Analysis of xx-ph-00016448-Kz1_b-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 98.7.....7...6......5..97..5....84....43...6.....2...1.5...49....91....2.......3. initial

Autosolve

position: 98.7.....7...6......5..97..5....84....43...6....42...1.5...49....91....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: 0:00:46.788935

The following important HDP chains were detected:

* DIS # D2: 2,8 # H2: 2,8 => CTR => H2: 1,4,9
* DIS # D2: 2,8 + H2: 1,4,9 # B4: 1,7 => CTR => B4: 2,3,6
* DIS # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 # C4: 1,7 => CTR => C4: 2,3,6
* DIS # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 # E8: 3,7 => CTR => E8: 8
* DIS # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 + E8: 8 # I9: 7,8 => CTR => I9: 4,6
* DIS # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 + E8: 8 + I9: 4,6 # H7: 1 => CTR => H7: 7,8
* DIS # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 + E8: 8 + I9: 4,6 + H7: 7,8 # C1: 1,3 => CTR => C1: 2,6
* DIS # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 + E8: 8 + I9: 4,6 + H7: 7,8 + C1: 2,6 # G2: 3 => CTR => G2: 2,8
* PRF # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 + E8: 8 + I9: 4,6 + H7: 7,8 + C1: 2,6 + G2: 2,8 # H3: 2,8 => SOL
* STA # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 + E8: 8 + I9: 4,6 + H7: 7,8 + C1: 2,6 + G2: 2,8 + H3: 2,8
* CNT   9 HDP CHAINS /  45 HYP OPENED

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

Details

Positions

98.7.....7...6......5..97..5....84....43...6.....2...1.5...49....91....2.......3. initial
98.7.....7...6......5..97..5....84....43...6....42...1.5...49....91....2.......3. autosolve
982753614743861295615249783536918427124375869897426351251634978369187542478592136 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (2)
D3: 2,8
D4: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H7,G9: 1.. / H7 = 1  =>  2 pairs (_) / G9 = 1  =>  3 pairs (_)
H4,G5: 2.. / H4 = 2  =>  3 pairs (_) / G5 = 2  =>  4 pairs (_)
I4,G6: 3.. / I4 = 3  =>  3 pairs (_) / G6 = 3  =>  4 pairs (_)
E1,E3: 4.. / E1 = 4  =>  2 pairs (_) / E3 = 4  =>  3 pairs (_)
H8,I9: 4.. / H8 = 4  =>  2 pairs (_) / I9 = 4  =>  2 pairs (_)
D2,D9: 5.. / D2 = 5  =>  2 pairs (_) / D9 = 5  =>  9 pairs (_)
D4,F6: 6.. / D4 = 6  =>  3 pairs (_) / F6 = 6  =>  6 pairs (_)
H2,I2: 9.. / H2 = 9  =>  3 pairs (_) / I2 = 9  =>  3 pairs (_)
D9,E9: 9.. / D9 = 9  =>  3 pairs (_) / E9 = 9  =>  6 pairs (_)
B6,H6: 9.. / B6 = 9  =>  2 pairs (_) / H6 = 9  =>  4 pairs (_)
D4,D9: 9.. / D4 = 9  =>  6 pairs (_) / D9 = 9  =>  3 pairs (_)
* DURATION: 0:00:06.707086  START: 10:15:36.550745  END: 10:15:43.257831 2020-10-26
* CP COUNT: (11)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:46.591311  START: 10:15:50.636669  END: 10:16:37.227980 2020-10-26
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00016448-Kz1_b-base-pr-002.dot
* REASONING
* DIS # D2: 2,8 # H2: 2,8 => CTR => H2: 1,4,9
* DIS # D2: 2,8 + H2: 1,4,9 # B4: 1,7 => CTR => B4: 2,3,6
* DIS # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 # C4: 1,7 => CTR => C4: 2,3,6
* DIS # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 # E8: 3,7 => CTR => E8: 8
* DIS # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 + E8: 8 # I9: 7,8 => CTR => I9: 4,6
* DIS # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 + E8: 8 + I9: 4,6 # H7: 1 => CTR => H7: 7,8
* DIS # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 + E8: 8 + I9: 4,6 + H7: 7,8 # C1: 1,3 => CTR => C1: 2,6
* DIS # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 + E8: 8 + I9: 4,6 + H7: 7,8 + C1: 2,6 # G2: 3 => CTR => G2: 2,8
* PRF # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 + E8: 8 + I9: 4,6 + H7: 7,8 + C1: 2,6 + G2: 2,8 # H3: 2,8 => SOL
* STA # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 + E8: 8 + I9: 4,6 + H7: 7,8 + C1: 2,6 + G2: 2,8 + H3: 2,8
* CNT   9 HDP CHAINS /  45 HYP OPENED

Header Info

16448;Kz1 b;GP;23;11.40;1.20;1.20

Solution

position: 982753614743861295615249783536918427124375869897426351251634978369187542478592136 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 # D2: 2,8 => UNS
* INC # D2: 5 => UNS
* INC # H3: 2,8 => UNS
* INC # H3: 1,4 => UNS
* INC # D7: 2,8 => UNS
* INC # D9: 2,8 => UNS
* INC # B4: 6,9 => UNS
* INC # B4: 1,2,3,7 => UNS
* INC # D9: 6,9 => UNS
* INC # D9: 2,5,8 => UNS
* CNT  10 HDP CHAINS /  10 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # D2: 2,8 => UNS
* INC # D2: 5 => UNS
* INC # H3: 2,8 => UNS
* INC # H3: 1,4 => UNS
* INC # D7: 2,8 => UNS
* INC # D9: 2,8 => UNS
* INC # B4: 6,9 => UNS
* INC # B4: 1,2,3,7 => UNS
* INC # D9: 6,9 => UNS
* INC # D9: 2,5,8 => UNS
* CNT  10 HDP CHAINS /  10 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # D2: 2,8 => UNS
* INC # D2: 5 => UNS
* INC # H3: 2,8 => UNS
* INC # H3: 1,4 => UNS
* INC # D7: 2,8 => UNS
* INC # D9: 2,8 => UNS
* INC # B4: 6,9 => UNS
* INC # B4: 1,2,3,7 => UNS
* INC # D9: 6,9 => UNS
* INC # D9: 2,5,8 => UNS
* INC # D2: 2,8 # G2: 2,8 => UNS
* DIS # D2: 2,8 # H2: 2,8 => CTR => H2: 1,4,9
* INC # D2: 2,8 + H2: 1,4,9 # G2: 2,8 => UNS
* INC # D2: 2,8 + H2: 1,4,9 # G2: 1,3 => UNS
* INC # D2: 2,8 + H2: 1,4,9 # G2: 2,8 => UNS
* INC # D2: 2,8 + H2: 1,4,9 # G2: 1,3 => UNS
* INC # D2: 2,8 + H2: 1,4,9 # H3: 2,8 => UNS
* INC # D2: 2,8 + H2: 1,4,9 # H3: 1,4 => UNS
* INC # D2: 2,8 + H2: 1,4,9 # C6: 3,8 => UNS
* INC # D2: 2,8 + H2: 1,4,9 # C6: 7 => UNS
* INC # D2: 2,8 + H2: 1,4,9 # G6: 3,8 => UNS
* INC # D2: 2,8 + H2: 1,4,9 # G6: 5 => UNS
* INC # D2: 2,8 + H2: 1,4,9 # A7: 3,8 => UNS
* INC # D2: 2,8 + H2: 1,4,9 # A8: 3,8 => UNS
* INC # D2: 2,8 + H2: 1,4,9 # E5: 1,7 => UNS
* INC # D2: 2,8 + H2: 1,4,9 # F5: 1,7 => UNS
* DIS # D2: 2,8 + H2: 1,4,9 # B4: 1,7 => CTR => B4: 2,3,6
* DIS # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 # C4: 1,7 => CTR => C4: 2,3,6
* INC # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 # A5: 2,8 => UNS
* INC # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 # A5: 1 => UNS
* INC # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 # G2: 2,8 => UNS
* INC # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 # G2: 1,3 => UNS
* INC # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 # E7: 3,7 => UNS
* DIS # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 # E8: 3,7 => CTR => E8: 8
* INC # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 + E8: 8 # B8: 3,7 => UNS
* INC # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 + E8: 8 # B8: 4,6 => UNS
* INC # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 + E8: 8 # H7: 7,8 => UNS
* DIS # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 + E8: 8 # I9: 7,8 => CTR => I9: 4,6
* INC # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 + E8: 8 + I9: 4,6 # H7: 7,8 => UNS
* DIS # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 + E8: 8 + I9: 4,6 # H7: 1 => CTR => H7: 7,8
* DIS # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 + E8: 8 + I9: 4,6 + H7: 7,8 # C1: 1,3 => CTR => C1: 2,6
* INC # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 + E8: 8 + I9: 4,6 + H7: 7,8 + C1: 2,6 # G2: 2,8 => UNS
* DIS # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 + E8: 8 + I9: 4,6 + H7: 7,8 + C1: 2,6 # G2: 3 => CTR => G2: 2,8
* PRF # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 + E8: 8 + I9: 4,6 + H7: 7,8 + C1: 2,6 + G2: 2,8 # H3: 2,8 => SOL
* STA # D2: 2,8 + H2: 1,4,9 + B4: 2,3,6 + C4: 2,3,6 + E8: 8 + I9: 4,6 + H7: 7,8 + C1: 2,6 + G2: 2,8 + H3: 2,8
* CNT  44 HDP CHAINS /  45 HYP OPENED