Analysis of xx-ph-00050991-12_10-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 98.76.54.7..9..8....6......8..5..9...3.....2...7.4....1...5.....791.......8..71.. initial

Autosolve

position: 98.76.54.7..9..8....6......8..5..9...3.....2..97.4....1...5.....791.......8..71.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # H6: 3,6 => CTR => H6: 1,5,8
* CNT   1 HDP CHAINS /  16 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 # H6: 3,6 => CTR => H6: 1,5,8
* STA H6: 1,5,8
* CNT   1 HDP CHAINS /  36 HYP OPENED

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

Pair Reduction Position

position: 98.76.54.7..9..8....6......8..5..9...3.....2..97.4....1...5.....791.......8..71.. pair_reduction
Pair Reduction

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

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:30.657842

The following important HDP chains were detected:

* DIS # F5: 6,8 # I1: 2,3 => CTR => I1: 1
* DIS # F5: 6,8 + I1: 1 # F6: 2,3 => CTR => F6: 1
* DIS # F5: 6,8 + I1: 1 + F6: 1 # D3: 2,3 => CTR => D3: 8
* DIS # F5: 6,8 + I1: 1 + F6: 1 + D3: 8 # E3: 2,3 => CTR => E3: 1
* DIS # F5: 6,8 + I1: 1 + F6: 1 + D3: 8 + E3: 1 # I5: 5 => CTR => I5: 4,7
* PRF # F5: 6,8 + I1: 1 + F6: 1 + D3: 8 + E3: 1 + I5: 4,7 # G7: 4,7 => SOL
* STA # F5: 6,8 + I1: 1 + F6: 1 + D3: 8 + E3: 1 + I5: 4,7 + G7: 4,7
* CNT   6 HDP CHAINS /  32 HYP OPENED

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

Details

Positions

98.76.54.7..9..8....6......8..5..9...3.....2...7.4....1...5.....791.......8..71.. initial
98.76.54.7..9..8....6......8..5..9...3.....2..97.4....1...5.....791.......8..71.. autosolve
98.76.54.7..9..8....6......8..5..9...3.....2..97.4....1...5.....791.......8..71.. pair_reduction
982763541715924836346815279864572913531698427297341685123459768479186352658237194 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (2)
D5: 6,8
G6: 3,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F2,F3: 5.. / F2 = 5  =>  5 pairs (_) / F3 = 5  =>  2 pairs (_)
C2,C5: 5.. / C2 = 5  =>  3 pairs (_) / C5 = 5  =>  5 pairs (_)
H2,I2: 6.. / H2 = 6  =>  2 pairs (_) / I2 = 6  =>  3 pairs (_)
E4,E5: 7.. / E4 = 7  =>  2 pairs (_) / E5 = 7  =>  3 pairs (_)
H3,I3: 9.. / H3 = 9  =>  2 pairs (_) / I3 = 9  =>  2 pairs (_)
E5,F5: 9.. / E5 = 9  =>  4 pairs (_) / F5 = 9  =>  2 pairs (_)
F7,E9: 9.. / F7 = 9  =>  4 pairs (_) / E9 = 9  =>  2 pairs (_)
E5,E9: 9.. / E5 = 9  =>  4 pairs (_) / E9 = 9  =>  2 pairs (_)
F5,F7: 9.. / F5 = 9  =>  2 pairs (_) / F7 = 9  =>  4 pairs (_)
* DURATION: 0:00:05.457271  START: 06:19:29.530756  END: 06:19:34.988027 2020-12-20
* CP COUNT: (9)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:30.495674  START: 06:19:56.842762  END: 06:20:27.338436 2020-12-20
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00050991-12_10-base-pr-002.dot
* REASONING
* DIS # F5: 6,8 # I1: 2,3 => CTR => I1: 1
* DIS # F5: 6,8 + I1: 1 # F6: 2,3 => CTR => F6: 1
* DIS # F5: 6,8 + I1: 1 + F6: 1 # D3: 2,3 => CTR => D3: 8
* DIS # F5: 6,8 + I1: 1 + F6: 1 + D3: 8 # E3: 2,3 => CTR => E3: 1
* DIS # F5: 6,8 + I1: 1 + F6: 1 + D3: 8 + E3: 1 # I5: 5 => CTR => I5: 4,7
* PRF # F5: 6,8 + I1: 1 + F6: 1 + D3: 8 + E3: 1 + I5: 4,7 # G7: 4,7 => SOL
* STA # F5: 6,8 + I1: 1 + F6: 1 + D3: 8 + E3: 1 + I5: 4,7 + G7: 4,7
* CNT   6 HDP CHAINS /  32 HYP OPENED

Header Info

50991;12_10;GP;25;11.30;1.20;1.20

Solution

position: 982763541715924836346815279864572913531698427297341685123459768479186352658237194 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 # F5: 6,8 => UNS
* INC # D6: 6,8 => UNS
* INC # F6: 6,8 => UNS
* INC # I5: 6,8 => UNS
* INC # I5: 1,4,5,7 => UNS
* INC # D7: 6,8 => UNS
* INC # D7: 2,3,4 => UNS
* INC # H4: 3,6 => UNS
* INC # I4: 3,6 => UNS
* DIS # H6: 3,6 => CTR => H6: 1,5,8
* INC # H6: 1,5,8 => UNS
* INC # I6: 3,6 => UNS
* INC # D6: 3,6 => UNS
* INC # F6: 3,6 => UNS
* INC # G7: 3,6 => UNS
* INC # G8: 3,6 => UNS
* CNT  16 HDP CHAINS /  16 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F5: 6,8 => UNS
* INC # D6: 6,8 => UNS
* INC # F6: 6,8 => UNS
* INC # I5: 6,8 => UNS
* INC # I5: 1,4,5,7 => UNS
* INC # D7: 6,8 => UNS
* INC # D7: 2,3,4 => UNS
* INC # H4: 3,6 => UNS
* INC # I4: 3,6 => UNS
* DIS # H6: 3,6 => CTR => H6: 1,5,8
* INC H6: 1,5,8 # I6: 3,6 => UNS
* INC H6: 1,5,8 # D6: 3,6 => UNS
* INC H6: 1,5,8 # F6: 3,6 => UNS
* INC H6: 1,5,8 # G7: 3,6 => UNS
* INC H6: 1,5,8 # G8: 3,6 => UNS
* INC H6: 1,5,8 # H4: 3,6 => UNS
* INC H6: 1,5,8 # I4: 3,6 => UNS
* INC H6: 1,5,8 # I6: 3,6 => UNS
* INC H6: 1,5,8 # D6: 3,6 => UNS
* INC H6: 1,5,8 # F6: 3,6 => UNS
* INC H6: 1,5,8 # G7: 3,6 => UNS
* INC H6: 1,5,8 # G8: 3,6 => UNS
* INC H6: 1,5,8 # F5: 6,8 => UNS
* INC H6: 1,5,8 # D6: 6,8 => UNS
* INC H6: 1,5,8 # F6: 6,8 => UNS
* INC H6: 1,5,8 # I5: 6,8 => UNS
* INC H6: 1,5,8 # I5: 1,4,5,7 => UNS
* INC H6: 1,5,8 # D7: 6,8 => UNS
* INC H6: 1,5,8 # D7: 2,3,4 => UNS
* INC H6: 1,5,8 # H4: 3,6 => UNS
* INC H6: 1,5,8 # I4: 3,6 => UNS
* INC H6: 1,5,8 # I6: 3,6 => UNS
* INC H6: 1,5,8 # D6: 3,6 => UNS
* INC H6: 1,5,8 # F6: 3,6 => UNS
* INC H6: 1,5,8 # G7: 3,6 => UNS
* INC H6: 1,5,8 # G8: 3,6 => UNS
* STA H6: 1,5,8
* CNT  36 HDP CHAINS /  36 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # F5: 6,8 => UNS
* INC # D6: 6,8 => UNS
* INC # F6: 6,8 => UNS
* INC # I5: 6,8 => UNS
* INC # I5: 1,4,5,7 => UNS
* INC # D7: 6,8 => UNS
* INC # D7: 2,3,4 => UNS
* INC # H4: 3,6 => UNS
* INC # I4: 3,6 => UNS
* INC # I6: 3,6 => UNS
* INC # D6: 3,6 => UNS
* INC # F6: 3,6 => UNS
* INC # G7: 3,6 => UNS
* INC # G8: 3,6 => UNS
* INC # F5: 6,8 # E2: 2,3 => UNS
* INC # F5: 6,8 # D3: 2,3 => UNS
* INC # F5: 6,8 # E3: 2,3 => UNS
* INC # F5: 6,8 # C1: 2,3 => UNS
* DIS # F5: 6,8 # I1: 2,3 => CTR => I1: 1
* INC # F5: 6,8 + I1: 1 # F4: 2,3 => UNS
* DIS # F5: 6,8 + I1: 1 # F6: 2,3 => CTR => F6: 1
* INC # F5: 6,8 + I1: 1 + F6: 1 # E2: 2,3 => UNS
* DIS # F5: 6,8 + I1: 1 + F6: 1 # D3: 2,3 => CTR => D3: 8
* DIS # F5: 6,8 + I1: 1 + F6: 1 + D3: 8 # E3: 2,3 => CTR => E3: 1
* INC # F5: 6,8 + I1: 1 + F6: 1 + D3: 8 + E3: 1 # I5: 4,5 => UNS
* INC # F5: 6,8 + I1: 1 + F6: 1 + D3: 8 + E3: 1 # I5: 7 => UNS
* INC # F5: 6,8 + I1: 1 + F6: 1 + D3: 8 + E3: 1 # D7: 2,3 => UNS
* INC # F5: 6,8 + I1: 1 + F6: 1 + D3: 8 + E3: 1 # D9: 2,3 => UNS
* INC # F5: 6,8 + I1: 1 + F6: 1 + D3: 8 + E3: 1 # I5: 4,7 => UNS
* DIS # F5: 6,8 + I1: 1 + F6: 1 + D3: 8 + E3: 1 # I5: 5 => CTR => I5: 4,7
* PRF # F5: 6,8 + I1: 1 + F6: 1 + D3: 8 + E3: 1 + I5: 4,7 # G7: 4,7 => SOL
* STA # F5: 6,8 + I1: 1 + F6: 1 + D3: 8 + E3: 1 + I5: 4,7 + G7: 4,7
* CNT  31 HDP CHAINS /  32 HYP OPENED