Analysis of xx-mith-te3-00015644-base.sdk

Contents

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

Original Sudoku

level: hard

position: 1.3..6...4.7...2...8......5..5.176.3..63.215...156..72........1...62.3.7...7..5.. initial

Autosolve

position: 1.3..6...4.7...2.668......5..5.176.3..63.215...156..72........1...62.3.7...7..5.. autosolve

Pair Reduction Variants

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A7: 5,9 => CTR => A7: 2,3,7
* CNT   1 HDP CHAINS /  22 HYP OPENED

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

Pair Reduction

The following important HDP chains were detected:

* DIS # A7: 5,9 => CTR => A7: 2,3,7
* STA A7: 2,3,7
* CNT   1 HDP CHAINS /  37 HYP OPENED

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

Pair Reduction Position

position: 1.3..6...4.7...2.668......5..5.176.3..63.215...156..72........15..62.3.7...7..5.. pair_reduction

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

Deep Pair Reduction

Time used: 0:00:10.929525

The following important HDP chains were detected:

* DIS # B1: 2 # E9: 8,9 => CTR => E9: 3,4
* PRF # B1: 2 + E9: 3,4 # H8: 8,9 => SOL
* STA # B1: 2 + E9: 3,4 + H8: 8,9
* CNT   2 HDP CHAINS /  42 HYP OPENED

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

Details

Positions

`1.3..6...4.7...2...8......5..5.176.3..63.215...156..72........1...62.3.7...7..5..`	initial
`1.3..6...4.7...2.668......5..5.176.3..63.215...156..72........1...62.3.7...7..5..`	autosolve
`1.3..6...4.7...2.668......5..5.176.3..63.215...156..72........15..62.3.7...7..5..`	pair_reduction
`123456789457189236689273415295817643746392158831564972372945861514628397968731524`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
B2: 5,9
C3: 2,9
H2: 1,3
H3: 1,3
A8: 5,9
B8: 1,9
H7: 2,6
H9: 2,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D2,D3: 1.. / D2 = 1  =>  6 pairs (_) / D3 = 1  => 14 pairs (_)
H2,H3: 1.. / H2 = 1  => 14 pairs (_) / H3 = 1  =>  6 pairs (_)
B8,B9: 1.. / B8 = 1  =>  7 pairs (_) / B9 = 1  => 14 pairs (_)
F8,F9: 1.. / F8 = 1  => 14 pairs (_) / F9 = 1  =>  7 pairs (_)
D2,H2: 1.. / D2 = 1  =>  6 pairs (_) / H2 = 1  => 14 pairs (_)
D3,H3: 1.. / D3 = 1  => 14 pairs (_) / H3 = 1  =>  6 pairs (_)
B8,F8: 1.. / B8 = 1  =>  7 pairs (_) / F8 = 1  => 14 pairs (_)
B9,F9: 1.. / B9 = 1  => 14 pairs (_) / F9 = 1  =>  7 pairs (_)
B1,C3: 2.. / B1 = 2  => 18 pairs (_) / C3 = 2  => 13 pairs (_)
D1,D3: 2.. / D1 = 2  => 13 pairs (_) / D3 = 2  => 18 pairs (_)
A4,B4: 2.. / A4 = 2  => 10 pairs (_) / B4 = 2  => 15 pairs (_)
H7,H9: 2.. / H7 = 2  =>  8 pairs (_) / H9 = 2  =>  6 pairs (_)
B1,D1: 2.. / B1 = 2  => 18 pairs (_) / D1 = 2  => 13 pairs (_)
C3,D3: 2.. / C3 = 2  => 13 pairs (_) / D3 = 2  => 18 pairs (_)
H2,H3: 3.. / H2 = 3  =>  6 pairs (_) / H3 = 3  => 14 pairs (_)
A6,B6: 3.. / A6 = 3  => 11 pairs (_) / B6 = 3  =>  9 pairs (_)
B1,B2: 5.. / B1 = 5  => 12 pairs (_) / B2 = 5  => 11 pairs (_)
A7,A8: 5.. / A7 = 5  =>  0 pairs (X) / A8 = 5  =>  7 pairs (_)
B1,E1: 5.. / B1 = 5  => 12 pairs (_) / E1 = 5  => 11 pairs (_)
A8,F8: 5.. / A8 = 5  =>  7 pairs (_) / F8 = 5  =>  0 pairs (X)
B7,B9: 6.. / B7 = 6  =>  8 pairs (_) / B9 = 6  =>  6 pairs (_)
H7,H9: 6.. / H7 = 6  =>  6 pairs (_) / H9 = 6  =>  8 pairs (_)
B7,H7: 6.. / B7 = 6  =>  8 pairs (_) / H7 = 6  =>  6 pairs (_)
B9,H9: 6.. / B9 = 6  =>  6 pairs (_) / H9 = 6  =>  8 pairs (_)
E1,E3: 7.. / E1 = 7  => 12 pairs (_) / E3 = 7  =>  9 pairs (_)
G1,G3: 7.. / G1 = 7  =>  9 pairs (_) / G3 = 7  => 12 pairs (_)
A5,B5: 7.. / A5 = 7  =>  8 pairs (_) / B5 = 7  =>  8 pairs (_)
A7,B7: 7.. / A7 = 7  =>  8 pairs (_) / B7 = 7  =>  8 pairs (_)
E1,G1: 7.. / E1 = 7  => 12 pairs (_) / G1 = 7  =>  9 pairs (_)
E3,G3: 7.. / E3 = 7  =>  9 pairs (_) / G3 = 7  => 12 pairs (_)
A5,A7: 7.. / A5 = 7  =>  8 pairs (_) / A7 = 7  =>  8 pairs (_)
B5,B7: 7.. / B5 = 7  =>  8 pairs (_) / B7 = 7  =>  8 pairs (_)
* DURATION: 0:00:10.957437  START: 07:43:45.901846  END: 07:43:56.859283 2025-04-04
* CP COUNT: (32)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:10.775552  START: 07:44:08.263841  END: 07:44:19.039393 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00015644-base-pr-002.dot
* REASONING
* DIS # B1: 2 # E9: 8,9 => CTR => E9: 3,4
* PRF # B1: 2 + E9: 3,4 # H8: 8,9 => SOL
* STA # B1: 2 + E9: 3,4 + H8: 8,9
* CNT   2 HDP CHAINS /  42 HYP OPENED

Header Info

rating: 3454; r2: 343585; index: 15644

Solution

position: 123456789457189236689273415295817643746392158831564972372945861514628397968731524 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 # B1: 5,9 => UNS
* INC # B1: 2 => UNS
* INC # E2: 5,9 => UNS
* INC # F2: 5,9 => UNS
* INC # B1: 2,9 => UNS
* INC # B1: 5 => UNS
* INC # D3: 2,9 => UNS
* INC # D3: 1,4 => UNS
* INC # C7: 2,9 => UNS
* INC # C9: 2,9 => UNS
* DIS # A7: 5,9 => CTR => A7: 2,3,7
* INC # A7: 2,3,7 => UNS
* INC # F8: 5,9 => UNS
* INC # F8: 1,4,8 => UNS
* INC # B9: 1,9 => UNS
* INC # B9: 2,3,6 => UNS
* INC # F8: 1,9 => UNS
* INC # F8: 4,5,8 => UNS
* INC # B7: 2,6 => UNS
* INC # B7: 3,7,9 => UNS
* INC # B9: 2,6 => UNS
* INC # B9: 1,3,9 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B1: 5,9 => UNS
* INC # B1: 2 => UNS
* INC # E2: 5,9 => UNS
* INC # F2: 5,9 => UNS
* INC # B1: 2,9 => UNS
* INC # B1: 5 => UNS
* INC # D3: 2,9 => UNS
* INC # D3: 1,4 => UNS
* INC # C7: 2,9 => UNS
* INC # C9: 2,9 => UNS
* DIS # A7: 5,9 => CTR => A7: 2,3,7
* INC A7: 2,3,7 # B9: 1,9 => UNS
* INC A7: 2,3,7 # B9: 2,3,6 => UNS
* INC A7: 2,3,7 # F8: 1,9 => UNS
* INC A7: 2,3,7 # F8: 4,8 => UNS
* INC A7: 2,3,7 # B7: 2,6 => UNS
* INC A7: 2,3,7 # B7: 3,7,9 => UNS
* INC A7: 2,3,7 # B9: 2,6 => UNS
* INC A7: 2,3,7 # B9: 1,3,9 => UNS
* INC A7: 2,3,7 # B1: 5,9 => UNS
* INC A7: 2,3,7 # B1: 2 => UNS
* INC A7: 2,3,7 # E2: 5,9 => UNS
* INC A7: 2,3,7 # F2: 5,9 => UNS
* INC A7: 2,3,7 # B1: 2,9 => UNS
* INC A7: 2,3,7 # B1: 5 => UNS
* INC A7: 2,3,7 # D3: 2,9 => UNS
* INC A7: 2,3,7 # D3: 1,4 => UNS
* INC A7: 2,3,7 # C7: 2,9 => UNS
* INC A7: 2,3,7 # C9: 2,9 => UNS
* INC A7: 2,3,7 # B9: 1,9 => UNS
* INC A7: 2,3,7 # B9: 2,3,6 => UNS
* INC A7: 2,3,7 # F8: 1,9 => UNS
* INC A7: 2,3,7 # F8: 4,8 => UNS
* INC A7: 2,3,7 # B7: 2,6 => UNS
* INC A7: 2,3,7 # B7: 3,7,9 => UNS
* INC A7: 2,3,7 # B9: 2,6 => UNS
* INC A7: 2,3,7 # B9: 1,3,9 => UNS
* STA A7: 2,3,7
* CNT  37 HDP CHAINS /  37 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # B1: 5,9 => UNS
* INC # B1: 2 => UNS
* INC # E2: 5,9 => UNS
* INC # F2: 5,9 => UNS
* INC # B1: 2,9 => UNS
* INC # B1: 5 => UNS
* INC # D3: 2,9 => UNS
* INC # D3: 1,4 => UNS
* INC # C7: 2,9 => UNS
* INC # C9: 2,9 => UNS
* INC # B9: 1,9 => UNS
* INC # B9: 2,3,6 => UNS
* INC # F8: 1,9 => UNS
* INC # F8: 4,8 => UNS
* INC # B7: 2,6 => UNS
* INC # B7: 3,7,9 => UNS
* INC # B9: 2,6 => UNS
* INC # B9: 1,3,9 => UNS
* INC # B1: 5,9 # E1: 5,9 => UNS
* INC # B1: 5,9 # E1: 4,7 => UNS
* INC # B1: 5,9 # E2: 5,9 => UNS
* INC # B1: 5,9 # F2: 5,9 => UNS
* INC # B1: 5,9 # B7: 2,7 => UNS
* INC # B1: 5,9 # B7: 6 => UNS
* INC # B1: 5,9 # B9: 2,3 => UNS
* INC # B1: 5,9 # B9: 6 => UNS
* INC # B1: 5,9 # E2: 3,5 => UNS
* INC # B1: 5,9 # E2: 8,9 => UNS
* INC # B1: 5,9 # F2: 3,5 => UNS
* INC # B1: 5,9 # F2: 8,9 => UNS
* INC # B1: 5,9 # B7: 2,6 => UNS
* INC # B1: 5,9 # B7: 7 => UNS
* INC # B1: 5,9 # B9: 2,6 => UNS
* INC # B1: 5,9 # B9: 3 => UNS
* INC # B1: 5,9 => UNS
* INC # B1: 2 # E5: 8,9 => UNS
* DIS # B1: 2 # E9: 8,9 => CTR => E9: 3,4
* INC # B1: 2 + E9: 3,4 # F8: 8,9 => UNS
* INC # B1: 2 + E9: 3,4 # F9: 8,9 => UNS
* INC # B1: 2 + E9: 3,4 # H4: 8,9 => UNS
* PRF # B1: 2 + E9: 3,4 # H8: 8,9 => SOL
* STA # B1: 2 + E9: 3,4 + H8: 8,9
* CNT  41 HDP CHAINS /  42 HYP OPENED