Analysis of xx-mith-te3-00147742-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 1..4.6.8.4..18....6...27.41......1...6.8.1.72.71.42.6...62.8....39......81......7 initial

Autosolve

position: 1..4.6.8.4..18....6...27.41......1...6.8.1.72.71.42.6...62.8....39......81......7 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: 0:00:19.696103

The following important HDP chains were detected:

* DIS # B4: 4,5 # D8: 5 => CTR => D8: 6,7
* DIS # C4: 4,5 # I4: 3,9 => CTR => I4: 4,5
* PRF # C4: 4,5 + I4: 4,5 # G6: 3,9 => SOL
* STA # C4: 4,5 + I4: 4,5 + G6: 3,9
* CNT   3 HDP CHAINS /  80 HYP OPENED

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

Details

Positions

1..4.6.8.4..18....6...27.41......1...6.8.1.72.71.42.6...62.8....39......81......7 initial
1..4.6.8.4..18....6...27.41......1...6.8.1.72.71.42.6...62.8....39......81......7 autosolve
123456789457189236698327541284763195365891472971542368546278913739615824812934657 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (6)
C5: 4,5
D4: 6,7
E4: 6,7
A7: 5,7
B7: 4,5
F8: 4,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E7,E8: 1.. / E7 = 1  =>  7 pairs (_) / E8 = 1  =>  7 pairs (_)
H7,H8: 1.. / H7 = 1  =>  7 pairs (_) / H8 = 1  =>  7 pairs (_)
E7,H7: 1.. / E7 = 1  =>  7 pairs (_) / H7 = 1  =>  7 pairs (_)
E8,H8: 1.. / E8 = 1  =>  7 pairs (_) / H8 = 1  =>  7 pairs (_)
A8,C9: 2.. / A8 = 2  => 12 pairs (_) / C9 = 2  => 13 pairs (_)
A4,A8: 2.. / A4 = 2  => 13 pairs (_) / A8 = 2  => 12 pairs (_)
I4,G5: 4.. / I4 = 4  =>  9 pairs (_) / G5 = 4  =>  0 pairs (*)
B7,C9: 4.. / B7 = 4  => 10 pairs (_) / C9 = 4  =>  0 pairs (X)
F8,F9: 4.. / F8 = 4  =>  5 pairs (_) / F9 = 4  => 18 pairs (_)
C5,G5: 4.. / C5 = 4  =>  9 pairs (_) / G5 = 4  =>  0 pairs (*)
B4,B7: 4.. / B4 = 4  =>  0 pairs (X) / B7 = 4  => 10 pairs (_)
G2,I2: 6.. / G2 = 6  =>  0 pairs (X) / I2 = 6  =>  6 pairs (_)
D4,E4: 6.. / D4 = 6  =>  4 pairs (_) / E4 = 6  =>  8 pairs (_)
I2,I8: 6.. / I2 = 6  =>  6 pairs (_) / I8 = 6  =>  0 pairs (X)
C1,C2: 7.. / C1 = 7  =>  6 pairs (_) / C2 = 7  =>  7 pairs (_)
G1,G2: 7.. / G1 = 7  =>  7 pairs (_) / G2 = 7  =>  6 pairs (_)
D4,E4: 7.. / D4 = 7  =>  8 pairs (_) / E4 = 7  =>  4 pairs (_)
A7,A8: 7.. / A7 = 7  =>  6 pairs (_) / A8 = 7  => 15 pairs (_)
C1,G1: 7.. / C1 = 7  =>  6 pairs (_) / G1 = 7  =>  7 pairs (_)
C2,G2: 7.. / C2 = 7  =>  7 pairs (_) / G2 = 7  =>  6 pairs (_)
A7,E7: 7.. / A7 = 7  =>  6 pairs (_) / E7 = 7  => 15 pairs (_)
D4,D8: 7.. / D4 = 7  =>  8 pairs (_) / D8 = 7  =>  4 pairs (_)
B3,C3: 8.. / B3 = 8  =>  7 pairs (_) / C3 = 8  => 13 pairs (_)
B4,C4: 8.. / B4 = 8  => 13 pairs (_) / C4 = 8  =>  7 pairs (_)
G6,I6: 8.. / G6 = 8  =>  6 pairs (_) / I6 = 8  =>  8 pairs (_)
G8,I8: 8.. / G8 = 8  =>  8 pairs (_) / I8 = 8  =>  6 pairs (_)
B3,B4: 8.. / B3 = 8  =>  7 pairs (_) / B4 = 8  => 13 pairs (_)
C3,C4: 8.. / C3 = 8  => 13 pairs (_) / C4 = 8  =>  7 pairs (_)
G6,G8: 8.. / G6 = 8  =>  6 pairs (_) / G8 = 8  =>  8 pairs (_)
I6,I8: 8.. / I6 = 8  =>  8 pairs (_) / I8 = 8  =>  6 pairs (_)
* DURATION: 0:00:07.796046  START: 14:20:52.539893  END: 14:21:00.335939 2025-04-05
* CP COUNT: (30)
* SOLUTION FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:19.521012  START: 14:21:07.561531  END: 14:21:27.082543 2025-04-05
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00147742-base-pr-002.dot
* REASONING
* DIS # B4: 4,5 # D8: 5 => CTR => D8: 6,7
* DIS # C4: 4,5 # I4: 3,9 => CTR => I4: 4,5
* PRF # C4: 4,5 + I4: 4,5 # G6: 3,9 => SOL
* STA # C4: 4,5 + I4: 4,5 + G6: 3,9
* CNT   3 HDP CHAINS /  80 HYP OPENED

Header Info

rating: 39622; r2: 725616; index: 147742

Solution

position: 123456789457189236698327541284763195365891472971542368546278913739615824812934657 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: 4,5 => UNS
* INC # C4: 4,5 => UNS
* INC # G5: 4,5 => UNS
* INC # G5: 3,9 => UNS
* INC # C9: 4,5 => UNS
* INC # C9: 2 => UNS
* INC # D8: 6,7 => UNS
* INC # D8: 5 => UNS
* INC # E8: 6,7 => UNS
* INC # E8: 1,5 => UNS
* INC # A8: 5,7 => UNS
* INC # A8: 2 => UNS
* INC # E7: 5,7 => UNS
* INC # E7: 1,3,9 => UNS
* INC # C9: 4,5 => UNS
* INC # C9: 2 => UNS
* INC # G7: 4,5 => UNS
* INC # I7: 4,5 => UNS
* INC # B4: 4,5 => UNS
* INC # B4: 2,8 => UNS
* INC # F9: 4,5 => UNS
* INC # F9: 3,9 => UNS
* INC # G8: 4,5 => UNS
* INC # I8: 4,5 => UNS
* CNT  24 HDP CHAINS /  24 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B4: 4,5 => UNS
* INC # C4: 4,5 => UNS
* INC # G5: 4,5 => UNS
* INC # G5: 3,9 => UNS
* INC # C9: 4,5 => UNS
* INC # C9: 2 => UNS
* INC # D8: 6,7 => UNS
* INC # D8: 5 => UNS
* INC # E8: 6,7 => UNS
* INC # E8: 1,5 => UNS
* INC # A8: 5,7 => UNS
* INC # A8: 2 => UNS
* INC # E7: 5,7 => UNS
* INC # E7: 1,3,9 => UNS
* INC # C9: 4,5 => UNS
* INC # C9: 2 => UNS
* INC # G7: 4,5 => UNS
* INC # I7: 4,5 => UNS
* INC # B4: 4,5 => UNS
* INC # B4: 2,8 => UNS
* INC # F9: 4,5 => UNS
* INC # F9: 3,9 => UNS
* INC # G8: 4,5 => UNS
* INC # I8: 4,5 => UNS
* CNT  24 HDP CHAINS /  24 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # B4: 4,5 => UNS
* INC # C4: 4,5 => UNS
* INC # G5: 4,5 => UNS
* INC # G5: 3,9 => UNS
* INC # C9: 4,5 => UNS
* INC # C9: 2 => UNS
* INC # D8: 6,7 => UNS
* INC # D8: 5 => UNS
* INC # E8: 6,7 => UNS
* INC # E8: 1,5 => UNS
* INC # A8: 5,7 => UNS
* INC # A8: 2 => UNS
* INC # E7: 5,7 => UNS
* INC # E7: 1,3,9 => UNS
* INC # C9: 4,5 => UNS
* INC # C9: 2 => UNS
* INC # G7: 4,5 => UNS
* INC # I7: 4,5 => UNS
* INC # B4: 4,5 => UNS
* INC # B4: 2,8 => UNS
* INC # F9: 4,5 => UNS
* INC # F9: 3,9 => UNS
* INC # G8: 4,5 => UNS
* INC # I8: 4,5 => UNS
* INC # B4: 4,5 # C1: 3,5 => UNS
* INC # B4: 4,5 # C2: 3,5 => UNS
* INC # B4: 4,5 # D3: 3,5 => UNS
* INC # B4: 4,5 # G3: 3,5 => UNS
* INC # B4: 4,5 # E5: 3,9 => UNS
* INC # B4: 4,5 # G5: 3,9 => UNS
* INC # B4: 4,5 # D6: 3,9 => UNS
* INC # B4: 4,5 # I6: 3,9 => UNS
* INC # B4: 4,5 # D8: 6,7 => UNS
* DIS # B4: 4,5 # D8: 5 => CTR => D8: 6,7
* INC # B4: 4,5 + D8: 6,7 # E5: 3,9 => UNS
* INC # B4: 4,5 + D8: 6,7 # D6: 3,9 => UNS
* INC # B4: 4,5 + D8: 6,7 # F2: 3,9 => UNS
* INC # B4: 4,5 + D8: 6,7 # F9: 3,9 => UNS
* INC # B4: 4,5 + D8: 6,7 # G5: 3,9 => UNS
* INC # B4: 4,5 + D8: 6,7 # I6: 3,9 => UNS
* INC # B4: 4,5 + D8: 6,7 # H2: 3,9 => UNS
* INC # B4: 4,5 + D8: 6,7 # H9: 3,9 => UNS
* INC # B4: 4,5 + D8: 6,7 # E7: 5,7 => UNS
* INC # B4: 4,5 + D8: 6,7 # E7: 3,9 => UNS
* INC # B4: 4,5 + D8: 6,7 # F9: 4,5 => UNS
* INC # B4: 4,5 + D8: 6,7 # F9: 3,9 => UNS
* INC # B4: 4,5 + D8: 6,7 # C1: 3,5 => UNS
* INC # B4: 4,5 + D8: 6,7 # C2: 3,5 => UNS
* INC # B4: 4,5 + D8: 6,7 # D3: 3,5 => UNS
* INC # B4: 4,5 + D8: 6,7 # G3: 3,5 => UNS
* INC # B4: 4,5 + D8: 6,7 # E5: 3,9 => UNS
* INC # B4: 4,5 + D8: 6,7 # G5: 3,9 => UNS
* INC # B4: 4,5 + D8: 6,7 # D6: 3,9 => UNS
* INC # B4: 4,5 + D8: 6,7 # I6: 3,9 => UNS
* INC # B4: 4,5 + D8: 6,7 # E5: 3,9 => UNS
* INC # B4: 4,5 + D8: 6,7 # D6: 3,9 => UNS
* INC # B4: 4,5 + D8: 6,7 # F2: 3,9 => UNS
* INC # B4: 4,5 + D8: 6,7 # F9: 3,9 => UNS
* INC # B4: 4,5 + D8: 6,7 # G5: 3,9 => UNS
* INC # B4: 4,5 + D8: 6,7 # I6: 3,9 => UNS
* INC # B4: 4,5 + D8: 6,7 # H2: 3,9 => UNS
* INC # B4: 4,5 + D8: 6,7 # H9: 3,9 => UNS
* INC # B4: 4,5 + D8: 6,7 # E7: 5,7 => UNS
* INC # B4: 4,5 + D8: 6,7 # E7: 3,9 => UNS
* INC # B4: 4,5 + D8: 6,7 # F9: 4,5 => UNS
* INC # B4: 4,5 + D8: 6,7 # F9: 3,9 => UNS
* INC # B4: 4,5 + D8: 6,7 => UNS
* INC # C4: 4,5 # B1: 5,9 => UNS
* INC # C4: 4,5 # B2: 5,9 => UNS
* INC # C4: 4,5 # D3: 5,9 => UNS
* INC # C4: 4,5 # G3: 5,9 => UNS
* INC # C4: 4,5 # I4: 4,5 => UNS
* DIS # C4: 4,5 # I4: 3,9 => CTR => I4: 4,5
* INC # C4: 4,5 + I4: 4,5 # E5: 3,9 => UNS
* INC # C4: 4,5 + I4: 4,5 # G5: 3,9 => UNS
* INC # C4: 4,5 + I4: 4,5 # G5: 4,5 => UNS
* INC # C4: 4,5 + I4: 4,5 # G5: 3,9 => UNS
* INC # C4: 4,5 + I4: 4,5 # D6: 3,9 => UNS
* PRF # C4: 4,5 + I4: 4,5 # G6: 3,9 => SOL
* STA # C4: 4,5 + I4: 4,5 + G6: 3,9
* CNT  79 HDP CHAINS /  80 HYP OPENED