Analysis of xx-mith-te3-00100279-base.sdk

Contents

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

Original Sudoku

level: hard

position: 1...5..89......2.68....215.239...6..58126....674.........59.8.......8.9...8.2156. initial

Autosolve

position: 1...56.89......2.68....215.239...61.58126....674....2....59.8.....6.8.9...8.2156. 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: 0:00:19.233471

The following important HDP chains were detected:

* PRF # B3: 4,9 # D3: 3,7 => SOL
* STA # B3: 4,9 + D3: 3,7
* CNT   1 HDP CHAINS /  72 HYP OPENED

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

Details

Positions

`1...5..89......2.68....215.239...6..58126....674.........59.8.......8.9...8.2156.`	initial
`1...56.89......2.68....215.239...61.58126....674....2....59.8.....6.8.9...8.2156.`	autosolve
`123456789457189236896372154239847615581263947674915328362594871715638492948721563`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
B1: 2,4
A2: 4,9
D2: 1,8
E2: 1,8
F5: 3,9
I4: 5,8
G6: 3,9
I6: 5,8
C7: 2,6
C8: 2,5
B9: 4,9
I7: 1,2
I8: 1,2

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D2,E2: 1.. / D2 = 1  => 12 pairs (_) / E2 = 1  => 14 pairs (_)
D6,E6: 1.. / D6 = 1  => 14 pairs (_) / E6 = 1  => 12 pairs (_)
B7,B8: 1.. / B7 = 1  => 12 pairs (_) / B8 = 1  => 12 pairs (_)
I7,I8: 1.. / I7 = 1  => 12 pairs (_) / I8 = 1  => 12 pairs (_)
B7,I7: 1.. / B7 = 1  => 12 pairs (_) / I7 = 1  => 12 pairs (_)
B8,I8: 1.. / B8 = 1  => 12 pairs (_) / I8 = 1  => 12 pairs (_)
D2,D6: 1.. / D2 = 1  => 12 pairs (_) / D6 = 1  => 14 pairs (_)
E2,E6: 1.. / E2 = 1  => 14 pairs (_) / E6 = 1  => 12 pairs (_)
B1,C1: 2.. / B1 = 2  => 15 pairs (_) / C1 = 2  => 14 pairs (_)
I7,I8: 2.. / I7 = 2  => 12 pairs (_) / I8 = 2  => 12 pairs (_)
B2,C2: 5.. / B2 = 5  => 14 pairs (_) / C2 = 5  => 13 pairs (_)
F4,F6: 5.. / F4 = 5  => 19 pairs (_) / F6 = 5  => 13 pairs (_)
I4,I6: 5.. / I4 = 5  => 13 pairs (_) / I6 = 5  => 19 pairs (_)
B8,C8: 5.. / B8 = 5  => 13 pairs (_) / C8 = 5  => 14 pairs (_)
F4,I4: 5.. / F4 = 5  => 19 pairs (_) / I4 = 5  => 13 pairs (_)
F6,I6: 5.. / F6 = 5  => 13 pairs (_) / I6 = 5  => 19 pairs (_)
B2,B8: 5.. / B2 = 5  => 14 pairs (_) / B8 = 5  => 13 pairs (_)
C2,C8: 5.. / C2 = 5  => 13 pairs (_) / C8 = 5  => 14 pairs (_)
B3,C3: 6.. / B3 = 6  => 14 pairs (_) / C3 = 6  => 11 pairs (_)
B7,C7: 6.. / B7 = 6  => 11 pairs (_) / C7 = 6  => 14 pairs (_)
B3,B7: 6.. / B3 = 6  => 14 pairs (_) / B7 = 6  => 11 pairs (_)
C3,C7: 6.. / C3 = 6  => 11 pairs (_) / C7 = 6  => 14 pairs (_)
D2,E2: 8.. / D2 = 8  => 14 pairs (_) / E2 = 8  => 12 pairs (_)
I4,I6: 8.. / I4 = 8  => 19 pairs (_) / I6 = 8  => 13 pairs (_)
F2,D3: 9.. / F2 = 9  => 15 pairs (_) / D3 = 9  => 14 pairs (_)
G5,G6: 9.. / G5 = 9  => 19 pairs (_) / G6 = 9  => 13 pairs (_)
A9,B9: 9.. / A9 = 9  => 20 pairs (_) / B9 = 9  => 13 pairs (_)
B3,D3: 9.. / B3 = 9  => 15 pairs (_) / D3 = 9  => 14 pairs (_)
F5,G5: 9.. / F5 = 9  => 13 pairs (_) / G5 = 9  => 19 pairs (_)
A2,A9: 9.. / A2 = 9  => 13 pairs (_) / A9 = 9  => 20 pairs (_)
D3,D6: 9.. / D3 = 9  => 14 pairs (_) / D6 = 9  => 15 pairs (_)
* DURATION: 0:00:12.222786  START: 01:02:50.384841  END: 01:03:02.607627 2025-04-05
* CP COUNT: (31)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:19.060154  START: 01:03:16.092799  END: 01:03:35.152953 2025-04-05
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00100279-base-pr-002.dot
* REASONING
* PRF # B3: 4,9 # D3: 3,7 => SOL
* STA # B3: 4,9 + D3: 3,7
* CNT   1 HDP CHAINS /  72 HYP OPENED

Header Info

rating: 25236; r2: 794895; index: 100279

Solution

position: 123456789457189236896372154239847615581263947674915328362594871715638492948721563 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 # B2: 4,9 => UNS
* INC # B3: 4,9 => UNS
* INC # F2: 4,9 => UNS
* INC # F2: 3,7 => UNS
* INC # A9: 4,9 => UNS
* INC # A9: 3,7 => UNS
* INC # D6: 1,8 => UNS
* INC # D6: 3,9 => UNS
* INC # E6: 1,8 => UNS
* INC # E6: 3 => UNS
* INC # D6: 3,9 => UNS
* INC # F6: 3,9 => UNS
* INC # G5: 3,9 => UNS
* INC # G5: 4,7 => UNS
* INC # F2: 3,9 => UNS
* INC # F2: 4,7 => UNS
* INC # G5: 3,9 => UNS
* INC # G5: 4,7 => UNS
* INC # D6: 3,9 => UNS
* INC # F6: 3,9 => UNS
* INC # B7: 2,6 => UNS
* INC # B7: 1 => UNS
* INC # B8: 2,5 => UNS
* INC # B8: 1 => UNS
* INC # A9: 4,9 => UNS
* INC # A9: 3,7 => UNS
* INC # B2: 4,9 => UNS
* INC # B3: 4,9 => UNS
* INC # B7: 1,2 => UNS
* INC # B7: 6 => UNS
* INC # B8: 1,2 => UNS
* INC # B8: 5 => UNS
* CNT  32 HDP CHAINS /  32 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B2: 4,9 => UNS
* INC # B3: 4,9 => UNS
* INC # F2: 4,9 => UNS
* INC # F2: 3,7 => UNS
* INC # A9: 4,9 => UNS
* INC # A9: 3,7 => UNS
* INC # D6: 1,8 => UNS
* INC # D6: 3,9 => UNS
* INC # E6: 1,8 => UNS
* INC # E6: 3 => UNS
* INC # D6: 3,9 => UNS
* INC # F6: 3,9 => UNS
* INC # G5: 3,9 => UNS
* INC # G5: 4,7 => UNS
* INC # F2: 3,9 => UNS
* INC # F2: 4,7 => UNS
* INC # G5: 3,9 => UNS
* INC # G5: 4,7 => UNS
* INC # D6: 3,9 => UNS
* INC # F6: 3,9 => UNS
* INC # B7: 2,6 => UNS
* INC # B7: 1 => UNS
* INC # B8: 2,5 => UNS
* INC # B8: 1 => UNS
* INC # A9: 4,9 => UNS
* INC # A9: 3,7 => UNS
* INC # B2: 4,9 => UNS
* INC # B3: 4,9 => UNS
* INC # B7: 1,2 => UNS
* INC # B7: 6 => UNS
* INC # B8: 1,2 => UNS
* INC # B8: 5 => UNS
* CNT  32 HDP CHAINS /  32 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # B2: 4,9 => UNS
* INC # B3: 4,9 => UNS
* INC # F2: 4,9 => UNS
* INC # F2: 3,7 => UNS
* INC # A9: 4,9 => UNS
* INC # A9: 3,7 => UNS
* INC # D6: 1,8 => UNS
* INC # D6: 3,9 => UNS
* INC # E6: 1,8 => UNS
* INC # E6: 3 => UNS
* INC # D6: 3,9 => UNS
* INC # F6: 3,9 => UNS
* INC # G5: 3,9 => UNS
* INC # G5: 4,7 => UNS
* INC # F2: 3,9 => UNS
* INC # F2: 4,7 => UNS
* INC # G5: 3,9 => UNS
* INC # G5: 4,7 => UNS
* INC # D6: 3,9 => UNS
* INC # F6: 3,9 => UNS
* INC # B7: 2,6 => UNS
* INC # B7: 1 => UNS
* INC # B8: 2,5 => UNS
* INC # B8: 1 => UNS
* INC # A9: 4,9 => UNS
* INC # A9: 3,7 => UNS
* INC # B2: 4,9 => UNS
* INC # B3: 4,9 => UNS
* INC # B7: 1,2 => UNS
* INC # B7: 6 => UNS
* INC # B8: 1,2 => UNS
* INC # B8: 5 => UNS
* INC # B2: 4,9 # D1: 3,7 => UNS
* INC # B2: 4,9 # G1: 3,7 => UNS
* INC # B2: 4,9 # A9: 4,9 => UNS
* INC # B2: 4,9 # A9: 3,7 => UNS
* INC # B2: 4,9 # E3: 3,7 => UNS
* INC # B2: 4,9 # I3: 3,7 => UNS
* INC # B2: 4,9 # D6: 1,8 => UNS
* INC # B2: 4,9 # D6: 3 => UNS
* INC # B2: 4,9 # E6: 1,8 => UNS
* INC # B2: 4,9 # E6: 3 => UNS
* INC # B2: 4,9 # D1: 3,7 => UNS
* INC # B2: 4,9 # E3: 3,7 => UNS
* INC # B2: 4,9 # F7: 3,7 => UNS
* INC # B2: 4,9 # F7: 4 => UNS
* INC # B2: 4,9 # G1: 3,7 => UNS
* INC # B2: 4,9 # I3: 3,7 => UNS
* INC # B2: 4,9 # H5: 3,7 => UNS
* INC # B2: 4,9 # H7: 3,7 => UNS
* INC # B2: 4,9 # F6: 3,9 => UNS
* INC # B2: 4,9 # F6: 5 => UNS
* INC # B2: 4,9 # G5: 3,9 => UNS
* INC # B2: 4,9 # G5: 4,7 => UNS
* INC # B2: 4,9 # G5: 3,9 => UNS
* INC # B2: 4,9 # G5: 4,7 => UNS
* INC # B2: 4,9 # F6: 3,9 => UNS
* INC # B2: 4,9 # F6: 5 => UNS
* INC # B2: 4,9 # A9: 4,9 => UNS
* INC # B2: 4,9 # A9: 3,7 => UNS
* INC # B2: 4,9 => UNS
* INC # B3: 4,9 # D1: 3,7 => UNS
* INC # B3: 4,9 # G1: 3,7 => UNS
* INC # B3: 4,9 # F2: 4,9 => UNS
* INC # B3: 4,9 # F2: 3,7 => UNS
* INC # B3: 4,9 # A9: 4,9 => UNS
* INC # B3: 4,9 # A9: 3,7 => UNS
* INC # B3: 4,9 # F2: 3,7 => UNS
* INC # B3: 4,9 # H2: 3,7 => UNS
* INC # B3: 4,9 # D3: 4,9 => UNS
* PRF # B3: 4,9 # D3: 3,7 => SOL
* STA # B3: 4,9 + D3: 3,7
* CNT  71 HDP CHAINS /  72 HYP OPENED