Analysis of xx-top500-259-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .7.3.....5......1......9.5..2....7.8...61.....4.......6..7..2..1.9............... initial

Autosolve

position: 97.351...56.4..91.41..69.57321945768.9561.....46...19565479.2.11.9524.7.2.71.6549 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # C2: 2,8 => SOL
* DIS # C2: 3 => CTR => C2: 2,8
* DIS # C3: 2,8 => CTR => C3: 3
* PRF # C3: 3 => SOL
* PRF # F2: 7,8 => SOL
* DIS # F2: 2 => CTR => F2: 7,8
* DIS # E6: 7,8 => CTR => E6: 3
* PRF # E6: 3 => SOL
* DIS # F2: 7 => CTR => F2: 2,8
* DIS # C3: 2,8 => CTR => C3: 3
* PRF # C3: 3 => SOL
* PRF # C2: 2,3 => SOL
* DIS # C2: 8 => CTR => C2: 2,3
* DIS # I5: 4 => CTR => I5: 2,3
* PRF # C3: 3,8 => SOL
* DIS # C3: 2 => CTR => C3: 3,8
* DIS # G8: 6 => CTR => G8: 3,8
* DIS # E6: 7,8 => CTR => E6: 3
* PRF # E6: 3 => SOL
* DIS # F6: 7,8 => CTR => F6: 2,3
* DIS # E6: 7,8 => CTR => E6: 3
* PRF # E6: 3 => SOL
* DIS # F6: 7,8 => CTR => F6: 2,3
* PRF # F2: 7,8 => SOL
* DIS # F2: 2 => CTR => F2: 7,8
* PRF # F6: 2,8 => SOL
* DIS # F6: 3,7 => CTR => F6: 2,8
* DIS # I5: 3,4 => CTR => I5: 2
* PRF # I5: 2 => SOL
* DIS # I5: 4 => CTR => I5: 2,3
* DIS # G8: 6 => CTR => G8: 3,8
* DIS # F6: 3,8 => CTR => F6: 2,7
* PRF # F6: 2,7 => SOL
* DIS # E6: 7 => CTR => E6: 3,8
* DIS # G8: 6 => CTR => G8: 3,8
* PRF # G8: 3,6 => SOL
* DIS # G8: 8 => CTR => G8: 3,6
* CNT  37 HDP CHAINS /  46 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* PRF # C2: 2,8 => SOL
* STA C2: 2,8
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

.7.3.....5......1......9.5..2....7.8...61.....4.......6..7..2..1.9............... initial
97.351...56.4..91.41..69.57321945768.9561.....46...19565479.2.11.9524.7.2.71.6549 autosolve
978351624562478913413269857321945768895617432746832195654793281189524376237186549 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (20)
C1: 2,8
E2: 7,8
D3: 2,8
G1: 4,6
H1: 2,8
I1: 4,6
I2: 2,3
G3: 3,8
A5: 7,8
A6: 7,8
F5: 7,8
D6: 2,8
G5: 3,4
H5: 2,3
B8: 3,8
B9: 3,8
F7: 3,8
E9: 3,8
H7: 3,8
I8: 3,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F2,D3: 2.. / F2 = 2  =>  0 pairs (X) / D3 = 2  =>  0 pairs (_)
H1,I2: 2.. / H1 = 2  =>  0 pairs (*) / I2 = 2  =>  0 pairs (X)
D6,F6: 2.. / D6 = 2  =>  0 pairs (X) / F6 = 2  =>  0 pairs (_)
H5,I5: 2.. / H5 = 2  =>  0 pairs (X) / I5 = 2  =>  0 pairs (_)
C1,H1: 2.. / C1 = 2  =>  0 pairs (X) / H1 = 2  =>  0 pairs (_)
C3,D3: 2.. / C3 = 2  =>  0 pairs (X) / D3 = 2  =>  0 pairs (_)
D3,D6: 2.. / D3 = 2  =>  0 pairs (*) / D6 = 2  =>  0 pairs (X)
F2,F6: 2.. / F2 = 2  =>  0 pairs (X) / F6 = 2  =>  0 pairs (_)
H1,H5: 2.. / H1 = 2  =>  0 pairs (*) / H5 = 2  =>  0 pairs (X)
I2,I5: 2.. / I2 = 2  =>  0 pairs (X) / I5 = 2  =>  0 pairs (_)
C2,C3: 3.. / C2 = 3  =>  0 pairs (X) / C3 = 3  =>  0 pairs (_)
I2,G3: 3.. / I2 = 3  =>  0 pairs (*) / G3 = 3  =>  0 pairs (X)
E6,F6: 3.. / E6 = 3  =>  0 pairs (*) / F6 = 3  =>  0 pairs (X)
B8,B9: 3.. / B8 = 3  =>  0 pairs (X) / B9 = 3  =>  0 pairs (_)
F7,E9: 3.. / F7 = 3  =>  0 pairs (*) / E9 = 3  =>  0 pairs (X)
C2,I2: 3.. / C2 = 3  =>  0 pairs (X) / I2 = 3  =>  0 pairs (_)
C3,G3: 3.. / C3 = 3  =>  0 pairs (*) / G3 = 3  =>  0 pairs (X)
F7,H7: 3.. / F7 = 3  =>  0 pairs (*) / H7 = 3  =>  0 pairs (X)
B9,E9: 3.. / B9 = 3  =>  0 pairs (*) / E9 = 3  =>  0 pairs (X)
E6,E9: 3.. / E6 = 3  =>  0 pairs (*) / E9 = 3  =>  0 pairs (X)
F6,F7: 3.. / F6 = 3  =>  0 pairs (X) / F7 = 3  =>  0 pairs (_)
H5,H7: 3.. / H5 = 3  =>  0 pairs (*) / H7 = 3  =>  0 pairs (X)
G1,I1: 4.. / G1 = 4  =>  0 pairs (X) / I1 = 4  => 18 pairs (_)
G5,I5: 4.. / G5 = 4  => 18 pairs (_) / I5 = 4  =>  0 pairs (X)
G1,G5: 4.. / G1 = 4  =>  0 pairs (X) / G5 = 4  => 18 pairs (_)
I1,I5: 4.. / I1 = 4  => 18 pairs (_) / I5 = 4  =>  0 pairs (X)
G1,I1: 6.. / G1 = 6  => 18 pairs (_) / I1 = 6  =>  0 pairs (X)
G8,I8: 6.. / G8 = 6  =>  0 pairs (X) / I8 = 6  => 18 pairs (_)
G1,G8: 6.. / G1 = 6  => 18 pairs (_) / G8 = 6  =>  0 pairs (X)
I1,I8: 6.. / I1 = 6  =>  0 pairs (X) / I8 = 6  => 18 pairs (_)
E2,F2: 7.. / E2 = 7  => 21 pairs (_) / F2 = 7  =>  0 pairs (X)
A5,A6: 7.. / A5 = 7  =>  0 pairs (X) / A6 = 7  => 18 pairs (_)
A5,F5: 7.. / A5 = 7  =>  0 pairs (X) / F5 = 7  => 18 pairs (_)
E2,E6: 7.. / E2 = 7  => 21 pairs (_) / E6 = 7  =>  0 pairs (X)
H1,G3: 8.. / H1 = 8  =>  0 pairs (X) / G3 = 8  =>  0 pairs (_)
A5,A6: 8.. / A5 = 8  => 18 pairs (_) / A6 = 8  =>  0 pairs (X)
B8,B9: 8.. / B8 = 8  =>  0 pairs (*) / B9 = 8  =>  0 pairs (X)
F7,E9: 8.. / F7 = 8  =>  0 pairs (X) / E9 = 8  =>  0 pairs (_)
H7,G8: 8.. / H7 = 8  =>  0 pairs (*) / G8 = 8  =>  0 pairs (X)
C1,H1: 8.. / C1 = 8  =>  0 pairs (*) / H1 = 8  =>  0 pairs (X)
A5,F5: 8.. / A5 = 8  => 18 pairs (_) / F5 = 8  =>  0 pairs (X)
F7,H7: 8.. / F7 = 8  =>  0 pairs (X) / H7 = 8  =>  0 pairs (_)
B8,G8: 8.. / B8 = 8  =>  0 pairs (*) / G8 = 8  =>  0 pairs (X)
B9,E9: 8.. / B9 = 8  =>  0 pairs (X) / E9 = 8  =>  0 pairs (_)
D3,D6: 8.. / D3 = 8  =>  0 pairs (X) / D6 = 8  =>  0 pairs (_)
G3,G8: 8.. / G3 = 8  =>  0 pairs (*) / G8 = 8  =>  0 pairs (X)
H1,H7: 8.. / H1 = 8  =>  0 pairs (X) / H7 = 8  =>  0 pairs (_)
* DURATION: 0:01:16.876403  START: 11:39:25.478638  END: 11:40:42.355041 2017-05-04
* CP COUNT: (47)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B8,B9,C1,D3,D6,E2,E9,F5,F7,G1,G3,G5,H1,H5,H7,I1,I2,I8)
* 97.351...56.4..91.41..69.57321945768.9561.....46...19565479.2.11.9524.7.2.71.6549
* PAIR C1: 2,8 BLK 1
C2: 2,8,3                                # reduction candidate for 2,8
C2: 2,8 => SOLVED
* 978351624562478913413269857321945768895617432746832195654793281189524376237186549
C2: 3 => CTR
* 97.351...5634..91241.269357321945768.9561.423.468.21956547932811.9524.7.2.71.6549
C3: 2,8,3                                # reduction candidate for 2,8
C3: 2,8 => CTR
* 97.351...5634..91241.269357321945768.9561.423.468.21956547932811.9524.7.2.71.6549
C3: 3 => SOLVED
* 978351624562478913413269857321945768895617432746832195654793281189524376237186549
* PAIR E2: 7,8 BLK 2
F2: 7,8,2                                # reduction candidate for 7,8
F2: 7,8 => SOLVED
* 978351624562478913413269857321945768895617432746832195654793281189524376237186549
F2: 2 => CTR
* 97.351...56.47291341..69.57321945768.9561.....46...19565479.2.11.9524.7.2.71.6549
* PAIR E2: 7,8 COL E
E6: 7,8,3                                # reduction candidate for 7,8
E6: 7,8 => CTR
* 97.35168456.4.291341..69.57321945768.9561.....46..3195654798231139524876287136549
E6: 3 => SOLVED
* 978351624562478913413269857321945768895617432746832195654793281189524376237186549
* PAIR D3: 2,8 BLK 2
F2: 2,8,7                                # reduction candidate for 2,8
F2: 7 => CTR
* 97.351...56.4.791.41.269.57321945768795618....46...19565479.2.11.9524.7.2.71.6549
F2: 2,8                                  # 21 pairs
* PAIR D3: 2,8 ROW 3
C3: 2,8,3                                # reduction candidate for 2,8
C3: 2,8 => CTR
* 97.351...5634..91241.269357321945768.9561.423.468.21956547932811.9524.7.2.71.6549
C3: 3 => SOLVED
* 978351624562478913413269857321945768895617432746832195654793281189524376237186549
* PAIR I2: 2,3 ROW 2
C2: 2,3,8                                # reduction candidate for 2,3
C2: 2,3 => SOLVED
* 978351624562478913413269857321945768895617432746832195654793281189524376237186549
C2: 8 => CTR
* 97.351...56847291341..69.57321945768.9561.....46...19565479.2.11.9524.7.2.71.6549
* PAIR I2: 2,3 COL I
I5: 2,3,4                                # reduction candidate for 2,3
I5: 4 => CTR
* 97.351...56.4..91241.269357321945768.9561.4...46...19565479.2.11.9524.7.2.71.6549
I5: 2,3                                  # 18 pairs
* PAIR G3: 3,8 ROW 3
C3: 3,8,2                                # reduction candidate for 3,8
C3: 3,8 => SOLVED
* 978351624562478913413269857321945768895617432746832195654793281189524376237186549
C3: 2 => CTR
* 97.351...5634..912412.69.57321945768.9561.....46...19565479.2.11.9524.7.2.71.6549
* PAIR G3: 3,8 COL G
G8: 3,8,6                                # reduction candidate for 3,8
G8: 6 => CTR
* 97.351...56.4..91.41..69857321945768.9561.32..46...19565479.2.11.9524.7.2.71.6549
G8: 3,8                                  # 18 pairs
* PAIR A6: 7,8 ROW 6
E6: 7,8,3                                # reduction candidate for 7,8
E6: 7,8 => CTR
* 97.35168456.4.291341..69.57321945768.9561.....46..3195654798231139524876287136549
E6: 3 => SOLVED
* 978351624562478913413269857321945768895617432746832195654793281189524376237186549
F6: 7,8,2,3                              # reduction candidate for 7,8
F6: 7,8 => CTR
* 97.351...56.4.291341..69.57321945768.9561.....46...19565479.2.11.9524.7.2.71.6549
F6: 2,3                                  # 21 pairs
* PAIR F5: 7,8 BLK 5
E6: 7,8,3                                # reduction candidate for 7,8
E6: 7,8 => CTR
* 97.35168456.4.291341..69.57321945768.9561.....46..3195654798231139524876287136549
E6: 3 => SOLVED
* 978351624562478913413269857321945768895617432746832195654793281189524376237186549
F6: 7,8,2,3                              # reduction candidate for 7,8
F6: 7,8 => CTR
* 97.351...56.4.291341..69.57321945768.9561.....46...19565479.2.11.9524.7.2.71.6549
F6: 2,3                                  # 21 pairs
* PAIR F5: 7,8 COL F
F2: 7,8,2                                # reduction candidate for 7,8
F2: 7,8 => SOLVED
* 978351624562478913413269857321945768895617432746832195654793281189524376237186549
F2: 2 => CTR
* 97.351...56.47291341..69.57321945768.9561.....46...19565479.2.11.9524.7.2.71.6549
* PAIR D6: 2,8 BLK 5
F6: 2,8,3,7                              # reduction candidate for 2,8
F6: 2,8 => SOLVED
* 978351624562478913413269857321945768895617432746832195654793281189524376237186549
F6: 3,7 => CTR
* 97.351...56.4.291341..69.57321945768.9561.....46...19565479.2.11.9524.7.2.71.6549
* PAIR G5: 3,4 BLK 6
I5: 3,4,2                                # reduction candidate for 3,4
I5: 3,4 => CTR
* 97.351...56.4..91241.269357321945768.9561.423.468.21956547932811.9524.7.2.71.6549
I5: 2 => SOLVED
* 978351624562478913413269857321945768895617432746832195654793281189524376237186549
* PAIR H5: 2,3 BLK 6
I5: 2,3,4                                # reduction candidate for 2,3
I5: 4 => CTR
* 97.351...56.4..91241.269357321945768.9561.4...46...19565479.2.11.9524.7.2.71.6549
I5: 2,3                                  # 18 pairs
* PAIR B8: 3,8 ROW 8
G8: 3,8,6                                # reduction candidate for 3,8
G8: 6 => CTR
* 97.351...56.4..91.41..69857321945768.9561.32..46...19565479.2.11.9524.7.2.71.6549
G8: 3,8                                  # 18 pairs
* PAIR F7: 3,8 COL F
F6: 3,8,2,7                              # reduction candidate for 3,8
F6: 3,8 => CTR
* 97.351...56.4.291341..69.57321945768.9561.....46...19565479.2.11.9524.7.2.71.6549
F6: 2,7 => SOLVED
* 978351624562478913413269857321945768895617432746832195654793281189524376237186549
* PAIR E9: 3,8 COL E
E6: 3,8,7                                # reduction candidate for 3,8
E6: 7 => CTR
* 97.351...56.4..91.41..69.57321945768.9561.....46.731956547982.11.9524.7.2.71.6549
E6: 3,8                                  # 21 pairs
* PAIR H7: 3,8 BLK 9
G8: 3,8,6                                # reduction candidate for 3,8
G8: 6 => CTR
* 97.351...56.4..91.41..69857321945768.9561.32..46...19565479.2.11.9524.7.2.71.6549
G8: 3,8                                  # 18 pairs
* PAIR I8: 3,6 BLK 9
G8: 3,6,8                                # reduction candidate for 3,6
G8: 3,6 => SOLVED
* 978351624562478913413269857321945768895617432746832195654793281189524376237186549
G8: 8 => CTR
* 97.35168456.4..91241.269357321945768.9561.423.468..19565479.2.11.9524876287136549
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-259-base-pr-000.dot
* REASONING
* PRF # C2: 2,8 => SOL
* DIS # C2: 3 => CTR => C2: 2,8
* DIS # C3: 2,8 => CTR => C3: 3
* PRF # C3: 3 => SOL
* PRF # F2: 7,8 => SOL
* DIS # F2: 2 => CTR => F2: 7,8
* DIS # E6: 7,8 => CTR => E6: 3
* PRF # E6: 3 => SOL
* DIS # F2: 7 => CTR => F2: 2,8
* DIS # C3: 2,8 => CTR => C3: 3
* PRF # C3: 3 => SOL
* PRF # C2: 2,3 => SOL
* DIS # C2: 8 => CTR => C2: 2,3
* DIS # I5: 4 => CTR => I5: 2,3
* PRF # C3: 3,8 => SOL
* DIS # C3: 2 => CTR => C3: 3,8
* DIS # G8: 6 => CTR => G8: 3,8
* DIS # E6: 7,8 => CTR => E6: 3
* PRF # E6: 3 => SOL
* DIS # F6: 7,8 => CTR => F6: 2,3
* DIS # E6: 7,8 => CTR => E6: 3
* PRF # E6: 3 => SOL
* DIS # F6: 7,8 => CTR => F6: 2,3
* PRF # F2: 7,8 => SOL
* DIS # F2: 2 => CTR => F2: 7,8
* PRF # F6: 2,8 => SOL
* DIS # F6: 3,7 => CTR => F6: 2,8
* DIS # I5: 3,4 => CTR => I5: 2
* PRF # I5: 2 => SOL
* DIS # I5: 4 => CTR => I5: 2,3
* DIS # G8: 6 => CTR => G8: 3,8
* DIS # F6: 3,8 => CTR => F6: 2,7
* PRF # F6: 2,7 => SOL
* DIS # E6: 7 => CTR => E6: 3,8
* DIS # G8: 6 => CTR => G8: 3,8
* PRF # G8: 3,6 => SOL
* DIS # G8: 8 => CTR => G8: 3,6
* CNT  37 HDP CHAINS /  46 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B8,B9,C1,D3,D6,E2,E9,F5,F7,G1,G3,G5,H1,H5,H7,I1,I2,I8)
* 97.351...56.4..91.41..69.57321945768.9561.....46...19565479.2.11.9524.7.2.71.6549
* PAIR C1: 2,8 BLK 1
C2: 2,8,3                                # reduction candidate for 2,8
C2: 2,8 => SOLVED
* 978351624562478913413269857321945768895617432746832195654793281189524376237186549
* DURATION: 0:00:01.956792  START: 11:41:28.383529  END: 11:41:30.340321 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-259-base-pr-001.dot
* REASONING
* PRF # C2: 2,8 => SOL
* STA C2: 2,8
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 259

solution: 978351624562478913413269857321945768895617432746832195654793281189524376237186549
info: 2081     FNBTWXY  S8.f     22615

http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/

Solution

position: 978351624562478913413269857321945768895617432746832195654793281189524376237186549 solved
Solution

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

Appendix: Full HDP Chains

A1. Pair Reduction Analysis

Full list of HDP chains traversed:

* PRF # C2: 2,8 => SOL
* DIS # C2: 3 => CTR => C2: 2,8
* DIS # C3: 2,8 => CTR => C3: 3
* PRF # C3: 3 => SOL
* PRF # F2: 7,8 => SOL
* DIS # F2: 2 => CTR => F2: 7,8
* DIS # E6: 7,8 => CTR => E6: 3
* PRF # E6: 3 => SOL
* INC # F2: 2,8 => UNS
* DIS # F2: 7 => CTR => F2: 2,8
* DIS # C3: 2,8 => CTR => C3: 3
* PRF # C3: 3 => SOL
* PRF # C2: 2,3 => SOL
* DIS # C2: 8 => CTR => C2: 2,3
* INC # I5: 2,3 => UNS
* DIS # I5: 4 => CTR => I5: 2,3
* PRF # C3: 3,8 => SOL
* DIS # C3: 2 => CTR => C3: 3,8
* INC # G8: 3,8 => UNS
* DIS # G8: 6 => CTR => G8: 3,8
* DIS # E6: 7,8 => CTR => E6: 3
* PRF # E6: 3 => SOL
* DIS # F6: 7,8 => CTR => F6: 2,3
* INC # F6: 2,3 => UNS
* DIS # E6: 7,8 => CTR => E6: 3
* PRF # E6: 3 => SOL
* DIS # F6: 7,8 => CTR => F6: 2,3
* INC # F6: 2,3 => UNS
* PRF # F2: 7,8 => SOL
* DIS # F2: 2 => CTR => F2: 7,8
* PRF # F6: 2,8 => SOL
* DIS # F6: 3,7 => CTR => F6: 2,8
* DIS # I5: 3,4 => CTR => I5: 2
* PRF # I5: 2 => SOL
* INC # I5: 2,3 => UNS
* DIS # I5: 4 => CTR => I5: 2,3
* INC # G8: 3,8 => UNS
* DIS # G8: 6 => CTR => G8: 3,8
* DIS # F6: 3,8 => CTR => F6: 2,7
* PRF # F6: 2,7 => SOL
* INC # E6: 3,8 => UNS
* DIS # E6: 7 => CTR => E6: 3,8
* INC # G8: 3,8 => UNS
* DIS # G8: 6 => CTR => G8: 3,8
* PRF # G8: 3,6 => SOL
* DIS # G8: 8 => CTR => G8: 3,6
* CNT  46 HDP CHAINS /  46 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # C2: 2,8 => SOL
* STA C2: 2,8
* CNT   1 HDP CHAINS /   1 HYP OPENED