Analysis of zz-www.sudokuoftheday.co.uk-20190331-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019
Autosolve
Pair Reduction Variants
- Pair Reduction Analysis
- Pair Reduction
Details
Solution
Appendix: Full HDP Chains
- A1. Pair Reduction Analysis
- A2. Pair Reduction

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019

level: medium

position: 6.4...85...5.4.....28.7..43..2.9.3......8....3....2....7...5..9.9...74..4.3.....5 initial

Autosolve

position: 6.4...8577.5.48...92857..43852.9.3..16..8.5..34..52..827.435.8959.8.743.483.....5 autosolve

Pair Reduction Variants

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # F1: 1,3 => SOL
* DIS # F1: 9 => CTR => F1: 1,3
* DIS # D2: 6 => CTR => D2: 1,3
* DIS # E9: 1,2 => CTR => E9: 6
* DIS # D2: 1,6 => CTR => D2: 3
* PRF # D2: 3 => SOL
* DIS # F4: 1,6 => CTR => F4: 4
* PRF # F4: 4 => SOL
* DIS # H2: 1,6 => CTR => H2: 2,9
* DIS # H2: 1,6 => CTR => H2: 2,9
* DIS # H5: 7,9 => CTR => H5: 2
* PRF # H5: 2 => SOL
* PRF # D4: 1,6 => SOL
* DIS # D4: 7 => CTR => D4: 1,6
* DIS # F4: 1,6 => CTR => F4: 4
* PRF # F4: 4 => SOL
* DIS # D2: 1,6 => CTR => D2: 3
* PRF # D2: 3 => SOL
* DIS # H5: 7,9 => CTR => H5: 2
* PRF # H5: 2 => SOL
* DIS # H4: 1,6 => CTR => H4: 7
* PRF # H4: 7 => SOL
* PRF # I4: 1,6 => SOL
* DIS # I4: 4 => CTR => I4: 1,6
* DIS # H2: 1,6 => CTR => H2: 2,9
* PRF # H9: 1,6 => SOL
* DIS # H9: 2,7 => CTR => H9: 1,6
* PRF # E8: 1,6 => SOL
* DIS # E8: 2 => CTR => E8: 1,6
* DIS # I8: 1,6 => CTR => I8: 2
* PRF # I8: 2 => SOL
* PRF # F1: 1,9 => SOL
* DIS # F1: 3 => CTR => F1: 1,9
* DIS # I8: 1,6 => CTR => I8: 2
* PRF # I8: 2 => SOL
* PRF # H9: 1,6 => SOL
* DIS # H9: 2,7 => CTR => H9: 1,6
* DIS # H9: 2,7 => CTR => H9: 1,6
* PRF # H9: 1,6 => SOL
* CNT  39 HDP CHAINS /  46 HYP OPENED

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

Pair Reduction

The following important HDP chains were detected:

* PRF # F1: 1,3 => SOL
* STA F1: 1,3
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

`6.4...85...5.4.....28.7..43..2.9.3......8....3....2....7...5..9.9...74..4.3.....5`	initial
`6.4...8577.5.48...92857..43852.9.3..16..8.5..34..52..827.435.8959.8.743.483.....5`	autosolve
`634921857715348296928576143852694371169783524347152968271435689596817432483269715`	solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (21)
B1: 1,3
B2: 1,3
D1: 2,9
E1: 1,2
F3: 1,6
G2: 2,9
G3: 1,6
C5: 7,9
C6: 7,9
D5: 3,7
F5: 3,4
D6: 1,6
I5: 2,4
G6: 7,9
H6: 1,6
C7: 1,6
C8: 1,6
D9: 2,9
F9: 1,9
G7: 1,6
G9: 2,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B1,B2: 1.. / B1 = 1  =>  0 pairs (X) / B2 = 1  =>  0 pairs (_)
C7,C8: 1.. / C7 = 1  => 21 pairs (_) / C8 = 1  =>  0 pairs (X)
F3,G3: 1.. / F3 = 1  =>  0 pairs (X) / G3 = 1  => 21 pairs (_)
D6,H6: 1.. / D6 = 1  => 25 pairs (_) / H6 = 1  =>  0 pairs (X)
C7,G7: 1.. / C7 = 1  => 21 pairs (_) / G7 = 1  =>  0 pairs (X)
G3,G7: 1.. / G3 = 1  => 21 pairs (_) / G7 = 1  =>  0 pairs (X)
D1,E1: 2.. / D1 = 2  =>  0 pairs (X) / E1 = 2  =>  0 pairs (_)
H5,I5: 2.. / H5 = 2  =>  0 pairs (*) / I5 = 2  =>  0 pairs (X)
E8,I8: 2.. / E8 = 2  =>  0 pairs (X) / I8 = 2  =>  0 pairs (_)
D1,D9: 2.. / D1 = 2  =>  0 pairs (X) / D9 = 2  =>  0 pairs (_)
G2,G9: 2.. / G2 = 2  => 18 pairs (_) / G9 = 2  =>  0 pairs (X)
B1,B2: 3.. / B1 = 3  =>  0 pairs (*) / B2 = 3  =>  0 pairs (X)
F1,D2: 3.. / F1 = 3  =>  0 pairs (X) / D2 = 3  =>  0 pairs (_)
D5,F5: 3.. / D5 = 3  =>  0 pairs (X) / F5 = 3  =>  0 pairs (_)
B1,F1: 3.. / B1 = 3  =>  0 pairs (*) / F1 = 3  =>  0 pairs (X)
B2,D2: 3.. / B2 = 3  =>  0 pairs (X) / D2 = 3  =>  0 pairs (_)
D2,D5: 3.. / D2 = 3  =>  0 pairs (*) / D5 = 3  =>  0 pairs (X)
F1,F5: 3.. / F1 = 3  =>  0 pairs (X) / F5 = 3  =>  0 pairs (_)
F4,F5: 4.. / F4 = 4  =>  0 pairs (*) / F5 = 4  =>  0 pairs (X)
I4,I5: 4.. / I4 = 4  =>  0 pairs (X) / I5 = 4  =>  0 pairs (_)
F4,I4: 4.. / F4 = 4  =>  0 pairs (*) / I4 = 4  =>  0 pairs (X)
F5,I5: 4.. / F5 = 4  =>  0 pairs (X) / I5 = 4  =>  0 pairs (_)
D2,F3: 6.. / D2 = 6  =>  0 pairs (X) / F3 = 6  => 21 pairs (_)
C7,C8: 6.. / C7 = 6  =>  0 pairs (X) / C8 = 6  => 21 pairs (_)
E8,E9: 6.. / E8 = 6  =>  0 pairs (X) / E9 = 6  => 22 pairs (_)
F3,G3: 6.. / F3 = 6  => 21 pairs (_) / G3 = 6  =>  0 pairs (X)
D6,H6: 6.. / D6 = 6  =>  0 pairs (X) / H6 = 6  => 25 pairs (_)
C7,G7: 6.. / C7 = 6  =>  0 pairs (X) / G7 = 6  => 21 pairs (_)
E9,H9: 6.. / E9 = 6  => 22 pairs (_) / H9 = 6  =>  0 pairs (X)
F3,F4: 6.. / F3 = 6  => 21 pairs (_) / F4 = 6  =>  0 pairs (X)
G3,G7: 6.. / G3 = 6  =>  0 pairs (X) / G7 = 6  => 21 pairs (_)
C5,C6: 7.. / C5 = 7  =>  0 pairs (X) / C6 = 7  => 18 pairs (_)
D4,D5: 7.. / D4 = 7  =>  0 pairs (X) / D5 = 7  =>  0 pairs (_)
G9,H9: 7.. / G9 = 7  => 18 pairs (_) / H9 = 7  =>  0 pairs (X)
D4,H4: 7.. / D4 = 7  =>  0 pairs (X) / H4 = 7  =>  0 pairs (_)
C6,G6: 7.. / C6 = 7  => 18 pairs (_) / G6 = 7  =>  0 pairs (X)
G6,G9: 7.. / G6 = 7  =>  0 pairs (X) / G9 = 7  => 18 pairs (_)
D1,F1: 9.. / D1 = 9  =>  0 pairs (*) / F1 = 9  =>  0 pairs (X)
G2,H2: 9.. / G2 = 9  =>  0 pairs (X) / H2 = 9  => 18 pairs (_)
C5,C6: 9.. / C5 = 9  => 18 pairs (_) / C6 = 9  =>  0 pairs (X)
H5,G6: 9.. / H5 = 9  =>  0 pairs (X) / G6 = 9  => 18 pairs (_)
D9,F9: 9.. / D9 = 9  =>  0 pairs (X) / F9 = 9  =>  0 pairs (_)
C5,H5: 9.. / C5 = 9  => 18 pairs (_) / H5 = 9  =>  0 pairs (X)
C6,G6: 9.. / C6 = 9  =>  0 pairs (X) / G6 = 9  => 18 pairs (_)
D1,D9: 9.. / D1 = 9  =>  0 pairs (*) / D9 = 9  =>  0 pairs (X)
F1,F9: 9.. / F1 = 9  =>  0 pairs (X) / F9 = 9  =>  0 pairs (_)
G2,G6: 9.. / G2 = 9  =>  0 pairs (X) / G6 = 9  => 18 pairs (_)
H2,H5: 9.. / H2 = 9  => 18 pairs (_) / H5 = 9  =>  0 pairs (X)
* DURATION: 0:01:05.633694  START: 04:56:42.521857  END: 04:57:48.155551 2019-05-01
* CP COUNT: (48)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B2,C5,C6,C7,C8,D1,D5,D6,D9,E1,F3,F5,F9,G2,G3,G6,G7,G9,H6,I5)
* 6.4...8577.5.48...92857..43852.9.3..16..8.5..34..52..827.435.8959.8.743.483.....5
* PAIR B1: 1,3 ROW 1
F1: 1,3,9                                # reduction candidate for 1,3
F1: 1,3 => SOLVED
* 634921857715348296928576143852694371169783524347152968271435689596817432483269715
F1: 9 => CTR
* 634.19857715348...928576143852.9.3..16.7835.4347.529.8271435689596827431483961725
* PAIR B2: 1,3 ROW 2
D2: 1,3,6                                # reduction candidate for 1,3
D2: 6 => CTR
* 6.4..3857735648...928571643852.963.416.3845.234.152.6827643518959182743.483.....5
D2: 1,3                                  # 21 pairs
* PAIR E1: 1,2 COL E
E8: 1,2,6                                # reduction candidate for 1,2
E8: 1,2                                  # 22 pairs
E9: 1,2,6                                # reduction candidate for 1,2
E9: 1,2 => CTR
* 6.4...8577.5.4829.92857.643852.963.416..8.5..34..52..827.435.8959.867432483...765
E9: 6                                    # 22 pairs
* PAIR F3: 1,6 BLK 2
D2: 1,6,3                                # reduction candidate for 1,6
D2: 1,6 => CTR
* 6.4..3857735.48...92857..43852.9.3..16.3845.234..52..827.435.8959.82743.4839....5
D2: 3 => SOLVED
* 634921857715348296928576143852694371169783524347152968271435689596817432483269715
* PAIR F3: 1,6 COL F
F4: 1,6,4                                # reduction candidate for 1,6
F4: 1,6 => CTR
* 6.4...8577.5.48...92857..43852.9.3.416..845.234..52..827.435.8959.82743.483961..5
F4: 4 => SOLVED
* 634921857715348296928576143852694371169783524347152968271435689596817432483269715
* PAIR G2: 2,9 BLK 3
H2: 2,9,1,6                              # reduction candidate for 2,9
H2: 1,6 => CTR
* 6.4...8577.5.489.292857..43852.9.3..16..8.5..34..52..827.435.8959.8.743.483.....5
H2: 2,9                                  # 23 pairs
* PAIR G3: 1,6 BLK 3
H2: 1,6,2,9                              # reduction candidate for 1,6
H2: 1,6 => CTR
* 6.4...8577.5.489.292857..43852.9.3..16..8.5..34..52..827.435.8959.8.743.483.....5
H2: 2,9                                  # 23 pairs
I2: 1,6,2                                # reduction candidate for 1,6
I2: 1,6                                  # 23 pairs
* PAIR C5: 7,9 ROW 5
H5: 7,9,2                                # reduction candidate for 7,9
H5: 7,9 => CTR
* 6.4219857715348..6928576.43852.9.3..16..8.5.234..52..827.435.8959.82743.483961..5
H5: 2 => SOLVED
* 634921857715348296928576143852694371169783524347152968271435689596817432483269715
* PAIR D6: 1,6 BLK 5
D4: 1,6,7                                # reduction candidate for 1,6
D4: 1,6 => SOLVED
* 634921857715348296928576143852694371169783524347152968271435689596817432483269715
D4: 7 => CTR
* 6.4...8577.5.48...92857..4385279.3..16.3845.234..52..827.435.8959.82743.483961..5
F4: 1,6,4                                # reduction candidate for 1,6
F4: 1,6 => CTR
* 6.4...8577.5.48...92857..43852.9.3.416..845.234..52..827.435.8959.82743.483961..5
F4: 4 => SOLVED
* 634921857715348296928576143852694371169783524347152968271435689596817432483269715
* PAIR D6: 1,6 COL D
D2: 1,6,3                                # reduction candidate for 1,6
D2: 1,6 => CTR
* 6.4..3857735.48...92857..43852.9.3..16.3845.234..52..827.435.8959.82743.4839....5
D2: 3 => SOLVED
* 634921857715348296928576143852694371169783524347152968271435689596817432483269715
* PAIR G6: 7,9 BLK 6
H5: 7,9,2                                # reduction candidate for 7,9
H5: 7,9 => CTR
* 6.4219857715348..6928576.43852.9.3..16..8.5.234..52..827.435.8959.82743.483961..5
H5: 2 => SOLVED
* 634921857715348296928576143852694371169783524347152968271435689596817432483269715
* PAIR H6: 1,6 BLK 6
H4: 1,6,7                                # reduction candidate for 1,6
H4: 1,6 => CTR
* 6.4...8577.5.48...92857..4385279.3..16.3845.234..52..827.435.8959.82743.483961..5
H4: 7 => SOLVED
* 634921857715348296928576143852694371169783524347152968271435689596817432483269715
I4: 1,6,4                                # reduction candidate for 1,6
I4: 1,6 => SOLVED
* 634921857715348296928576143852694371169783524347152968271435689596817432483269715
I4: 4 => CTR
* 6.4...8577.5.48...92857..43852.9.3.416..845.234..52..827.435.8959.82743.483961..5
* PAIR H6: 1,6 COL H
H2: 1,6,2,9                              # reduction candidate for 1,6
H2: 1,6 => CTR
* 6.4...8577.5.489.292857..43852.9.3..16..8.5..34..52..827.435.8959.8.743.483.....5
H2: 2,9                                  # 23 pairs
H9: 1,6,2,7                              # reduction candidate for 1,6
H9: 1,6 => SOLVED
* 634921857715348296928576143852694371169783524347152968271435689596817432483269715
H9: 2,7 => CTR
* 6.4.19857715348...928576143852.943..16.7835.4347.529.8271435689596827431483961725
* PAIR C8: 1,6 ROW 8
E8: 1,6,2                                # reduction candidate for 1,6
E8: 1,6 => SOLVED
* 634921857715348296928576143852694371169783524347152968271435689596817432483269715
E8: 2 => CTR
* 6.4219857715348...928576143852.943..16.7835.4347.529.8271435689596827431483961725
I8: 1,6,2                                # reduction candidate for 1,6
I8: 1,6 => CTR
* 6.4219857715348...928576143852.943..16.7835.4347.529.8271435689596827431483961725
I8: 2 => SOLVED
* 634921857715348296928576143852694371169783524347152968271435689596817432483269715
* PAIR F9: 1,9 COL F
F1: 1,9,3                                # reduction candidate for 1,9
F1: 1,9 => SOLVED
* 634921857715348296928576143852694371169783524347152968271435689596817432483269715
F1: 3 => CTR
* 6.4923857735.48...92857..43852.9.3..16.3845.234..52..827.435.8959.8.743.4832.97.5
* PAIR G7: 1,6 BLK 9
I8: 1,6,2                                # reduction candidate for 1,6
I8: 1,6 => CTR
* 6.4219857715348...928576143852.943..16.7835.4347.529.8271435689596827431483961725
I8: 2 => SOLVED
* 634921857715348296928576143852694371169783524347152968271435689596817432483269715
H9: 1,6,2,7                              # reduction candidate for 1,6
H9: 1,6 => SOLVED
* 634921857715348296928576143852694371169783524347152968271435689596817432483269715
H9: 2,7 => CTR
* 6.4.19857715348...928576143852.943..16.7835.4347.529.8271435689596827431483961725
* PAIR G9: 2,7 BLK 9
H9: 2,7,1,6                              # reduction candidate for 2,7
H9: 2,7 => CTR
* 6.4.19857715348...928576143852.943..16.7835.4347.529.8271435689596827431483961725
H9: 1,6 => SOLVED
* 634921857715348296928576143852694371169783524347152968271435689596817432483269715
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190331-absurd-base-pr-000.dot
* REASONING
* PRF # F1: 1,3 => SOL
* DIS # F1: 9 => CTR => F1: 1,3
* DIS # D2: 6 => CTR => D2: 1,3
* DIS # E9: 1,2 => CTR => E9: 6
* DIS # D2: 1,6 => CTR => D2: 3
* PRF # D2: 3 => SOL
* DIS # F4: 1,6 => CTR => F4: 4
* PRF # F4: 4 => SOL
* DIS # H2: 1,6 => CTR => H2: 2,9
* DIS # H2: 1,6 => CTR => H2: 2,9
* DIS # H5: 7,9 => CTR => H5: 2
* PRF # H5: 2 => SOL
* PRF # D4: 1,6 => SOL
* DIS # D4: 7 => CTR => D4: 1,6
* DIS # F4: 1,6 => CTR => F4: 4
* PRF # F4: 4 => SOL
* DIS # D2: 1,6 => CTR => D2: 3
* PRF # D2: 3 => SOL
* DIS # H5: 7,9 => CTR => H5: 2
* PRF # H5: 2 => SOL
* DIS # H4: 1,6 => CTR => H4: 7
* PRF # H4: 7 => SOL
* PRF # I4: 1,6 => SOL
* DIS # I4: 4 => CTR => I4: 1,6
* DIS # H2: 1,6 => CTR => H2: 2,9
* PRF # H9: 1,6 => SOL
* DIS # H9: 2,7 => CTR => H9: 1,6
* PRF # E8: 1,6 => SOL
* DIS # E8: 2 => CTR => E8: 1,6
* DIS # I8: 1,6 => CTR => I8: 2
* PRF # I8: 2 => SOL
* PRF # F1: 1,9 => SOL
* DIS # F1: 3 => CTR => F1: 1,9
* DIS # I8: 1,6 => CTR => I8: 2
* PRF # I8: 2 => SOL
* PRF # H9: 1,6 => SOL
* DIS # H9: 2,7 => CTR => H9: 1,6
* DIS # H9: 2,7 => CTR => H9: 1,6
* PRF # H9: 1,6 => SOL
* CNT  39 HDP CHAINS /  46 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B2,C5,C6,C7,C8,D1,D5,D6,D9,E1,F3,F5,F9,G2,G3,G6,G7,G9,H6,I5)
* 6.4...8577.5.48...92857..43852.9.3..16..8.5..34..52..827.435.8959.8.743.483.....5
* PAIR B1: 1,3 ROW 1
F1: 1,3,9                                # reduction candidate for 1,3
F1: 1,3 => SOLVED
* 634921857715348296928576143852694371169783524347152968271435689596817432483269715
* DURATION: 0:00:01.576279  START: 04:58:26.203125  END: 04:58:27.779404 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190331-absurd-base-pr-001.dot
* REASONING
* PRF # F1: 1,3 => SOL
* STA F1: 1,3
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190331, absurd

Solution

position: 634921857715348296928576143852694371169783524347152968271435689596817432483269715 solved

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:

* PRF # F1: 1,3 => SOL
* DIS # F1: 9 => CTR => F1: 1,3
* INC # D2: 1,3 => UNS
* DIS # D2: 6 => CTR => D2: 1,3
* INC # E8: 1,2 => UNS
* DIS # E9: 1,2 => CTR => E9: 6
* INC # E9: 6 => UNS
* DIS # D2: 1,6 => CTR => D2: 3
* PRF # D2: 3 => SOL
* DIS # F4: 1,6 => CTR => F4: 4
* PRF # F4: 4 => SOL
* INC # H2: 2,9 => UNS
* DIS # H2: 1,6 => CTR => H2: 2,9
* DIS # H2: 1,6 => CTR => H2: 2,9
* INC # H2: 2,9 => UNS
* INC # I2: 1,6 => UNS
* DIS # H5: 7,9 => CTR => H5: 2
* PRF # H5: 2 => SOL
* PRF # D4: 1,6 => SOL
* DIS # D4: 7 => CTR => D4: 1,6
* DIS # F4: 1,6 => CTR => F4: 4
* PRF # F4: 4 => SOL
* DIS # D2: 1,6 => CTR => D2: 3
* PRF # D2: 3 => SOL
* DIS # H5: 7,9 => CTR => H5: 2
* PRF # H5: 2 => SOL
* DIS # H4: 1,6 => CTR => H4: 7
* PRF # H4: 7 => SOL
* PRF # I4: 1,6 => SOL
* DIS # I4: 4 => CTR => I4: 1,6
* DIS # H2: 1,6 => CTR => H2: 2,9
* INC # H2: 2,9 => UNS
* PRF # H9: 1,6 => SOL
* DIS # H9: 2,7 => CTR => H9: 1,6
* PRF # E8: 1,6 => SOL
* DIS # E8: 2 => CTR => E8: 1,6
* DIS # I8: 1,6 => CTR => I8: 2
* PRF # I8: 2 => SOL
* PRF # F1: 1,9 => SOL
* DIS # F1: 3 => CTR => F1: 1,9
* DIS # I8: 1,6 => CTR => I8: 2
* PRF # I8: 2 => SOL
* PRF # H9: 1,6 => SOL
* DIS # H9: 2,7 => CTR => H9: 1,6
* DIS # H9: 2,7 => CTR => H9: 1,6
* PRF # H9: 1,6 => SOL
* CNT  46 HDP CHAINS /  46 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # F1: 1,3 => SOL
* STA F1: 1,3
* CNT   1 HDP CHAINS /   1 HYP OPENED