Analysis of xx-ph-00016300-Kz1_b-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 98.7.....6...9.7....7..5...5....4.3..2......1..86..5....95..8......3...4.....1.2. initial

Autosolve

position: 98.7.....6...9.7....7..5...5....4.3..2..5...1..86..5....95..8......3...4.....1.2. 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: 0:00:35.768333

The following important HDP chains were detected:

* DIS # B4: 1,6 # A5: 3,4 => CTR => A5: 7
* DIS # B4: 1,6 + A5: 7 # I4: 2,7 => CTR => I4: 8,9
* DIS # B4: 1,6 + A5: 7 + I4: 8,9 # A3: 3,4 => CTR => A3: 1,2
* PRF # B4: 1,6 + A5: 7 + I4: 8,9 + A3: 1,2 # A7: 3,4 => SOL
* STA # B4: 1,6 + A5: 7 + I4: 8,9 + A3: 1,2 + A7: 3,4
* CNT   4 HDP CHAINS /  29 HYP OPENED

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

Details

Positions

98.7.....6...9.7....7..5...5....4.3..2......1..86..5....95..8......3...4.....1.2. initial
98.7.....6...9.7....7..5...5....4.3..2..5...1..86..5....95..8......3...4.....1.2. autosolve
985746312642193758137285496561874239724359681398612547419527863256938174873461925 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
C4: 1,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H8,I9: 5.. / H8 = 5  =>  1 pairs (_) / I9 = 5  =>  1 pairs (_)
I4,H5: 8.. / I4 = 8  =>  1 pairs (_) / H5 = 8  =>  2 pairs (_)
A8,A9: 8.. / A8 = 8  =>  2 pairs (_) / A9 = 8  =>  2 pairs (_)
B4,B6: 9.. / B4 = 9  =>  2 pairs (_) / B6 = 9  =>  3 pairs (_)
* DURATION: 0:00:03.044513  START: 16:15:59.798210  END: 16:16:02.842723 2020-12-04
* CP COUNT: (4)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:35.623235  START: 16:16:06.891539  END: 16:16:42.514774 2020-12-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00016300-Kz1_b-base-pr-002.dot
* REASONING
* DIS # B4: 1,6 # A5: 3,4 => CTR => A5: 7
* DIS # B4: 1,6 + A5: 7 # I4: 2,7 => CTR => I4: 8,9
* DIS # B4: 1,6 + A5: 7 + I4: 8,9 # A3: 3,4 => CTR => A3: 1,2
* PRF # B4: 1,6 + A5: 7 + I4: 8,9 + A3: 1,2 # A7: 3,4 => SOL
* STA # B4: 1,6 + A5: 7 + I4: 8,9 + A3: 1,2 + A7: 3,4
* CNT   4 HDP CHAINS /  29 HYP OPENED

Header Info

16300;Kz1 b;GP;23;11.30;1.20;1.20

Solution

position: 985746312642193758137285496561874239724359681398612547419527863256938174873461925 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 # B4: 1,6 => UNS
* INC # B4: 7,9 => UNS
* INC # C8: 1,6 => UNS
* INC # C8: 2,5 => UNS
* CNT   4 HDP CHAINS /   4 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B4: 1,6 => UNS
* INC # B4: 7,9 => UNS
* INC # C8: 1,6 => UNS
* INC # C8: 2,5 => UNS
* CNT   4 HDP CHAINS /   4 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # B4: 1,6 => UNS
* INC # B4: 7,9 => UNS
* INC # C8: 1,6 => UNS
* INC # C8: 2,5 => UNS
* INC # B4: 1,6 # B7: 1,6 => UNS
* INC # B4: 1,6 # B8: 1,6 => UNS
* INC # B4: 1,6 # C8: 1,6 => UNS
* INC # B4: 1,6 # C8: 2,5 => UNS
* DIS # B4: 1,6 # A5: 3,4 => CTR => A5: 7
* INC # B4: 1,6 + A5: 7 # C1: 3,4 => UNS
* INC # B4: 1,6 + A5: 7 # C2: 3,4 => UNS
* INC # B4: 1,6 + A5: 7 # C9: 3,4 => UNS
* INC # B4: 1,6 + A5: 7 # I4: 2,9 => UNS
* INC # B4: 1,6 + A5: 7 # I4: 7,8 => UNS
* INC # B4: 1,6 + A5: 7 # D4: 2,9 => UNS
* INC # B4: 1,6 + A5: 7 # D4: 8 => UNS
* INC # B4: 1,6 + A5: 7 # G3: 2,9 => UNS
* INC # B4: 1,6 + A5: 7 # G3: 1,3,4,6 => UNS
* DIS # B4: 1,6 + A5: 7 # I4: 2,7 => CTR => I4: 8,9
* INC # B4: 1,6 + A5: 7 + I4: 8,9 # B7: 1,6 => UNS
* INC # B4: 1,6 + A5: 7 + I4: 8,9 # B8: 1,6 => UNS
* INC # B4: 1,6 + A5: 7 + I4: 8,9 # C8: 1,6 => UNS
* INC # B4: 1,6 + A5: 7 + I4: 8,9 # C8: 2,5 => UNS
* INC # B4: 1,6 + A5: 7 + I4: 8,9 # C1: 3,4 => UNS
* INC # B4: 1,6 + A5: 7 + I4: 8,9 # C2: 3,4 => UNS
* INC # B4: 1,6 + A5: 7 + I4: 8,9 # C9: 3,4 => UNS
* DIS # B4: 1,6 + A5: 7 + I4: 8,9 # A3: 3,4 => CTR => A3: 1,2
* PRF # B4: 1,6 + A5: 7 + I4: 8,9 + A3: 1,2 # A7: 3,4 => SOL
* STA # B4: 1,6 + A5: 7 + I4: 8,9 + A3: 1,2 + A7: 3,4
* CNT  28 HDP CHAINS /  29 HYP OPENED