,8 => CTR => A6: 9
* PRF # D1: 5,7 => SOL
* DIS # D1: 7,8 => CTR => D1: 3,5
* PRF # D1: 3,5 => SOL
* DIS # F9: 7,8 => CTR => F9: 9
* DIS # B3: 3,4 => CTR => B3: 6,8
* PRF # D1: 3,5 => SOL
* DIS # D1: 7,8 => CTR => D1: 3,5
* DIS # D2: 2,3 => CTR => D2: 9
* DIS # A6: 6,8 => CTR => A6: 9
* DIS # C3: 6,8 => CTR => C3: 3,4
* DIS # C7: 6,8 => CTR => C7: 2,5
* DIS # E7: 7,9 => CTR => E7: 2
* PRF # E7: 2 => SOL
* DIS # F9: 8 => CTR => F9: 7,9
* PRF # D1: 3,5 => SOL
* DIS # D1: 7,8 => CTR => D1: 3,5
* DIS # C7: 2,8 => CTR => C7: 5,6
* PRF # C9: 2,8 => SOL
* DIS # C9: 4 => CTR => C9: 2,8
* DIS # D7: 2,9 => CTR => D7: 7,8
* DIS # B8: 7,8 => CTR => B8: 9
* DIS # B9: 7,8 => CTR => B9: 4,9
* PRF # D9: 7,8 => SOL
* DIS # D9: 2,9 => CTR => D9: 7,8
* DIS # F9: 7,8 => CTR => F9: 9
* CNT  28 HDP CHAINS /  50 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 # B3: 3,4 => CTR => B3: 6,8
* DIS B3: 6,8 # A6: 6,8 => CTR => A6: 9
* PRF B3: 6,8 + A6: 9 # D1: 5,7 => SOL
* STA B3: 6,8 + A6: 9 + D1: 5,7
* CNT   3 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

2.9....4...7..68......1..9....18.46.42.6.............7............435..63...6.5.1 initial
219...64.5.7..681.....1.79.7..1824694216..358......127.....1.341..435..63...6.5.1 autosolve
219578643537946812864213795753182469421697358986354127675821934198435276342769581 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (22)
B2: 3,4
A3: 6,8
E1: 5,7
F1: 7,8
D3: 2,5
F3: 3,4
I1: 3,5
I2: 2,3
I3: 2,5
B4: 3,5
C4: 3,5
C6: 6,8
E5: 7,9
F5: 7,9
D6: 3,5
E6: 4,5
F6: 3,4
C8: 2,8
G7: 2,9
G8: 2,9
H8: 7,8
H9: 7,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
I2,I3: 2.. / I2 = 2  =>  0 pairs (*) / I3 = 2  =>  0 pairs (X)
G7,G8: 2.. / G7 = 2  =>  0 pairs (X) / G8 = 2  => 21 pairs (_)
D3,I3: 2.. / D3 = 2  =>  0 pairs (*) / I3 = 2  =>  0 pairs (X)
C8,G8: 2.. / C8 = 2  =>  0 pairs (X) / G8 = 2  => 21 pairs (_)
C9,D9: 2.. / C9 = 2  =>  0 pairs (*) / D9 = 2  =>  0 pairs (X)
E2,E7: 2.. / E2 = 2  =>  0 pairs (X) / E7 = 2  =>  0 pairs (_)
I1,I2: 3.. / I1 = 3  =>  0 pairs (*) / I2 = 3  =>  0 pairs (X)
B4,C4: 3.. / B4 = 3  =>  0 pairs (X) / C4 = 3  => 20 pairs (_)
D6,F6: 3.. / D6 = 3  =>  0 pairs (*) / F6 = 3  =>  0 pairs (X)
D1,I1: 3.. / D1 = 3  =>  0 pairs (X) / I1 = 3  =>  0 pairs (_)
C3,C4: 3.. / C3 = 3  =>  0 pairs (X) / C4 = 3  => 20 pairs (_)
F3,F6: 3.. / F3 = 3  =>  0 pairs (*) / F6 = 3  =>  0 pairs (X)
E2,F3: 4.. / E2 = 4  =>  0 pairs (*) / F3 = 4  =>  0 pairs (X)
E6,F6: 4.. / E6 = 4  =>  0 pairs (X) / F6 = 4  =>  0 pairs (_)
B9,C9: 4.. / B9 = 4  =>  0 pairs (*) / C9 = 4  =>  0 pairs (X)
B2,E2: 4.. / B2 = 4  =>  0 pairs (X) / E2 = 4  =>  0 pairs (_)
C3,C9: 4.. / C3 = 4  =>  0 pairs (*) / C9 = 4  =>  0 pairs (X)
E2,E6: 4.. / E2 = 4  =>  0 pairs (*) / E6 = 4  =>  0 pairs (X)
F3,F6: 4.. / F3 = 4  =>  0 pairs (X) / F6 = 4  =>  0 pairs (_)
I1,I3: 5.. / I1 = 5  =>  0 pairs (X) / I3 = 5  =>  0 pairs (_)
B4,C4: 5.. / B4 = 5  => 20 pairs (_) / C4 = 5  =>  0 pairs (X)
D6,E6: 5.. / D6 = 5  =>  0 pairs (X) / E6 = 5  =>  0 pairs (_)
B7,C7: 5.. / B7 = 5  =>  0 pairs (X) / C7 = 5  => 20 pairs (_)
D3,I3: 5.. / D3 = 5  =>  0 pairs (X) / I3 = 5  =>  0 pairs (_)
B4,B7: 5.. / B4 = 5  => 20 pairs (_) / B7 = 5  =>  0 pairs (X)
C4,C7: 5.. / C4 = 5  =>  0 pairs (X) / C7 = 5  => 20 pairs (_)
E1,E6: 5.. / E1 = 5  =>  0 pairs (X) / E6 = 5  =>  0 pairs (_)
E5,F5: 7.. / E5 = 7  =>  0 pairs (X) / F5 = 7  => 21 pairs (_)
H8,H9: 7.. / H8 = 7  => 23 pairs (_) / H9 = 7  =>  0 pairs (X)
B8,H8: 7.. / B8 = 7  =>  0 pairs (X) / H8 = 7  => 23 pairs (_)
D1,F1: 8.. / D1 = 8  =>  0 pairs (X) / F1 = 8  => 22 pairs (_)
H8,H9: 8.. / H8 = 8  =>  0 pairs (X) / H9 = 8  => 23 pairs (_)
F1,F9: 8.. / F1 = 8  => 22 pairs (_) / F9 = 8  =>  0 pairs (X)
D2,E2: 9.. / D2 = 9  => 23 pairs (_) / E2 = 9  =>  0 pairs (X)
A6,B6: 9.. / A6 = 9  => 24 pairs (_) / B6 = 9  =>  0 pairs (X)
E5,F5: 9.. / E5 = 9  => 21 pairs (_) / F5 = 9  =>  0 pairs (X)
G7,G8: 9.. / G7 = 9  => 21 pairs (_) / G8 = 9  =>  0 pairs (X)
B8,G8: 9.. / B8 = 9  => 21 pairs (_) / G8 = 9  =>  0 pairs (X)
A6,A7: 9.. / A6 = 9  => 24 pairs (_) / A7 = 9  =>  0 pairs (X)
F5,F9: 9.. / F5 = 9  =>  0 pairs (X) / F9 = 9  => 21 pairs (_)
* DURATION: 0:00:53.361764  START: 05:12:36.434518  END: 05:13:29.796282 2019-05-01
* CP COUNT: (40)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B2,B4,C4,C6,C8,D3,D6,E1,E5,E6,F1,F3,F5,F6,G7,G8,H8,H9,I1,I2,I3)
* 219...64.5.7..681.....1.79.7..1824694216..358......127.....1.341..435..63...6.5.1
* PAIR B2: 3,4 BLK 1
B3: 3,4,6,8                              # reduction candidate for 3,4
B3: 3,4 => CTR
* 219...64.5.7.26813.3.5147927531824694216..358...3..127..5..1.341.24359.63.426.5.1
B3: 6,8                                  # 24 pairs
C3: 3,4,6,8                              # reduction candidate for 3,4
C3: 3,4                                  # 24 pairs
* PAIR A3: 6,8 BLK 1
B3: 6,8,3,4                              # reduction candidate for 6,8
B3: 6,8                                  # 24 pairs
C3: 6,8,3,4                              # reduction candidate for 6,8
C3: 6,8 => CTR
* 219...64.5.7.26813.3.5147927531824694216..358...3..127..5..1.341..435..63.426.5.1
C3: 3,4                                  # 24 pairs
* PAIR A3: 6,8 COL A
A6: 6,8,9                                # reduction candidate for 6,8
A6: 6,8 => CTR
* 219..864.5.7926813...5147927..18246942169.358.9....1279....12341.24359.63..2695.1
A6: 9                                    # 24 pairs
A7: 6,8,9                                # reduction candidate for 6,8
A7: 6,8                                  # 24 pairs
* PAIR E1: 5,7 BLK 2
D1: 5,7,3,8                              # reduction candidate for 5,7
D1: 5,7 => SOLVED
* 219578643537946812864213795753182469421697358986354127675821934198435276342769581
D1: 3,8                                  # 28 pairs
* PAIR F1: 7,8 BLK 2
D1: 7,8,3,5                              # reduction candidate for 7,8
D1: 7,8 => CTR
* 219.58643547396812...2147957..1824694216793589..543127...821934198435276372.6.581
D1: 3,5 => SOLVED
* 219578643537946812864213795753182469421697358986354127675821934198435276342769581
* PAIR F1: 7,8 COL F
F9: 7,8,9                                # reduction candidate for 7,8
F9: 7,8 => CTR
* 219.58643547396812...2147957..1824694216793589..543127...82193419843527637296.581
F9: 9                                    # 21 pairs
* PAIR F3: 3,4 ROW 3
B3: 3,4,6,8                              # reduction candidate for 3,4
B3: 3,4 => CTR
* 219...64.5.7.26813.3.5147927531824694216..358...3..127..5..1.341.24359.63.426.5.1
B3: 6,8                                  # 24 pairs
C3: 3,4,6,8                              # reduction candidate for 3,4
C3: 3,4                                  # 24 pairs
* PAIR I1: 3,5 ROW 1
D1: 3,5,7,8                              # reduction candidate for 3,5
D1: 3,5 => SOLVED
* 219578643537946812864213795753182469421697358986354127675821934198435276342769581
D1: 7,8 => CTR
* 219.58643547396812...2147957..1824694216793589..543127...821934198435276372.6.581
* PAIR I2: 2,3 ROW 2
D2: 2,3,9                                # reduction candidate for 2,3
D2: 2,3 => CTR
* 219...64.5.7.9681.....1479.7..182469421679358....43127....2193419.435..63...6.5.1
D2: 9                                    # 23 pairs
* PAIR C6: 6,8 BLK 4
A6: 6,8,9                                # reduction candidate for 6,8
A6: 6,8 => CTR
* 219..864.5.7926813...5147927..18246942169.358.9....1279....12341.24359.63..2695.1
A6: 9                                    # 24 pairs
B6: 6,8,9                                # reduction candidate for 6,8
B6: 6,8                                  # 24 pairs
* PAIR C6: 6,8 COL C
C3: 6,8,3,4                              # reduction candidate for 6,8
C3: 6,8 => CTR
* 219...64.5.7.26813.3.5147927531824694216..358...3..127..5..1.341..435..63.426.5.1
C3: 3,4                                  # 24 pairs
C7: 6,8,2,5                              # reduction candidate for 6,8
C7: 6,8 => CTR
* 219...64.5.7..681...3.1479.7351824694216..358....43127.5...1.341..435..63.426.5.1
C7: 2,5                                  # 23 pairs
* PAIR E5: 7,9 COL E
E7: 7,9,2                                # reduction candidate for 7,9
E7: 7,9 => CTR
* 219...64.5.7.26813...5147927..1824694216..358...3..127.....1.341..435..63...6.5.1
E7: 2 => SOLVED
* 219578643537946812864213795753182469421697358986354127675821934198435276342769581
* PAIR F5: 7,9 COL F
F9: 7,9,8                                # reduction candidate for 7,9
F9: 8 => CTR
* 2198.76435.7..6812...21.7957..182469421679358...543127...7219341..435..63...68571
F9: 7,9                                  # 22 pairs
* PAIR D6: 3,5 COL D
D1: 3,5,7,8                              # reduction candidate for 3,5
D1: 3,5 => SOLVED
* 219578643537946812864213795753182469421697358986354127675821934198435276342769581
D1: 7,8 => CTR
* 219.58643547396812...2147957..1824694216793589..543127...821934198435276372.6.581
* PAIR C8: 2,8 BLK 7
C7: 2,8,5,6                              # reduction candidate for 2,8
C7: 2,8 => CTR
* 219...64.5.7..681...3.1479.7351824694216..358..6.4312765...1.341..435..63.426.5.1
C7: 5,6                                  # 23 pairs
C9: 2,8,4                                # reduction candidate for 2,8
C9: 2,8 => SOLVED
* 219578643537946812864213795753182469421697358986354127675821934198435276342769581
C9: 4 => CTR
* 219...64.5.7.26813...5147927..1824694216..358...3..127.....1.341..435..63.426.5.1
* PAIR G7: 2,9 ROW 7
D7: 2,9,7,8                              # reduction candidate for 2,9
D7: 2,9 => CTR
* 2197586435.7..6812...21.7957..1824694216.7358...54.127.....1.341..435.863...6.571
D7: 7,8                                  # 23 pairs
E7: 2,9,7                                # reduction candidate for 2,9
E7: 2,9                                  # 26 pairs
* PAIR H8: 7,8 ROW 8
B8: 7,8,9                                # reduction candidate for 7,8
B8: 7,8 => CTR
* 219...64.5.7.26813...5147927..1824694216..358...3..127.....12341.24359.63..26.5.1
B8: 9                                    # 21 pairs
* PAIR H9: 7,8 ROW 9
B9: 7,8,4,9                              # reduction candidate for 7,8
B9: 7,8 => CTR
* 219..864.5.7926813...5147927..18246942169.358......127.....1.341..435..63.42695.1
B9: 4,9                                  # 23 pairs
D9: 7,8,2,9                              # reduction candidate for 7,8
D9: 7,8 => SOLVED
* 219578643537946812864213795753182469421697358986354127675821934198435276342769581
D9: 2,9 => CTR
* 219.58643547396812...2147957..1824694216793589..543127...82193419843527637296.581
F9: 7,8,9                                # reduction candidate for 7,8
F9: 7,8 => CTR
* 219.58643547396812...2147957..1824694216793589..543127...82193419843527637296.581
F9: 9                                    # 21 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190411-absurd-base-pr-000.dot
* REASONING
* DIS # B3: 3,4 => CTR => B3: 6,8
* DIS # C3: 6,8 => CTR => C3: 3,4
* DIS # A6: 6,8 => CTR => A6: 9
* PRF # D1: 5,7 => SOL
* DIS # D1: 7,8 => CTR => D1: 3,5
* PRF # D1: 3,5 => SOL
* DIS # F9: 7,8 => CTR => F9: 9
* DIS # B3: 3,4 => CTR => B3: 6,8
* PRF # D1: 3,5 => SOL
* DIS # D1: 7,8 => CTR => D1: 3,5
* DIS # D2: 2,3 => CTR => D2: 9
* DIS # A6: 6,8 => CTR => A6: 9
* DIS # C3: 6,8 => CTR => C3: 3,4
* DIS # C7: 6,8 => CTR => C7: 2,5
* DIS # E7: 7,9 => CTR => E7: 2
* PRF # E7: 2 => SOL
* DIS # F9: 8 => CTR => F9: 7,9
* PRF # D1: 3,5 => SOL
* DIS # D1: 7,8 => CTR => D1: 3,5
* DIS # C7: 2,8 => CTR => C7: 5,6
* PRF # C9: 2,8 => SOL
* DIS # C9: 4 => CTR => C9: 2,8
* DIS # D7: 2,9 => CTR => D7: 7,8
* DIS # B8: 7,8 => CTR => B8: 9
* DIS # B9: 7,8 => CTR => B9: 4,9
* PRF # D9: 7,8 => SOL
* DIS # D9: 2,9 => CTR => D9: 7,8
* DIS # F9: 7,8 => CTR => F9: 9
* CNT  28 HDP CHAINS /  50 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B2,B4,C4,C6,C8,D3,D6,E1,E5,E6,F1,F3,F5,F6,G7,G8,H8,H9,I1,I2,I3)
* 219...64.5.7..681.....1.79.7..1824694216..358......127.....1.341..435..63...6.5.1
* PAIR B2: 3,4 BLK 1
B3: 3,4,6,8                              # reduction candidate for 3,4
B3: 3,4 => CTR
* 219...64.5.7.26813.3.5147927531824694216..358...3..127..5..1.341.24359.63.426.5.1
* RESTART
* PAIR A3: 6,8 COL A
A6: 6,8,9                                # reduction candidate for 6,8
A6: 6,8 => CTR
* 219..864.5.7926813..351479273518246942169.358.9....1279....12341.24359.63..2695.1
* RESTART
* PAIR RESTART
* PAIR E1: 5,7 BLK 2
D1: 5,7,3,8                              # reduction candidate for 5,7
D1: 5,7 => SOLVED
* 219578643537946812864213795753182469421697358986354127675821934198435276342769581
* DURATION: 0:00:03.484174  START: 05:14:08.089319  END: 05:14:11.573493 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190411-absurd-base-pr-001.dot
* REASONING
* DIS # B3: 3,4 => CTR => B3: 6,8
* DIS B3: 6,8 # A6: 6,8 => CTR => A6: 9
* PRF B3: 6,8 + A6: 9 # D1: 5,7 => SOL
* STA B3: 6,8 + A6: 9 + D1: 5,7
* CNT   3 HDP CHAINS /   3 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190411, absurd

Solution

position: 219578643537946812864213795753182469421697358986354127675821934198435276342769581 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 # B3: 3,4 => CTR => B3: 6,8
* INC # B3: 6,8 => UNS
* INC # C3: 3,4 => UNS
* INC # B3: 6,8 => UNS
* DIS # C3: 6,8 => CTR => C3: 3,4
* INC # C3: 3,4 => UNS
* DIS # A6: 6,8 => CTR => A6: 9
* INC # A6: 9 => UNS
* INC # A7: 6,8 => UNS
* PRF # D1: 5,7 => SOL
* INC # D1: 3,8 => UNS
* DIS # D1: 7,8 => CTR => D1: 3,5
* PRF # D1: 3,5 => SOL
* DIS # F9: 7,8 => CTR => F9: 9
* INC # F9: 9 => UNS
* DIS # B3: 3,4 => CTR => B3: 6,8
* INC # B3: 6,8 => UNS
* INC # C3: 3,4 => UNS
* PRF # D1: 3,5 => SOL
* DIS # D1: 7,8 => CTR => D1: 3,5
* DIS # D2: 2,3 => CTR => D2: 9
* INC # D2: 9 => UNS
* DIS # A6: 6,8 => CTR => A6: 9
* INC # A6: 9 => UNS
* INC # B6: 6,8 => UNS
* DIS # C3: 6,8 => CTR => C3: 3,4
* INC # C3: 3,4 => UNS
* DIS # C7: 6,8 => CTR => C7: 2,5
* INC # C7: 2,5 => UNS
* DIS # E7: 7,9 => CTR => E7: 2
* PRF # E7: 2 => SOL
* INC # F9: 7,9 => UNS
* DIS # F9: 8 => CTR => F9: 7,9
* PRF # D1: 3,5 => SOL
* DIS # D1: 7,8 => CTR => D1: 3,5
* DIS # C7: 2,8 => CTR => C7: 5,6
* INC # C7: 5,6 => UNS
* PRF # C9: 2,8 => SOL
* DIS # C9: 4 => CTR => C9: 2,8
* DIS # D7: 2,9 => CTR => D7: 7,8
* INC # D7: 7,8 => UNS
* INC # E7: 2,9 => UNS
* DIS # B8: 7,8 => CTR => B8: 9
* INC # B8: 9 => UNS
* DIS # B9: 7,8 => CTR => B9: 4,9
* INC # B9: 4,9 => UNS
* PRF # D9: 7,8 => SOL
* DIS # D9: 2,9 => CTR => D9: 7,8
* DIS # F9: 7,8 => CTR => F9: 9
* INC # F9: 9 => UNS
* CNT  50 HDP CHAINS /  50 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B3: 3,4 => CTR => B3: 6,8
* DIS B3: 6,8 # A6: 6,8 => CTR => A6: 9
* PRF B3: 6,8 + A6: 9 # D1: 5,7 => SOL
* STA B3: 6,8 + A6: 9 + D1: 5,7
* CNT   3 HDP CHAINS /   3 HYP OPENED