Analysis of xx-ph-00041155-12_07-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 98.7..6..7..5.......4.8..9.8...7.43..4...2.....3.....73.......1.7..9..8.......9.6 initial

Autosolve

position: 98.7..6..7..5.9.....4.8.79.8...7.43..47..2.....3.....73.......1.7..9..8.......9.6 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: 0:00:53.260611

The following important HDP chains were detected:

* DIS # H7: 2,5 # B4: 6,9 => CTR => B4: 1,2,5
* DIS # G8: 2,5 # F9: 1,3 => CTR => F9: 4,5,7,8
* DIS # G8: 2,5 + F9: 4,5,7,8 # F6: 1,6 => CTR => F6: 4,5,8
* DIS # G8: 2,5 + F9: 4,5,7,8 + F6: 4,5,8 # H1: 5 => CTR => H1: 1,2
* DIS # G8: 2,5 + F9: 4,5,7,8 + F6: 4,5,8 + H1: 1,2 # D5: 3,6 => CTR => D5: 1,8
* DIS # G8: 2,5 + F9: 4,5,7,8 + F6: 4,5,8 + H1: 1,2 + D5: 1,8 # D6: 1,8 => CTR => D6: 4,6,9
* PRF # G8: 2,5 + F9: 4,5,7,8 + F6: 4,5,8 + H1: 1,2 + D5: 1,8 + D6: 4,6,9 # E7: 2,5 => SOL
* STA # G8: 2,5 + F9: 4,5,7,8 + F6: 4,5,8 + H1: 1,2 + D5: 1,8 + D6: 4,6,9 + E7: 2,5
* CNT   7 HDP CHAINS /  62 HYP OPENED

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

Details

Positions

98.7..6..7..5.......4.8..9.8...7.43..4...2.....3.....73.......1.7..9..8.......9.6 initial
98.7..6..7..5.9.....4.8.79.8...7.43..47..2.....3.....73.......1.7..9..8.......9.6 autosolve
985713624726549318134286795869175432547832169213964857398657241672491583451328976 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
G7: 2,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B2,B3: 3.. / B2 = 3  =>  1 pairs (_) / B3 = 3  =>  3 pairs (_)
D5,E5: 3.. / D5 = 3  =>  2 pairs (_) / E5 = 3  =>  1 pairs (_)
G8,I8: 3.. / G8 = 3  =>  1 pairs (_) / I8 = 3  => 12 pairs (_)
G2,G8: 3.. / G2 = 3  => 12 pairs (_) / G8 = 3  =>  1 pairs (_)
A8,A9: 4.. / A8 = 4  =>  4 pairs (_) / A9 = 4  =>  1 pairs (_)
H5,H6: 6.. / H5 = 6  =>  2 pairs (_) / H6 = 6  =>  2 pairs (_)
F7,F9: 7.. / F7 = 7  =>  1 pairs (_) / F9 = 7  =>  1 pairs (_)
H7,H9: 7.. / H7 = 7  =>  1 pairs (_) / H9 = 7  =>  1 pairs (_)
F7,H7: 7.. / F7 = 7  =>  1 pairs (_) / H7 = 7  =>  1 pairs (_)
F9,H9: 7.. / F9 = 7  =>  1 pairs (_) / H9 = 7  =>  1 pairs (_)
G2,I2: 8.. / G2 = 8  =>  4 pairs (_) / I2 = 8  =>  2 pairs (_)
C7,C9: 8.. / C7 = 8  =>  4 pairs (_) / C9 = 8  =>  1 pairs (_)
I2,I5: 8.. / I2 = 8  =>  2 pairs (_) / I5 = 8  =>  4 pairs (_)
I4,I5: 9.. / I4 = 9  =>  3 pairs (_) / I5 = 9  =>  2 pairs (_)
B7,C7: 9.. / B7 = 9  =>  3 pairs (_) / C7 = 9  =>  1 pairs (_)
D5,I5: 9.. / D5 = 9  =>  3 pairs (_) / I5 = 9  =>  2 pairs (_)
B6,D6: 9.. / B6 = 9  =>  1 pairs (_) / D6 = 9  =>  3 pairs (_)
C4,C7: 9.. / C4 = 9  =>  3 pairs (_) / C7 = 9  =>  1 pairs (_)
* DURATION: 0:00:14.703942  START: 18:35:44.792475  END: 18:35:59.496417 2020-12-18
* CP COUNT: (18)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:52.998261  START: 18:36:10.032688  END: 18:37:03.030949 2020-12-18
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00041155-12_07-base-pr-002.dot
* REASONING
* DIS # H7: 2,5 # B4: 6,9 => CTR => B4: 1,2,5
* DIS # G8: 2,5 # F9: 1,3 => CTR => F9: 4,5,7,8
* DIS # G8: 2,5 + F9: 4,5,7,8 # F6: 1,6 => CTR => F6: 4,5,8
* DIS # G8: 2,5 + F9: 4,5,7,8 + F6: 4,5,8 # H1: 5 => CTR => H1: 1,2
* DIS # G8: 2,5 + F9: 4,5,7,8 + F6: 4,5,8 + H1: 1,2 # D5: 3,6 => CTR => D5: 1,8
* DIS # G8: 2,5 + F9: 4,5,7,8 + F6: 4,5,8 + H1: 1,2 + D5: 1,8 # D6: 1,8 => CTR => D6: 4,6,9
* PRF # G8: 2,5 + F9: 4,5,7,8 + F6: 4,5,8 + H1: 1,2 + D5: 1,8 + D6: 4,6,9 # E7: 2,5 => SOL
* STA # G8: 2,5 + F9: 4,5,7,8 + F6: 4,5,8 + H1: 1,2 + D5: 1,8 + D6: 4,6,9 + E7: 2,5
* CNT   7 HDP CHAINS /  62 HYP OPENED

Header Info

41155;12_07;GP;24;11.30;1.20;1.20

Solution

position: 985713624726549318134286795869175432547832169213964857398657241672491583451328976 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 # H7: 2,5 => UNS
* INC # G8: 2,5 => UNS
* INC # I8: 2,5 => UNS
* INC # H9: 2,5 => UNS
* INC # B7: 2,5 => UNS
* INC # C7: 2,5 => UNS
* INC # E7: 2,5 => UNS
* INC # G6: 2,5 => UNS
* INC # G6: 1,8 => UNS
* CNT   9 HDP CHAINS /   9 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # H7: 2,5 => UNS
* INC # G8: 2,5 => UNS
* INC # I8: 2,5 => UNS
* INC # H9: 2,5 => UNS
* INC # B7: 2,5 => UNS
* INC # C7: 2,5 => UNS
* INC # E7: 2,5 => UNS
* INC # G6: 2,5 => UNS
* INC # G6: 1,8 => UNS
* CNT   9 HDP CHAINS /   9 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # H7: 2,5 => UNS
* INC # G8: 2,5 => UNS
* INC # I8: 2,5 => UNS
* INC # H9: 2,5 => UNS
* INC # B7: 2,5 => UNS
* INC # C7: 2,5 => UNS
* INC # E7: 2,5 => UNS
* INC # G6: 2,5 => UNS
* INC # G6: 1,8 => UNS
* INC # H7: 2,5 # C7: 6,9 => UNS
* INC # H7: 2,5 # C7: 8 => UNS
* DIS # H7: 2,5 # B4: 6,9 => CTR => B4: 1,2,5
* INC # H7: 2,5 + B4: 1,2,5 # B6: 6,9 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # B6: 6,9 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # B6: 1,2,5 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # C7: 6,9 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # C7: 8 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # B6: 6,9 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # B6: 1,2,5 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # D7: 4,6 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # D7: 8 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # E2: 4,6 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # E6: 4,6 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # G6: 2,5 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # G6: 1,8 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # H1: 2,5 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # H6: 2,5 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # C7: 6,9 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # C7: 8 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # B6: 6,9 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # B6: 1,2,5 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # D7: 4,6 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # D7: 8 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # E2: 4,6 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # E6: 4,6 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # G6: 2,5 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # G6: 1,8 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # H1: 2,5 => UNS
* INC # H7: 2,5 + B4: 1,2,5 # H6: 2,5 => UNS
* INC # H7: 2,5 + B4: 1,2,5 => UNS
* INC # G8: 2,5 # E1: 1,3 => UNS
* INC # G8: 2,5 # E1: 2 => UNS
* DIS # G8: 2,5 # F9: 1,3 => CTR => F9: 4,5,7,8
* INC # G8: 2,5 + F9: 4,5,7,8 # D3: 1,6 => UNS
* INC # G8: 2,5 + F9: 4,5,7,8 # D3: 2 => UNS
* INC # G8: 2,5 + F9: 4,5,7,8 # F4: 1,6 => UNS
* DIS # G8: 2,5 + F9: 4,5,7,8 # F6: 1,6 => CTR => F6: 4,5,8
* INC # G8: 2,5 + F9: 4,5,7,8 + F6: 4,5,8 # F8: 1,6 => UNS
* INC # G8: 2,5 + F9: 4,5,7,8 + F6: 4,5,8 # D3: 1,6 => UNS
* INC # G8: 2,5 + F9: 4,5,7,8 + F6: 4,5,8 # D3: 2 => UNS
* INC # G8: 2,5 + F9: 4,5,7,8 + F6: 4,5,8 # F4: 1,6 => UNS
* INC # G8: 2,5 + F9: 4,5,7,8 + F6: 4,5,8 # F8: 1,6 => UNS
* INC # G8: 2,5 + F9: 4,5,7,8 + F6: 4,5,8 # H1: 1,2 => UNS
* DIS # G8: 2,5 + F9: 4,5,7,8 + F6: 4,5,8 # H1: 5 => CTR => H1: 1,2
* INC # G8: 2,5 + F9: 4,5,7,8 + F6: 4,5,8 + H1: 1,2 # B2: 1,2 => UNS
* INC # G8: 2,5 + F9: 4,5,7,8 + F6: 4,5,8 + H1: 1,2 # C2: 1,2 => UNS
* INC # G8: 2,5 + F9: 4,5,7,8 + F6: 4,5,8 + H1: 1,2 # D5: 1,8 => UNS
* DIS # G8: 2,5 + F9: 4,5,7,8 + F6: 4,5,8 + H1: 1,2 # D5: 3,6 => CTR => D5: 1,8
* DIS # G8: 2,5 + F9: 4,5,7,8 + F6: 4,5,8 + H1: 1,2 + D5: 1,8 # D6: 1,8 => CTR => D6: 4,6,9
* INC # G8: 2,5 + F9: 4,5,7,8 + F6: 4,5,8 + H1: 1,2 + D5: 1,8 + D6: 4,6,9 # B7: 2,5 => UNS
* PRF # G8: 2,5 + F9: 4,5,7,8 + F6: 4,5,8 + H1: 1,2 + D5: 1,8 + D6: 4,6,9 # E7: 2,5 => SOL
* STA # G8: 2,5 + F9: 4,5,7,8 + F6: 4,5,8 + H1: 1,2 + D5: 1,8 + D6: 4,6,9 + E7: 2,5
* CNT  61 HDP CHAINS /  62 HYP OPENED