Analysis of xx-mith-te3-00145390-base.sdk

Contents

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

Original Sudoku

level: hard

position: 12..56..9.571.9...6.927....2.1..........2184........3.51.......7.6.1259..92..56.. initial

Autosolve

position: 12..56..9.571.9...6.927....2.1...9......2184........3.51.......7.6.1259..92..56.. 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: 0:00:13.095910

The following important HDP chains were detected:

* DIS # H9: 7,8 # E6: 4,8 => CTR => E6: 6,9
* PRF # H9: 7,8 + E6: 6,9 # D9: 3,4 => SOL
* STA # H9: 7,8 + E6: 6,9 + D9: 3,4
* CNT   2 HDP CHAINS /  47 HYP OPENED

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

Details

Positions

`12..56..9.571.9...6.927....2.1..........2184........3.51.......7.6.1259..92..56..`	initial
`12..56..9.571.9...6.927....2.1...9......2184........3.51.......7.6.1259..92..56..`	autosolve
`123456789457189263689273415241738956365921847978564132514697328736812594892345671`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
H1: 7,8
A5: 3,9
C5: 3,5
G6: 1,2
I6: 1,2
D7: 6,9
E7: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G6,I6: 1.. / G6 = 1  =>  8 pairs (_) / I6 = 1  =>  9 pairs (_)
H9,I9: 1.. / H9 = 1  =>  8 pairs (_) / I9 = 1  =>  9 pairs (_)
G3,G6: 1.. / G3 = 1  =>  9 pairs (_) / G6 = 1  =>  8 pairs (_)
H3,H9: 1.. / H3 = 1  =>  9 pairs (_) / H9 = 1  =>  8 pairs (_)
G6,I6: 2.. / G6 = 2  =>  9 pairs (_) / I6 = 2  =>  8 pairs (_)
H2,H7: 2.. / H2 = 2  => 12 pairs (_) / H7 = 2  =>  8 pairs (_)
H3,I3: 5.. / H3 = 5  =>  8 pairs (_) / I3 = 5  => 10 pairs (_)
C5,C6: 5.. / C5 = 5  =>  8 pairs (_) / C6 = 5  =>  9 pairs (_)
C6,D6: 5.. / C6 = 5  =>  9 pairs (_) / D6 = 5  =>  8 pairs (_)
H3,H4: 5.. / H3 = 5  =>  8 pairs (_) / H4 = 5  => 10 pairs (_)
H2,I2: 6.. / H2 = 6  =>  8 pairs (_) / I2 = 6  => 11 pairs (_)
D7,E7: 6.. / D7 = 6  =>  5 pairs (_) / E7 = 6  =>  5 pairs (_)
H2,H4: 6.. / H2 = 6  =>  8 pairs (_) / H4 = 6  => 11 pairs (_)
G1,H1: 7.. / G1 = 7  => 12 pairs (_) / H1 = 7  => 10 pairs (_)
F7,D9: 7.. / F7 = 7  => 19 pairs (_) / D9 = 7  =>  8 pairs (_)
G1,G7: 7.. / G1 = 7  => 12 pairs (_) / G7 = 7  => 10 pairs (_)
A5,A6: 9.. / A5 = 9  =>  7 pairs (_) / A6 = 9  =>  8 pairs (_)
D7,E7: 9.. / D7 = 9  =>  5 pairs (_) / E7 = 9  =>  5 pairs (_)
A5,D5: 9.. / A5 = 9  =>  7 pairs (_) / D5 = 9  =>  8 pairs (_)
E6,E7: 9.. / E6 = 9  =>  5 pairs (_) / E7 = 9  =>  5 pairs (_)
* DURATION: 0:00:05.461948  START: 22:04:01.290774  END: 22:04:06.752722 2025-04-06
* CP COUNT: (20)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:12.927712  START: 22:04:10.211832  END: 22:04:23.139544 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00145390-base-pr-002.dot
* REASONING
* DIS # H9: 7,8 # E6: 4,8 => CTR => E6: 6,9
* PRF # H9: 7,8 + E6: 6,9 # D9: 3,4 => SOL
* STA # H9: 7,8 + E6: 6,9 + D9: 3,4
* CNT   2 HDP CHAINS /  47 HYP OPENED

Header Info

rating: 38844; r2: 718862; index: 145390

Solution

position: 123456789457189263689273415241738956365921847978564132514697328736812594892345671 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 # H7: 7,8 => UNS
* INC # H9: 7,8 => UNS
* INC # D5: 3,9 => UNS
* INC # D5: 5,6,7 => UNS
* INC # D5: 3,5 => UNS
* INC # D5: 6,7,9 => UNS
* INC # D5: 6,9 => UNS
* INC # D6: 6,9 => UNS
* INC # E6: 6,9 => UNS
* INC # E6: 4,8 => UNS
* CNT  10 HDP CHAINS /  10 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # H7: 7,8 => UNS
* INC # H9: 7,8 => UNS
* INC # D5: 3,9 => UNS
* INC # D5: 5,6,7 => UNS
* INC # D5: 3,5 => UNS
* INC # D5: 6,7,9 => UNS
* INC # D5: 6,9 => UNS
* INC # D6: 6,9 => UNS
* INC # E6: 6,9 => UNS
* INC # E6: 4,8 => UNS
* CNT  10 HDP CHAINS /  10 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # H7: 7,8 => UNS
* INC # H9: 7,8 => UNS
* INC # D5: 3,9 => UNS
* INC # D5: 5,6,7 => UNS
* INC # D5: 3,5 => UNS
* INC # D5: 6,7,9 => UNS
* INC # D5: 6,9 => UNS
* INC # D6: 6,9 => UNS
* INC # E6: 6,9 => UNS
* INC # E6: 4,8 => UNS
* INC # H7: 7,8 # G1: 3,4 => UNS
* INC # H7: 7,8 # G3: 3,4 => UNS
* INC # H7: 7,8 # I3: 3,4 => UNS
* INC # H7: 7,8 # A2: 3,4 => UNS
* INC # H7: 7,8 # E2: 3,4 => UNS
* INC # H7: 7,8 # G7: 3,4 => UNS
* INC # H7: 7,8 # G7: 2,7 => UNS
* INC # H7: 7,8 # D5: 3,9 => UNS
* INC # H7: 7,8 # D5: 5,6 => UNS
* INC # H7: 7,8 # D5: 3,5 => UNS
* INC # H7: 7,8 # D5: 6,9 => UNS
* INC # H7: 7,8 # D5: 6,9 => UNS
* INC # H7: 7,8 # D6: 6,9 => UNS
* INC # H7: 7,8 # D5: 6,9 => UNS
* INC # H7: 7,8 # D6: 6,9 => UNS
* INC # H7: 7,8 => UNS
* INC # H9: 7,8 # G1: 3,4 => UNS
* INC # H9: 7,8 # I2: 3,4 => UNS
* INC # H9: 7,8 # B3: 3,4 => UNS
* INC # H9: 7,8 # F3: 3,4 => UNS
* INC # H9: 7,8 # G7: 3,4 => UNS
* INC # H9: 7,8 # G7: 7 => UNS
* INC # H9: 7,8 # D5: 3,9 => UNS
* INC # H9: 7,8 # D5: 5,6,7 => UNS
* INC # H9: 7,8 # D5: 3,5 => UNS
* INC # H9: 7,8 # D5: 6,7,9 => UNS
* INC # H9: 7,8 # B4: 6,7 => UNS
* INC # H9: 7,8 # D4: 6,7 => UNS
* INC # H9: 7,8 # B5: 6,7 => UNS
* INC # H9: 7,8 # D5: 6,7 => UNS
* INC # H9: 7,8 # D5: 6,9 => UNS
* INC # H9: 7,8 # D6: 6,9 => UNS
* INC # H9: 7,8 # E6: 6,9 => UNS
* DIS # H9: 7,8 # E6: 4,8 => CTR => E6: 6,9
* INC # H9: 7,8 + E6: 6,9 # D9: 7,8 => UNS
* PRF # H9: 7,8 + E6: 6,9 # D9: 3,4 => SOL
* STA # H9: 7,8 + E6: 6,9 + D9: 3,4
* CNT  46 HDP CHAINS /  47 HYP OPENED