Analysis of zz-www.sudokuoftheday.co.uk-20060710-absurd-base.sdk

Contents

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

level: medium

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

position: .1...23...63.9.....9..43.62....3.4218....5..9.....95....1.........25....6.5...2.7 initial

Autosolve

position: .1...239.263.9.....9..43.62.5..3.42183...56791....9583.213.....3..25....6.59..237 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 5,7 => CTR => A1: 4
* DIS # C1: 4 => CTR => C1: 7,8
* DIS # G3: 7,8 => CTR => G3: 1
* DIS # C4: 7,9 => CTR => C4: 6
* DIS # A7: 4 => CTR => A7: 7,9
* PRF # C6: 2,4 => SOL
* DIS # C6: 6,7 => CTR => C6: 2,4
* DIS # C6: 4,7 => CTR => C6: 2,6
* DIS # D6: 6 => CTR => D6: 4,7
* PRF # B8: 4,7 => SOL
* DIS # B8: 8 => CTR => B8: 4,7
* PRF # B8: 4,8 => SOL
* DIS # B8: 7 => CTR => B8: 4,8
* PRF # F9: 4,8 => SOL
* DIS # F9: 1 => CTR => F9: 4,8
* DIS # F9: 1,8 => CTR => F9: 4
* PRF # F9: 4 => SOL
* DIS # G8: 1 => CTR => G8: 8,9
* DIS # H2: 1 => CTR => H2: 4,5
* CNT  19 HDP CHAINS /  41 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 # A1: 5,7 => CTR => A1: 4
* DIS A1: 4 # G3: 7,8 => CTR => G3: 1
* PRF A1: 4 + G3: 1 # D1: 6,7 => SOL
* STA A1: 4 + G3: 1 + D1: 6,7
* CNT   3 HDP CHAINS /   7 HYP OPENED

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

Details

Positions

.1...23...63.9.....9..43.62....3.4218....5..9.....95....1.........25....6.5...2.7 initial
.1...239.263.9.....9..43.62.5..3.42183...56791....9583.213.....3..25....6.59..237 autosolve
418672395263591748597843162956738421834125679172469583721386954349257816685914237 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
A3: 5,7
C3: 7,8
I1: 5,8
A4: 7,9
C5: 2,4
B6: 4,7
D5: 1,4
E5: 1,2
B9: 4,8
E9: 1,8
G7: 8,9
H7: 4,5
H8: 1,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D5,E5: 1.. / D5 = 1  =>  0 pairs (*) / E5 = 1  =>  0 pairs (X)
E9,F9: 1.. / E9 = 1  =>  0 pairs (*) / F9 = 1  =>  0 pairs (X)
G8,H8: 1.. / G8 = 1  =>  0 pairs (X) / H8 = 1  => 17 pairs (_)
D3,G3: 1.. / D3 = 1  =>  0 pairs (X) / G3 = 1  => 16 pairs (_)
E5,E9: 1.. / E5 = 1  =>  0 pairs (X) / E9 = 1  =>  0 pairs (_)
F2,F9: 1.. / F2 = 1  =>  0 pairs (*) / F9 = 1  =>  0 pairs (X)
H2,H8: 1.. / H2 = 1  =>  0 pairs (X) / H8 = 1  => 17 pairs (_)
C5,C6: 2.. / C5 = 2  =>  0 pairs (X) / C6 = 2  =>  0 pairs (_)
E5,E6: 2.. / E5 = 2  =>  0 pairs (*) / E6 = 2  =>  0 pairs (X)
C5,E5: 2.. / C5 = 2  =>  0 pairs (X) / E5 = 2  =>  0 pairs (_)
C6,E6: 2.. / C6 = 2  =>  0 pairs (*) / E6 = 2  =>  0 pairs (X)
A1,C1: 4.. / A1 = 4  => 16 pairs (_) / C1 = 4  =>  0 pairs (X)
H2,I2: 4.. / H2 = 4  => 17 pairs (_) / I2 = 4  => 15 pairs (_)
D5,D6: 4.. / D5 = 4  =>  0 pairs (X) / D6 = 4  =>  0 pairs (_)
C5,D5: 4.. / C5 = 4  =>  0 pairs (*) / D5 = 4  =>  0 pairs (X)
B9,F9: 4.. / B9 = 4  =>  0 pairs (X) / F9 = 4  =>  0 pairs (_)
A1,A7: 4.. / A1 = 4  => 16 pairs (_) / A7 = 4  =>  0 pairs (X)
A1,A3: 5.. / A1 = 5  =>  0 pairs (X) / A3 = 5  => 13 pairs (_)
H7,I7: 5.. / H7 = 5  => 13 pairs (_) / I7 = 5  => 20 pairs (_)
A3,D3: 5.. / A3 = 5  => 13 pairs (_) / D3 = 5  =>  0 pairs (X)
H2,H7: 5.. / H2 = 5  => 20 pairs (_) / H7 = 5  => 13 pairs (_)
D1,E1: 6.. / D1 = 6  => 18 pairs (_) / E1 = 6  => 17 pairs (_)
C4,C6: 6.. / C4 = 6  => 18 pairs (_) / C6 = 6  =>  0 pairs (X)
I7,I8: 6.. / I7 = 6  => 19 pairs (_) / I8 = 6  => 13 pairs (_)
F8,I8: 6.. / F8 = 6  => 19 pairs (_) / I8 = 6  => 13 pairs (_)
G2,G3: 7.. / G2 = 7  => 15 pairs (_) / G3 = 7  =>  0 pairs (X)
B6,B8: 7.. / B6 = 7  =>  0 pairs (*) / B8 = 7  =>  0 pairs (X)
C1,C3: 8.. / C1 = 8  => 20 pairs (_) / C3 = 8  => 14 pairs (_)
D4,F4: 8.. / D4 = 8  => 14 pairs (_) / F4 = 8  => 18 pairs (_)
B8,B9: 8.. / B8 = 8  =>  0 pairs (X) / B9 = 8  =>  0 pairs (_)
A4,C4: 9.. / A4 = 9  => 14 pairs (_) / C4 = 9  =>  0 pairs (X)
A7,C8: 9.. / A7 = 9  =>  0 pairs (X) / C8 = 9  => 14 pairs (_)
G7,G8: 9.. / G7 = 9  => 14 pairs (_) / G8 = 9  =>  0 pairs (X)
A7,G7: 9.. / A7 = 9  =>  0 pairs (X) / G7 = 9  => 14 pairs (_)
C8,G8: 9.. / C8 = 9  => 14 pairs (_) / G8 = 9  =>  0 pairs (X)
A4,A7: 9.. / A4 = 9  => 14 pairs (_) / A7 = 9  =>  0 pairs (X)
C4,C8: 9.. / C4 = 9  =>  0 pairs (X) / C8 = 9  => 14 pairs (_)
* DURATION: 0:00:40.999414  START: 00:35:11.317940  END: 00:35:52.317354 2019-05-01
* CP COUNT: (37)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B6,B9,C3,C5,D5,E5,E9,G7,H7,H8,I1)
* .1...239.263.9.....9..43.62.5..3.42183...56791....9583.213.....3..25....6.59..237
* PAIR A3: 5,7 BLK 1
A1: 5,7,4                                # reduction candidate for 5,7
A1: 5,7 => CTR
* .14..239.263.9.....98.43.62.5..3.42183241567914..295834213..95.37925....6859..237
A1: 4                                    # 16 pairs
* PAIR A3: 5,7 ROW 3
D3: 5,7,1,8                              # reduction candidate for 5,7
D3: 5,7                                  # 17 pairs
D3: 1,8                                  # 14 pairs
* PAIR C3: 7,8 BLK 1
C1: 7,8,4                                # reduction candidate for 7,8
C1: 4 => CTR
* .14..239.263.9.....98.43.62.5..3.42183241567914..295834213..95.37925....6859..237
C1: 7,8                                  # 16 pairs
* PAIR C3: 7,8 ROW 3
D3: 7,8,1,5                              # reduction candidate for 7,8
D3: 7,8                                  # 17 pairs
G3: 7,8,1                                # reduction candidate for 7,8
G3: 7,8 => CTR
* 41...239.263.9....59.143.62.5..3.42183241567917462958372136....38.25....645981237
G3: 1                                    # 16 pairs
* PAIR I1: 5,8 BLK 3
I2: 5,8,4                                # reduction candidate for 5,8
I2: 5,8                                  # 17 pairs
I2: 4                                    # 15 pairs
* PAIR I1: 5,8 ROW 1
D1: 5,8,6,7                              # reduction candidate for 5,8
D1: 5,8                                  # 20 pairs
D1: 6,7                                  # 14 pairs
* PAIR I1: 5,8 COL I
I7: 5,8,4,6                              # reduction candidate for 5,8
I7: 5,8                                  # 15 pairs
I7: 4,6                                  # 14 pairs
* PAIR A4: 7,9 BLK 4
C4: 7,9,6                                # reduction candidate for 7,9
C4: 7,9 => CTR
* .1...239.263.9.....9..43.62.5..3.421832415679146729583.213.....37.25....6859..237
C4: 6                                    # 18 pairs
* PAIR A4: 7,9 COL A
A7: 7,9,4                                # reduction candidate for 7,9
A7: 4 => CTR
* .14..239.263.91.4..98.4316295..3.421832..56791....95834213..95.3.925....685914237
A7: 7,9                                  # 16 pairs
* PAIR C5: 2,4 BLK 4
C6: 2,4,6,7                              # reduction candidate for 2,4
C6: 2,4 => SOLVED
* 418672395263591748597843162956738421834125679172469583721386954349257816685914237
C6: 6,7 => CTR
* .1...239.263.9.....9..43.62.5..3.42183241567914..29583.213.....37.25....6859..237
* PAIR B6: 4,7 BLK 4
C6: 4,7,2,6                              # reduction candidate for 4,7
C6: 4,7 => CTR
* .1...239.263.9.....9..43.62956.3.4218324156791..629583.213..9.8389257146645981237
C6: 2,6                                  # 14 pairs
* PAIR B6: 4,7 ROW 6
D6: 4,7,6                                # reduction candidate for 4,7
D6: 6 => CTR
* .1..6239.263.9.....9..43.62.56.3.4218324156791..629583.2137....38.25....6.5981237
D6: 4,7                                  # 16 pairs
* PAIR B6: 4,7 COL B
B8: 4,7,8                                # reduction candidate for 4,7
B8: 4,7 => SOLVED
* 418672395263591748597843162956738421834125679172469583721386954349257816685914237
B8: 8 => CTR
* 41...239.263.9....59..43.62956.3.42183...567917...95837213..9.83892571466459..237
* PAIR B9: 4,8 BLK 7
B8: 4,8,7                                # reduction candidate for 4,8
B8: 4,8 => SOLVED
* 418672395263591748597843162956738421834125679172469583721386954349257816685914237
B8: 7 => CTR
* .1...239.263.91....9..43162.5..3.42183.12567914...9583.213.....37.25....685914237
* PAIR B9: 4,8 ROW 9
F9: 4,8,1                                # reduction candidate for 4,8
F9: 4,8 => SOLVED
* 418672395263591748597843162956738421834125679172469583721386954349257816685914237
F9: 1 => CTR
* 41.672395263598714597143.62.5..3.42183..1567917..29583721364958389257146645981237
* PAIR E9: 1,8 BLK 8
F9: 1,8,4                                # reduction candidate for 1,8
F9: 1,8 => CTR
* 41..7239.263.9.71459714386295673842183...567917...95837213..9..3892571466459..237
F9: 4 => SOLVED
* 418672395263591748597843162956738421834125679172469583721386954349257816685914237
* PAIR G7: 8,9 BLK 9
G8: 8,9,1                                # reduction candidate for 8,9
G8: 1 => CTR
* 41..72395263598714597143862956.3.4218324156791...29583.213.4958389257146645981237
G8: 8,9                                  # 17 pairs
* PAIR H7: 4,5 BLK 9
I7: 4,5,6,8                              # reduction candidate for 4,5
I7: 4,5                                  # 20 pairs
I7: 6,8                                  # 16 pairs
* PAIR H7: 4,5 COL H
H2: 4,5,1                                # reduction candidate for 4,5
H2: 1 => CTR
* 41..72395263598714597143862956.3.4218324156791...29583.213.4958389257146645981237
H2: 4,5                                  # 17 pairs
* PAIR H8: 1,4 COL H
H2: 1,4,5                                # reduction candidate for 1,4
H2: 5                                    # 20 pairs
H2: 1,4                                  # 13 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060710-absurd-base-pr-000.dot
* REASONING
* DIS # A1: 5,7 => CTR => A1: 4
* DIS # C1: 4 => CTR => C1: 7,8
* DIS # G3: 7,8 => CTR => G3: 1
* DIS # C4: 7,9 => CTR => C4: 6
* DIS # A7: 4 => CTR => A7: 7,9
* PRF # C6: 2,4 => SOL
* DIS # C6: 6,7 => CTR => C6: 2,4
* DIS # C6: 4,7 => CTR => C6: 2,6
* DIS # D6: 6 => CTR => D6: 4,7
* PRF # B8: 4,7 => SOL
* DIS # B8: 8 => CTR => B8: 4,7
* PRF # B8: 4,8 => SOL
* DIS # B8: 7 => CTR => B8: 4,8
* PRF # F9: 4,8 => SOL
* DIS # F9: 1 => CTR => F9: 4,8
* DIS # F9: 1,8 => CTR => F9: 4
* PRF # F9: 4 => SOL
* DIS # G8: 1 => CTR => G8: 8,9
* DIS # H2: 1 => CTR => H2: 4,5
* CNT  19 HDP CHAINS /  41 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B6,B9,C3,C5,D5,E5,E9,G7,H7,H8,I1)
* .1...239.263.9.....9..43.62.5..3.42183...56791....9583.213.....3..25....6.59..237
* PAIR A3: 5,7 BLK 1
A1: 5,7,4                                # reduction candidate for 5,7
A1: 5,7 => CTR
* .14..239.263.9.....98.43.62.5..3.42183241567914..295834213..95.37925....6859..237
* PAIR C3: 7,8 ROW 3
D3: 7,8,1                                # reduction candidate for 7,8
D3: 7,8                                  # 20 pairs
G3: 7,8,1                                # reduction candidate for 7,8
G3: 7,8 => CTR
* 41..7239.263.98714597143862.5.83642183241567917..29583.213.....38.257..6645981237
* RESTART
* PAIR RESTART
* PAIR I1: 5,8 BLK 3
I2: 5,8,4                                # reduction candidate for 5,8
I2: 4                                    # 21 pairs
I2: 5,8                                  # 20 pairs
* PAIR I1: 5,8 ROW 1
D1: 5,8,6,7                              # reduction candidate for 5,8
D1: 6,7 => SOLVED
* 418672395263591748597843162956738421834125679172469583721386954349257816685914237
* DURATION: 0:00:06.619527  START: 00:36:18.404036  END: 00:36:25.023563 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060710-absurd-base-pr-001.dot
* REASONING
* DIS # A1: 5,7 => CTR => A1: 4
* DIS A1: 4 # G3: 7,8 => CTR => G3: 1
* PRF A1: 4 + G3: 1 # D1: 6,7 => SOL
* STA A1: 4 + G3: 1 + D1: 6,7
* CNT   3 HDP CHAINS /   7 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060710, absurd

Solution

position: 418672395263591748597843162956738421834125679172469583721386954349257816685914237 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 # A1: 5,7 => CTR => A1: 4
* INC # A1: 4 => UNS
* INC # D3: 5,7 => UNS
* INC # D3: 1,8 => UNS
* INC # C1: 7,8 => UNS
* DIS # C1: 4 => CTR => C1: 7,8
* INC # D3: 7,8 => UNS
* DIS # G3: 7,8 => CTR => G3: 1
* INC # G3: 1 => UNS
* INC # I2: 5,8 => UNS
* INC # I2: 4 => UNS
* INC # D1: 5,8 => UNS
* INC # D1: 6,7 => UNS
* INC # I7: 5,8 => UNS
* INC # I7: 4,6 => UNS
* DIS # C4: 7,9 => CTR => C4: 6
* INC # C4: 6 => UNS
* INC # A7: 7,9 => UNS
* DIS # A7: 4 => CTR => A7: 7,9
* PRF # C6: 2,4 => SOL
* DIS # C6: 6,7 => CTR => C6: 2,4
* DIS # C6: 4,7 => CTR => C6: 2,6
* INC # C6: 2,6 => UNS
* INC # D6: 4,7 => UNS
* DIS # D6: 6 => CTR => D6: 4,7
* PRF # B8: 4,7 => SOL
* DIS # B8: 8 => CTR => B8: 4,7
* PRF # B8: 4,8 => SOL
* DIS # B8: 7 => CTR => B8: 4,8
* PRF # F9: 4,8 => SOL
* DIS # F9: 1 => CTR => F9: 4,8
* DIS # F9: 1,8 => CTR => F9: 4
* PRF # F9: 4 => SOL
* INC # G8: 8,9 => UNS
* DIS # G8: 1 => CTR => G8: 8,9
* INC # I7: 4,5 => UNS
* INC # I7: 6,8 => UNS
* INC # H2: 4,5 => UNS
* DIS # H2: 1 => CTR => H2: 4,5
* INC # H2: 1,4 => UNS
* INC # H2: 5 => UNS
* CNT  41 HDP CHAINS /  41 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A1: 5,7 => CTR => A1: 4
* INC A1: 4 # D3: 7,8 => UNS
* DIS A1: 4 # G3: 7,8 => CTR => G3: 1
* INC A1: 4 + G3: 1 # I2: 5,8 => UNS
* INC A1: 4 + G3: 1 # I2: 4 => UNS
* INC A1: 4 + G3: 1 # D1: 5,8 => UNS
* PRF A1: 4 + G3: 1 # D1: 6,7 => SOL
* STA A1: 4 + G3: 1 + D1: 6,7
* CNT   7 HDP CHAINS /   7 HYP OPENED