Analysis of xx-mith-te3-00069590-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 1.34.6.......8.2....9..7.....8.9.15.5......989.1...3.2.1........953.182.8.25...1. initial

Autosolve

position: 1.34.6.......8.2....9..7.....8.9.15.5......989.1...3.2.1........953.182.8.25...1. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # F7: 4,9 => CTR => F7: 2,8
* DIS # I9: 4,9 => CTR => I9: 3,6,7
* CNT   2 HDP CHAINS /  13 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # F7: 4,9 => CTR => F7: 2,8
* DIS F7: 2,8 # I9: 4,9 => CTR => I9: 3,6,7
* STA F7: 2,8 + I9: 3,6,7
* CNT   2 HDP CHAINS /  27 HYP OPENED

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

Pair Reduction Position

position: 1.34.6.......8.2....9..7.....8.9.15.5......989.1...3.2.1........953.182.8.25...1. pair_reduction
Pair Reduction

See section Pair Reduction for the HDP chains leading to this result.

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:20.383973

The following important HDP chains were detected:

* DIS # D5: 6,7 # E6: 6,7 => CTR => E6: 4,5
* PRF # I3: 1,3 # A2: 4,6 => SOL
* STA # I3: 1,3 + A2: 4,6
* CNT   2 HDP CHAINS / 100 HYP OPENED

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

Details

Positions

1.34.6.......8.2....9..7.....8.9.15.5......989.1...3.2.1........953.182.8.25...1. initial
1.34.6.......8.2....9..7.....8.9.15.5......989.1...3.2.1........953.182.8.25...1. autosolve
1.34.6.......8.2....9..7.....8.9.15.5......989.1...3.2.1........953.182.8.25...1. pair_reduction
123456789457189236689237541248693157536712498971845362314928675795361824862574913 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
E1: 2,5
D2: 1,9
D3: 1,2
E3: 1,3
H1: 7,8
E5: 1,3
F9: 4,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
I2,I3: 1.. / I2 = 1  =>  7 pairs (_) / I3 = 1  => 15 pairs (_)
D5,E5: 1.. / D5 = 1  => 10 pairs (_) / E5 = 1  =>  6 pairs (_)
D2,I2: 1.. / D2 = 1  => 15 pairs (_) / I2 = 1  =>  7 pairs (_)
E3,E5: 1.. / E3 = 1  => 10 pairs (_) / E5 = 1  =>  6 pairs (_)
E1,D3: 2.. / E1 = 2  => 10 pairs (_) / D3 = 2  => 10 pairs (_)
B1,E1: 2.. / B1 = 2  => 10 pairs (_) / E1 = 2  => 10 pairs (_)
A3,A4: 2.. / A3 = 2  => 10 pairs (_) / A4 = 2  => 10 pairs (_)
E1,E7: 2.. / E1 = 2  => 10 pairs (_) / E7 = 2  => 10 pairs (_)
F2,E3: 3.. / F2 = 3  => 10 pairs (_) / E3 = 3  =>  6 pairs (_)
A7,B9: 3.. / A7 = 3  =>  7 pairs (_) / B9 = 3  =>  0 pairs (X)
B9,I9: 3.. / B9 = 3  =>  0 pairs (X) / I9 = 3  =>  7 pairs (_)
A4,A7: 3.. / A4 = 3  =>  0 pairs (X) / A7 = 3  =>  7 pairs (_)
E3,E5: 3.. / E3 = 3  =>  6 pairs (_) / E5 = 3  => 10 pairs (_)
E1,F2: 5.. / E1 = 5  => 10 pairs (_) / F2 = 5  => 10 pairs (_)
E6,F6: 5.. / E6 = 5  => 10 pairs (_) / F6 = 5  => 10 pairs (_)
G7,I7: 5.. / G7 = 5  =>  9 pairs (_) / I7 = 5  =>  8 pairs (_)
E1,E6: 5.. / E1 = 5  => 10 pairs (_) / E6 = 5  => 10 pairs (_)
F2,F6: 5.. / F2 = 5  => 10 pairs (_) / F6 = 5  => 10 pairs (_)
B1,B3: 8.. / B1 = 8  => 13 pairs (_) / B3 = 8  =>  9 pairs (_)
H1,H3: 8.. / H1 = 8  =>  9 pairs (_) / H3 = 8  => 13 pairs (_)
D6,F6: 8.. / D6 = 8  =>  9 pairs (_) / F6 = 8  => 10 pairs (_)
D7,F7: 8.. / D7 = 8  => 10 pairs (_) / F7 = 8  =>  9 pairs (_)
B1,H1: 8.. / B1 = 8  => 13 pairs (_) / H1 = 8  =>  9 pairs (_)
B3,H3: 8.. / B3 = 8  =>  9 pairs (_) / H3 = 8  => 13 pairs (_)
D6,D7: 8.. / D6 = 8  =>  9 pairs (_) / D7 = 8  => 10 pairs (_)
F6,F7: 8.. / F6 = 8  => 10 pairs (_) / F7 = 8  =>  9 pairs (_)
D2,F2: 9.. / D2 = 9  =>  7 pairs (_) / F2 = 9  => 15 pairs (_)
G1,I1: 9.. / G1 = 9  =>  8 pairs (_) / I1 = 9  =>  8 pairs (_)
D2,D7: 9.. / D2 = 9  =>  7 pairs (_) / D7 = 9  => 15 pairs (_)
* DURATION: 0:00:08.763520  START: 10:05:45.218904  END: 10:05:53.982424 2025-04-06
* CP COUNT: (29)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:20.160193  START: 10:06:01.092409  END: 10:06:21.252602 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00069590-base-pr-002.dot
* REASONING
* DIS # D5: 6,7 # E6: 6,7 => CTR => E6: 4,5
* PRF # I3: 1,3 # A2: 4,6 => SOL
* STA # I3: 1,3 + A2: 4,6
* CNT   2 HDP CHAINS / 100 HYP OPENED

Header Info

rating: 15383; r2: 430513; index: 69590

Solution

position: 123456789457189236689237541248693157536712498971845362314928675795361824862574913 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 # B1: 2,5 => UNS
* INC # B1: 7,8 => UNS
* INC # D5: 1,2 => UNS
* INC # D5: 6,7 => UNS
* INC # I3: 1,3 => UNS
* INC # I3: 4,5,6 => UNS
* INC # B1: 7,8 => UNS
* INC # B1: 2,5 => UNS
* DIS # F7: 4,9 => CTR => F7: 2,8
* INC # F7: 2,8 => UNS
* INC # G9: 4,9 => UNS
* DIS # I9: 4,9 => CTR => I9: 3,6,7
* INC # I9: 3,6,7 => UNS
* CNT  13 HDP CHAINS /  13 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B1: 2,5 => UNS
* INC # B1: 7,8 => UNS
* INC # D5: 1,2 => UNS
* INC # D5: 6,7 => UNS
* INC # I3: 1,3 => UNS
* INC # I3: 4,5,6 => UNS
* INC # B1: 7,8 => UNS
* INC # B1: 2,5 => UNS
* DIS # F7: 4,9 => CTR => F7: 2,8
* INC F7: 2,8 # G9: 4,9 => UNS
* DIS F7: 2,8 # I9: 4,9 => CTR => I9: 3,6,7
* INC F7: 2,8 + I9: 3,6,7 # G9: 4,9 => UNS
* INC F7: 2,8 + I9: 3,6,7 # G9: 6,7 => UNS
* INC F7: 2,8 + I9: 3,6,7 # G9: 4,9 => UNS
* INC F7: 2,8 + I9: 3,6,7 # G9: 6,7 => UNS
* INC F7: 2,8 + I9: 3,6,7 # B1: 2,5 => UNS
* INC F7: 2,8 + I9: 3,6,7 # B1: 7,8 => UNS
* INC F7: 2,8 + I9: 3,6,7 # D5: 1,2 => UNS
* INC F7: 2,8 + I9: 3,6,7 # D5: 6,7 => UNS
* INC F7: 2,8 + I9: 3,6,7 # I3: 1,3 => UNS
* INC F7: 2,8 + I9: 3,6,7 # I3: 4,5,6 => UNS
* INC F7: 2,8 + I9: 3,6,7 # B1: 7,8 => UNS
* INC F7: 2,8 + I9: 3,6,7 # B1: 2,5 => UNS
* INC F7: 2,8 + I9: 3,6,7 # D7: 2,8 => UNS
* INC F7: 2,8 + I9: 3,6,7 # D7: 6,7,9 => UNS
* INC F7: 2,8 + I9: 3,6,7 # G9: 4,9 => UNS
* INC F7: 2,8 + I9: 3,6,7 # G9: 6,7 => UNS
* STA F7: 2,8 + I9: 3,6,7
* CNT  27 HDP CHAINS /  27 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # B1: 2,5 => UNS
* INC # B1: 7,8 => UNS
* INC # D5: 1,2 => UNS
* INC # D5: 6,7 => UNS
* INC # I3: 1,3 => UNS
* INC # I3: 4,5,6 => UNS
* INC # B1: 7,8 => UNS
* INC # B1: 2,5 => UNS
* INC # D7: 2,8 => UNS
* INC # D7: 6,7,9 => UNS
* INC # G9: 4,9 => UNS
* INC # G9: 6,7 => UNS
* INC # B1: 2,5 # D5: 1,2 => UNS
* INC # B1: 2,5 # D5: 6,7 => UNS
* INC # B1: 2,5 # I3: 1,3 => UNS
* INC # B1: 2,5 # I3: 4,5,6 => UNS
* INC # B1: 2,5 # G7: 7,9 => UNS
* INC # B1: 2,5 # G9: 7,9 => UNS
* INC # B1: 2,5 # I7: 7,9 => UNS
* INC # B1: 2,5 # I7: 3,4,5,6 => UNS
* INC # B1: 2,5 # D7: 2,8 => UNS
* INC # B1: 2,5 # D7: 6,7,9 => UNS
* INC # B1: 2,5 # G9: 4,9 => UNS
* INC # B1: 2,5 # G9: 6,7 => UNS
* INC # B1: 2,5 => UNS
* INC # B1: 7,8 # G5: 4,6 => UNS
* INC # B1: 7,8 # G9: 4,6 => UNS
* INC # B1: 7,8 # I4: 4,6 => UNS
* INC # B1: 7,8 # I8: 4,6 => UNS
* INC # B1: 7,8 # F4: 2,3 => UNS
* INC # B1: 7,8 # F4: 4 => UNS
* INC # B1: 7,8 # F5: 2,3 => UNS
* INC # B1: 7,8 # F5: 4 => UNS
* INC # B1: 7,8 # I4: 4,6 => UNS
* INC # B1: 7,8 # G5: 4,6 => UNS
* INC # B1: 7,8 # B6: 4,6 => UNS
* INC # B1: 7,8 # B6: 7 => UNS
* INC # B1: 7,8 # I8: 4,6 => UNS
* INC # B1: 7,8 # G9: 4,6 => UNS
* INC # B1: 7,8 # C7: 4,6 => UNS
* INC # B1: 7,8 # E7: 4,6 => UNS
* INC # B1: 7,8 => UNS
* INC # D5: 1,2 # B1: 2,5 => UNS
* INC # D5: 1,2 # B1: 7,8 => UNS
* INC # D5: 1,2 # B1: 7,8 => UNS
* INC # D5: 1,2 # B1: 2,5 => UNS
* INC # D5: 1,2 # D6: 6,7 => UNS
* INC # D5: 1,2 # E6: 6,7 => UNS
* INC # D5: 1,2 # A4: 6,7 => UNS
* INC # D5: 1,2 # B4: 6,7 => UNS
* INC # D5: 1,2 # I4: 6,7 => UNS
* INC # D5: 1,2 # D7: 6,7 => UNS
* INC # D5: 1,2 # D7: 8 => UNS
* INC # D5: 1,2 # G1: 5,9 => UNS
* INC # D5: 1,2 # G1: 7 => UNS
* INC # D5: 1,2 # I1: 5,9 => UNS
* INC # D5: 1,2 # I1: 7 => UNS
* INC # D5: 1,2 => UNS
* INC # D5: 6,7 # B1: 2,5 => UNS
* INC # D5: 6,7 # B1: 7,8 => UNS
* INC # D5: 6,7 # B1: 7,8 => UNS
* INC # D5: 6,7 # B1: 2,5 => UNS
* INC # D5: 6,7 # A4: 2,3 => UNS
* INC # D5: 6,7 # B4: 2,3 => UNS
* INC # D5: 6,7 # D4: 6,7 => UNS
* INC # D5: 6,7 # D6: 6,7 => UNS
* DIS # D5: 6,7 # E6: 6,7 => CTR => E6: 4,5
* INC # D5: 6,7 + E6: 4,5 # C5: 6,7 => UNS
* INC # D5: 6,7 + E6: 4,5 # G5: 6,7 => UNS
* INC # D5: 6,7 + E6: 4,5 # D4: 6,7 => UNS
* INC # D5: 6,7 + E6: 4,5 # D6: 6,7 => UNS
* INC # D5: 6,7 + E6: 4,5 # C5: 6,7 => UNS
* INC # D5: 6,7 + E6: 4,5 # G5: 6,7 => UNS
* INC # D5: 6,7 + E6: 4,5 # F4: 2,3 => UNS
* INC # D5: 6,7 + E6: 4,5 # F4: 4 => UNS
* INC # D5: 6,7 + E6: 4,5 # D7: 2,8 => UNS
* INC # D5: 6,7 + E6: 4,5 # D7: 9 => UNS
* INC # D5: 6,7 + E6: 4,5 # G9: 4,9 => UNS
* INC # D5: 6,7 + E6: 4,5 # G9: 6,7 => UNS
* INC # D5: 6,7 + E6: 4,5 # B1: 2,5 => UNS
* INC # D5: 6,7 + E6: 4,5 # B1: 7,8 => UNS
* INC # D5: 6,7 + E6: 4,5 # B1: 7,8 => UNS
* INC # D5: 6,7 + E6: 4,5 # B1: 2,5 => UNS
* INC # D5: 6,7 + E6: 4,5 # A4: 2,3 => UNS
* INC # D5: 6,7 + E6: 4,5 # B4: 2,3 => UNS
* INC # D5: 6,7 + E6: 4,5 # D4: 6,7 => UNS
* INC # D5: 6,7 + E6: 4,5 # D6: 6,7 => UNS
* INC # D5: 6,7 + E6: 4,5 # C5: 6,7 => UNS
* INC # D5: 6,7 + E6: 4,5 # G5: 6,7 => UNS
* INC # D5: 6,7 + E6: 4,5 # F4: 2,3 => UNS
* INC # D5: 6,7 + E6: 4,5 # F4: 4 => UNS
* INC # D5: 6,7 + E6: 4,5 # F6: 4,5 => UNS
* INC # D5: 6,7 + E6: 4,5 # F6: 8 => UNS
* INC # D5: 6,7 + E6: 4,5 # D7: 2,8 => UNS
* INC # D5: 6,7 + E6: 4,5 # D7: 9 => UNS
* INC # D5: 6,7 + E6: 4,5 # G9: 4,9 => UNS
* INC # D5: 6,7 + E6: 4,5 # G9: 6,7 => UNS
* INC # D5: 6,7 + E6: 4,5 => UNS
* PRF # I3: 1,3 # A2: 4,6 => SOL
* STA # I3: 1,3 + A2: 4,6
* CNT  99 HDP CHAINS / 100 HYP OPENED