Analysis of xx-ph-00009472-cy4-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 98.7..6....5.4.........9.3.6.....9...3.....8...4.7...52...1......14.5........7..1 initial

Autosolve

position: 98.7..6....5.4.........9.3.6.....9...3.....8...4.7...52...1......14.5........7..1 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: 0:00:36.684023

The following important HDP chains were detected:

* DIS # H1: 2,4 # I5: 2,4 => CTR => I5: 6
* DIS # H1: 2,4 + I5: 6 # I4: 3 => CTR => I4: 2,4
* DIS # H1: 2,4 + I5: 6 + I4: 2,4 # I7: 8,9 => CTR => I7: 3
* DIS # H1: 2,4 + I5: 6 + I4: 2,4 + I7: 3 # D5: 2,9 => CTR => D5: 1,5
* PRF # H1: 2,4 + I5: 6 + I4: 2,4 + I7: 3 + D5: 1,5 # D6: 1,8 => SOL
* STA # H1: 2,4 + I5: 6 + I4: 2,4 + I7: 3 + D5: 1,5 + D6: 1,8
* CNT   5 HDP CHAINS /  48 HYP OPENED

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

Details

Positions

98.7..6....5.4.........9.3.6.....9...3.....8...4.7...52...1......14.5........7..1 initial
98.7..6....5.4.........9.3.6.....9...3.....8...4.7...52...1......14.5........7..1 autosolve
983751642725643198416289537678532914532194786194876325257918463361425879849367251 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (3)
C1: 2,3
I1: 2,4
A6: 1,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F1,H1: 1.. / F1 = 1  =>  3 pairs (_) / H1 = 1  =>  4 pairs (_)
C1,A2: 3.. / C1 = 3  =>  5 pairs (_) / A2 = 3  =>  8 pairs (_)
I4,G6: 3.. / I4 = 3  =>  4 pairs (_) / G6 = 3  =>  3 pairs (_)
A3,B3: 4.. / A3 = 4  =>  3 pairs (_) / B3 = 4  =>  4 pairs (_)
H1,I1: 4.. / H1 = 4  => 12 pairs (_) / I1 = 4  =>  2 pairs (_)
F4,F5: 4.. / F4 = 4  =>  3 pairs (_) / F5 = 4  =>  3 pairs (_)
A3,A9: 4.. / A3 = 4  =>  3 pairs (_) / A9 = 4  =>  4 pairs (_)
H1,G3: 5.. / H1 = 5  =>  3 pairs (_) / G3 = 5  =>  3 pairs (_)
B4,A5: 5.. / B4 = 5  =>  4 pairs (_) / A5 = 5  =>  3 pairs (_)
E1,H1: 5.. / E1 = 5  =>  3 pairs (_) / H1 = 5  =>  3 pairs (_)
A5,A9: 5.. / A5 = 5  =>  3 pairs (_) / A9 = 5  =>  4 pairs (_)
I5,H6: 6.. / I5 = 6  =>  4 pairs (_) / H6 = 6  =>  3 pairs (_)
C4,A6: 8.. / C4 = 8  =>  8 pairs (_) / A6 = 8  =>  4 pairs (_)
H2,I2: 9.. / H2 = 9  =>  3 pairs (_) / I2 = 9  =>  3 pairs (_)
C5,B6: 9.. / C5 = 9  =>  4 pairs (_) / B6 = 9  =>  5 pairs (_)
B6,D6: 9.. / B6 = 9  =>  5 pairs (_) / D6 = 9  =>  4 pairs (_)
* DURATION: 0:00:09.728243  START: 07:49:01.266011  END: 07:49:10.994254 2020-12-01
* CP COUNT: (16)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:36.380465  START: 07:49:17.354459  END: 07:49:53.734924 2020-12-01
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00009472-cy4-base-pr-002.dot
* REASONING
* DIS # H1: 2,4 # I5: 2,4 => CTR => I5: 6
* DIS # H1: 2,4 + I5: 6 # I4: 3 => CTR => I4: 2,4
* DIS # H1: 2,4 + I5: 6 + I4: 2,4 # I7: 8,9 => CTR => I7: 3
* DIS # H1: 2,4 + I5: 6 + I4: 2,4 + I7: 3 # D5: 2,9 => CTR => D5: 1,5
* PRF # H1: 2,4 + I5: 6 + I4: 2,4 + I7: 3 + D5: 1,5 # D6: 1,8 => SOL
* STA # H1: 2,4 + I5: 6 + I4: 2,4 + I7: 3 + D5: 1,5 + D6: 1,8
* CNT   5 HDP CHAINS /  48 HYP OPENED

Header Info

9472;cy4;GP;22;11.30;11.30;2.60

Solution

position: 983751642725643198416289537678532914532194786194876325257918463361425879849367251 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 # E1: 2,3 => UNS
* INC # F1: 2,3 => UNS
* INC # H1: 2,4 => UNS
* INC # H1: 1,5 => UNS
* INC # I4: 2,4 => UNS
* INC # I5: 2,4 => UNS
* INC # D6: 1,8 => UNS
* INC # F6: 1,8 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E1: 2,3 => UNS
* INC # F1: 2,3 => UNS
* INC # H1: 2,4 => UNS
* INC # H1: 1,5 => UNS
* INC # I4: 2,4 => UNS
* INC # I5: 2,4 => UNS
* INC # D6: 1,8 => UNS
* INC # F6: 1,8 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # E1: 2,3 => UNS
* INC # F1: 2,3 => UNS
* INC # H1: 2,4 => UNS
* INC # H1: 1,5 => UNS
* INC # I4: 2,4 => UNS
* INC # I5: 2,4 => UNS
* INC # D6: 1,8 => UNS
* INC # F6: 1,8 => UNS
* INC # E1: 2,3 # D2: 2,3 => UNS
* INC # E1: 2,3 # F2: 2,3 => UNS
* INC # E1: 2,3 # E4: 2,3 => UNS
* INC # E1: 2,3 # E8: 2,3 => UNS
* INC # E1: 2,3 # E9: 2,3 => UNS
* INC # E1: 2,3 # D6: 1,8 => UNS
* INC # E1: 2,3 # D6: 2,3,6,9 => UNS
* INC # E1: 2,3 => UNS
* INC # F1: 2,3 # D2: 2,3 => UNS
* INC # F1: 2,3 # F2: 2,3 => UNS
* INC # F1: 2,3 # F4: 2,3 => UNS
* INC # F1: 2,3 # F6: 2,3 => UNS
* INC # F1: 2,3 # D6: 1,8 => UNS
* INC # F1: 2,3 # F6: 1,8 => UNS
* INC # F1: 2,3 # I5: 2,6 => UNS
* INC # F1: 2,3 # I5: 7 => UNS
* INC # F1: 2,3 # D6: 2,6 => UNS
* INC # F1: 2,3 # F6: 2,6 => UNS
* INC # F1: 2,3 # H8: 2,6 => UNS
* INC # F1: 2,3 # H9: 2,6 => UNS
* INC # F1: 2,3 => UNS
* INC # H1: 2,4 # D2: 2,6 => UNS
* INC # H1: 2,4 # F2: 2,6 => UNS
* INC # H1: 2,4 # D3: 2,6 => UNS
* INC # H1: 2,4 # E3: 2,6 => UNS
* INC # H1: 2,4 # H4: 2,4 => UNS
* INC # H1: 2,4 # H9: 2,4 => UNS
* INC # H1: 2,4 # I4: 2,4 => UNS
* DIS # H1: 2,4 # I5: 2,4 => CTR => I5: 6
* INC # H1: 2,4 + I5: 6 # I4: 2,4 => UNS
* DIS # H1: 2,4 + I5: 6 # I4: 3 => CTR => I4: 2,4
* DIS # H1: 2,4 + I5: 6 + I4: 2,4 # I7: 8,9 => CTR => I7: 3
* INC # H1: 2,4 + I5: 6 + I4: 2,4 + I7: 3 # B4: 1,5 => UNS
* INC # H1: 2,4 + I5: 6 + I4: 2,4 + I7: 3 # B4: 2,7 => UNS
* INC # H1: 2,4 + I5: 6 + I4: 2,4 + I7: 3 # D5: 1,5 => UNS
* DIS # H1: 2,4 + I5: 6 + I4: 2,4 + I7: 3 # D5: 2,9 => CTR => D5: 1,5
* INC # H1: 2,4 + I5: 6 + I4: 2,4 + I7: 3 + D5: 1,5 # B4: 1,5 => UNS
* INC # H1: 2,4 + I5: 6 + I4: 2,4 + I7: 3 + D5: 1,5 # B4: 2,7 => UNS
* PRF # H1: 2,4 + I5: 6 + I4: 2,4 + I7: 3 + D5: 1,5 # D6: 1,8 => SOL
* STA # H1: 2,4 + I5: 6 + I4: 2,4 + I7: 3 + D5: 1,5 + D6: 1,8
* CNT  47 HDP CHAINS /  48 HYP OPENED