Analysis of xx-mith-te3-00133424-base.sdk

Contents

Original Sudoku
Autosolve
Pair Reduction Variants
Details
Solution
Appendix: Full HDP Chains

Original Sudoku

level: hard

position: 1..4.678....18..36....7....2.8......396.1.....71...3.8...6...43......6.7..473.81. initial

Autosolve

position: 1..4.678....18..36....7....2.8......396.1.....71...3.8...6...43......6.7..473.81. autosolve

Pair Reduction Variants

Pair Reduction Analysis

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

Pair Reduction

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

Deep Pair Reduction

Time used: 0:00:11.528374

The following important HDP chains were detected:

* DIS # G4: 5,9 # B2: 2 => CTR => B2: 4,5
* PRF # G4: 5,9 + B2: 4,5 # D4: 5,9 => SOL
* STA # G4: 5,9 + B2: 4,5 + D4: 5,9
* CNT   2 HDP CHAINS /  49 HYP OPENED

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

Details

Positions

`1..4.678....18..36....7....2.8......396.1.....71...3.8...6...43......6.7..473.81.`	initial
`1..4.678....18..36....7....2.8......396.1.....71...3.8...6...43......6.7..473.81.`	autosolve
`123456789457189236689372154248563971396817425571924368712698543835241697964735812`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (6)
A3: 6,8
B3: 6,8
G3: 1,4
I3: 1,4
B4: 4,5
A6: 4,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G3,I3: 1.. / G3 = 1  =>  5 pairs (_) / I3 = 1  =>  5 pairs (_)
G4,I4: 1.. / G4 = 1  =>  5 pairs (_) / I4 = 1  =>  5 pairs (_)
B7,B8: 1.. / B7 = 1  =>  6 pairs (_) / B8 = 1  =>  7 pairs (_)
F7,F8: 1.. / F7 = 1  =>  7 pairs (_) / F8 = 1  =>  6 pairs (_)
B7,F7: 1.. / B7 = 1  =>  6 pairs (_) / F7 = 1  =>  7 pairs (_)
B8,F8: 1.. / B8 = 1  =>  7 pairs (_) / F8 = 1  =>  6 pairs (_)
G3,G4: 1.. / G3 = 1  =>  5 pairs (_) / G4 = 1  =>  5 pairs (_)
I3,I4: 1.. / I3 = 1  =>  5 pairs (_) / I4 = 1  =>  5 pairs (_)
B1,C1: 3.. / B1 = 3  =>  6 pairs (_) / C1 = 3  =>  7 pairs (_)
D3,F3: 3.. / D3 = 3  => 17 pairs (_) / F3 = 3  =>  6 pairs (_)
D4,F4: 3.. / D4 = 3  =>  6 pairs (_) / F4 = 3  => 17 pairs (_)
B8,C8: 3.. / B8 = 3  =>  7 pairs (_) / C8 = 3  =>  6 pairs (_)
B1,B8: 3.. / B1 = 3  =>  6 pairs (_) / B8 = 3  =>  7 pairs (_)
C1,C8: 3.. / C1 = 3  =>  7 pairs (_) / C8 = 3  =>  6 pairs (_)
D3,D4: 3.. / D3 = 3  => 17 pairs (_) / D4 = 3  =>  6 pairs (_)
F3,F4: 3.. / F3 = 3  =>  6 pairs (_) / F4 = 3  => 17 pairs (_)
A2,B2: 4.. / A2 = 4  => 11 pairs (_) / B2 = 4  =>  8 pairs (_)
G3,I3: 4.. / G3 = 4  =>  5 pairs (_) / I3 = 4  =>  5 pairs (_)
B4,A6: 4.. / B4 = 4  => 11 pairs (_) / A6 = 4  =>  8 pairs (_)
E8,F8: 4.. / E8 = 4  =>  6 pairs (_) / F8 = 4  => 10 pairs (_)
A2,A6: 4.. / A2 = 4  => 11 pairs (_) / A6 = 4  =>  8 pairs (_)
B2,B4: 4.. / B2 = 4  =>  8 pairs (_) / B4 = 4  => 11 pairs (_)
B4,A6: 5.. / B4 = 5  =>  8 pairs (_) / A6 = 5  => 11 pairs (_)
A3,B3: 6.. / A3 = 6  =>  5 pairs (_) / B3 = 6  =>  9 pairs (_)
E4,E6: 6.. / E4 = 6  =>  8 pairs (_) / E6 = 6  =>  6 pairs (_)
H4,H6: 6.. / H4 = 6  =>  6 pairs (_) / H6 = 6  =>  8 pairs (_)
A9,B9: 6.. / A9 = 6  =>  9 pairs (_) / B9 = 6  =>  5 pairs (_)
E4,H4: 6.. / E4 = 6  =>  8 pairs (_) / H4 = 6  =>  6 pairs (_)
E6,H6: 6.. / E6 = 6  =>  6 pairs (_) / H6 = 6  =>  8 pairs (_)
A3,A9: 6.. / A3 = 6  =>  5 pairs (_) / A9 = 6  =>  9 pairs (_)
B3,B9: 6.. / B3 = 6  =>  9 pairs (_) / B9 = 6  =>  5 pairs (_)
A2,C2: 7.. / A2 = 7  =>  9 pairs (_) / C2 = 7  =>  8 pairs (_)
F4,F5: 7.. / F4 = 7  =>  6 pairs (_) / F5 = 7  => 12 pairs (_)
H4,H5: 7.. / H4 = 7  => 12 pairs (_) / H5 = 7  =>  6 pairs (_)
A7,C7: 7.. / A7 = 7  =>  8 pairs (_) / C7 = 7  =>  9 pairs (_)
F4,H4: 7.. / F4 = 7  =>  6 pairs (_) / H4 = 7  => 12 pairs (_)
F5,H5: 7.. / F5 = 7  => 12 pairs (_) / H5 = 7  =>  6 pairs (_)
A2,A7: 7.. / A2 = 7  =>  9 pairs (_) / A7 = 7  =>  8 pairs (_)
C2,C7: 7.. / C2 = 7  =>  8 pairs (_) / C7 = 7  =>  9 pairs (_)
A3,B3: 8.. / A3 = 8  =>  9 pairs (_) / B3 = 8  =>  5 pairs (_)
D5,F5: 8.. / D5 = 8  =>  8 pairs (_) / F5 = 8  =>  8 pairs (_)
D5,D8: 8.. / D5 = 8  =>  8 pairs (_) / D8 = 8  =>  8 pairs (_)
* DURATION: 0:00:12.454063  START: 20:11:43.482789  END: 20:11:55.936852 2025-04-06
* CP COUNT: (42)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:11.391564  START: 20:12:00.624096  END: 20:12:12.015660 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00133424-base-pr-002.dot
* REASONING
* DIS # G4: 5,9 # B2: 2 => CTR => B2: 4,5
* PRF # G4: 5,9 + B2: 4,5 # D4: 5,9 => SOL
* STA # G4: 5,9 + B2: 4,5 + D4: 5,9
* CNT   2 HDP CHAINS /  49 HYP OPENED

Header Info

rating: 35294; r2: 742263; index: 133424

Solution

position: 123456789457189236689372154248563971396817425571924368712698543835241697964735812 solved

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 # G4: 1,4 => UNS
* INC # G4: 5,9 => UNS
* INC # I4: 1,4 => UNS
* INC # I4: 5,9 => UNS
* INC # E4: 4,5 => UNS
* INC # F4: 4,5 => UNS
* INC # G4: 4,5 => UNS
* INC # I4: 4,5 => UNS
* INC # B2: 4,5 => UNS
* INC # B2: 2 => UNS
* INC # E6: 4,5 => UNS
* INC # F6: 4,5 => UNS
* INC # A2: 4,5 => UNS
* INC # A2: 7,9 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G4: 1,4 => UNS
* INC # G4: 5,9 => UNS
* INC # I4: 1,4 => UNS
* INC # I4: 5,9 => UNS
* INC # E4: 4,5 => UNS
* INC # F4: 4,5 => UNS
* INC # G4: 4,5 => UNS
* INC # I4: 4,5 => UNS
* INC # B2: 4,5 => UNS
* INC # B2: 2 => UNS
* INC # E6: 4,5 => UNS
* INC # F6: 4,5 => UNS
* INC # A2: 4,5 => UNS
* INC # A2: 7,9 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # G4: 1,4 => UNS
* INC # G4: 5,9 => UNS
* INC # I4: 1,4 => UNS
* INC # I4: 5,9 => UNS
* INC # E4: 4,5 => UNS
* INC # F4: 4,5 => UNS
* INC # G4: 4,5 => UNS
* INC # I4: 4,5 => UNS
* INC # B2: 4,5 => UNS
* INC # B2: 2 => UNS
* INC # E6: 4,5 => UNS
* INC # F6: 4,5 => UNS
* INC # A2: 4,5 => UNS
* INC # A2: 7,9 => UNS
* INC # G4: 1,4 # I4: 1,4 => UNS
* INC # G4: 1,4 # I4: 5,9 => UNS
* INC # G4: 1,4 # E4: 4,5 => UNS
* INC # G4: 1,4 # F4: 4,5 => UNS
* INC # G4: 1,4 # I4: 4,5 => UNS
* INC # G4: 1,4 # B2: 4,5 => UNS
* INC # G4: 1,4 # B2: 2 => UNS
* INC # G4: 1,4 # E6: 4,5 => UNS
* INC # G4: 1,4 # F6: 4,5 => UNS
* INC # G4: 1,4 # A2: 4,5 => UNS
* INC # G4: 1,4 # A2: 7,9 => UNS
* INC # G4: 1,4 # I4: 1,4 => UNS
* INC # G4: 1,4 # I4: 5,9 => UNS
* INC # G4: 1,4 # H5: 2,5 => UNS
* INC # G4: 1,4 # I5: 2,5 => UNS
* INC # G4: 1,4 # H6: 2,5 => UNS
* INC # G4: 1,4 # D5: 2,5 => UNS
* INC # G4: 1,4 # F5: 2,5 => UNS
* INC # G4: 1,4 # G2: 2,5 => UNS
* INC # G4: 1,4 # G7: 2,5 => UNS
* INC # G4: 1,4 => UNS
* INC # G4: 5,9 # E4: 4,5 => UNS
* INC # G4: 5,9 # F4: 4,5 => UNS
* INC # G4: 5,9 # B2: 4,5 => UNS
* DIS # G4: 5,9 # B2: 2 => CTR => B2: 4,5
* INC # G4: 5,9 + B2: 4,5 # E4: 4,5 => UNS
* INC # G4: 5,9 + B2: 4,5 # F4: 4,5 => UNS
* INC # G4: 5,9 + B2: 4,5 # E6: 4,5 => UNS
* INC # G4: 5,9 + B2: 4,5 # F6: 4,5 => UNS
* INC # G4: 5,9 + B2: 4,5 # A2: 4,5 => UNS
* INC # G4: 5,9 + B2: 4,5 # A2: 7,9 => UNS
* INC # G4: 5,9 + B2: 4,5 # H4: 5,9 => UNS
* INC # G4: 5,9 + B2: 4,5 # H6: 5,9 => UNS
* PRF # G4: 5,9 + B2: 4,5 # D4: 5,9 => SOL
* STA # G4: 5,9 + B2: 4,5 + D4: 5,9
* CNT  48 HDP CHAINS /  49 HYP OPENED