Analysis of xx-top95-066-work.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 34.6.......7.......2..8.57......5....7..1..2....4......36.2..1.......9.......7.82 initial

Autosolve

position: 345671298..725.....2..8.57....7.5....7..1..2....4.2....36.2..1.......9.......7.82 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C4: 1,9 => CTR => C4: 2,3,4,8
* DIS # D5: 3,9 => CTR => D5: 8
* DIS # F5: 8,9 => CTR => F5: 3,6
* CNT   3 HDP CHAINS /  22 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 # C4: 1,9 => CTR => C4: 2,3,4,8
* DIS C4: 2,3,4,8 # D5: 3,9 => CTR => D5: 8
* STA C4: 2,3,4,8 + D5: 8
* CNT   2 HDP CHAINS /  46 HYP OPENED

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

Pair Reduction Position

position: 345671298..725.....2..8.57....7.5....7.81..2....4.2....36.2..1.......9.......7.82 pair_reduction
Pair Reduction

See section Pair Reduction for the HDP chains leading to this result.

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:48.915553

The following important HDP chains were detected:

* DIS # A2: 1,9 # C6: 1,9 => CTR => C6: 3,8
* DIS # A2: 1,9 + C6: 3,8 # I5: 3,6 => CTR => I5: 4,5,9
* PRF # A2: 1,9 + C6: 3,8 + I5: 4,5,9 # G5: 4 => SOL
* STA # A2: 1,9 + C6: 3,8 + I5: 4,5,9 + G5: 4
* CNT   3 HDP CHAINS /  37 HYP OPENED

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

Details

Positions

34.6.......7.......2..8.57......5....7..1..2....4......36.2..1.......9.......7.82 initial
345671298..725.....2..8.57....7.5....7..1..2....4.2....36.2..1.......9.......7.82 autosolve
345671298..725.....2..8.57....7.5....7.81..2....4.2....36.2..1.......9.......7.82 pair_reduction
345671298987253146621984573264795831573816429198432657836529714712348965459167382 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (4)
C3: 1,9
D3: 3,9
F7: 8,9
G7: 4,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D8,D9: 1.. / D8 = 1  =>  5 pairs (_) / D9 = 1  => 11 pairs (_)
A4,C4: 2.. / A4 = 2  =>  4 pairs (_) / C4 = 2  => 16 pairs (_)
A8,C8: 2.. / A8 = 2  => 16 pairs (_) / C8 = 2  =>  4 pairs (_)
A4,A8: 2.. / A4 = 2  =>  4 pairs (_) / A8 = 2  => 16 pairs (_)
C4,C8: 2.. / C4 = 2  => 16 pairs (_) / C8 = 2  =>  4 pairs (_)
F2,F3: 4.. / F2 = 4  =>  9 pairs (_) / F3 = 4  =>  5 pairs (_)
E8,E9: 4.. / E8 = 4  =>  4 pairs (_) / E9 = 4  =>  0 pairs (X)
F3,I3: 4.. / F3 = 4  =>  5 pairs (_) / I3 = 4  =>  9 pairs (_)
A5,I5: 5.. / A5 = 5  =>  4 pairs (_) / I5 = 5  => 11 pairs (_)
H6,H8: 5.. / H6 = 5  =>  4 pairs (_) / H8 = 5  =>  9 pairs (_)
A3,I3: 6.. / A3 = 6  =>  4 pairs (_) / I3 = 6  => 12 pairs (_)
E9,G9: 6.. / E9 = 6  => 11 pairs (_) / G9 = 6  =>  7 pairs (_)
F5,F8: 6.. / F5 = 6  => 11 pairs (_) / F8 = 6  => 11 pairs (_)
G6,I6: 7.. / G6 = 7  =>  6 pairs (_) / I6 = 7  =>  4 pairs (_)
A7,A8: 7.. / A7 = 7  => 17 pairs (_) / A8 = 7  =>  4 pairs (_)
A8,I8: 7.. / A8 = 7  =>  4 pairs (_) / I8 = 7  => 17 pairs (_)
G6,G7: 7.. / G6 = 7  =>  6 pairs (_) / G7 = 7  =>  4 pairs (_)
A2,B2: 8.. / A2 = 8  =>  5 pairs (_) / B2 = 8  => 11 pairs (_)
D5,F5: 8.. / D5 = 8  =>  5 pairs (_) / F5 = 8  =>  0 pairs (X)
G4,G6: 8.. / G4 = 8  =>  4 pairs (_) / G6 = 8  =>  6 pairs (_)
* DURATION: 0:00:24.575664  START: 00:21:15.224458  END: 00:21:39.800122 2017-05-04
* CP COUNT: (20)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:48.710737  START: 00:22:32.986819  END: 00:23:21.697556 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top95-066-work-pr-002.dot
* REASONING
* DIS # A2: 1,9 # C6: 1,9 => CTR => C6: 3,8
* DIS # A2: 1,9 + C6: 3,8 # I5: 3,6 => CTR => I5: 4,5,9
* PRF # A2: 1,9 + C6: 3,8 + I5: 4,5,9 # G5: 4 => SOL
* STA # A2: 1,9 + C6: 3,8 + I5: 4,5,9 + G5: 4
* CNT   3 HDP CHAINS /  37 HYP OPENED

Header Info

Top 95 Sudokus 066
[sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt

* REASONING for PRR
* DIS # A2: 1,9 # C6: 1,9 => CTR => C6: 3,8
* DIS # A2: 1,9 + C6: 3,8 # I5: 3,6 => CTR => I5: 4,5,9
* PRF # A2: 1,9 + C6: 3,8 + I5: 4,5,9 # G5: 4 => SOL
* STA # A2: 1,9 + C6: 3,8 + I5: 4,5,9 # G5: 4

Solution

position: 345671298987253146621984573264795831573816429198432657836529714712348965459167382 solved
Solution

See section Deep 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: 1,9 => UNS
* INC # B2: 1,9 => UNS
* INC # A3: 1,9 => UNS
* DIS # C4: 1,9 => CTR => C4: 2,3,4,8
* INC # C4: 2,3,4,8 => UNS
* INC # C6: 1,9 => UNS
* INC # C9: 1,9 => UNS
* INC # F2: 3,9 => UNS
* INC # F3: 3,9 => UNS
* DIS # D5: 3,9 => CTR => D5: 8
* INC # D5: 8 => UNS
* INC # D9: 3,9 => UNS
* INC # D7: 8,9 => UNS
* INC # D7: 5 => UNS
* INC # A7: 8,9 => UNS
* INC # A7: 4,5,7 => UNS
* DIS # F5: 8,9 => CTR => F5: 3,6
* INC # F5: 3,6 => UNS
* INC # I7: 4,7 => UNS
* INC # I8: 4,7 => UNS
* INC # A7: 4,7 => UNS
* INC # A7: 5,8,9 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A2: 1,9 => UNS
* INC # B2: 1,9 => UNS
* INC # A3: 1,9 => UNS
* DIS # C4: 1,9 => CTR => C4: 2,3,4,8
* INC C4: 2,3,4,8 # C6: 1,9 => UNS
* INC C4: 2,3,4,8 # C9: 1,9 => UNS
* INC C4: 2,3,4,8 # A2: 1,9 => UNS
* INC C4: 2,3,4,8 # B2: 1,9 => UNS
* INC C4: 2,3,4,8 # A3: 1,9 => UNS
* INC C4: 2,3,4,8 # C6: 1,9 => UNS
* INC C4: 2,3,4,8 # C9: 1,9 => UNS
* INC C4: 2,3,4,8 # F2: 3,9 => UNS
* INC C4: 2,3,4,8 # F3: 3,9 => UNS
* DIS C4: 2,3,4,8 # D5: 3,9 => CTR => D5: 8
* INC C4: 2,3,4,8 + D5: 8 # D9: 3,9 => UNS
* INC C4: 2,3,4,8 + D5: 8 # D9: 3,9 => UNS
* INC C4: 2,3,4,8 + D5: 8 # D9: 1,5 => UNS
* INC C4: 2,3,4,8 + D5: 8 # F2: 3,9 => UNS
* INC C4: 2,3,4,8 + D5: 8 # F3: 3,9 => UNS
* INC C4: 2,3,4,8 + D5: 8 # D9: 3,9 => UNS
* INC C4: 2,3,4,8 + D5: 8 # D9: 1,5 => UNS
* INC C4: 2,3,4,8 + D5: 8 # A7: 8,9 => UNS
* INC C4: 2,3,4,8 + D5: 8 # A7: 4,5,7 => UNS
* INC C4: 2,3,4,8 + D5: 8 # I7: 4,7 => UNS
* INC C4: 2,3,4,8 + D5: 8 # I8: 4,7 => UNS
* INC C4: 2,3,4,8 + D5: 8 # A7: 4,7 => UNS
* INC C4: 2,3,4,8 + D5: 8 # A7: 5,8,9 => UNS
* INC C4: 2,3,4,8 + D5: 8 # A2: 1,9 => UNS
* INC C4: 2,3,4,8 + D5: 8 # B2: 1,9 => UNS
* INC C4: 2,3,4,8 + D5: 8 # A3: 1,9 => UNS
* INC C4: 2,3,4,8 + D5: 8 # C6: 1,9 => UNS
* INC C4: 2,3,4,8 + D5: 8 # C9: 1,9 => UNS
* INC C4: 2,3,4,8 + D5: 8 # F2: 3,9 => UNS
* INC C4: 2,3,4,8 + D5: 8 # F3: 3,9 => UNS
* INC C4: 2,3,4,8 + D5: 8 # D9: 3,9 => UNS
* INC C4: 2,3,4,8 + D5: 8 # D9: 1,5 => UNS
* INC C4: 2,3,4,8 + D5: 8 # D9: 5,9 => UNS
* INC C4: 2,3,4,8 + D5: 8 # D9: 1,3 => UNS
* INC C4: 2,3,4,8 + D5: 8 # A7: 5,9 => UNS
* INC C4: 2,3,4,8 + D5: 8 # A7: 4,7,8 => UNS
* INC C4: 2,3,4,8 + D5: 8 # A7: 8,9 => UNS
* INC C4: 2,3,4,8 + D5: 8 # A7: 4,5,7 => UNS
* INC C4: 2,3,4,8 + D5: 8 # I7: 4,7 => UNS
* INC C4: 2,3,4,8 + D5: 8 # I8: 4,7 => UNS
* INC C4: 2,3,4,8 + D5: 8 # A7: 4,7 => UNS
* INC C4: 2,3,4,8 + D5: 8 # A7: 5,8,9 => UNS
* STA C4: 2,3,4,8 + D5: 8
* CNT  46 HDP CHAINS /  46 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # A2: 1,9 => UNS
* INC # B2: 1,9 => UNS
* INC # A3: 1,9 => UNS
* INC # C6: 1,9 => UNS
* INC # C9: 1,9 => UNS
* INC # F2: 3,9 => UNS
* INC # F3: 3,9 => UNS
* INC # D9: 3,9 => UNS
* INC # D9: 1,5 => UNS
* INC # D9: 5,9 => UNS
* INC # D9: 1,3 => UNS
* INC # A7: 5,9 => UNS
* INC # A7: 4,7,8 => UNS
* INC # A7: 8,9 => UNS
* INC # A7: 4,5,7 => UNS
* INC # I7: 4,7 => UNS
* INC # I8: 4,7 => UNS
* INC # A7: 4,7 => UNS
* INC # A7: 5,8,9 => UNS
* INC # A2: 1,9 # A4: 1,9 => UNS
* INC # A2: 1,9 # A6: 1,9 => UNS
* INC # A2: 1,9 # A9: 1,9 => UNS
* DIS # A2: 1,9 # C6: 1,9 => CTR => C6: 3,8
* INC # A2: 1,9 + C6: 3,8 # C9: 1,9 => UNS
* INC # A2: 1,9 + C6: 3,8 # C9: 1,9 => UNS
* INC # A2: 1,9 + C6: 3,8 # C9: 4 => UNS
* INC # A2: 1,9 + C6: 3,8 # C9: 1,9 => UNS
* INC # A2: 1,9 + C6: 3,8 # C9: 4 => UNS
* INC # A2: 1,9 + C6: 3,8 # F2: 3,9 => UNS
* INC # A2: 1,9 + C6: 3,8 # F3: 3,9 => UNS
* INC # A2: 1,9 + C6: 3,8 # E4: 3,6 => UNS
* INC # A2: 1,9 + C6: 3,8 # E6: 3,6 => UNS
* INC # A2: 1,9 + C6: 3,8 # G5: 3,6 => UNS
* DIS # A2: 1,9 + C6: 3,8 # I5: 3,6 => CTR => I5: 4,5,9
* INC # A2: 1,9 + C6: 3,8 + I5: 4,5,9 # G5: 3,6 => UNS
* PRF # A2: 1,9 + C6: 3,8 + I5: 4,5,9 # G5: 4 => SOL
* STA # A2: 1,9 + C6: 3,8 + I5: 4,5,9 + G5: 4
* CNT  36 HDP CHAINS /  37 HYP OPENED