Analysis of zz-www.sudokuoftheday.co.uk-20060703-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: 12....5........1374.7...........38.6.6.....2..5.9..3...46..1.......58..28...6.... initial

Autosolve

position: 12....5..6.5..21374.7...2.......38.6.6.....2..5.9.63..546..1.......586.28.2.6.... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B3: 3,9 => CTR => B3: 8
* DIS # B3: 3 => CTR => B3: 8,9
* DIS # E2: 8,9 => CTR => E2: 4
* DIS # F9: 4 => CTR => F9: 7,9
* DIS # E2: 9 => CTR => E2: 4,8
* DIS # D5: 4,8 => CTR => D5: 1,5,7
* DIS # H3: 8,9 => CTR => H3: 6
* DIS # E3: 8,9 => CTR => E3: 1,3
* PRF # I7: 8,9 => SOL
* PRF # H4: 1,4 => SOL
* DIS # I5: 1,4 => CTR => I5: 5,9
* DIS # I9: 1,4 => CTR => I9: 3,5,9
* PRF # H7: 7,9 => SOL
* DIS # H8: 7,9 => CTR => H8: 1,4
* DIS # G9: 7,9 => CTR => G9: 4
* DIS # H9: 7,9 => CTR => H9: 1,4,5
* DIS # G5: 4 => CTR => G5: 7,9
* CNT  17 HDP CHAINS /  52 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: 3,9 => CTR => B3: 8
* DIS B3: 8 # F9: 4 => CTR => F9: 7,9
* DIS B3: 8 + F9: 7,9 # A4: 2,7 => CTR => A4: 9
* DIS B3: 8 + F9: 7,9 + A4: 9 # C6: 8 => CTR => C6: 1,4
* DIS B3: 8 + F9: 7,9 + A4: 9 + C6: 1,4 # D4: 1,2 => CTR => D4: 5
* PRF B3: 8 + F9: 7,9 + A4: 9 + C6: 1,4 + D4: 5 => SOL
* STA B3: 8 + F9: 7,9 + A4: 9 + C6: 1,4 + D4: 5
* CNT   6 HDP CHAINS /   7 HYP OPENED

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

Details

Positions

12....5........1374.7...........38.6.6.....2..5.9..3...46..1.......58..28...6.... initial
12....5..6.5..21374.7...2.......38.6.6.....2..5.9.63..546..1.......586.28.2.6.... autosolve
123697584695842137487315269971523846368174925254986371546231798739458612812769453 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
C1: 3,9
B2: 8,9
F1: 7,9
D2: 4,8
F3: 5,9
I3: 8,9
A6: 2,7
I6: 1,4
G7: 7,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D3,E3: 1.. / D3 = 1  =>  9 pairs (_) / E3 = 1  =>  9 pairs (_)
A4,A6: 2.. / A4 = 2  =>  0 pairs (X) / A6 = 2  =>  9 pairs (_)
D7,E7: 2.. / D7 = 2  =>  9 pairs (_) / E7 = 2  =>  0 pairs (X)
A6,E6: 2.. / A6 = 2  =>  9 pairs (_) / E6 = 2  =>  0 pairs (X)
D4,D7: 2.. / D4 = 2  =>  0 pairs (X) / D7 = 2  =>  9 pairs (_)
C1,B3: 3.. / C1 = 3  => 14 pairs (_) / B3 = 3  =>  0 pairs (X)
A5,C5: 3.. / A5 = 3  => 10 pairs (_) / C5 = 3  =>  0 pairs (X)
I7,I9: 3.. / I7 = 3  => 11 pairs (_) / I9 = 3  =>  0 pairs (*)
A5,A8: 3.. / A5 = 3  => 10 pairs (_) / A8 = 3  =>  0 pairs (X)
D2,E2: 4.. / D2 = 4  =>  0 pairs (X) / E2 = 4  => 14 pairs (_)
H1,I1: 4.. / H1 = 4  => 19 pairs (_) / I1 = 4  => 11 pairs (_)
D8,H8: 4.. / D8 = 4  => 19 pairs (_) / H8 = 4  =>  0 pairs (X)
F5,F9: 4.. / F5 = 4  => 19 pairs (_) / F9 = 4  =>  0 pairs (X)
G5,G9: 4.. / G5 = 4  =>  0 pairs (X) / G9 = 4  => 19 pairs (_)
D3,F3: 5.. / D3 = 5  =>  0 pairs (X) / F3 = 5  =>  9 pairs (_)
H4,I5: 5.. / H4 = 5  => 13 pairs (_) / I5 = 5  =>  9 pairs (_)
H9,I9: 5.. / H9 = 5  =>  9 pairs (_) / I9 = 5  => 13 pairs (_)
D4,H4: 5.. / D4 = 5  =>  9 pairs (_) / H4 = 5  => 13 pairs (_)
F3,F5: 5.. / F3 = 5  =>  9 pairs (_) / F5 = 5  =>  0 pairs (X)
H4,H9: 5.. / H4 = 5  => 13 pairs (_) / H9 = 5  =>  9 pairs (_)
I5,I9: 5.. / I5 = 5  =>  9 pairs (_) / I9 = 5  => 13 pairs (_)
D1,D3: 6.. / D1 = 6  =>  9 pairs (_) / D3 = 6  =>  0 pairs (X)
H1,H3: 6.. / H1 = 6  =>  0 pairs (X) / H3 = 6  =>  9 pairs (_)
D1,H1: 6.. / D1 = 6  =>  9 pairs (_) / H1 = 6  =>  0 pairs (X)
D3,H3: 6.. / D3 = 6  =>  0 pairs (X) / H3 = 6  =>  9 pairs (_)
B2,B3: 8.. / B2 = 8  =>  0 pairs (X) / B3 = 8  => 16 pairs (_)
C5,C6: 8.. / C5 = 8  => 18 pairs (_) / C6 = 8  =>  9 pairs (_)
H7,I7: 8.. / H7 = 8  => 11 pairs (_) / I7 = 8  =>  0 pairs (*)
C6,E6: 8.. / C6 = 8  =>  9 pairs (_) / E6 = 8  => 18 pairs (_)
E7,F9: 9.. / E7 = 9  =>  0 pairs (X) / F9 = 9  => 16 pairs (_)
B2,E2: 9.. / B2 = 9  => 16 pairs (_) / E2 = 9  =>  0 pairs (X)
* DURATION: 0:00:30.677789  START: 00:17:53.906591  END: 00:18:24.584380 2019-05-01
* CP COUNT: (31)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B2,C1,D2,F1,F3,G7,I3,I6)
* 12....5..6.5..21374.7...2.......38.6.6.....2..5.9.63..546..1.......586.28.2.6....
* PAIR C1: 3,9 BLK 1
B3: 3,9,8                                # reduction candidate for 3,9
B3: 3,9 => CTR
* 12....5..6854921374.7..52.......38.6.6.....2..5.9.63..546..1.......586.28.2.6....
B3: 8                                    # 16 pairs
* PAIR C1: 3,9 ROW 1
E1: 3,9,7,8                              # reduction candidate for 3,9
E1: 3,9                                  # 16 pairs
E1: 7,8                                  # 12 pairs
* PAIR C1: 3,9 COL C
C5: 3,9,1,4,8                            # reduction candidate for 3,9
C5: 3,9                                  # 16 pairs
C8: 3,9,1                                # reduction candidate for 3,9
C8: 3,9                                  # 13 pairs
* PAIR B2: 8,9 BLK 1
B3: 8,9,3                                # reduction candidate for 8,9
B3: 3 => CTR
* 12....5..685492137437..52.......38.6.6.....2..5.9.63..546..1.......586.28.2.6....
B3: 8,9                                  # 14 pairs
* PAIR B2: 8,9 ROW 2
E2: 8,9,4                                # reduction candidate for 8,9
E2: 8,9 => CTR
* 12....5.4695482137487...2.9.....38.6.6....42..5.9.63.1546.91783....586428.2.64915
E2: 4                                    # 14 pairs
* PAIR F1: 7,9 BLK 2
E1: 7,9,3,8                              # reduction candidate for 7,9
E1: 7,9                                  # 16 pairs
E1: 3,8                                  # 10 pairs
* PAIR F1: 7,9 COL F
F9: 7,9,4                                # reduction candidate for 7,9
F9: 4 => CTR
* 12....5..695..2137487...2.9.....3896.6....425.5.9.63..546.91783....586.28.2.649..
F9: 7,9                                  # 19 pairs
* PAIR D2: 4,8 BLK 2
E2: 4,8,9                                # reduction candidate for 4,8
E2: 9 => CTR
* 12....5..6.54921374.7..52.......38.6.6.....2..5.9.63..546..1.......586.28.2.6....
E2: 4,8                                  # 16 pairs
* PAIR D2: 4,8 COL D
D5: 4,8,1,5,7                            # reduction candidate for 4,8
D5: 4,8 => CTR
* 12.6875946.5..21374.7...26......38.6.6....42..5.9.63.1546291783....586428.2.64915
D5: 1,5,7                                # 14 pairs
* PAIR I3: 8,9 BLK 3
H1: 8,9,4,6                              # reduction candidate for 8,9
H1: 8,9                                  # 12 pairs
I1: 8,9,4                                # reduction candidate for 8,9
I1: 8,9                                  # 19 pairs
H3: 8,9,6                                # reduction candidate for 8,9
H3: 8,9 => CTR
* 129..75646854921374376152.......38.6.6...4.2..5.9.63.1546..1.......586.28.2.6....
H3: 6                                    #  9 pairs
* PAIR I3: 8,9 ROW 3
B3: 8,9,3                                # reduction candidate for 8,9
B3: 8,9                                  # 14 pairs
E3: 8,9,1,3                              # reduction candidate for 8,9
E3: 8,9 => CTR
* 1296375..685..21374371.526......38.6.6...4.2..5.9.63..546..1.......586.28.2.694..
E3: 1,3                                  # 10 pairs
* PAIR I3: 8,9 COL I
I7: 8,9,3                                # reduction candidate for 8,9
I7: 8,9 => SOLVED
* 123697584695842137487315269971523846368174925254986371546231798739458612812769453
I7: 3                                    # 11 pairs
* PAIR A6: 2,7 BLK 4
A4: 2,7,9                                # reduction candidate for 2,7
A4: 2,7                                  # 13 pairs
A4: 9                                    # 12 pairs
* PAIR A6: 2,7 ROW 6
E6: 2,7,1,4,8                            # reduction candidate for 2,7
E6: 2,7                                  # 22 pairs
E6: 1,4,8                                # 11 pairs
* PAIR I6: 1,4 BLK 6
H4: 1,4,5,7,9                            # reduction candidate for 1,4
H4: 1,4 => SOLVED
* 123697584695842137487315269971523846368174925254986371546231798739458612812769453
H4: 5,7,9                                #  9 pairs
I5: 1,4,5,9                              # reduction candidate for 1,4
I5: 1,4 => CTR
* 12.679548695842137487.35269..4..3856.6.584921258916374546291783.3.4586.28.23674.5
I5: 5,9                                  # 10 pairs
H6: 1,4,7                                # reduction candidate for 1,4
H6: 1,4                                  # 22 pairs
* PAIR I6: 1,4 ROW 6
C6: 1,4,8                                # reduction candidate for 1,4
C6: 1,4                                  # 18 pairs
E6: 1,4,2,7,8                            # reduction candidate for 1,4
E6: 1,4                                  # 12 pairs
* PAIR I6: 1,4 COL I
I9: 1,4,3,5,9                            # reduction candidate for 1,4
I9: 1,4 => CTR
* 12.6..54.6.5842137487135269..45.38.6.6.7.4925.5.9.63.4546291783.3.45869289236..5.
I9: 3,5,9                                # 10 pairs
* PAIR G7: 7,9 BLK 9
H7: 7,9,8                                # reduction candidate for 7,9
H7: 7,9 => SOLVED
* 123697584695842137487315269971523846368174925254986371546231798739458612812769453
H7: 8                                    # 11 pairs
H8: 7,9,1,4                              # reduction candidate for 7,9
H8: 7,9 => CTR
* 123697548695842137487135269.14..3896369584721.5.9.63.4546..19839314586728723694..
H8: 1,4                                  # 10 pairs
G9: 7,9,4                                # reduction candidate for 7,9
G9: 7,9 => CTR
* 12....5.4695..2137487...2.9.....38.6.6....42..5.9.6371546.91783....586428.2.64915
G9: 4                                    # 19 pairs
H9: 7,9,1,4,5                            # reduction candidate for 7,9
H9: 7,9 => CTR
* 12....5..6.5842137487.352.9..4..3856.6.5.4921.51986374546.91783.39458612812367495
H9: 1,4,5                                #  9 pairs
* PAIR G7: 7,9 ROW 7
E7: 7,9,2,3                              # reduction candidate for 7,9
E7: 2,3                                  # 20 pairs
E7: 7,9                                  # 11 pairs
* PAIR G7: 7,9 COL G
G5: 7,9,4                                # reduction candidate for 7,9
G5: 4 => CTR
* 12....5.4695..2137487...2.9.....38.6.6....42..5.9.6371546.91783....586428.2.64915
G5: 7,9                                  # 19 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060703-absurd-base-pr-000.dot
* REASONING
* DIS # B3: 3,9 => CTR => B3: 8
* DIS # B3: 3 => CTR => B3: 8,9
* DIS # E2: 8,9 => CTR => E2: 4
* DIS # F9: 4 => CTR => F9: 7,9
* DIS # E2: 9 => CTR => E2: 4,8
* DIS # D5: 4,8 => CTR => D5: 1,5,7
* DIS # H3: 8,9 => CTR => H3: 6
* DIS # E3: 8,9 => CTR => E3: 1,3
* PRF # I7: 8,9 => SOL
* PRF # H4: 1,4 => SOL
* DIS # I5: 1,4 => CTR => I5: 5,9
* DIS # I9: 1,4 => CTR => I9: 3,5,9
* PRF # H7: 7,9 => SOL
* DIS # H8: 7,9 => CTR => H8: 1,4
* DIS # G9: 7,9 => CTR => G9: 4
* DIS # H9: 7,9 => CTR => H9: 1,4,5
* DIS # G5: 4 => CTR => G5: 7,9
* CNT  17 HDP CHAINS /  52 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B2,C1,D2,F1,F3,G7,I3,I6)
* 12....5..6.5..21374.7...2.......38.6.6.....2..5.9.63..546..1.......586.28.2.6....
* PAIR C1: 3,9 BLK 1
B3: 3,9,8                                # reduction candidate for 3,9
B3: 3,9 => CTR
* 12....5..6854921374.7..52.......38.6.6.....2..5.9.63..546..1.......586.28.2.6....
* PAIR F1: 7,9 COL F
F9: 7,9,4                                # reduction candidate for 7,9
F9: 4 => CTR
* 123679548695..2137487.35269.....3896369..7425.58946371546.91783....586.28.2.649..
* PAIR RESTART
* PAIR A6: 2,7 BLK 4
A4: 2,7,9                                # reduction candidate for 2,7
A4: 2,7 => CTR
* 123697548695842137487135269.14..3896369584721.5.9.63..546..19839314586728723694..
* PAIR I6: 1,4 ROW 6
C6: 1,4,8                                # reduction candidate for 1,4
C6: 8 => CTR
* 1236..5..695842137487..5269974..3856361..492.25.9.637.546..17..739458612812.6.4..
* PAIR RESTART

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (C4,C6,D3,D7,D9,E1,E3,E4,E5,F1,F9,H1,H4,H7,H9,I1,I5,I6,I7,I9)
* 1236..5..695842137487..526997...38.6368..492.25.98637.546..17..739458612812.6.4..
* PAIR E4: 1,2 BLK 5
D4: 1,2,5                                # reduction candidate for 1,2
D4: 1,2 => CTR
* 1236..5..695842137487..526997...3856368574921251986374546..17..7394586128127694..
D4: 5 => SOLVED
* 123697584695842137487315269971523846368174925254986371546231798739458612812769453
* DURATION: 0:00:08.189382  START: 00:18:54.191484  END: 00:19:02.380866 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060703-absurd-base-pr-001.dot
* REASONING
* DIS # B3: 3,9 => CTR => B3: 8
* DIS B3: 8 # F9: 4 => CTR => F9: 7,9
* DIS B3: 8 + F9: 7,9 # A4: 2,7 => CTR => A4: 9
* DIS B3: 8 + F9: 7,9 + A4: 9 # C6: 8 => CTR => C6: 1,4
* DIS B3: 8 + F9: 7,9 + A4: 9 + C6: 1,4 # D4: 1,2 => CTR => D4: 5
* PRF B3: 8 + F9: 7,9 + A4: 9 + C6: 1,4 + D4: 5 => SOL
* STA B3: 8 + F9: 7,9 + A4: 9 + C6: 1,4 + D4: 5
* CNT   6 HDP CHAINS /   7 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060703, absurd

Solution

position: 123697584695842137487315269971523846368174925254986371546231798739458612812769453 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: 3,9 => CTR => B3: 8
* INC # B3: 8 => UNS
* INC # E1: 3,9 => UNS
* INC # E1: 7,8 => UNS
* INC # C5: 3,9 => UNS
* INC # C8: 3,9 => UNS
* INC # B3: 8,9 => UNS
* DIS # B3: 3 => CTR => B3: 8,9
* DIS # E2: 8,9 => CTR => E2: 4
* INC # E2: 4 => UNS
* INC # E1: 7,9 => UNS
* INC # E1: 3,8 => UNS
* INC # F9: 7,9 => UNS
* DIS # F9: 4 => CTR => F9: 7,9
* INC # E2: 4,8 => UNS
* DIS # E2: 9 => CTR => E2: 4,8
* DIS # D5: 4,8 => CTR => D5: 1,5,7
* INC # D5: 1,5,7 => UNS
* INC # H1: 8,9 => UNS
* INC # I1: 8,9 => UNS
* DIS # H3: 8,9 => CTR => H3: 6
* INC # H3: 6 => UNS
* INC # B3: 8,9 => UNS
* DIS # E3: 8,9 => CTR => E3: 1,3
* INC # E3: 1,3 => UNS
* PRF # I7: 8,9 => SOL
* INC # I7: 3 => UNS
* INC # A4: 2,7 => UNS
* INC # A4: 9 => UNS
* INC # E6: 2,7 => UNS
* INC # E6: 1,4,8 => UNS
* PRF # H4: 1,4 => SOL
* INC # H4: 5,7,9 => UNS
* DIS # I5: 1,4 => CTR => I5: 5,9
* INC # I5: 5,9 => UNS
* INC # H6: 1,4 => UNS
* INC # C6: 1,4 => UNS
* INC # E6: 1,4 => UNS
* DIS # I9: 1,4 => CTR => I9: 3,5,9
* INC # I9: 3,5,9 => UNS
* PRF # H7: 7,9 => SOL
* INC # H7: 8 => UNS
* DIS # H8: 7,9 => CTR => H8: 1,4
* INC # H8: 1,4 => UNS
* DIS # G9: 7,9 => CTR => G9: 4
* INC # G9: 4 => UNS
* DIS # H9: 7,9 => CTR => H9: 1,4,5
* INC # H9: 1,4,5 => UNS
* INC # E7: 7,9 => UNS
* INC # E7: 2,3 => UNS
* INC # G5: 7,9 => UNS
* DIS # G5: 4 => CTR => G5: 7,9
* CNT  52 HDP CHAINS /  52 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B3: 3,9 => CTR => B3: 8
* INC B3: 8 # F9: 7,9 => UNS
* DIS B3: 8 # F9: 4 => CTR => F9: 7,9
* DIS B3: 8 + F9: 7,9 # A4: 2,7 => CTR => A4: 9
* INC B3: 8 + F9: 7,9 + A4: 9 # C6: 1,4 => UNS
* DIS B3: 8 + F9: 7,9 + A4: 9 # C6: 8 => CTR => C6: 1,4
* DIS B3: 8 + F9: 7,9 + A4: 9 + C6: 1,4 # D4: 1,2 => CTR => D4: 5
* PRF B3: 8 + F9: 7,9 + A4: 9 + C6: 1,4 + D4: 5 => SOL
* STA B3: 8 + F9: 7,9 + A4: 9 + C6: 1,4 + D4: 5
* CNT   8 HDP CHAINS /   7 HYP OPENED