Analysis of xx-ph-00011683-kz0-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 98.7.....6...8.7....7..5....4..3..2...65..9.......1..4..86..5......5..1......2..3 initial

Autosolve

position: 98.7.....6...8.7....7..5....4..3..2...65..9.......1..4..86..5......5..1......2..3 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: 0:00:34.007009

The following important HDP chains were detected:

* DIS # F4: 8,9 # H3: 3,4,9 => CTR => H3: 6,8
* DIS # F4: 8,9 + H3: 6,8 # A4: 7 => CTR => A4: 1,5
* DIS # F4: 8,9 + H3: 6,8 + A4: 1,5 # A5: 8 => CTR => A5: 2,3
* DIS # F4: 8,9 + H3: 6,8 + A4: 1,5 + A5: 2,3 # D8: 8,9 => CTR => D8: 3,4
* PRF # F4: 8,9 + H3: 6,8 + A4: 1,5 + A5: 2,3 + D8: 3,4 # D9: 1,4 => SOL
* STA # F4: 8,9 + H3: 6,8 + A4: 1,5 + A5: 2,3 + D8: 3,4 + D9: 1,4
* CNT   5 HDP CHAINS /  25 HYP OPENED

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

Details

Positions

98.7.....6...8.7....7..5....4..3..2...65..9.......1..4..86..5......5..1......2..3 initial
98.7.....6...8.7....7..5....4..3..2...65..9.......1..4..86..5......5..1......2..3 autosolve
982716435651384792437925168145839627326547981879261354218673549793458216564192873 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
D4: 8,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E5,F5: 4.. / E5 = 4  =>  2 pairs (_) / F5 = 4  =>  4 pairs (_)
I4,H6: 5.. / I4 = 5  =>  2 pairs (_) / H6 = 5  =>  1 pairs (_)
F4,E6: 6.. / F4 = 6  =>  3 pairs (_) / E6 = 6  =>  2 pairs (_)
B8,B9: 6.. / B8 = 6  =>  1 pairs (_) / B9 = 6  =>  2 pairs (_)
F1,F4: 6.. / F1 = 6  =>  2 pairs (_) / F4 = 6  =>  3 pairs (_)
* DURATION: 0:00:02.940274  START: 22:09:06.864107  END: 22:09:09.804381 2020-12-01
* CP COUNT: (5)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:33.865290  START: 22:09:13.709571  END: 22:09:47.574861 2020-12-01
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00011683-kz0-base-pr-002.dot
* REASONING
* DIS # F4: 8,9 # H3: 3,4,9 => CTR => H3: 6,8
* DIS # F4: 8,9 + H3: 6,8 # A4: 7 => CTR => A4: 1,5
* DIS # F4: 8,9 + H3: 6,8 + A4: 1,5 # A5: 8 => CTR => A5: 2,3
* DIS # F4: 8,9 + H3: 6,8 + A4: 1,5 + A5: 2,3 # D8: 8,9 => CTR => D8: 3,4
* PRF # F4: 8,9 + H3: 6,8 + A4: 1,5 + A5: 2,3 + D8: 3,4 # D9: 1,4 => SOL
* STA # F4: 8,9 + H3: 6,8 + A4: 1,5 + A5: 2,3 + D8: 3,4 + D9: 1,4
* CNT   5 HDP CHAINS /  25 HYP OPENED

Header Info

11683;kz0;GP;23;11.30;11.30;9.50

Solution

position: 982716435651384792437925168145839627326547981879261354218673549793458216564192873 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 # F4: 8,9 => UNS
* INC # D6: 8,9 => UNS
* INC # D8: 8,9 => UNS
* INC # D9: 8,9 => UNS
* CNT   4 HDP CHAINS /   4 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F4: 8,9 => UNS
* INC # D6: 8,9 => UNS
* INC # D8: 8,9 => UNS
* INC # D9: 8,9 => UNS
* CNT   4 HDP CHAINS /   4 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # F4: 8,9 => UNS
* INC # D6: 8,9 => UNS
* INC # D8: 8,9 => UNS
* INC # D9: 8,9 => UNS
* INC # F4: 8,9 # I2: 2,5 => UNS
* INC # F4: 8,9 # I2: 9 => UNS
* INC # F4: 8,9 # C1: 2,5 => UNS
* INC # F4: 8,9 # C1: 1,3,4 => UNS
* INC # F4: 8,9 # H3: 6,8 => UNS
* DIS # F4: 8,9 # H3: 3,4,9 => CTR => H3: 6,8
* INC # F4: 8,9 + H3: 6,8 # A4: 1,5 => UNS
* DIS # F4: 8,9 + H3: 6,8 # A4: 7 => CTR => A4: 1,5
* INC # F4: 8,9 + H3: 6,8 + A4: 1,5 # C1: 1,5 => UNS
* INC # F4: 8,9 + H3: 6,8 + A4: 1,5 # C2: 1,5 => UNS
* INC # F4: 8,9 + H3: 6,8 + A4: 1,5 # C9: 1,5 => UNS
* INC # F4: 8,9 + H3: 6,8 + A4: 1,5 # A5: 2,3 => UNS
* DIS # F4: 8,9 + H3: 6,8 + A4: 1,5 # A5: 8 => CTR => A5: 2,3
* INC # F4: 8,9 + H3: 6,8 + A4: 1,5 + A5: 2,3 # B3: 2,3 => UNS
* INC # F4: 8,9 + H3: 6,8 + A4: 1,5 + A5: 2,3 # B7: 2,3 => UNS
* INC # F4: 8,9 + H3: 6,8 + A4: 1,5 + A5: 2,3 # B8: 2,3 => UNS
* DIS # F4: 8,9 + H3: 6,8 + A4: 1,5 + A5: 2,3 # D8: 8,9 => CTR => D8: 3,4
* INC # F4: 8,9 + H3: 6,8 + A4: 1,5 + A5: 2,3 + D8: 3,4 # D9: 8,9 => UNS
* INC # F4: 8,9 + H3: 6,8 + A4: 1,5 + A5: 2,3 + D8: 3,4 # D9: 8,9 => UNS
* PRF # F4: 8,9 + H3: 6,8 + A4: 1,5 + A5: 2,3 + D8: 3,4 # D9: 1,4 => SOL
* STA # F4: 8,9 + H3: 6,8 + A4: 1,5 + A5: 2,3 + D8: 3,4 + D9: 1,4
* CNT  24 HDP CHAINS /  25 HYP OPENED