Analysis of xx-mith-te3-00051014-base.sdk

Contents

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

Original Sudoku

level: hard

position: 1...56.8.....8....6..3.7....7563.1..3.1...6.7....71...53....4.171....9.2.......5. initial

Autosolve

position: 1...56.8..5..8....68.3.7....7563.1..3.1...6.7....71...53....4.171....9.2.......5. autosolve

Pair Reduction Variants

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # E9: 4,6 => CTR => E9: 1,2,9
* CNT   1 HDP CHAINS /  20 HYP OPENED

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

Pair Reduction

The following important HDP chains were detected:

* DIS # E9: 4,6 => CTR => E9: 1,2,9
* STA E9: 1,2,9
* CNT   1 HDP CHAINS /  37 HYP OPENED

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

Pair Reduction Position

position: 1...56.8..5..8....68.3.7....7563.1..3.1...6.7....71...53....4.171....9.2.......5. pair_reduction

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

Deep Pair Reduction

Time used: 0:00:30.370641

The following important HDP chains were detected:

* DIS # G1: 3,7 # G9: 3,7 => CTR => G9: 8
* DIS # G1: 2 # B6: 4,9 => CTR => B6: 2,6
* DIS # H2: 3,7 # B1: 4,9 => CTR => B1: 2
* PRF # H2: 3,7 + B1: 2 # A9: 4,9 => SOL
* STA # H2: 3,7 + B1: 2 + A9: 4,9
* CNT   4 HDP CHAINS / 138 HYP OPENED

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

Details

Positions

`1...56.8.....8....6..3.7....7563.1..3.1...6.7....71...53....4.171....9.2.......5.`	initial
`1...56.8..5..8....68.3.7....7563.1..3.1...6.7....71...53....4.171....9.2.......5.`	autosolve
`1...56.8..5..8....68.3.7....7563.1..3.1...6.7....71...53....4.171....9.2.......5.`	pair_reduction
`123456789457189236689327514275634198341895627896271345532968471718543962964712853`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
C1: 3,7
C2: 3,7
G3: 2,5
D5: 5,8
F5: 5,8
E8: 4,6
H7: 6,7
H8: 3,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D2,E3: 1.. / D2 = 1  =>  8 pairs (_) / E3 = 1  =>  0 pairs (X)
H2,H3: 1.. / H2 = 1  =>  0 pairs (X) / H3 = 1  =>  8 pairs (_)
D9,E9: 1.. / D9 = 1  =>  0 pairs (X) / E9 = 1  =>  8 pairs (_)
D2,H2: 1.. / D2 = 1  =>  8 pairs (_) / H2 = 1  =>  0 pairs (X)
E3,H3: 1.. / E3 = 1  =>  0 pairs (X) / H3 = 1  =>  8 pairs (_)
D2,D9: 1.. / D2 = 1  =>  8 pairs (_) / D9 = 1  =>  0 pairs (X)
E3,E9: 1.. / E3 = 1  =>  0 pairs (X) / E9 = 1  =>  8 pairs (_)
C1,C2: 3.. / C1 = 3  =>  8 pairs (_) / C2 = 3  =>  8 pairs (_)
F8,F9: 3.. / F8 = 3  => 10 pairs (_) / F9 = 3  => 10 pairs (_)
F8,H8: 3.. / F8 = 3  => 10 pairs (_) / H8 = 3  => 10 pairs (_)
G3,I3: 5.. / G3 = 5  =>  8 pairs (_) / I3 = 5  => 12 pairs (_)
D5,F5: 5.. / D5 = 5  => 10 pairs (_) / F5 = 5  =>  6 pairs (_)
G6,I6: 5.. / G6 = 5  => 12 pairs (_) / I6 = 5  =>  8 pairs (_)
D8,F8: 5.. / D8 = 5  =>  6 pairs (_) / F8 = 5  => 10 pairs (_)
D5,D8: 5.. / D5 = 5  => 10 pairs (_) / D8 = 5  =>  6 pairs (_)
F5,F8: 5.. / F5 = 5  =>  6 pairs (_) / F8 = 5  => 10 pairs (_)
G3,G6: 5.. / G3 = 5  =>  8 pairs (_) / G6 = 5  => 12 pairs (_)
I3,I6: 5.. / I3 = 5  => 12 pairs (_) / I6 = 5  =>  8 pairs (_)
H2,I2: 6.. / H2 = 6  => 10 pairs (_) / I2 = 6  =>  9 pairs (_)
B6,C6: 6.. / B6 = 6  =>  8 pairs (_) / C6 = 6  => 10 pairs (_)
B6,B9: 6.. / B6 = 6  =>  8 pairs (_) / B9 = 6  => 10 pairs (_)
I2,I9: 6.. / I2 = 6  =>  9 pairs (_) / I9 = 6  => 10 pairs (_)
C1,C2: 7.. / C1 = 7  =>  8 pairs (_) / C2 = 7  =>  8 pairs (_)
D7,D9: 7.. / D7 = 7  =>  0 pairs (X) / D9 = 7  =>  8 pairs (_)
H7,G9: 7.. / H7 = 7  =>  8 pairs (_) / G9 = 7  =>  0 pairs (X)
C1,G1: 7.. / C1 = 7  =>  8 pairs (_) / G1 = 7  =>  8 pairs (_)
D7,H7: 7.. / D7 = 7  =>  0 pairs (X) / H7 = 7  =>  8 pairs (_)
D9,G9: 7.. / D9 = 7  =>  8 pairs (_) / G9 = 7  =>  0 pairs (X)
H2,H7: 7.. / H2 = 7  =>  0 pairs (X) / H7 = 7  =>  8 pairs (_)
A4,A6: 8.. / A4 = 8  => 15 pairs (_) / A6 = 8  =>  8 pairs (_)
D5,F5: 8.. / D5 = 8  =>  6 pairs (_) / F5 = 8  => 10 pairs (_)
C7,C8: 8.. / C7 = 8  => 13 pairs (_) / C8 = 8  =>  9 pairs (_)
G9,I9: 8.. / G9 = 8  =>  8 pairs (_) / I9 = 8  => 10 pairs (_)
A4,I4: 8.. / A4 = 8  => 15 pairs (_) / I4 = 8  =>  8 pairs (_)
G6,G9: 8.. / G6 = 8  => 10 pairs (_) / G9 = 8  =>  8 pairs (_)
* DURATION: 0:00:11.292262  START: 08:48:21.293863  END: 08:48:32.586125 2025-04-06
* CP COUNT: (35)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:30.138983  START: 08:48:44.301943  END: 08:49:14.440926 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00051014-base-pr-002.dot
* REASONING
* DIS # G1: 3,7 # G9: 3,7 => CTR => G9: 8
* DIS # G1: 2 # B6: 4,9 => CTR => B6: 2,6
* DIS # H2: 3,7 # B1: 4,9 => CTR => B1: 2
* PRF # H2: 3,7 + B1: 2 # A9: 4,9 => SOL
* STA # H2: 3,7 + B1: 2 + A9: 4,9
* CNT   4 HDP CHAINS / 138 HYP OPENED

Header Info

rating: 10451; r2: 367019; index: 51014

Solution

position: 123456789457189236689327514275634198341895627896271345532968471718543962964712853 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 # G1: 3,7 => UNS
* INC # G1: 2 => UNS
* INC # G2: 3,7 => UNS
* INC # H2: 3,7 => UNS
* INC # G6: 2,5 => UNS
* INC # G6: 3,8 => UNS
* INC # D8: 5,8 => UNS
* INC # D8: 4 => UNS
* INC # F8: 5,8 => UNS
* INC # F8: 3,4 => UNS
* DIS # E9: 4,6 => CTR => E9: 1,2,9
* INC # E9: 1,2,9 => UNS
* INC # C8: 4,6 => UNS
* INC # C8: 8 => UNS
* INC # H2: 6,7 => UNS
* INC # H2: 1,2,3,4,9 => UNS
* INC # I9: 3,6 => UNS
* INC # I9: 8 => UNS
* INC # H2: 3,6 => UNS
* INC # H2: 1,2,4,7,9 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G1: 3,7 => UNS
* INC # G1: 2 => UNS
* INC # G2: 3,7 => UNS
* INC # H2: 3,7 => UNS
* INC # G6: 2,5 => UNS
* INC # G6: 3,8 => UNS
* INC # D8: 5,8 => UNS
* INC # D8: 4 => UNS
* INC # F8: 5,8 => UNS
* INC # F8: 3,4 => UNS
* DIS # E9: 4,6 => CTR => E9: 1,2,9
* INC E9: 1,2,9 # C8: 4,6 => UNS
* INC E9: 1,2,9 # C8: 8 => UNS
* INC E9: 1,2,9 # H2: 6,7 => UNS
* INC E9: 1,2,9 # H2: 1,2,3,4,9 => UNS
* INC E9: 1,2,9 # I9: 3,6 => UNS
* INC E9: 1,2,9 # I9: 8 => UNS
* INC E9: 1,2,9 # H2: 3,6 => UNS
* INC E9: 1,2,9 # H2: 1,2,4,7,9 => UNS
* INC E9: 1,2,9 # G1: 3,7 => UNS
* INC E9: 1,2,9 # G1: 2 => UNS
* INC E9: 1,2,9 # G2: 3,7 => UNS
* INC E9: 1,2,9 # H2: 3,7 => UNS
* INC E9: 1,2,9 # G6: 2,5 => UNS
* INC E9: 1,2,9 # G6: 3,8 => UNS
* INC E9: 1,2,9 # D8: 5,8 => UNS
* INC E9: 1,2,9 # D8: 4 => UNS
* INC E9: 1,2,9 # F8: 5,8 => UNS
* INC E9: 1,2,9 # F8: 3,4 => UNS
* INC E9: 1,2,9 # C8: 4,6 => UNS
* INC E9: 1,2,9 # C8: 8 => UNS
* INC E9: 1,2,9 # H2: 6,7 => UNS
* INC E9: 1,2,9 # H2: 1,2,3,4,9 => UNS
* INC E9: 1,2,9 # I9: 3,6 => UNS
* INC E9: 1,2,9 # I9: 8 => UNS
* INC E9: 1,2,9 # H2: 3,6 => UNS
* INC E9: 1,2,9 # H2: 1,2,4,7,9 => UNS
* STA E9: 1,2,9
* CNT  37 HDP CHAINS /  37 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # G1: 3,7 => UNS
* INC # G1: 2 => UNS
* INC # G2: 3,7 => UNS
* INC # H2: 3,7 => UNS
* INC # G6: 2,5 => UNS
* INC # G6: 3,8 => UNS
* INC # D8: 5,8 => UNS
* INC # D8: 4 => UNS
* INC # F8: 5,8 => UNS
* INC # F8: 3,4 => UNS
* INC # C8: 4,6 => UNS
* INC # C8: 8 => UNS
* INC # H2: 6,7 => UNS
* INC # H2: 1,2,3,4,9 => UNS
* INC # I9: 3,6 => UNS
* INC # I9: 8 => UNS
* INC # H2: 3,6 => UNS
* INC # H2: 1,2,4,7,9 => UNS
* INC # G1: 3,7 # G2: 3,7 => UNS
* INC # G1: 3,7 # H2: 3,7 => UNS
* INC # G1: 3,7 # G2: 3,7 => UNS
* INC # G1: 3,7 # H2: 3,7 => UNS
* DIS # G1: 3,7 # G9: 3,7 => CTR => G9: 8
* INC # G1: 3,7 + G9: 8 # G2: 3,7 => UNS
* INC # G1: 3,7 + G9: 8 # G2: 2 => UNS
* INC # G1: 3,7 + G9: 8 # H2: 4,9 => UNS
* INC # G1: 3,7 + G9: 8 # I2: 4,9 => UNS
* INC # G1: 3,7 + G9: 8 # I3: 4,9 => UNS
* INC # G1: 3,7 + G9: 8 # B1: 4,9 => UNS
* INC # G1: 3,7 + G9: 8 # D1: 4,9 => UNS
* INC # G1: 3,7 + G9: 8 # I4: 4,9 => UNS
* INC # G1: 3,7 + G9: 8 # I6: 4,9 => UNS
* INC # G1: 3,7 + G9: 8 # G6: 2,5 => UNS
* INC # G1: 3,7 + G9: 8 # G6: 3 => UNS
* INC # G1: 3,7 + G9: 8 # D8: 5,8 => UNS
* INC # G1: 3,7 + G9: 8 # D8: 4 => UNS
* INC # G1: 3,7 + G9: 8 # F8: 5,8 => UNS
* INC # G1: 3,7 + G9: 8 # F8: 3,4 => UNS
* INC # G1: 3,7 + G9: 8 # C8: 4,6 => UNS
* INC # G1: 3,7 + G9: 8 # C8: 8 => UNS
* INC # G1: 3,7 + G9: 8 # H2: 3,6 => UNS
* INC # G1: 3,7 + G9: 8 # H2: 2,4,9 => UNS
* INC # G1: 3,7 + G9: 8 # G2: 3,7 => UNS
* INC # G1: 3,7 + G9: 8 # G2: 2 => UNS
* INC # G1: 3,7 + G9: 8 # G2: 3,7 => UNS
* INC # G1: 3,7 + G9: 8 # G2: 2 => UNS
* INC # G1: 3,7 + G9: 8 # H2: 4,9 => UNS
* INC # G1: 3,7 + G9: 8 # I2: 4,9 => UNS
* INC # G1: 3,7 + G9: 8 # I3: 4,9 => UNS
* INC # G1: 3,7 + G9: 8 # B1: 4,9 => UNS
* INC # G1: 3,7 + G9: 8 # D1: 4,9 => UNS
* INC # G1: 3,7 + G9: 8 # I4: 4,9 => UNS
* INC # G1: 3,7 + G9: 8 # I6: 4,9 => UNS
* INC # G1: 3,7 + G9: 8 # G6: 2,5 => UNS
* INC # G1: 3,7 + G9: 8 # G6: 3 => UNS
* INC # G1: 3,7 + G9: 8 # D8: 5,8 => UNS
* INC # G1: 3,7 + G9: 8 # D8: 4 => UNS
* INC # G1: 3,7 + G9: 8 # F8: 5,8 => UNS
* INC # G1: 3,7 + G9: 8 # F8: 3,4 => UNS
* INC # G1: 3,7 + G9: 8 # C8: 4,6 => UNS
* INC # G1: 3,7 + G9: 8 # C8: 8 => UNS
* INC # G1: 3,7 + G9: 8 # H2: 3,6 => UNS
* INC # G1: 3,7 + G9: 8 # H2: 2,4,9 => UNS
* INC # G1: 3,7 + G9: 8 # I2: 3,6 => UNS
* INC # G1: 3,7 + G9: 8 # I2: 4,9 => UNS
* INC # G1: 3,7 + G9: 8 => UNS
* INC # G1: 2 # A2: 4,9 => UNS
* INC # G1: 2 # C3: 4,9 => UNS
* INC # G1: 2 # B5: 4,9 => UNS
* DIS # G1: 2 # B6: 4,9 => CTR => B6: 2,6
* INC # G1: 2 + B6: 2,6 # B9: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # A2: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # C3: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # B5: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # B9: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # F2: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # E3: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # D6: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # D6: 2 => UNS
* INC # G1: 2 + B6: 2,6 # H2: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # I2: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # C3: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # E3: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # I4: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # I4: 8 => UNS
* INC # G1: 2 + B6: 2,6 # D8: 5,8 => UNS
* INC # G1: 2 + B6: 2,6 # D8: 4 => UNS
* INC # G1: 2 + B6: 2,6 # F8: 5,8 => UNS
* INC # G1: 2 + B6: 2,6 # F8: 3,4 => UNS
* INC # G1: 2 + B6: 2,6 # C8: 4,6 => UNS
* INC # G1: 2 + B6: 2,6 # C8: 8 => UNS
* INC # G1: 2 + B6: 2,6 # A2: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # C3: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # B5: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # B9: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # F2: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # E3: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # D6: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # D6: 2 => UNS
* INC # G1: 2 + B6: 2,6 # H2: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # I2: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # C3: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # E3: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # I4: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # I4: 8 => UNS
* INC # G1: 2 + B6: 2,6 # C6: 2,6 => UNS
* INC # G1: 2 + B6: 2,6 # C6: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # B9: 2,6 => UNS
* INC # G1: 2 + B6: 2,6 # B9: 4,9 => UNS
* INC # G1: 2 + B6: 2,6 # D8: 5,8 => UNS
* INC # G1: 2 + B6: 2,6 # D8: 4 => UNS
* INC # G1: 2 + B6: 2,6 # F8: 5,8 => UNS
* INC # G1: 2 + B6: 2,6 # F8: 3,4 => UNS
* INC # G1: 2 + B6: 2,6 # C8: 4,6 => UNS
* INC # G1: 2 + B6: 2,6 # C8: 8 => UNS
* INC # G1: 2 + B6: 2,6 => UNS
* INC # G2: 3,7 # G1: 3,7 => UNS
* INC # G2: 3,7 # G1: 2 => UNS
* INC # G2: 3,7 # G1: 3,7 => UNS
* INC # G2: 3,7 # G1: 2 => UNS
* INC # G2: 3,7 # G6: 2,5 => UNS
* INC # G2: 3,7 # G6: 3,8 => UNS
* INC # G2: 3,7 # D8: 5,8 => UNS
* INC # G2: 3,7 # D8: 4 => UNS
* INC # G2: 3,7 # F8: 5,8 => UNS
* INC # G2: 3,7 # F8: 3,4 => UNS
* INC # G2: 3,7 # C8: 4,6 => UNS
* INC # G2: 3,7 # C8: 8 => UNS
* INC # G2: 3,7 # I9: 3,6 => UNS
* INC # G2: 3,7 # I9: 8 => UNS
* INC # G2: 3,7 # I9: 3,8 => UNS
* INC # G2: 3,7 # I9: 6 => UNS
* INC # G2: 3,7 # G6: 3,8 => UNS
* INC # G2: 3,7 # G6: 2,5 => UNS
* INC # G2: 3,7 => UNS
* DIS # H2: 3,7 # B1: 4,9 => CTR => B1: 2
* PRF # H2: 3,7 + B1: 2 # A9: 4,9 => SOL
* STA # H2: 3,7 + B1: 2 + A9: 4,9
* CNT 137 HDP CHAINS / 138 HYP OPENED