Analysis of xx-ph-00041138-12_07-base.sdk

Contents

Original Sudoku

level: very deep

Original Sudoku

position: 98.7..6..7..5.........98...5..6..7....4....3......2.9.1...6...7.5.1...69.....51.. initial

Autosolve

position: 98.7..6..7..5.69......98.7.5..6..7....4....3......2.9.1...6...7.5.1...69.....51.. 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: 0:00:06.856523

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

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Time used: 0:00:00.000014

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

Very Deep Constraint Pair Analysis

Very Deep Constraint Pair Analysis

Time used: 0:00:39.513876

List of important HDP chains detected for H1,H7: 5..:

* DIS # H1: 5 # D7: 8,9 # E5: 1,7 => CTR => E5: 5
* DIS # H1: 5 # D7: 8,9 + E5: 5 # B2: 2,3 => CTR => B2: 4
* DIS # H1: 5 # D7: 8,9 + E5: 5 + B2: 4 # A6: 6,8 => CTR => A6: 3
* DIS # H1: 5 # D7: 8,9 + E5: 5 + B2: 4 + A6: 3 => CTR => D7: 2,3,4
* DIS # H1: 5 + D7: 2,3,4 # D9: 8,9 # E4: 3,4 => CTR => E4: 8
* DIS # H1: 5 + D7: 2,3,4 # D9: 8,9 + E4: 8 # D3: 3,4 => CTR => D3: 2
* DIS # H1: 5 + D7: 2,3,4 # D9: 8,9 + E4: 8 + D3: 2 => CTR => D9: 2,3,4
* DIS # H1: 5 + D7: 2,3,4 + D9: 2,3,4 # I1: 2,3 => CTR => I1: 1,4
* DIS # H1: 5 + D7: 2,3,4 + D9: 2,3,4 + I1: 1,4 # I2: 2,3 => CTR => I2: 1,4,8
* DIS # H1: 5 + D7: 2,3,4 + D9: 2,3,4 + I1: 1,4 + I2: 1,4,8 # I3: 2,3 => CTR => I3: 1,4
* DIS # H1: 5 + D7: 2,3,4 + D9: 2,3,4 + I1: 1,4 + I2: 1,4,8 + I3: 1,4 => CTR => H1: 1,2,4
* STA H1: 1,2,4
* CNT  11 HDP CHAINS /  54 HYP OPENED

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

Details

This sudoku is very deep. Here is some information that may be helpful on how to proceed.

Positions

98.7..6..7..5.........98...5..6..7....4....3......2.9.1...6...7.5.1...69.....51.. initial
98.7..6..7..5.69......98.7.5..6..7....4....3......2.9.1...6...7.5.1...69.....51.. autosolve

Classification

level: very deep

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
D5: 8,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C1,C3: 5.. / C1 = 5  =>  1 pairs (_) / C3 = 5  =>  1 pairs (_)
E5,E6: 5.. / E5 = 5  =>  2 pairs (_) / E6 = 5  =>  2 pairs (_)
G7,H7: 5.. / G7 = 5  =>  6 pairs (_) / H7 = 5  =>  1 pairs (_)
H1,H7: 5.. / H1 = 5  =>  6 pairs (_) / H7 = 5  =>  1 pairs (_)
I5,I6: 6.. / I5 = 6  =>  2 pairs (_) / I6 = 6  =>  2 pairs (_)
F5,F8: 7.. / F5 = 7  =>  2 pairs (_) / F8 = 7  =>  4 pairs (_)
H2,I2: 8.. / H2 = 8  =>  2 pairs (_) / I2 = 8  =>  1 pairs (_)
* DURATION: 0:00:04.465138  START: 05:26:23.165100  END: 05:26:27.630238 2020-10-27
* CP COUNT: (7)
* INCONCLUSIVE

--------------------------------------------------
* DEEP CONSTRAINT PAIRS (PAIR REDUCTION)
H1,H7: 5.. / H1 = 5 ==>  6 pairs (_) / H7 = 5 ==>  1 pairs (_)
G7,H7: 5.. / G7 = 5 ==>  6 pairs (_) / H7 = 5 ==>  1 pairs (_)
F5,F8: 7.. / F5 = 7 ==>  2 pairs (_) / F8 = 7 ==>  4 pairs (_)
I5,I6: 6.. / I5 = 6 ==>  2 pairs (_) / I6 = 6 ==>  2 pairs (_)
E5,E6: 5.. / E5 = 5 ==>  2 pairs (_) / E6 = 5 ==>  2 pairs (_)
H2,I2: 8.. / H2 = 8 ==>  2 pairs (_) / I2 = 8 ==>  1 pairs (_)
C1,C3: 5.. / C1 = 5 ==>  1 pairs (_) / C3 = 5 ==>  1 pairs (_)
* DURATION: 0:01:00.172090  START: 05:26:36.501754  END: 05:27:36.673844 2020-10-27
* DCP COUNT: (7)
* INCONCLUSIVE

--------------------------------------------------
* VERY DEEP CONSTRAINT PAIRS (PAIR REDUCTION, RECURSIVE)
H1,H7: 5.. / H1 = 5 ==>  0 pairs (X) / H7 = 5  =>  1 pairs (_)
* DURATION: 0:00:39.509659  START: 05:27:36.751293  END: 05:28:16.260952 2020-10-27
* REASONING H1,H7: 5..
* DIS # H1: 5 # D7: 8,9 # E5: 1,7 => CTR => E5: 5
* DIS # H1: 5 # D7: 8,9 + E5: 5 # B2: 2,3 => CTR => B2: 4
* DIS # H1: 5 # D7: 8,9 + E5: 5 + B2: 4 # A6: 6,8 => CTR => A6: 3
* DIS # H1: 5 # D7: 8,9 + E5: 5 + B2: 4 + A6: 3 => CTR => D7: 2,3,4
* DIS # H1: 5 + D7: 2,3,4 # D9: 8,9 # E4: 3,4 => CTR => E4: 8
* DIS # H1: 5 + D7: 2,3,4 # D9: 8,9 + E4: 8 # D3: 3,4 => CTR => D3: 2
* DIS # H1: 5 + D7: 2,3,4 # D9: 8,9 + E4: 8 + D3: 2 => CTR => D9: 2,3,4
* DIS # H1: 5 + D7: 2,3,4 + D9: 2,3,4 # I1: 2,3 => CTR => I1: 1,4
* DIS # H1: 5 + D7: 2,3,4 + D9: 2,3,4 + I1: 1,4 # I2: 2,3 => CTR => I2: 1,4,8
* DIS # H1: 5 + D7: 2,3,4 + D9: 2,3,4 + I1: 1,4 + I2: 1,4,8 # I3: 2,3 => CTR => I3: 1,4
* DIS # H1: 5 + D7: 2,3,4 + D9: 2,3,4 + I1: 1,4 + I2: 1,4,8 + I3: 1,4 => CTR => H1: 1,2,4
* STA H1: 1,2,4
* CNT  11 HDP CHAINS /  54 HYP OPENED
* VDCP COUNT: (1)
* CLUE FOUND

Header Info

41138;12_07;GP;24;11.40;1.20;1.20

Appendix: Full HDP Chains

A1. Pair Reduction Analysis

Full list of HDP chains traversed:

* INC # D7: 8,9 => UNS
* INC # D9: 8,9 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # D7: 8,9 => UNS
* INC # D9: 8,9 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # D7: 8,9 => UNS
* INC # D9: 8,9 => UNS
* INC # D7: 8,9 # E4: 3,4 => UNS
* INC # D7: 8,9 # F4: 3,4 => UNS
* INC # D7: 8,9 # E6: 3,4 => UNS
* INC # D7: 8,9 # D3: 3,4 => UNS
* INC # D7: 8,9 # D9: 3,4 => UNS
* INC # D7: 8,9 => UNS
* INC # D9: 8,9 # E4: 3,4 => UNS
* INC # D9: 8,9 # F4: 3,4 => UNS
* INC # D9: 8,9 # E6: 3,4 => UNS
* INC # D9: 8,9 # D3: 3,4 => UNS
* INC # D9: 8,9 # D7: 3,4 => UNS
* INC # D9: 8,9 # C9: 8,9 => UNS
* INC # D9: 8,9 # C9: 2,3,6,7 => UNS
* INC # D9: 8,9 => UNS
* CNT  16 HDP CHAINS /  16 HYP OPENED

A4. Deep Constraint Pair Analysis

Full list of HDP chains traversed for H1,H7: 5..:

* INC # H1: 5 # D7: 8,9 => UNS
* INC # H1: 5 # D9: 8,9 => UNS
* INC # H1: 5 # E5: 1,7 => UNS
* INC # H1: 5 # E6: 1,7 => UNS
* INC # H1: 5 # B5: 1,7 => UNS
* INC # H1: 5 # B5: 2,6,9 => UNS
* INC # H1: 5 # H4: 2,8 => UNS
* INC # H1: 5 # I4: 2,8 => UNS
* INC # H1: 5 # A5: 2,8 => UNS
* INC # H1: 5 # A5: 6 => UNS
* INC # H1: 5 # G8: 2,8 => UNS
* INC # H1: 5 # G8: 3,4 => UNS
* INC # H1: 5 # H4: 4,8 => UNS
* INC # H1: 5 # I4: 4,8 => UNS
* INC # H1: 5 # D6: 4,8 => UNS
* INC # H1: 5 # D6: 3 => UNS
* INC # H1: 5 # G8: 4,8 => UNS
* INC # H1: 5 # G8: 2,3 => UNS
* INC # H1: 5 => UNS
* INC # H7: 5 # D7: 8,9 => UNS
* INC # H7: 5 # D9: 8,9 => UNS
* INC # H7: 5 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

Full list of HDP chains traversed for G7,H7: 5..:

* INC # G7: 5 # D7: 8,9 => UNS
* INC # G7: 5 # D9: 8,9 => UNS
* INC # G7: 5 # E5: 1,7 => UNS
* INC # G7: 5 # E6: 1,7 => UNS
* INC # G7: 5 # B5: 1,7 => UNS
* INC # G7: 5 # B5: 2,6,9 => UNS
* INC # G7: 5 # H4: 2,8 => UNS
* INC # G7: 5 # I4: 2,8 => UNS
* INC # G7: 5 # A5: 2,8 => UNS
* INC # G7: 5 # A5: 6 => UNS
* INC # G7: 5 # G8: 2,8 => UNS
* INC # G7: 5 # G8: 3,4 => UNS
* INC # G7: 5 # H4: 4,8 => UNS
* INC # G7: 5 # I4: 4,8 => UNS
* INC # G7: 5 # D6: 4,8 => UNS
* INC # G7: 5 # D6: 3 => UNS
* INC # G7: 5 # G8: 4,8 => UNS
* INC # G7: 5 # G8: 2,3 => UNS
* INC # G7: 5 => UNS
* INC # H7: 5 # D7: 8,9 => UNS
* INC # H7: 5 # D9: 8,9 => UNS
* INC # H7: 5 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

Full list of HDP chains traversed for F5,F8: 7..:

* INC # F8: 7 # D7: 8,9 => UNS
* INC # F8: 7 # D9: 8,9 => UNS
* INC # F8: 7 # F4: 1,9 => UNS
* INC # F8: 7 # F4: 3,4 => UNS
* INC # F8: 7 # B5: 1,9 => UNS
* INC # F8: 7 # B5: 2,6,7 => UNS
* INC # F8: 7 => UNS
* INC # F5: 7 # D7: 8,9 => UNS
* INC # F5: 7 # D9: 8,9 => UNS
* INC # F5: 7 # D7: 3,4 => UNS
* INC # F5: 7 # F7: 3,4 => UNS
* INC # F5: 7 # E8: 3,4 => UNS
* INC # F5: 7 # D9: 3,4 => UNS
* INC # F5: 7 # E9: 3,4 => UNS
* INC # F5: 7 # A8: 3,4 => UNS
* INC # F5: 7 # G8: 3,4 => UNS
* INC # F5: 7 # F1: 3,4 => UNS
* INC # F5: 7 # F4: 3,4 => UNS
* INC # F5: 7 => UNS
* CNT  19 HDP CHAINS /  19 HYP OPENED

Full list of HDP chains traversed for I5,I6: 6..:

* INC # I5: 6 # C4: 2,8 => UNS
* INC # I5: 6 # C4: 1,3,9 => UNS
* INC # I5: 6 # G5: 2,8 => UNS
* INC # I5: 6 # G5: 5 => UNS
* INC # I5: 6 # A8: 2,8 => UNS
* INC # I5: 6 # A9: 2,8 => UNS
* INC # I5: 6 # D7: 8,9 => UNS
* INC # I5: 6 # D9: 8,9 => UNS
* INC # I5: 6 => UNS
* INC # I6: 6 # C4: 3,8 => UNS
* INC # I6: 6 # C6: 3,8 => UNS
* INC # I6: 6 # D6: 3,8 => UNS
* INC # I6: 6 # E6: 3,8 => UNS
* INC # I6: 6 # A8: 3,8 => UNS
* INC # I6: 6 # A9: 3,8 => UNS
* INC # I6: 6 # D7: 8,9 => UNS
* INC # I6: 6 # D9: 8,9 => UNS
* INC # I6: 6 => UNS
* CNT  18 HDP CHAINS /  18 HYP OPENED

Full list of HDP chains traversed for E5,E6: 5..:

* INC # E5: 5 # D7: 8,9 => UNS
* INC # E5: 5 # D9: 8,9 => UNS
* INC # E5: 5 # H4: 2,8 => UNS
* INC # E5: 5 # I4: 2,8 => UNS
* INC # E5: 5 # I5: 2,8 => UNS
* INC # E5: 5 # A5: 2,8 => UNS
* INC # E5: 5 # A5: 6 => UNS
* INC # E5: 5 # G7: 2,8 => UNS
* INC # E5: 5 # G8: 2,8 => UNS
* INC # E5: 5 => UNS
* INC # E6: 5 # D7: 8,9 => UNS
* INC # E6: 5 # D9: 8,9 => UNS
* INC # E6: 5 # H4: 4,8 => UNS
* INC # E6: 5 # I4: 4,8 => UNS
* INC # E6: 5 # I6: 4,8 => UNS
* INC # E6: 5 # D6: 4,8 => UNS
* INC # E6: 5 # D6: 3 => UNS
* INC # E6: 5 # G7: 4,8 => UNS
* INC # E6: 5 # G8: 4,8 => UNS
* INC # E6: 5 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

Full list of HDP chains traversed for H2,I2: 8..:

* INC # H2: 8 # D7: 8,9 => UNS
* INC # H2: 8 # D9: 8,9 => UNS
* INC # H2: 8 # G7: 2,4 => UNS
* INC # H2: 8 # H7: 2,4 => UNS
* INC # H2: 8 # G8: 2,4 => UNS
* INC # H2: 8 # I9: 2,4 => UNS
* INC # H2: 8 # A9: 2,4 => UNS
* INC # H2: 8 # B9: 2,4 => UNS
* INC # H2: 8 # D9: 2,4 => UNS
* INC # H2: 8 # E9: 2,4 => UNS
* INC # H2: 8 # H1: 2,4 => UNS
* INC # H2: 8 # H4: 2,4 => UNS
* INC # H2: 8 => UNS
* INC # I2: 8 # D7: 8,9 => UNS
* INC # I2: 8 # D9: 8,9 => UNS
* INC # I2: 8 => UNS
* CNT  16 HDP CHAINS /  16 HYP OPENED

Full list of HDP chains traversed for C1,C3: 5..:

* INC # C1: 5 # D7: 8,9 => UNS
* INC # C1: 5 # D9: 8,9 => UNS
* INC # C1: 5 => UNS
* INC # C3: 5 # D7: 8,9 => UNS
* INC # C3: 5 # D9: 8,9 => UNS
* INC # C3: 5 => UNS
* CNT   6 HDP CHAINS /   6 HYP OPENED

A5. Very Deep Constraint Pair Analysis

Full list of HDP chains traversed for H1,H7: 5..:

* INC # H1: 5 # D7: 8,9 => UNS
* INC # H1: 5 # D9: 8,9 => UNS
* INC # H1: 5 # E5: 1,7 => UNS
* INC # H1: 5 # E6: 1,7 => UNS
* INC # H1: 5 # B5: 1,7 => UNS
* INC # H1: 5 # B5: 2,6,9 => UNS
* INC # H1: 5 # H4: 2,8 => UNS
* INC # H1: 5 # I4: 2,8 => UNS
* INC # H1: 5 # A5: 2,8 => UNS
* INC # H1: 5 # A5: 6 => UNS
* INC # H1: 5 # G8: 2,8 => UNS
* INC # H1: 5 # G8: 3,4 => UNS
* INC # H1: 5 # H4: 4,8 => UNS
* INC # H1: 5 # I4: 4,8 => UNS
* INC # H1: 5 # D6: 4,8 => UNS
* INC # H1: 5 # D6: 3 => UNS
* INC # H1: 5 # G8: 4,8 => UNS
* INC # H1: 5 # G8: 2,3 => UNS
* DIS # H1: 5 # D7: 8,9 # E5: 1,7 => CTR => E5: 5
* INC # H1: 5 # D7: 8,9 + E5: 5 # D3: 3,4 => UNS
* INC # H1: 5 # D7: 8,9 + E5: 5 # D9: 3,4 => UNS
* DIS # H1: 5 # D7: 8,9 + E5: 5 # B2: 2,3 => CTR => B2: 4
* DIS # H1: 5 # D7: 8,9 + E5: 5 + B2: 4 # A6: 6,8 => CTR => A6: 3
* DIS # H1: 5 # D7: 8,9 + E5: 5 + B2: 4 + A6: 3 => CTR => D7: 2,3,4
* INC # H1: 5 + D7: 2,3,4 # D9: 8,9 => UNS
* INC # H1: 5 + D7: 2,3,4 # D9: 2,3,4 => UNS
* INC # H1: 5 + D7: 2,3,4 # E5: 1,7 => UNS
* INC # H1: 5 + D7: 2,3,4 # E6: 1,7 => UNS
* INC # H1: 5 + D7: 2,3,4 # B5: 1,7 => UNS
* INC # H1: 5 + D7: 2,3,4 # B5: 2,6,9 => UNS
* INC # H1: 5 + D7: 2,3,4 # H4: 2,8 => UNS
* INC # H1: 5 + D7: 2,3,4 # I4: 2,8 => UNS
* INC # H1: 5 + D7: 2,3,4 # A5: 2,8 => UNS
* INC # H1: 5 + D7: 2,3,4 # A5: 6 => UNS
* INC # H1: 5 + D7: 2,3,4 # G8: 2,8 => UNS
* INC # H1: 5 + D7: 2,3,4 # G8: 3,4 => UNS
* INC # H1: 5 + D7: 2,3,4 # H4: 4,8 => UNS
* INC # H1: 5 + D7: 2,3,4 # I4: 4,8 => UNS
* INC # H1: 5 + D7: 2,3,4 # D6: 4,8 => UNS
* INC # H1: 5 + D7: 2,3,4 # D6: 3 => UNS
* INC # H1: 5 + D7: 2,3,4 # G8: 4,8 => UNS
* INC # H1: 5 + D7: 2,3,4 # G8: 2,3 => UNS
* INC # H1: 5 + D7: 2,3,4 # D9: 8,9 # E5: 1,7 => UNS
* INC # H1: 5 + D7: 2,3,4 # D9: 8,9 # E6: 1,7 => UNS
* INC # H1: 5 + D7: 2,3,4 # D9: 8,9 # B5: 1,7 => UNS
* INC # H1: 5 + D7: 2,3,4 # D9: 8,9 # B5: 2,6,9 => UNS
* DIS # H1: 5 + D7: 2,3,4 # D9: 8,9 # E4: 3,4 => CTR => E4: 8
* DIS # H1: 5 + D7: 2,3,4 # D9: 8,9 + E4: 8 # D3: 3,4 => CTR => D3: 2
* DIS # H1: 5 + D7: 2,3,4 # D9: 8,9 + E4: 8 + D3: 2 => CTR => D9: 2,3,4
* DIS # H1: 5 + D7: 2,3,4 + D9: 2,3,4 # I1: 2,3 => CTR => I1: 1,4
* DIS # H1: 5 + D7: 2,3,4 + D9: 2,3,4 + I1: 1,4 # I2: 2,3 => CTR => I2: 1,4,8
* DIS # H1: 5 + D7: 2,3,4 + D9: 2,3,4 + I1: 1,4 + I2: 1,4,8 # I3: 2,3 => CTR => I3: 1,4
* DIS # H1: 5 + D7: 2,3,4 + D9: 2,3,4 + I1: 1,4 + I2: 1,4,8 + I3: 1,4 => CTR => H1: 1,2,4
* INC H1: 1,2,4 # H7: 5 => UNS
* STA H1: 1,2,4
* CNT  54 HDP CHAINS /  54 HYP OPENED