Analysis of zz-www.sudokuoftheday.co.uk-20190413-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: ..5.....2......65.2..97........6...96.....1.5...24.....89.....6.2.4.8.7..7....23. initial

Autosolve

position: ..5....92......65.26.975.1...256.4896.....125.5.24..6..89...546.264.8971.7....238 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # G1: 3,8 => CTR => G1: 7
* DIS # C3: 4 => CTR => C3: 3,8
* DIS # I2: 7 => CTR => I2: 3,4
* DIS # C3: 8 => CTR => C3: 3,4
* PRF # F4: 3 => SOL
* PRF # A1: 1,7 => SOL
* DIS # A2: 1,7 => CTR => A2: 4,8,9
* PRF # F4: 1,3 => SOL
* DIS # F4: 7 => CTR => F4: 1,3
* DIS # B2: 1,3 => CTR => B2: 4,9
* DIS # A6: 1,8 => CTR => A6: 9
* DIS # C2: 1,8 => CTR => C2: 3,4,7
* DIS # A6: 8 => CTR => A6: 1,9
* DIS # G1: 8 => CTR => G1: 3,7
* DIS # I2: 4 => CTR => I2: 3,7
* DIS # D7: 1,3 => CTR => D7: 7
* DIS # A9: 5 => CTR => A9: 1,4
* DIS # C2: 1,4 => CTR => C2: 3,7,8
* PRF # D1: 3,8 => SOL
* CNT  19 HDP CHAINS /  38 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 # G1: 3,8 => CTR => G1: 7
* PRF G1: 7 # F4: 3 => SOL
* STA G1: 7 + F4: 3
* CNT   2 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

..5.....2......65.2..97........6...96.....1.5...24.....89.....6.2.4.8.7..7....23. initial
..5....92......65.26.975.1...256.4896.....125.5.24..6..89...546.264.8971.7....238 autosolve
145386792897124653263975814712563489634897125958241367389712546526438971471659238 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
G3: 3,8
I3: 3,4
A4: 1,7
B4: 1,3
C6: 1,8
F6: 1,9
G6: 3,7
I6: 3,7
A7: 1,3
A8: 3,5
C9: 1,4
E8: 3,5
D9: 1,6
F9: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F4,F6: 1.. / F4 = 1  =>  0 pairs (X) / F6 = 1  => 15 pairs (_)
E2,F2: 2.. / E2 = 2  => 19 pairs (_) / F2 = 2  =>  0 pairs (X)
E7,F7: 2.. / E7 = 2  =>  0 pairs (X) / F7 = 2  => 19 pairs (_)
E2,E7: 2.. / E2 = 2  => 19 pairs (_) / E7 = 2  =>  0 pairs (X)
F2,F7: 2.. / F2 = 2  =>  0 pairs (X) / F7 = 2  => 19 pairs (_)
G6,I6: 3.. / G6 = 3  => 13 pairs (_) / I6 = 3  =>  0 pairs (X)
A7,A8: 3.. / A7 = 3  => 16 pairs (_) / A8 = 3  =>  0 pairs (X)
B4,F4: 3.. / B4 = 3  => 17 pairs (_) / F4 = 3  =>  0 pairs (*)
A8,E8: 3.. / A8 = 3  =>  0 pairs (X) / E8 = 3  => 16 pairs (_)
F1,F2: 4.. / F1 = 4  =>  0 pairs (X) / F2 = 4  => 20 pairs (_)
I2,I3: 4.. / I2 = 4  =>  0 pairs (X) / I3 = 4  => 15 pairs (_)
B5,C5: 4.. / B5 = 4  => 16 pairs (_) / C5 = 4  =>  0 pairs (*)
A9,C9: 4.. / A9 = 4  =>  0 pairs (*) / C9 = 4  =>  0 pairs (X)
C3,I3: 4.. / C3 = 4  =>  0 pairs (X) / I3 = 4  => 15 pairs (_)
A8,A9: 5.. / A8 = 5  => 16 pairs (_) / A9 = 5  =>  0 pairs (X)
E8,E9: 5.. / E8 = 5  =>  0 pairs (X) / E9 = 5  => 16 pairs (_)
A8,E8: 5.. / A8 = 5  => 16 pairs (_) / E8 = 5  =>  0 pairs (X)
A9,E9: 5.. / A9 = 5  =>  0 pairs (X) / E9 = 5  => 16 pairs (_)
D1,F1: 6.. / D1 = 6  =>  0 pairs (X) / F1 = 6  => 20 pairs (_)
D9,F9: 6.. / D9 = 6  => 20 pairs (_) / F9 = 6  =>  0 pairs (X)
D1,D9: 6.. / D1 = 6  =>  0 pairs (X) / D9 = 6  => 20 pairs (_)
F1,F9: 6.. / F1 = 6  => 20 pairs (_) / F9 = 6  =>  0 pairs (X)
G1,I2: 7.. / G1 = 7  => 13 pairs (_) / I2 = 7  =>  0 pairs (X)
A4,C5: 7.. / A4 = 7  =>  0 pairs (*) / C5 = 7  =>  0 pairs (X)
G6,I6: 7.. / G6 = 7  =>  0 pairs (X) / I6 = 7  => 13 pairs (_)
D7,F7: 7.. / D7 = 7  => 16 pairs (_) / F7 = 7  =>  0 pairs (X)
A1,G1: 7.. / A1 = 7  =>  0 pairs (X) / G1 = 7  => 13 pairs (_)
A4,F4: 7.. / A4 = 7  =>  0 pairs (*) / F4 = 7  =>  0 pairs (X)
C2,C5: 7.. / C2 = 7  =>  0 pairs (*) / C5 = 7  =>  0 pairs (X)
D5,D7: 7.. / D5 = 7  =>  0 pairs (X) / D7 = 7  => 16 pairs (_)
G1,G6: 7.. / G1 = 7  => 13 pairs (_) / G6 = 7  =>  0 pairs (X)
I2,I6: 7.. / I2 = 7  =>  0 pairs (X) / I6 = 7  => 13 pairs (_)
G1,G3: 8.. / G1 = 8  =>  0 pairs (X) / G3 = 8  => 15 pairs (_)
A6,C6: 8.. / A6 = 8  =>  0 pairs (X) / C6 = 8  => 15 pairs (_)
D5,E5: 8.. / D5 = 8  => 20 pairs (_) / E5 = 8  =>  0 pairs (X)
C3,G3: 8.. / C3 = 8  =>  0 pairs (X) / G3 = 8  => 15 pairs (_)
A2,B2: 9.. / A2 = 9  =>  0 pairs (X) / B2 = 9  => 15 pairs (_)
B5,A6: 9.. / B5 = 9  =>  0 pairs (X) / A6 = 9  => 15 pairs (_)
E9,F9: 9.. / E9 = 9  =>  0 pairs (X) / F9 = 9  => 20 pairs (_)
A6,F6: 9.. / A6 = 9  => 15 pairs (_) / F6 = 9  =>  0 pairs (X)
A2,A6: 9.. / A2 = 9  =>  0 pairs (X) / A6 = 9  => 15 pairs (_)
B2,B5: 9.. / B2 = 9  => 15 pairs (_) / B5 = 9  =>  0 pairs (X)
E5,E9: 9.. / E5 = 9  => 20 pairs (_) / E9 = 9  =>  0 pairs (X)
* DURATION: 0:00:54.035138  START: 05:16:03.087889  END: 05:16:57.123027 2019-05-01
* CP COUNT: (43)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,A8,B4,C6,C9,D9,E8,F6,F9,G3,G6,I3,I6)
* ..5....92......65.26.975.1...256.4896.....125.5.24..6..89...546.264.8971.7....238
* PAIR G3: 3,8 BLK 3
G1: 3,8,7                                # reduction candidate for 3,8
G1: 3,8 => CTR
* 7.5.86392894...65726.975.141325674896.7...125.58241763389712546526438971471659238
G1: 7                                    # 13 pairs
* PAIR G3: 3,8 ROW 3
C3: 3,8,4                                # reduction candidate for 3,8
C3: 4 => CTR
* ..5....92......65.264975813..256.48964....125958241367.89...546.264.8971471659238
C3: 3,8                                  # 15 pairs
* PAIR I3: 3,4 BLK 3
I2: 3,4,7                                # reduction candidate for 3,4
I2: 7 => CTR
* 7.5....92......65726.975.14132567489647...125958241763389712546526438971471659238
I2: 3,4                                  # 13 pairs
* PAIR I3: 3,4 ROW 3
C3: 3,4,8                                # reduction candidate for 3,4
C3: 8 => CTR
* ..5....92......65.268975314..256.4896.....125851249763.89...546.264.8971.74.96238
C3: 3,4                                  # 15 pairs
* PAIR A4: 1,7 ROW 4
F4: 1,7,3                                # reduction candidate for 1,7
F4: 3 => SOLVED
* 145386792897124653263975814712563489634897125958241367389712546526438971471659238
F4: 1,7                                  # 17 pairs
* PAIR A4: 1,7 COL A
A1: 1,7,4,8                              # reduction candidate for 1,7
A1: 1,7 => SOLVED
* 145386792897124653263975814712563489634897125958241367389712546526438971471659238
A1: 4,8                                  # 14 pairs
A2: 1,7,4,8,9                            # reduction candidate for 1,7
A2: 1,7 => CTR
* 8.5..6792.9...4653263975814..256.4896.4.9.125958241367389..2546526438971471659238
A2: 4,8,9                                # 14 pairs
* PAIR B4: 1,3 ROW 4
F4: 1,3,7                                # reduction candidate for 1,3
F4: 1,3 => SOLVED
* 145386792897124653263975814712563489634897125958241367389712546526438971471659238
F4: 7 => CTR
* ..5....92......65.26.975.1.132567489647...125958241.6.389712546526438971471659238
* PAIR B4: 1,3 COL B
B1: 1,3,4                                # reduction candidate for 1,3
B1: 1,3                                  # 17 pairs
B2: 1,3,4,9                              # reduction candidate for 1,3
B2: 1,3 => CTR
* ..5....929.....65.26.975.1...256.489694...125.5.249.6..89...546.264.8971471...238
B2: 4,9                                  # 15 pairs
* PAIR C6: 1,8 BLK 4
A6: 1,8,9                                # reduction candidate for 1,8
A6: 1,8 => CTR
* ..5....929.....65.26.975.1...256.489694...125.5.249.6..89...546.264.8971471...238
A6: 9                                    # 15 pairs
* PAIR C6: 1,8 COL C
C2: 1,8,3,4,7                            # reduction candidate for 1,8
C2: 1,8 => CTR
* ..5....92......65.263975814132567489647...12595824..6..897..546.264.8971.7....238
C2: 3,4,7                                # 14 pairs
* PAIR F6: 1,9 ROW 6
A6: 1,9,8                                # reduction candidate for 1,9
A6: 8 => CTR
* ..5....929.....65.26.975.1...256.489694...12585124..6..89...546.264.8971.7....238
A6: 1,9                                  # 15 pairs
* PAIR G6: 3,7 COL G
G1: 3,7,8                                # reduction candidate for 3,7
G1: 8 => CTR
* 7.5...892......6572689753141.256.4896.....125.5.24..6..89...546.264.8971.7....238
G1: 3,7                                  # 15 pairs
* PAIR I6: 3,7 COL I
I2: 3,7,4                                # reduction candidate for 3,7
I2: 4 => CTR
* ..5...792......654264975813..256.48964....125958241367.89...546.264.8971471659238
I2: 3,7                                  # 15 pairs
* PAIR A7: 1,3 ROW 7
D7: 1,3,7                                # reduction candidate for 1,3
D7: 1,3 => CTR
* ..56.4792497812653263975.1.7.256.4896..78.125.5.24..67.89327546326458971574196238
D7: 7                                    # 16 pairs
E7: 1,3,2                                # reduction candidate for 1,3
E7: 1,3                                  # 19 pairs
* PAIR C9: 1,4 BLK 7
A9: 1,4,5                                # reduction candidate for 1,4
A9: 5 => CTR
* ..5....92.91...65.263975.14..256.48964....125958241.6.189...546326458971574...238
A9: 1,4                                  # 16 pairs
* PAIR C9: 1,4 COL C
C2: 1,4,3,7,8                            # reduction candidate for 1,4
C2: 1,4 => CTR
* ..5....92......65.263975814132567489647...125958241.6.389712546526438971471659238
C2: 3,7,8                                # 14 pairs
* PAIR D9: 1,6 COL D
D1: 1,6,3,8                              # reduction candidate for 1,6
D1: 3,8 => SOLVED
* 145386792897124653263975814712563489634897125958241367389712546526438971471659238
D1: 1,6                                  # 17 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190413-absurd-base-pr-000.dot
* REASONING
* DIS # G1: 3,8 => CTR => G1: 7
* DIS # C3: 4 => CTR => C3: 3,8
* DIS # I2: 7 => CTR => I2: 3,4
* DIS # C3: 8 => CTR => C3: 3,4
* PRF # F4: 3 => SOL
* PRF # A1: 1,7 => SOL
* DIS # A2: 1,7 => CTR => A2: 4,8,9
* PRF # F4: 1,3 => SOL
* DIS # F4: 7 => CTR => F4: 1,3
* DIS # B2: 1,3 => CTR => B2: 4,9
* DIS # A6: 1,8 => CTR => A6: 9
* DIS # C2: 1,8 => CTR => C2: 3,4,7
* DIS # A6: 8 => CTR => A6: 1,9
* DIS # G1: 8 => CTR => G1: 3,7
* DIS # I2: 4 => CTR => I2: 3,7
* DIS # D7: 1,3 => CTR => D7: 7
* DIS # A9: 5 => CTR => A9: 1,4
* DIS # C2: 1,4 => CTR => C2: 3,7,8
* PRF # D1: 3,8 => SOL
* CNT  19 HDP CHAINS /  38 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,A8,B4,C6,C9,D9,E8,F6,F9,G3,G6,I3,I6)
* ..5....92......65.26.975.1...256.4896.....125.5.24..6..89...546.264.8971.7....238
* PAIR G3: 3,8 BLK 3
G1: 3,8,7                                # reduction candidate for 3,8
G1: 3,8 => CTR
* 7.5.86392894...65726.975.141325674896.7...125.58241763389712546526438971471659238
* PAIR A4: 1,7 ROW 4
F4: 1,7,3                                # reduction candidate for 1,7
F4: 3 => SOLVED
* 145386792897124653263975814712563489634897125958241367389712546526438971471659238
* DURATION: 0:00:03.806540  START: 05:17:23.205191  END: 05:17:27.011731 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190413-absurd-base-pr-001.dot
* REASONING
* DIS # G1: 3,8 => CTR => G1: 7
* PRF G1: 7 # F4: 3 => SOL
* STA G1: 7 + F4: 3
* CNT   2 HDP CHAINS /   3 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190413, absurd

Solution

position: 145386792897124653263975814712563489634897125958241367389712546526438971471659238 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 # G1: 3,8 => CTR => G1: 7
* INC # G1: 7 => UNS
* INC # C3: 3,8 => UNS
* DIS # C3: 4 => CTR => C3: 3,8
* INC # I2: 3,4 => UNS
* DIS # I2: 7 => CTR => I2: 3,4
* INC # C3: 3,4 => UNS
* DIS # C3: 8 => CTR => C3: 3,4
* INC # F4: 1,7 => UNS
* PRF # F4: 3 => SOL
* PRF # A1: 1,7 => SOL
* INC # A1: 4,8 => UNS
* DIS # A2: 1,7 => CTR => A2: 4,8,9
* INC # A2: 4,8,9 => UNS
* PRF # F4: 1,3 => SOL
* DIS # F4: 7 => CTR => F4: 1,3
* INC # B1: 1,3 => UNS
* DIS # B2: 1,3 => CTR => B2: 4,9
* INC # B2: 4,9 => UNS
* DIS # A6: 1,8 => CTR => A6: 9
* INC # A6: 9 => UNS
* DIS # C2: 1,8 => CTR => C2: 3,4,7
* INC # C2: 3,4,7 => UNS
* INC # A6: 1,9 => UNS
* DIS # A6: 8 => CTR => A6: 1,9
* INC # G1: 3,7 => UNS
* DIS # G1: 8 => CTR => G1: 3,7
* INC # I2: 3,7 => UNS
* DIS # I2: 4 => CTR => I2: 3,7
* DIS # D7: 1,3 => CTR => D7: 7
* INC # D7: 7 => UNS
* INC # E7: 1,3 => UNS
* INC # A9: 1,4 => UNS
* DIS # A9: 5 => CTR => A9: 1,4
* DIS # C2: 1,4 => CTR => C2: 3,7,8
* INC # C2: 3,7,8 => UNS
* INC # D1: 1,6 => UNS
* PRF # D1: 3,8 => SOL
* CNT  38 HDP CHAINS /  38 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # G1: 3,8 => CTR => G1: 7
* INC G1: 7 # F4: 1,7 => UNS
* PRF G1: 7 # F4: 3 => SOL
* STA G1: 7 + F4: 3
* CNT   3 HDP CHAINS /   3 HYP OPENED