Analysis of xx-ph-00000998-H242-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 9876.....65....7............4..8..1...65..9.......2..3..59..8......3..2......1..4 initial

Autosolve

position: 9876.....65....7............4..8..1...65..9.......2..3..59..8......3..2......1..4 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: 0:00:38.975848

The following important HDP chains were detected:

* DIS # F5: 4 # I5: 7,8 => CTR => I5: 2
* DIS # F5: 4 + I5: 2 # E7: 6,7 => CTR => E7: 2,4
* DIS # F5: 4 + I5: 2 + E7: 2,4 # B7: 6,7 => CTR => B7: 1,2,3
* PRF # F5: 4 + I5: 2 + E7: 2,4 + B7: 1,2,3 # H7: 6,7 => SOL
* STA # F5: 4 + I5: 2 + E7: 2,4 + B7: 1,2,3 + H7: 6,7
* CNT   4 HDP CHAINS /  46 HYP OPENED

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

Details

Positions

9876.....65....7............4..8..1...65..9.......2..3..59..8......3..2......1..4 initial
9876.....65....7............4..8..1...65..9.......2..3..59..8......3..2......1..4 autosolve
987613245651428739423795168542389617316574982879162453235946871194837526768251394 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (3)
D4: 3,7
F4: 6,9
E6: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E5,D6: 1.. / E5 = 1  =>  4 pairs (_) / D6 = 1  =>  7 pairs (_)
D4,F5: 3.. / D4 = 3  =>  4 pairs (_) / F5 = 3  =>  7 pairs (_)
A4,A6: 5.. / A4 = 5  =>  4 pairs (_) / A6 = 5  =>  4 pairs (_)
F8,E9: 5.. / F8 = 5  =>  5 pairs (_) / E9 = 5  =>  4 pairs (_)
F4,E6: 6.. / F4 = 6  =>  5 pairs (_) / E6 = 6  =>  3 pairs (_)
F4,E6: 9.. / F4 = 9  =>  3 pairs (_) / E6 = 9  =>  5 pairs (_)
I8,H9: 9.. / I8 = 9  =>  3 pairs (_) / H9 = 9  =>  3 pairs (_)
C4,F4: 9.. / C4 = 9  =>  5 pairs (_) / F4 = 9  =>  3 pairs (_)
* DURATION: 0:00:05.987943  START: 22:50:05.041642  END: 22:50:11.029585 2020-11-23
* CP COUNT: (8)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:38.649532  START: 22:50:16.526344  END: 22:50:55.175876 2020-11-23
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00000998-H242-base-pr-002.dot
* REASONING
* DIS # F5: 4 # I5: 7,8 => CTR => I5: 2
* DIS # F5: 4 + I5: 2 # E7: 6,7 => CTR => E7: 2,4
* DIS # F5: 4 + I5: 2 + E7: 2,4 # B7: 6,7 => CTR => B7: 1,2,3
* PRF # F5: 4 + I5: 2 + E7: 2,4 + B7: 1,2,3 # H7: 6,7 => SOL
* STA # F5: 4 + I5: 2 + E7: 2,4 + B7: 1,2,3 + H7: 6,7
* CNT   4 HDP CHAINS /  46 HYP OPENED

Header Info

998;H242;GP;22;11.30;11.30;3.40

Solution

position: 987613245651428739423795168542389617316574982879162453235946871194837526768251394 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: 3,7 => UNS
* INC # F5: 4 => UNS
* INC # A4: 3,7 => UNS
* INC # A4: 2,5 => UNS
* INC # D3: 3,7 => UNS
* INC # D3: 1,2,4,8 => UNS
* CNT   6 HDP CHAINS /   6 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F5: 3,7 => UNS
* INC # F5: 4 => UNS
* INC # A4: 3,7 => UNS
* INC # A4: 2,5 => UNS
* INC # D3: 3,7 => UNS
* INC # D3: 1,2,4,8 => UNS
* CNT   6 HDP CHAINS /   6 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # F5: 3,7 => UNS
* INC # F5: 4 => UNS
* INC # A4: 3,7 => UNS
* INC # A4: 2,5 => UNS
* INC # D3: 3,7 => UNS
* INC # D3: 1,2,4,8 => UNS
* INC # F5: 3,7 # A4: 3,7 => UNS
* INC # F5: 3,7 # A4: 2,5 => UNS
* INC # F5: 3,7 # D3: 3,7 => UNS
* INC # F5: 3,7 # D3: 1,2,4,8 => UNS
* INC # F5: 3,7 # E1: 1,4 => UNS
* INC # F5: 3,7 # E2: 1,4 => UNS
* INC # F5: 3,7 # E3: 1,4 => UNS
* INC # F5: 3,7 # A5: 3,7 => UNS
* INC # F5: 3,7 # B5: 3,7 => UNS
* INC # F5: 3,7 # F3: 3,7 => UNS
* INC # F5: 3,7 # F3: 4,5,8,9 => UNS
* INC # F5: 3,7 # D2: 1,4 => UNS
* INC # F5: 3,7 # D3: 1,4 => UNS
* INC # F5: 3,7 => UNS
* INC # F5: 4 # F3: 3,5 => UNS
* INC # F5: 4 # F3: 7,8,9 => UNS
* INC # F5: 4 # G1: 3,5 => UNS
* INC # F5: 4 # H1: 3,5 => UNS
* INC # F5: 4 # C9: 2,9 => UNS
* INC # F5: 4 # C9: 3,8 => UNS
* INC # F5: 4 # A5: 1,7 => UNS
* INC # F5: 4 # B5: 1,7 => UNS
* INC # F5: 4 # E3: 1,7 => UNS
* INC # F5: 4 # E3: 2,4,5,9 => UNS
* INC # F5: 4 # A6: 1,7 => UNS
* INC # F5: 4 # B6: 1,7 => UNS
* INC # F5: 4 # D3: 1,7 => UNS
* INC # F5: 4 # D3: 2,4,8 => UNS
* DIS # F5: 4 # I5: 7,8 => CTR => I5: 2
* INC # F5: 4 + I5: 2 # H6: 7,8 => UNS
* INC # F5: 4 + I5: 2 # H6: 7,8 => UNS
* INC # F5: 4 + I5: 2 # H6: 4,5,6 => UNS
* INC # F5: 4 + I5: 2 # A5: 7,8 => UNS
* INC # F5: 4 + I5: 2 # A5: 1,3 => UNS
* DIS # F5: 4 + I5: 2 # E7: 6,7 => CTR => E7: 2,4
* INC # F5: 4 + I5: 2 + E7: 2,4 # F8: 6,7 => UNS
* INC # F5: 4 + I5: 2 + E7: 2,4 # E9: 6,7 => UNS
* DIS # F5: 4 + I5: 2 + E7: 2,4 # B7: 6,7 => CTR => B7: 1,2,3
* PRF # F5: 4 + I5: 2 + E7: 2,4 + B7: 1,2,3 # H7: 6,7 => SOL
* STA # F5: 4 + I5: 2 + E7: 2,4 + B7: 1,2,3 + H7: 6,7
* CNT  45 HDP CHAINS /  46 HYP OPENED