Analysis of xx-mith-te3-00153914-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 12..5...9.57......6.9.2.1..27....3.8......42....5.2.6..6..97...7..61.....1.2.5.7. initial

Autosolve

position: 12..5...9.57......6.9.2.1..27....3.8......42....5.2.6..6..97...7..61.....1.2.5.7. 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: 0:00:14.840193

The following important HDP chains were detected:

* DIS # D4: 1,9 # C5: 3,8 => CTR => C5: 1,5,6
* DIS # D4: 1,9 + C5: 1,5,6 # D3: 3,8 => CTR => D3: 4,7
* PRF # D4: 1,9 + C5: 1,5,6 + D3: 4,7 # I3: 4,7 => SOL
* STA # D4: 1,9 + C5: 1,5,6 + D3: 4,7 + I3: 4,7
* CNT   3 HDP CHAINS /  48 HYP OPENED

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

Details

Positions

12..5...9.57......6.9.2.1..27....3.8......42....5.2.6..6..97...7..61.....1.2.5.7. initial
12..5...9.57......6.9.2.1..27....3.8......42....5.2.6..6..97...7..61.....1.2.5.7. autosolve
123456789457189236689723154275964318396871425841532967562397841734618592918245673 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
D2: 1,9
F2: 1,9
E4: 4,6
G6: 7,9
I6: 1,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D2,F2: 1.. / D2 = 1  =>  4 pairs (_) / F2 = 1  =>  4 pairs (_)
H7,I7: 1.. / H7 = 1  =>  7 pairs (_) / I7 = 1  => 12 pairs (_)
C6,I6: 1.. / C6 = 1  =>  8 pairs (_) / I6 = 1  => 10 pairs (_)
H4,H7: 1.. / H4 = 1  => 12 pairs (_) / H7 = 1  =>  7 pairs (_)
G2,I2: 2.. / G2 = 2  =>  6 pairs (_) / I2 = 2  => 11 pairs (_)
C7,C8: 2.. / C7 = 2  =>  6 pairs (_) / C8 = 2  =>  7 pairs (_)
H3,I3: 5.. / H3 = 5  => 12 pairs (_) / I3 = 5  =>  8 pairs (_)
H4,I5: 5.. / H4 = 5  =>  8 pairs (_) / I5 = 5  => 12 pairs (_)
G7,G8: 5.. / G7 = 5  => 10 pairs (_) / G8 = 5  =>  6 pairs (_)
C4,H4: 5.. / C4 = 5  => 12 pairs (_) / H4 = 5  =>  8 pairs (_)
C8,G8: 5.. / C8 = 5  => 10 pairs (_) / G8 = 5  =>  6 pairs (_)
A5,A7: 5.. / A5 = 5  => 10 pairs (_) / A7 = 5  => 12 pairs (_)
H3,H4: 5.. / H3 = 5  => 12 pairs (_) / H4 = 5  =>  8 pairs (_)
I3,I5: 5.. / I3 = 5  =>  8 pairs (_) / I5 = 5  => 12 pairs (_)
F1,E2: 6.. / F1 = 6  =>  8 pairs (_) / E2 = 6  =>  0 pairs (X)
C4,C5: 6.. / C4 = 6  => 13 pairs (_) / C5 = 6  =>  5 pairs (_)
G9,I9: 6.. / G9 = 6  =>  8 pairs (_) / I9 = 6  =>  6 pairs (_)
F1,G1: 6.. / F1 = 6  =>  8 pairs (_) / G1 = 6  =>  0 pairs (X)
I2,I9: 6.. / I2 = 6  =>  8 pairs (_) / I9 = 6  =>  6 pairs (_)
D1,D3: 7.. / D1 = 7  =>  0 pairs (X) / D3 = 7  =>  8 pairs (_)
G1,I3: 7.. / G1 = 7  =>  8 pairs (_) / I3 = 7  =>  0 pairs (X)
E5,E6: 7.. / E5 = 7  =>  6 pairs (_) / E6 = 7  => 10 pairs (_)
D1,G1: 7.. / D1 = 7  =>  0 pairs (X) / G1 = 7  =>  8 pairs (_)
D3,I3: 7.. / D3 = 7  =>  8 pairs (_) / I3 = 7  =>  0 pairs (X)
E5,I5: 7.. / E5 = 7  =>  6 pairs (_) / I5 = 7  => 10 pairs (_)
G1,G6: 7.. / G1 = 7  =>  8 pairs (_) / G6 = 7  =>  0 pairs (X)
D2,F2: 9.. / D2 = 9  =>  4 pairs (_) / F2 = 9  =>  4 pairs (_)
H4,G6: 9.. / H4 = 9  =>  0 pairs (X) / G6 = 9  =>  8 pairs (_)
B8,A9: 9.. / B8 = 9  =>  0 pairs (X) / A9 = 9  =>  6 pairs (_)
A9,G9: 9.. / A9 = 9  =>  6 pairs (_) / G9 = 9  =>  0 pairs (X)
H4,H8: 9.. / H4 = 9  =>  0 pairs (X) / H8 = 9  =>  8 pairs (_)
* DURATION: 0:00:08.753954  START: 22:54:05.203217  END: 22:54:13.957171 2025-04-06
* CP COUNT: (31)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:14.675976  START: 22:54:17.765601  END: 22:54:32.441577 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00153914-base-pr-002.dot
* REASONING
* DIS # D4: 1,9 # C5: 3,8 => CTR => C5: 1,5,6
* DIS # D4: 1,9 + C5: 1,5,6 # D3: 3,8 => CTR => D3: 4,7
* PRF # D4: 1,9 + C5: 1,5,6 + D3: 4,7 # I3: 4,7 => SOL
* STA # D4: 1,9 + C5: 1,5,6 + D3: 4,7 + I3: 4,7
* CNT   3 HDP CHAINS /  48 HYP OPENED

Header Info

rating: 42359; r2: 814532; index: 153914

Solution

position: 123456789457189236689723154275964318396871425841532967562397841734618592918245673 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 # D4: 1,9 => UNS
* INC # D5: 1,9 => UNS
* INC # F4: 1,9 => UNS
* INC # F5: 1,9 => UNS
* INC # F4: 4,6 => UNS
* INC # F4: 1,9 => UNS
* INC # C4: 4,6 => UNS
* INC # C4: 1,5 => UNS
* INC # E2: 4,6 => UNS
* INC # E2: 3,8 => UNS
* INC # I5: 1,7 => UNS
* INC # I5: 5 => UNS
* CNT  12 HDP CHAINS /  12 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # D4: 1,9 => UNS
* INC # D5: 1,9 => UNS
* INC # F4: 1,9 => UNS
* INC # F5: 1,9 => UNS
* INC # F4: 4,6 => UNS
* INC # F4: 1,9 => UNS
* INC # C4: 4,6 => UNS
* INC # C4: 1,5 => UNS
* INC # E2: 4,6 => UNS
* INC # E2: 3,8 => UNS
* INC # I5: 1,7 => UNS
* INC # I5: 5 => UNS
* CNT  12 HDP CHAINS /  12 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # D4: 1,9 => UNS
* INC # D5: 1,9 => UNS
* INC # F4: 1,9 => UNS
* INC # F5: 1,9 => UNS
* INC # F4: 4,6 => UNS
* INC # F4: 1,9 => UNS
* INC # C4: 4,6 => UNS
* INC # C4: 1,5 => UNS
* INC # E2: 4,6 => UNS
* INC # E2: 3,8 => UNS
* INC # I5: 1,7 => UNS
* INC # I5: 5 => UNS
* INC # D4: 1,9 # F4: 1,9 => UNS
* INC # D4: 1,9 # F5: 1,9 => UNS
* INC # D4: 1,9 # F4: 1,9 => UNS
* INC # D4: 1,9 # F5: 1,9 => UNS
* INC # D4: 1,9 # H4: 1,9 => UNS
* INC # D4: 1,9 # H4: 5 => UNS
* INC # D4: 1,9 # F4: 4,6 => UNS
* INC # D4: 1,9 # F4: 1,9 => UNS
* INC # D4: 1,9 # C4: 4,6 => UNS
* INC # D4: 1,9 # C4: 1,5 => UNS
* INC # D4: 1,9 # E2: 4,6 => UNS
* INC # D4: 1,9 # E2: 3,8 => UNS
* INC # D4: 1,9 # E5: 3,8 => UNS
* INC # D4: 1,9 # F5: 3,8 => UNS
* INC # D4: 1,9 # E6: 3,8 => UNS
* INC # D4: 1,9 # A5: 3,8 => UNS
* INC # D4: 1,9 # B5: 3,8 => UNS
* DIS # D4: 1,9 # C5: 3,8 => CTR => C5: 1,5,6
* INC # D4: 1,9 + C5: 1,5,6 # D1: 3,8 => UNS
* DIS # D4: 1,9 + C5: 1,5,6 # D3: 3,8 => CTR => D3: 4,7
* INC # D4: 1,9 + C5: 1,5,6 + D3: 4,7 # D7: 3,8 => UNS
* INC # D4: 1,9 + C5: 1,5,6 + D3: 4,7 # E5: 3,8 => UNS
* INC # D4: 1,9 + C5: 1,5,6 + D3: 4,7 # F5: 3,8 => UNS
* INC # D4: 1,9 + C5: 1,5,6 + D3: 4,7 # E6: 3,8 => UNS
* INC # D4: 1,9 + C5: 1,5,6 + D3: 4,7 # A5: 3,8 => UNS
* INC # D4: 1,9 + C5: 1,5,6 + D3: 4,7 # B5: 3,8 => UNS
* INC # D4: 1,9 + C5: 1,5,6 + D3: 4,7 # D1: 3,8 => UNS
* INC # D4: 1,9 + C5: 1,5,6 + D3: 4,7 # D7: 3,8 => UNS
* INC # D4: 1,9 + C5: 1,5,6 + D3: 4,7 # I5: 1,7 => UNS
* INC # D4: 1,9 + C5: 1,5,6 + D3: 4,7 # I5: 5 => UNS
* INC # D4: 1,9 + C5: 1,5,6 + D3: 4,7 # F4: 1,9 => UNS
* INC # D4: 1,9 + C5: 1,5,6 + D3: 4,7 # F5: 1,9 => UNS
* INC # D4: 1,9 + C5: 1,5,6 + D3: 4,7 # D1: 4,7 => UNS
* INC # D4: 1,9 + C5: 1,5,6 + D3: 4,7 # D1: 3,8 => UNS
* PRF # D4: 1,9 + C5: 1,5,6 + D3: 4,7 # I3: 4,7 => SOL
* STA # D4: 1,9 + C5: 1,5,6 + D3: 4,7 + I3: 4,7
* CNT  47 HDP CHAINS /  48 HYP OPENED