Analysis of zz-www.sudokuoftheday.co.uk-20060501-absurd-base.sdk

Contents

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

level: medium

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

position: ....4.....2.9..3.759.1.7....3..2.7......34892.........1...729.........2..6.89.1.. initial

Autosolve

position: ...243..9.2.95.3.75931.72...3..2.7......34892.........1...729.........2..6.89517. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # H2: 6,8 => CTR => H2: 1
* DIS # H3: 6,8 => CTR => H3: 4
* DIS # H1: 1,8 => CTR => H1: 5,6
* DIS # G6: 5,6 => CTR => G6: 4
* PRF # G6: 4 => SOL
* DIS # A6: 6,7 => CTR => A6: 2,4,8,9
* DIS # C4: 5,6 => CTR => C4: 4,8,9
* DIS # I4: 5,6 => CTR => I4: 1,4
* DIS # A9: 2,4 => CTR => A9: 3
* PRF # A9: 3 => SOL
* DIS # C6: 2,4 => CTR => C6: 5,6,7,8,9
* DIS # H7: 3,4 => CTR => H7: 5,6,8
* DIS # I7: 3,4 => CTR => I7: 5,6,8
* DIS # A8: 3,4 => CTR => A8: 7,8,9
* PRF # A8: 7,8,9 => SOL
* PRF # I8: 3,4 => SOL
* DIS # H7: 4,5 => CTR => H7: 3,6,8
* DIS # I7: 4,5 => CTR => I7: 3,6,8
* DIS # I8: 4,5 => CTR => I8: 3,8
* DIS # B8: 4,5 => CTR => B8: 7,8
* DIS # C8: 4,5 => CTR => C8: 7,8,9
* DIS # G6: 6 => CTR => G6: 4,5
* DIS # H7: 3,4 => CTR => H7: 5,6,8
* DIS # I7: 3,4 => CTR => I7: 5,6,8
* PRF # I8: 3,4 => SOL
* DIS # A9: 2 => CTR => A9: 3,4
* DIS # I6: 3,4 => CTR => I6: 1,5,6
* CNT  27 HDP CHAINS /  62 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 # H2: 6,8 => CTR => H2: 1
* DIS H2: 1 # H3: 6,8 => CTR => H3: 4
* PRF H2: 1 + H3: 4 # H1: 5,6 => SOL
* STA H2: 1 + H3: 4 + H1: 5,6
* CNT   3 HDP CHAINS /   7 HYP OPENED

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

Details

Positions

....4.....2.9..3.759.1.7....3..2.7......34892.........1...729.........2..6.89.1.. initial
...243..9.2.95.3.75931.72...3..2.7......34892.........1...729.........2..6.89517. autosolve
718243659426958317593167248834529761651734892279681435145372986987416523362895174 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
F2: 6,8
E3: 6,8
G1: 5,6
A5: 6,7
D4: 5,6
E6: 1,8
C9: 2,4
D7: 3,4
D8: 3,4
E8: 1,6
F8: 1,6
G8: 4,5
I9: 3,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H1,H2: 1.. / H1 = 1  =>  0 pairs (X) / H2 = 1  => 13 pairs (_)
B5,C5: 1.. / B5 = 1  => 14 pairs (_) / C5 = 1  => 14 pairs (_)
I4,I6: 1.. / I4 = 1  => 14 pairs (_) / I6 = 1  =>  0 pairs (X)
E8,F8: 1.. / E8 = 1  => 14 pairs (_) / F8 = 1  =>  0 pairs (X)
C2,H2: 1.. / C2 = 1  =>  0 pairs (X) / H2 = 1  => 13 pairs (_)
F4,I4: 1.. / F4 = 1  =>  0 pairs (X) / I4 = 1  => 14 pairs (_)
B1,B5: 1.. / B1 = 1  => 14 pairs (_) / B5 = 1  => 14 pairs (_)
E6,E8: 1.. / E6 = 1  =>  0 pairs (X) / E8 = 1  => 14 pairs (_)
A6,C6: 2.. / A6 = 2  => 13 pairs (_) / C6 = 2  =>  0 pairs (X)
A9,C9: 2.. / A9 = 2  =>  0 pairs (X) / C9 = 2  => 13 pairs (_)
A6,A9: 2.. / A6 = 2  => 13 pairs (_) / A9 = 2  =>  0 pairs (X)
C6,C9: 2.. / C6 = 2  =>  0 pairs (X) / C9 = 2  => 13 pairs (_)
H6,I6: 3.. / H6 = 3  => 13 pairs (_) / I6 = 3  =>  0 pairs (X)
A8,A9: 3.. / A8 = 3  =>  0 pairs (X) / A9 = 3  =>  0 pairs (_)
D7,D8: 3.. / D7 = 3  =>  0 pairs (*) / D8 = 3  =>  0 pairs (X)
A9,I9: 3.. / A9 = 3  =>  0 pairs (*) / I9 = 3  =>  0 pairs (X)
H6,H7: 3.. / H6 = 3  => 13 pairs (_) / H7 = 3  =>  0 pairs (X)
A2,C2: 4.. / A2 = 4  => 14 pairs (_) / C2 = 4  => 17 pairs (_)
H3,I3: 4.. / H3 = 4  => 16 pairs (_) / I3 = 4  =>  0 pairs (X)
D7,D8: 4.. / D7 = 4  =>  0 pairs (X) / D8 = 4  =>  0 pairs (_)
G6,G8: 4.. / G6 = 4  =>  0 pairs (*) / G8 = 4  =>  0 pairs (X)
G1,H1: 5.. / G1 = 5  =>  0 pairs (X) / H1 = 5  => 16 pairs (_)
F2,E3: 6.. / F2 = 6  =>  0 pairs (X) / E3 = 6  => 14 pairs (_)
E8,F8: 6.. / E8 = 6  =>  0 pairs (X) / F8 = 6  => 14 pairs (_)
H7,I7: 6.. / H7 = 6  => 17 pairs (_) / I7 = 6  => 14 pairs (_)
E3,E8: 6.. / E3 = 6  => 14 pairs (_) / E8 = 6  =>  0 pairs (X)
F2,F8: 6.. / F2 = 6  =>  0 pairs (X) / F8 = 6  => 14 pairs (_)
G1,G6: 6.. / G1 = 6  => 16 pairs (_) / G6 = 6  =>  0 pairs (X)
D5,D6: 7.. / D5 = 7  => 17 pairs (_) / D6 = 7  => 14 pairs (_)
F2,E3: 8.. / F2 = 8  => 14 pairs (_) / E3 = 8  =>  0 pairs (X)
E3,E6: 8.. / E3 = 8  =>  0 pairs (X) / E6 = 8  => 14 pairs (_)
F4,F6: 9.. / F4 = 9  => 18 pairs (_) / F6 = 9  => 14 pairs (_)
A8,C8: 9.. / A8 = 9  =>  0 pairs (*) / C8 = 9  =>  0 pairs (X)
* DURATION: 0:00:34.483886  START: 22:47:59.024726  END: 22:48:33.508612 2019-04-30
* CP COUNT: (33)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,C9,D4,D7,D8,E3,E6,E8,F2,F8,G1,G8,I9)
* ...243..9.2.95.3.75931.72...3..2.7......34892.........1...729.........2..6.89517.
* PAIR F2: 6,8 ROW 2
A2: 6,8,4                                # reduction candidate for 6,8
A2: 6,8                                  # 17 pairs
C2: 6,8,1,4                              # reduction candidate for 6,8
C2: 6,8                                  # 15 pairs
H2: 6,8,1                                # reduction candidate for 6,8
H2: 6,8 => CTR
* ...24351942195.3.75931.72...3..2.7...1..34892......6..1...729........42..64895173
H2: 1                                    # 13 pairs
* PAIR E3: 6,8 ROW 3
H3: 6,8,4                                # reduction candidate for 6,8
H3: 6,8 => CTR
* ...243659.2.95.317593167284.3..2.7......34892....8.43.14.3729..3.94..528.6.895173
H3: 4                                    # 16 pairs
I3: 6,8,4                                # reduction candidate for 6,8
I3: 6,8                                  # 16 pairs
* PAIR G1: 5,6 BLK 3
H1: 5,6,1,8                              # reduction candidate for 5,6
H1: 1,8 => CTR
* ...2435.9.2.95.3.75931.72...3..2.7......34892......6..1...729........42..6.895173
H1: 5,6                                  # 16 pairs
* PAIR G1: 5,6 COL G
G6: 5,6,4                                # reduction candidate for 5,6
G6: 5,6 => CTR
* ...243..9.2.95.3.75931.72...3..2.7......34892.........1...729........42..6.895173
G6: 4 => SOLVED
* 718243659426958317593167248834529761651734892279681435145372986987416523362895174
* PAIR A5: 6,7 BLK 4
C5: 6,7,1,5                              # reduction candidate for 6,7
C5: 6,7                                  # 15 pairs
A6: 6,7,2,4,8,9                          # reduction candidate for 6,7
A6: 6,7 => CTR
* ...243..942.95.3.75931.72...3..2.7......34892.42.89.311..3729..3.9416528264895173
A6: 2,4,8,9                              # 13 pairs
C6: 6,7,2,4,5,8,9                        # reduction candidate for 6,7
C6: 6,7                                  # 19 pairs
* PAIR A5: 6,7 ROW 5
D5: 6,7,5                                # reduction candidate for 6,7
D5: 6,7                                  # 16 pairs
D5: 5                                    # 14 pairs
* PAIR A5: 6,7 COL A
A1: 6,7,8                                # reduction candidate for 6,7
A1: 8                                    # 15 pairs
A1: 6,7                                  # 15 pairs
* PAIR D4: 5,6 BLK 5
D5: 5,6,7                                # reduction candidate for 5,6
D5: 5,6                                  # 14 pairs
D6: 5,6,7                                # reduction candidate for 5,6
D6: 5,6                                  # 17 pairs
* PAIR D4: 5,6 ROW 4
C4: 5,6,4,8,9                            # reduction candidate for 5,6
C4: 5,6 => CTR
* ...243..9.2.95.3.75931.72...3..2.741....34892...7.....1...729........42..6.895173
C4: 4,8,9                                # 13 pairs
H4: 5,6,4                                # reduction candidate for 5,6
H4: 5,6                                  # 15 pairs
I4: 5,6,1,4                              # reduction candidate for 5,6
I4: 5,6 => CTR
* ...243..9.2.9583.75931672...3..2174.....34892....89.311...729......1642..6.895173
I4: 1,4                                  # 14 pairs
* PAIR E6: 1,8 BLK 5
F4: 1,8,9                                # reduction candidate for 1,8
F4: 1,8                                  # 14 pairs
F6: 1,8,9                                # reduction candidate for 1,8
F6: 1,8                                  # 18 pairs
* PAIR C9: 2,4 BLK 7
A9: 2,4,3                                # reduction candidate for 2,4
A9: 2,4 => CTR
* ...243659.2.95.317593167284.3..2.7......34892....8.43.14..729..3.94..528.6.895173
A9: 3 => SOLVED
* 718243659426958317593167248834529761651734892279681435145372986987416523362895174
* PAIR C9: 2,4 COL C
C6: 2,4,5,6,7,8,9                        # reduction candidate for 2,4
C6: 2,4 => CTR
* ...243..942.95.3.75931.72...3..2.7......34892.........1...729........42..64895173
C6: 5,6,7,8,9                            # 13 pairs
* PAIR D7: 3,4 ROW 7
H7: 3,4,5,6,8                            # reduction candidate for 3,4
H7: 3,4 => CTR
* ...243659.2.95.317593167284.3..2.7......34892....8.43.1..37294634....528.6.895173
H7: 5,6,8                                # 13 pairs
I7: 3,4,5,6,8                            # reduction candidate for 3,4
I7: 3,4 => CTR
* ...243659.2.95.317593167284.3..2.74.....34892.......3.1...7296.......528.6.89517.
I7: 5,6,8                                # 13 pairs
* PAIR D8: 3,4 ROW 8
A8: 3,4,7,8,9                            # reduction candidate for 3,4
A8: 3,4 => CTR
* ...243659.2.95.317593167284.3..2.7......34892....8.4..14..729...79...528.6.89517.
A8: 7,8,9 => SOLVED
* 718243659426958317593167248834529761651734892279681435145372986987416523362895174
I8: 3,4,5,8                              # reduction candidate for 3,4
I8: 3,4 => SOLVED
* 718243659426958317593167248834529761651734892279681435145372986987416523362895174
I8: 5,8                                  # 14 pairs
* PAIR G8: 4,5 BLK 9
H7: 4,5,3,6,8                            # reduction candidate for 4,5
H7: 4,5 => CTR
* ...243659.2.95.317593167284.3..2.76.....34892....8.43.14.3729.63.94..528.6.895173
H7: 3,6,8                                # 13 pairs
I7: 4,5,3,6,8                            # reduction candidate for 4,5
I7: 4,5 => CTR
* ...243659.2.95.317593167284.3..2.7......34892.......3.1..37296.3.94..528.6.895173
I7: 3,6,8                                # 13 pairs
I8: 4,5,3,8                              # reduction candidate for 4,5
I8: 4,5 => CTR
* ...243..9.2.95.3.75931.72...3..2.7......34892.........1...729.........2..6.89517.
I8: 3,8                                  # 14 pairs
* PAIR G8: 4,5 ROW 8
B8: 4,5,7,8                              # reduction candidate for 4,5
B8: 4,5 => CTR
* ...243..9.2.95.3.75931.72...3..2.7......348922........1..4729...4.3..528362895174
B8: 7,8                                  # 14 pairs
C8: 4,5,7,8,9                            # reduction candidate for 4,5
C8: 4,5 => CTR
* ...243..9.2.95.3.75931.7246.3..2.7......348922........1...729..97.....28362895174
C8: 7,8,9                                # 13 pairs
* PAIR G8: 4,5 COL G
G6: 4,5,6                                # reduction candidate for 4,5
G6: 6 => CTR
* ...243..9.2.95.3.75931.72...3..2.7......34892......6..1...729........42..6.895173
G6: 4,5                                  # 16 pairs
* PAIR I9: 3,4 BLK 9
H7: 3,4,5,6,8                            # reduction candidate for 3,4
H7: 3,4 => CTR
* ...243659.2.95.317593167284.3..2.7......34892....8.43.1..37294634....528.6.895173
H7: 5,6,8                                # 13 pairs
I7: 3,4,5,6,8                            # reduction candidate for 3,4
I7: 3,4 => CTR
* ...243659.2.95.317593167284.3..2.74.....34892.......3.1...7296.......528.6.89517.
I7: 5,6,8                                # 13 pairs
I8: 3,4,5,8                              # reduction candidate for 3,4
I8: 3,4 => SOLVED
* 718243659426958317593167248834529761651734892279681435145372986987416523362895174
I8: 5,8                                  # 14 pairs
* PAIR I9: 3,4 ROW 9
A9: 3,4,2                                # reduction candidate for 3,4
A9: 2 => CTR
* ...243659426958317593167284.3..2.74.....34892.........1...729..3.94..528264895173
A9: 3,4                                  # 13 pairs
* PAIR I9: 3,4 COL I
I6: 3,4,1,5,6                            # reduction candidate for 3,4
I6: 3,4 => CTR
* ...243..9.2.95.3.75931.72...3..2.7.1....34892.........1...729........42..6.895173
I6: 1,5,6                                # 13 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060501-absurd-base-pr-000.dot
* REASONING
* DIS # H2: 6,8 => CTR => H2: 1
* DIS # H3: 6,8 => CTR => H3: 4
* DIS # H1: 1,8 => CTR => H1: 5,6
* DIS # G6: 5,6 => CTR => G6: 4
* PRF # G6: 4 => SOL
* DIS # A6: 6,7 => CTR => A6: 2,4,8,9
* DIS # C4: 5,6 => CTR => C4: 4,8,9
* DIS # I4: 5,6 => CTR => I4: 1,4
* DIS # A9: 2,4 => CTR => A9: 3
* PRF # A9: 3 => SOL
* DIS # C6: 2,4 => CTR => C6: 5,6,7,8,9
* DIS # H7: 3,4 => CTR => H7: 5,6,8
* DIS # I7: 3,4 => CTR => I7: 5,6,8
* DIS # A8: 3,4 => CTR => A8: 7,8,9
* PRF # A8: 7,8,9 => SOL
* PRF # I8: 3,4 => SOL
* DIS # H7: 4,5 => CTR => H7: 3,6,8
* DIS # I7: 4,5 => CTR => I7: 3,6,8
* DIS # I8: 4,5 => CTR => I8: 3,8
* DIS # B8: 4,5 => CTR => B8: 7,8
* DIS # C8: 4,5 => CTR => C8: 7,8,9
* DIS # G6: 6 => CTR => G6: 4,5
* DIS # H7: 3,4 => CTR => H7: 5,6,8
* DIS # I7: 3,4 => CTR => I7: 5,6,8
* PRF # I8: 3,4 => SOL
* DIS # A9: 2 => CTR => A9: 3,4
* DIS # I6: 3,4 => CTR => I6: 1,5,6
* CNT  27 HDP CHAINS /  62 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,C9,D4,D7,D8,E3,E6,E8,F2,F8,G1,G8,I9)
* ...243..9.2.95.3.75931.72...3..2.7......34892.........1...729.........2..6.89517.
* PAIR F2: 6,8 ROW 2
A2: 6,8,4                                # reduction candidate for 6,8
A2: 6,8                                  # 17 pairs
C2: 6,8,1,4                              # reduction candidate for 6,8
C2: 6,8                                  # 15 pairs
H2: 6,8,1                                # reduction candidate for 6,8
H2: 6,8 => CTR
* ...24351942195.3.75931.72...3..2.7...1..34892......6..1...729........42..64895173
* PAIR RESTART
* PAIR F2: 6,8 ROW 2
A2: 6,8,4                                # reduction candidate for 6,8
A2: 6,8                                  # 17 pairs
C2: 6,8,4                                # reduction candidate for 6,8
C2: 6,8                                  # 15 pairs
* PAIR E3: 6,8 ROW 3
H3: 6,8,4                                # reduction candidate for 6,8
H3: 6,8 => CTR
* ...243659.2.95.317593167284.3..2.7......34892....8.43.14.3729..3.94..528.6.895173
* RESTART
* PAIR RESTART
* PAIR G1: 5,6 BLK 3
H1: 5,6,8                                # reduction candidate for 5,6
H1: 5,6 => SOLVED
* 718243659426958317593167248834529761651734892279681435145372986987416523362895174
* DURATION: 0:00:05.504763  START: 22:49:09.832983  END: 22:49:15.337746 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060501-absurd-base-pr-001.dot
* REASONING
* DIS # H2: 6,8 => CTR => H2: 1
* DIS H2: 1 # H3: 6,8 => CTR => H3: 4
* PRF H2: 1 + H3: 4 # H1: 5,6 => SOL
* STA H2: 1 + H3: 4 + H1: 5,6
* CNT   3 HDP CHAINS /   7 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060501, absurd

Solution

position: 718243659426958317593167248834529761651734892279681435145372986987416523362895174 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 # A2: 6,8 => UNS
* INC # C2: 6,8 => UNS
* DIS # H2: 6,8 => CTR => H2: 1
* INC # H2: 1 => UNS
* DIS # H3: 6,8 => CTR => H3: 4
* INC # H3: 4 => UNS
* INC # I3: 6,8 => UNS
* INC # H1: 5,6 => UNS
* DIS # H1: 1,8 => CTR => H1: 5,6
* DIS # G6: 5,6 => CTR => G6: 4
* PRF # G6: 4 => SOL
* INC # C5: 6,7 => UNS
* DIS # A6: 6,7 => CTR => A6: 2,4,8,9
* INC # A6: 2,4,8,9 => UNS
* INC # C6: 6,7 => UNS
* INC # D5: 6,7 => UNS
* INC # D5: 5 => UNS
* INC # A1: 6,7 => UNS
* INC # A1: 8 => UNS
* INC # D5: 5,6 => UNS
* INC # D6: 5,6 => UNS
* DIS # C4: 5,6 => CTR => C4: 4,8,9
* INC # C4: 4,8,9 => UNS
* INC # H4: 5,6 => UNS
* DIS # I4: 5,6 => CTR => I4: 1,4
* INC # I4: 1,4 => UNS
* INC # F4: 1,8 => UNS
* INC # F6: 1,8 => UNS
* DIS # A9: 2,4 => CTR => A9: 3
* PRF # A9: 3 => SOL
* DIS # C6: 2,4 => CTR => C6: 5,6,7,8,9
* INC # C6: 5,6,7,8,9 => UNS
* DIS # H7: 3,4 => CTR => H7: 5,6,8
* INC # H7: 5,6,8 => UNS
* DIS # I7: 3,4 => CTR => I7: 5,6,8
* INC # I7: 5,6,8 => UNS
* DIS # A8: 3,4 => CTR => A8: 7,8,9
* PRF # A8: 7,8,9 => SOL
* PRF # I8: 3,4 => SOL
* INC # I8: 5,8 => UNS
* DIS # H7: 4,5 => CTR => H7: 3,6,8
* INC # H7: 3,6,8 => UNS
* DIS # I7: 4,5 => CTR => I7: 3,6,8
* INC # I7: 3,6,8 => UNS
* DIS # I8: 4,5 => CTR => I8: 3,8
* INC # I8: 3,8 => UNS
* DIS # B8: 4,5 => CTR => B8: 7,8
* INC # B8: 7,8 => UNS
* DIS # C8: 4,5 => CTR => C8: 7,8,9
* INC # C8: 7,8,9 => UNS
* INC # G6: 4,5 => UNS
* DIS # G6: 6 => CTR => G6: 4,5
* DIS # H7: 3,4 => CTR => H7: 5,6,8
* INC # H7: 5,6,8 => UNS
* DIS # I7: 3,4 => CTR => I7: 5,6,8
* INC # I7: 5,6,8 => UNS
* PRF # I8: 3,4 => SOL
* INC # I8: 5,8 => UNS
* INC # A9: 3,4 => UNS
* DIS # A9: 2 => CTR => A9: 3,4
* DIS # I6: 3,4 => CTR => I6: 1,5,6
* INC # I6: 1,5,6 => UNS
* CNT  62 HDP CHAINS /  62 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A2: 6,8 => UNS
* INC # C2: 6,8 => UNS
* DIS # H2: 6,8 => CTR => H2: 1
* INC H2: 1 # A2: 6,8 => UNS
* INC H2: 1 # C2: 6,8 => UNS
* DIS H2: 1 # H3: 6,8 => CTR => H3: 4
* PRF H2: 1 + H3: 4 # H1: 5,6 => SOL
* STA H2: 1 + H3: 4 + H1: 5,6
* CNT   7 HDP CHAINS /   7 HYP OPENED