Analysis of xx-ph-00011216-kz0-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 9..8..7...8..6..5...4..3..88.......9.2..3..6...7...4...1.3.......6.2...1.....5.2. initial

Autosolve

position: 9..8..7...8..6..5...4..3..88.......9.2..3..6...7...4...1.3.......6.2...1.....5.2. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

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

Pair Reduction

Pair Reduction

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

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:12.880763

The following important HDP chains were detected:

* PRF # G3: 1,9 # C1: 3,5 => SOL
* STA # G3: 1,9 + C1: 3,5
* CNT   1 HDP CHAINS /  27 HYP OPENED

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

Details

Positions

9..8..7...8..6..5...4..3..88.......9.2..3..6...7...4...1.3.......6.2...1.....5.2. initial
9..8..7...8..6..5...4..3..88.......9.2..3..6...7...4...1.3.......6.2...1.....5.2. autosolve
935812746781964352264573198843651279129437865657289413512346987496728531378195624 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (2)
H3: 1,9
I5: 5,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D9,E9: 1.. / D9 = 1  =>  2 pairs (_) / E9 = 1  =>  3 pairs (_)
G4,I6: 2.. / G4 = 2  =>  3 pairs (_) / I6 = 2  =>  3 pairs (_)
A7,C7: 2.. / A7 = 2  =>  2 pairs (_) / C7 = 2  =>  3 pairs (_)
B4,A5: 4.. / B4 = 4  =>  3 pairs (_) / A5 = 4  =>  3 pairs (_)
I1,G3: 6.. / I1 = 6  =>  3 pairs (_) / G3 = 6  =>  3 pairs (_)
F7,D9: 6.. / F7 = 6  =>  2 pairs (_) / D9 = 6  =>  3 pairs (_)
B1,I1: 6.. / B1 = 6  =>  3 pairs (_) / I1 = 6  =>  3 pairs (_)
A3,A6: 6.. / A3 = 6  =>  4 pairs (_) / A6 = 6  =>  2 pairs (_)
H4,I5: 7.. / H4 = 7  =>  5 pairs (_) / I5 = 7  =>  2 pairs (_)
G5,H6: 8.. / G5 = 8  =>  3 pairs (_) / H6 = 8  =>  3 pairs (_)
C7,C9: 8.. / C7 = 8  =>  3 pairs (_) / C9 = 8  =>  2 pairs (_)
F5,G5: 8.. / F5 = 8  =>  3 pairs (_) / G5 = 8  =>  3 pairs (_)
C5,B6: 9.. / C5 = 9  =>  3 pairs (_) / B6 = 9  =>  5 pairs (_)
* DURATION: 0:00:07.419597  START: 14:36:02.234148  END: 14:36:09.653745 2020-12-01
* CP COUNT: (13)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:12.734342  START: 14:36:15.420373  END: 14:36:28.154715 2020-12-01
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00011216-kz0-base-pr-002.dot
* REASONING
* PRF # G3: 1,9 # C1: 3,5 => SOL
* STA # G3: 1,9 + C1: 3,5
* CNT   1 HDP CHAINS /  27 HYP OPENED

Header Info

11216;kz0;GP;23;11.30;11.30;7.60

Solution

position: 935812746781964352264573198843651279129437865657289413512346987496728531378195624 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 # G2: 1,9 => UNS
* INC # G3: 1,9 => UNS
* INC # D3: 1,9 => UNS
* INC # E3: 1,9 => UNS
* INC # D5: 5,7 => UNS
* INC # D5: 1,4,9 => UNS
* INC # I7: 5,7 => UNS
* INC # I7: 4,6 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G2: 1,9 => UNS
* INC # G3: 1,9 => UNS
* INC # D3: 1,9 => UNS
* INC # E3: 1,9 => UNS
* INC # D5: 5,7 => UNS
* INC # D5: 1,4,9 => UNS
* INC # I7: 5,7 => UNS
* INC # I7: 4,6 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # G2: 1,9 => UNS
* INC # G3: 1,9 => UNS
* INC # D3: 1,9 => UNS
* INC # E3: 1,9 => UNS
* INC # D5: 5,7 => UNS
* INC # D5: 1,4,9 => UNS
* INC # I7: 5,7 => UNS
* INC # I7: 4,6 => UNS
* INC # G2: 1,9 # I1: 3,4 => UNS
* INC # G2: 1,9 # I2: 3,4 => UNS
* INC # G2: 1,9 # H8: 3,4 => UNS
* INC # G2: 1,9 # H8: 7,8,9 => UNS
* INC # G2: 1,9 # D2: 1,9 => UNS
* INC # G2: 1,9 # F2: 1,9 => UNS
* INC # G2: 1,9 # I1: 2,6 => UNS
* INC # G2: 1,9 # I1: 3,4 => UNS
* INC # G2: 1,9 # A3: 2,6 => UNS
* INC # G2: 1,9 # A3: 1,5,7 => UNS
* INC # G2: 1,9 # D3: 1,9 => UNS
* INC # G2: 1,9 # E3: 1,9 => UNS
* INC # G2: 1,9 # D5: 5,7 => UNS
* INC # G2: 1,9 # D5: 1,4,9 => UNS
* INC # G2: 1,9 # I7: 5,7 => UNS
* INC # G2: 1,9 # I7: 4,6 => UNS
* INC # G2: 1,9 => UNS
* PRF # G3: 1,9 # C1: 3,5 => SOL
* STA # G3: 1,9 + C1: 3,5
* CNT  26 HDP CHAINS /  27 HYP OPENED