Analysis of xx-ph-00026375-KC40b-base.sdk

Contents

Original Sudoku

level: very deep

Original Sudoku

position: 98.7..6..75..4......3..8.7.5....9.3...9.....2....1...63.....2...9...5.8....4....1 initial

Autosolve

position: 98.7..6..75..4......3..8.7.5....9.3...9.....2....1...63.....2...9...5.8....4....1 autosolve
Autosolve

Pair Reduction Variants

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Time used: 0:00:00.000012

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

Very Deep Constraint Pair Analysis

Very Deep Constraint Pair Analysis

Time used: 0:01:26.237916

List of important HDP chains detected for I2,I4: 8..:

* DIS # I4: 8 # D2: 1,2,6 # D3: 2,6 => CTR => D3: 1,5,9
* DIS # I4: 8 # B4: 2,6 # C7: 1,4 => CTR => C7: 5,6,7,8
* DIS # I4: 8 # B4: 2,6 + C7: 5,6,7,8 # G5: 1,4 => CTR => G5: 5,7
* PRF # I4: 8 # B4: 2,6 + C7: 5,6,7,8 + G5: 5,7 # H5: 5 => SOL
* STA # I4: 8 # B4: 2,6 + C7: 5,6,7,8 + G5: 5,7 + H5: 5
* CNT   4 HDP CHAINS / 119 HYP OPENED

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

Details

This sudoku is very deep. Here is some information that may be helpful on how to proceed.

Positions

98.7..6..75..4......3..8.7.5....9.3...9.....2....1...63.....2...9...5.8....4....1 initial
98.7..6..75..4......3..8.7.5....9.3...9.....2....1...63.....2...9...5.8....4....1 autosolve

Classification

level: very deep

Pairing Analysis

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H1,H2: 2.. / H1 = 2  =>  4 pairs (_) / H2 = 2  =>  1 pairs (_)
B5,B6: 3.. / B5 = 3  =>  0 pairs (_) / B6 = 3  =>  0 pairs (_)
F5,F6: 4.. / F5 = 4  =>  1 pairs (_) / F6 = 4  =>  2 pairs (_)
C7,C9: 5.. / C7 = 5  =>  0 pairs (_) / C9 = 5  =>  1 pairs (_)
H7,H9: 6.. / H7 = 6  =>  2 pairs (_) / H9 = 6  =>  2 pairs (_)
G2,I2: 8.. / G2 = 8  =>  4 pairs (_) / I2 = 8  =>  1 pairs (_)
I2,I4: 8.. / I2 = 8  =>  1 pairs (_) / I4 = 8  =>  4 pairs (_)
G6,H6: 9.. / G6 = 9  =>  1 pairs (_) / H6 = 9  =>  2 pairs (_)
* DURATION: 0:00:06.303759  START: 02:30:09.044310  END: 02:30:15.348069 2020-10-20
* CP COUNT: (8)
* INCONCLUSIVE

--------------------------------------------------
* DEEP CONSTRAINT PAIRS (PAIR REDUCTION)
I2,I4: 8.. / I2 = 8 ==>  1 pairs (_) / I4 = 8 ==>  4 pairs (_)
G2,I2: 8.. / G2 = 8 ==>  4 pairs (_) / I2 = 8 ==>  1 pairs (_)
H1,H2: 2.. / H1 = 2 ==>  4 pairs (_) / H2 = 2 ==>  1 pairs (_)
H7,H9: 6.. / H7 = 6 ==>  2 pairs (_) / H9 = 6 ==>  2 pairs (_)
G6,H6: 9.. / G6 = 9 ==>  1 pairs (_) / H6 = 9 ==>  2 pairs (_)
F5,F6: 4.. / F5 = 4 ==>  1 pairs (_) / F6 = 4 ==>  2 pairs (_)
C7,C9: 5.. / C7 = 5 ==>  0 pairs (_) / C9 = 5 ==>  1 pairs (_)
B5,B6: 3.. / B5 = 3 ==>  0 pairs (_) / B6 = 3 ==>  0 pairs (_)
* DURATION: 0:01:07.665288  START: 02:30:15.348995  END: 02:31:23.014283 2020-10-20
* DCP COUNT: (8)
* INCONCLUSIVE

--------------------------------------------------
* VERY DEEP CONSTRAINT PAIRS (PAIR REDUCTION, RECURSIVE)
I2,I4: 8.. / I2 = 8  =>  0 pairs (X) / I4 = 8 ==>  0 pairs (*)
* DURATION: 0:01:26.236693  START: 02:31:23.101072  END: 02:32:49.337765 2020-10-20
* REASONING I2,I4: 8..
* DIS # I4: 8 # D2: 1,2,6 # D3: 2,6 => CTR => D3: 1,5,9
* DIS # I4: 8 # B4: 2,6 # C7: 1,4 => CTR => C7: 5,6,7,8
* DIS # I4: 8 # B4: 2,6 + C7: 5,6,7,8 # G5: 1,4 => CTR => G5: 5,7
* PRF # I4: 8 # B4: 2,6 + C7: 5,6,7,8 + G5: 5,7 # H5: 5 => SOL
* STA # I4: 8 # B4: 2,6 + C7: 5,6,7,8 + G5: 5,7 + H5: 5
* CNT   4 HDP CHAINS / 119 HYP OPENED
* VDCP COUNT: (1)
* SOLUTION FOUND

Header Info

26375;KC40b;GP;24;11.40;11.40;11.10

Appendix: Full HDP Chains

A1. Deep Constraint Pair Analysis

Full list of HDP chains traversed for I2,I4: 8..:

* INC # I4: 8 # D2: 3,9 => UNS
* INC # I4: 8 # D2: 1,2,6 => UNS
* INC # I4: 8 # E4: 2,6 => UNS
* INC # I4: 8 # E4: 7 => UNS
* INC # I4: 8 # B4: 2,6 => UNS
* INC # I4: 8 # C4: 2,6 => UNS
* INC # I4: 8 # D2: 2,6 => UNS
* INC # I4: 8 # D3: 2,6 => UNS
* INC # I4: 8 # D8: 2,6 => UNS
* INC # I4: 8 # I7: 4,7 => UNS
* INC # I4: 8 # I7: 5,9 => UNS
* INC # I4: 8 # C8: 4,7 => UNS
* INC # I4: 8 # C8: 1,2,6 => UNS
* INC # I4: 8 => UNS
* INC # I2: 8 # G4: 4,7 => UNS
* INC # I2: 8 # G5: 4,7 => UNS
* INC # I2: 8 # G6: 4,7 => UNS
* INC # I2: 8 # B4: 4,7 => UNS
* INC # I2: 8 # C4: 4,7 => UNS
* INC # I2: 8 # I7: 4,7 => UNS
* INC # I2: 8 # I8: 4,7 => UNS
* INC # I2: 8 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

Full list of HDP chains traversed for G2,I2: 8..:

* INC # G2: 8 # D2: 3,9 => UNS
* INC # G2: 8 # D2: 1,2,6 => UNS
* INC # G2: 8 # E4: 2,6 => UNS
* INC # G2: 8 # E4: 7 => UNS
* INC # G2: 8 # B4: 2,6 => UNS
* INC # G2: 8 # C4: 2,6 => UNS
* INC # G2: 8 # D2: 2,6 => UNS
* INC # G2: 8 # D3: 2,6 => UNS
* INC # G2: 8 # D8: 2,6 => UNS
* INC # G2: 8 # I7: 4,7 => UNS
* INC # G2: 8 # I7: 5,9 => UNS
* INC # G2: 8 # C8: 4,7 => UNS
* INC # G2: 8 # C8: 1,2,6 => UNS
* INC # G2: 8 => UNS
* INC # I2: 8 # G4: 4,7 => UNS
* INC # I2: 8 # G5: 4,7 => UNS
* INC # I2: 8 # G6: 4,7 => UNS
* INC # I2: 8 # B4: 4,7 => UNS
* INC # I2: 8 # C4: 4,7 => UNS
* INC # I2: 8 # I7: 4,7 => UNS
* INC # I2: 8 # I8: 4,7 => UNS
* INC # I2: 8 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

Full list of HDP chains traversed for H1,H2: 2..:

* INC # H1: 2 # A3: 1,4 => UNS
* INC # H1: 2 # B3: 1,4 => UNS
* INC # H1: 2 # C4: 1,4 => UNS
* INC # H1: 2 # C7: 1,4 => UNS
* INC # H1: 2 # C8: 1,4 => UNS
* INC # H1: 2 # I1: 3,5 => UNS
* INC # H1: 2 # I1: 4 => UNS
* INC # H1: 2 # E5: 3,5 => UNS
* INC # H1: 2 # E5: 6,7,8 => UNS
* INC # H1: 2 # D2: 1,3 => UNS
* INC # H1: 2 # F2: 1,3 => UNS
* INC # H1: 2 # G2: 1,9 => UNS
* INC # H1: 2 # G3: 1,9 => UNS
* INC # H1: 2 # D2: 1,9 => UNS
* INC # H1: 2 # D2: 2,3,6 => UNS
* INC # H1: 2 => UNS
* INC # H2: 2 # A3: 1,6 => UNS
* INC # H2: 2 # B3: 1,6 => UNS
* INC # H2: 2 # D2: 1,6 => UNS
* INC # H2: 2 # F2: 1,6 => UNS
* INC # H2: 2 # C4: 1,6 => UNS
* INC # H2: 2 # C7: 1,6 => UNS
* INC # H2: 2 # C8: 1,6 => UNS
* INC # H2: 2 => UNS
* CNT  24 HDP CHAINS /  24 HYP OPENED

Full list of HDP chains traversed for H7,H9: 6..:

* INC # H7: 6 # B7: 1,7 => UNS
* INC # H7: 6 # C7: 1,7 => UNS
* INC # H7: 6 # I7: 5,9 => UNS
* INC # H7: 6 # G9: 5,9 => UNS
* INC # H7: 6 # H6: 5,9 => UNS
* INC # H7: 6 # H6: 4 => UNS
* INC # H7: 6 => UNS
* INC # H9: 6 # C9: 2,8 => UNS
* INC # H9: 6 # C9: 5,7 => UNS
* INC # H9: 6 # E9: 2,8 => UNS
* INC # H9: 6 # E9: 3,7,9 => UNS
* INC # H9: 6 # A6: 2,8 => UNS
* INC # H9: 6 # A6: 4 => UNS
* INC # H9: 6 # C8: 2,7 => UNS
* INC # H9: 6 # C9: 2,7 => UNS
* INC # H9: 6 # E9: 2,7 => UNS
* INC # H9: 6 # F9: 2,7 => UNS
* INC # H9: 6 # B4: 2,7 => UNS
* INC # H9: 6 # B6: 2,7 => UNS
* INC # H9: 6 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

Full list of HDP chains traversed for G6,H6: 9..:

* INC # H6: 9 # H1: 1,2 => UNS
* INC # H6: 9 # H1: 4,5 => UNS
* INC # H6: 9 # C2: 1,2 => UNS
* INC # H6: 9 # D2: 1,2 => UNS
* INC # H6: 9 # F2: 1,2 => UNS
* INC # H6: 9 # H7: 5,6 => UNS
* INC # H6: 9 # H7: 4 => UNS
* INC # H6: 9 # C9: 5,6 => UNS
* INC # H6: 9 # C9: 2,7,8 => UNS
* INC # H6: 9 => UNS
* INC # G6: 9 # G5: 4,5 => UNS
* INC # G6: 9 # H5: 4,5 => UNS
* INC # G6: 9 # H1: 4,5 => UNS
* INC # G6: 9 # H7: 4,5 => UNS
* INC # G6: 9 => UNS
* CNT  15 HDP CHAINS /  15 HYP OPENED

Full list of HDP chains traversed for F5,F6: 4..:

* INC # F6: 4 # C4: 2,8 => UNS
* INC # F6: 4 # C6: 2,8 => UNS
* INC # F6: 4 # D6: 2,8 => UNS
* INC # F6: 4 # D6: 3,5 => UNS
* INC # F6: 4 # A9: 2,8 => UNS
* INC # F6: 4 # A9: 6 => UNS
* INC # F6: 4 # G6: 5,9 => UNS
* INC # F6: 4 # G6: 7,8 => UNS
* INC # F6: 4 # H7: 5,9 => UNS
* INC # F6: 4 # H9: 5,9 => UNS
* INC # F6: 4 => UNS
* INC # F5: 4 # G5: 1,5 => UNS
* INC # F5: 4 # G5: 7,8 => UNS
* INC # F5: 4 # H1: 1,5 => UNS
* INC # F5: 4 # H1: 2,4 => UNS
* INC # F5: 4 => UNS
* CNT  16 HDP CHAINS /  16 HYP OPENED

Full list of HDP chains traversed for C7,C9: 5..:

* INC # C9: 5 # H7: 6,9 => UNS
* INC # C9: 5 # H7: 4,5 => UNS
* INC # C9: 5 # E9: 6,9 => UNS
* INC # C9: 5 # E9: 2,3,7,8 => UNS
* INC # C9: 5 => UNS
* INC # C7: 5 => UNS
* CNT   6 HDP CHAINS /   6 HYP OPENED

Full list of HDP chains traversed for B5,B6: 3..:

* INC # B5: 3 => UNS
* INC # B6: 3 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED

A2. Very Deep Constraint Pair Analysis

Full list of HDP chains traversed for I2,I4: 8..:

* INC # I4: 8 # D2: 3,9 => UNS
* INC # I4: 8 # D2: 1,2,6 => UNS
* INC # I4: 8 # E4: 2,6 => UNS
* INC # I4: 8 # E4: 7 => UNS
* INC # I4: 8 # B4: 2,6 => UNS
* INC # I4: 8 # C4: 2,6 => UNS
* INC # I4: 8 # D2: 2,6 => UNS
* INC # I4: 8 # D3: 2,6 => UNS
* INC # I4: 8 # D8: 2,6 => UNS
* INC # I4: 8 # I7: 4,7 => UNS
* INC # I4: 8 # I7: 5,9 => UNS
* INC # I4: 8 # C8: 4,7 => UNS
* INC # I4: 8 # C8: 1,2,6 => UNS
* INC # I4: 8 # D2: 3,9 # H1: 1,2 => UNS
* INC # I4: 8 # D2: 3,9 # H1: 4,5 => UNS
* INC # I4: 8 # D2: 3,9 # C2: 1,2 => UNS
* INC # I4: 8 # D2: 3,9 # F2: 1,2 => UNS
* INC # I4: 8 # D2: 3,9 # E4: 2,6 => UNS
* INC # I4: 8 # D2: 3,9 # E4: 7 => UNS
* INC # I4: 8 # D2: 3,9 # B4: 2,6 => UNS
* INC # I4: 8 # D2: 3,9 # C4: 2,6 => UNS
* INC # I4: 8 # D2: 3,9 # D3: 2,6 => UNS
* INC # I4: 8 # D2: 3,9 # D8: 2,6 => UNS
* INC # I4: 8 # D2: 3,9 # I7: 4,7 => UNS
* INC # I4: 8 # D2: 3,9 # I7: 5,9 => UNS
* INC # I4: 8 # D2: 3,9 # C8: 4,7 => UNS
* INC # I4: 8 # D2: 3,9 # C8: 1,2,6 => UNS
* INC # I4: 8 # D2: 3,9 => UNS
* INC # I4: 8 # D2: 1,2,6 # H1: 4,5 => UNS
* INC # I4: 8 # D2: 1,2,6 # I1: 4,5 => UNS
* INC # I4: 8 # D2: 1,2,6 # G3: 4,5 => UNS
* INC # I4: 8 # D2: 1,2,6 # I7: 4,5 => UNS
* INC # I4: 8 # D2: 1,2,6 # I7: 7,9 => UNS
* INC # I4: 8 # D2: 1,2,6 # E4: 2,6 => UNS
* INC # I4: 8 # D2: 1,2,6 # E4: 7 => UNS
* INC # I4: 8 # D2: 1,2,6 # B4: 2,6 => UNS
* INC # I4: 8 # D2: 1,2,6 # C4: 2,6 => UNS
* INC # I4: 8 # D2: 1,2,6 # D2: 2,6 => UNS
* DIS # I4: 8 # D2: 1,2,6 # D3: 2,6 => CTR => D3: 1,5,9
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # D8: 2,6 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # E4: 2,6 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # E4: 7 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # B4: 2,6 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # C4: 2,6 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # D2: 2,6 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # D8: 2,6 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # I7: 4,7 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # I7: 5,9 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # C8: 4,7 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # C8: 1,2,6 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # H1: 4,5 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # I1: 4,5 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # G3: 4,5 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # I7: 4,5 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # I7: 7,9 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # E4: 2,6 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # E4: 7 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # B4: 2,6 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # C4: 2,6 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # D2: 2,6 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # D8: 2,6 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # I7: 4,7 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # I7: 5,9 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # C8: 4,7 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 # C8: 1,2,6 => UNS
* INC # I4: 8 # D2: 1,2,6 + D3: 1,5,9 => UNS
* INC # I4: 8 # E4: 2,6 # D2: 3,9 => UNS
* INC # I4: 8 # E4: 2,6 # D2: 1,2,6 => UNS
* INC # I4: 8 # E4: 2,6 # D2: 2,6 => UNS
* INC # I4: 8 # E4: 2,6 # D3: 2,6 => UNS
* INC # I4: 8 # E4: 2,6 # D8: 2,6 => UNS
* INC # I4: 8 # E4: 2,6 # E3: 2,6 => UNS
* INC # I4: 8 # E4: 2,6 # E8: 2,6 => UNS
* INC # I4: 8 # E4: 2,6 # E9: 2,6 => UNS
* INC # I4: 8 # E4: 2,6 # I7: 4,7 => UNS
* INC # I4: 8 # E4: 2,6 # I7: 5,9 => UNS
* INC # I4: 8 # E4: 2,6 # C8: 4,7 => UNS
* INC # I4: 8 # E4: 2,6 # C8: 1,2,6 => UNS
* INC # I4: 8 # E4: 2,6 => UNS
* INC # I4: 8 # E4: 7 # D2: 3,9 => UNS
* INC # I4: 8 # E4: 7 # D2: 1,2,6 => UNS
* INC # I4: 8 # E4: 7 # B4: 2,6 => UNS
* INC # I4: 8 # E4: 7 # C4: 2,6 => UNS
* INC # I4: 8 # E4: 7 # D2: 2,6 => UNS
* INC # I4: 8 # E4: 7 # D3: 2,6 => UNS
* INC # I4: 8 # E4: 7 # D8: 2,6 => UNS
* INC # I4: 8 # E4: 7 # G5: 1,4 => UNS
* INC # I4: 8 # E4: 7 # H5: 1,4 => UNS
* INC # I4: 8 # E4: 7 # B4: 1,4 => UNS
* INC # I4: 8 # E4: 7 # C4: 1,4 => UNS
* INC # I4: 8 # E4: 7 # G3: 1,4 => UNS
* INC # I4: 8 # E4: 7 # G3: 5,9 => UNS
* INC # I4: 8 # E4: 7 # I7: 4,7 => UNS
* INC # I4: 8 # E4: 7 # I7: 5,9 => UNS
* INC # I4: 8 # E4: 7 # C8: 4,7 => UNS
* INC # I4: 8 # E4: 7 # C8: 1,2,6 => UNS
* INC # I4: 8 # E4: 7 => UNS
* INC # I4: 8 # B4: 2,6 # D2: 3,9 => UNS
* INC # I4: 8 # B4: 2,6 # D2: 1,2,6 => UNS
* INC # I4: 8 # B4: 2,6 # B3: 2,6 => UNS
* INC # I4: 8 # B4: 2,6 # B9: 2,6 => UNS
* INC # I4: 8 # B4: 2,6 # A5: 1,4 => UNS
* INC # I4: 8 # B4: 2,6 # B5: 1,4 => UNS
* INC # I4: 8 # B4: 2,6 # C1: 1,4 => UNS
* DIS # I4: 8 # B4: 2,6 # C7: 1,4 => CTR => C7: 5,6,7,8
* INC # I4: 8 # B4: 2,6 + C7: 5,6,7,8 # C8: 1,4 => UNS
* INC # I4: 8 # B4: 2,6 + C7: 5,6,7,8 # A5: 1,4 => UNS
* INC # I4: 8 # B4: 2,6 + C7: 5,6,7,8 # B5: 1,4 => UNS
* INC # I4: 8 # B4: 2,6 + C7: 5,6,7,8 # C1: 1,4 => UNS
* INC # I4: 8 # B4: 2,6 + C7: 5,6,7,8 # C8: 1,4 => UNS
* INC # I4: 8 # B4: 2,6 + C7: 5,6,7,8 # D2: 2,6 => UNS
* INC # I4: 8 # B4: 2,6 + C7: 5,6,7,8 # D3: 2,6 => UNS
* INC # I4: 8 # B4: 2,6 + C7: 5,6,7,8 # D8: 2,6 => UNS
* DIS # I4: 8 # B4: 2,6 + C7: 5,6,7,8 # G5: 1,4 => CTR => G5: 5,7
* INC # I4: 8 # B4: 2,6 + C7: 5,6,7,8 + G5: 5,7 # H5: 1,4 => UNS
* INC # I4: 8 # B4: 2,6 + C7: 5,6,7,8 + G5: 5,7 # H5: 1,4 => UNS
* PRF # I4: 8 # B4: 2,6 + C7: 5,6,7,8 + G5: 5,7 # H5: 5 => SOL
* STA # I4: 8 # B4: 2,6 + C7: 5,6,7,8 + G5: 5,7 + H5: 5
* CNT 117 HDP CHAINS / 119 HYP OPENED