Analysis of xx-top500-194-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ...3.2...6.....4....1......78.5.........4.6........1..5......32.3.....8.....1.... initial

Autosolve

position: 94.3.28166281..4.33.148629.7845613291.324.6..26..3.14.5168.4.3243.625.818.2.13564 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # E2: 5,7 => CTR => E2: 9
* PRF # E2: 9 => SOL
* PRF # E2: 7,9 => SOL
* DIS # E2: 5 => CTR => E2: 7,9
* PRF # F6: 7,9 => SOL
* DIS # E2: 5,7 => CTR => E2: 9
* PRF # E2: 9 => SOL
* PRF # I5: 5,7 => SOL
* PRF # F6: 7,9 => SOL
* PRF # I5: 5,7 => SOL
* PRF # E2: 7,9 => SOL
* DIS # E2: 5 => CTR => E2: 7,9
* CNT  12 HDP CHAINS /  20 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # E2: 5,7 => CTR => E2: 9
* PRF E2: 9 => SOL
* STA E2: 9
* CNT   2 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

...3.2...6.....4....1......78.5.........4.6........1..5......32.3.....8.....1.... initial
94.3.28166281..4.33.148629.7845613291.324.6..26..3.14.5168.4.3243.625.818.2.13564 autosolve
947352816628197453351486297784561329193248675265739148516874932439625781872913564 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (16)
C1: 5,7
B3: 5,7
E1: 5,7
F2: 7,9
H2: 5,7
I3: 5,7
B5: 5,9
C6: 5,9
D6: 7,9
H5: 5,7
C8: 7,9
B9: 7,9
E7: 7,9
D9: 7,9
G7: 7,9
G8: 7,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C1,B3: 5.. / C1 = 5  =>  0 pairs (X) / B3 = 5  =>  0 pairs (_)
E1,E2: 5.. / E1 = 5  =>  0 pairs (*) / E2 = 5  =>  0 pairs (X)
H2,I3: 5.. / H2 = 5  =>  0 pairs (*) / I3 = 5  =>  0 pairs (X)
B5,C6: 5.. / B5 = 5  =>  0 pairs (X) / C6 = 5  =>  0 pairs (_)
C1,E1: 5.. / C1 = 5  =>  0 pairs (X) / E1 = 5  =>  0 pairs (_)
E2,H2: 5.. / E2 = 5  =>  0 pairs (X) / H2 = 5  =>  0 pairs (_)
B3,I3: 5.. / B3 = 5  =>  0 pairs (*) / I3 = 5  =>  0 pairs (X)
C6,I6: 5.. / C6 = 5  =>  0 pairs (*) / I6 = 5  =>  0 pairs (X)
B3,B5: 5.. / B3 = 5  =>  0 pairs (*) / B5 = 5  =>  0 pairs (X)
C1,C6: 5.. / C1 = 5  =>  0 pairs (X) / C6 = 5  =>  0 pairs (_)
H2,H5: 5.. / H2 = 5  =>  0 pairs (*) / H5 = 5  =>  0 pairs (X)
C1,B3: 7.. / C1 = 7  =>  0 pairs (*) / B3 = 7  =>  0 pairs (X)
H2,I3: 7.. / H2 = 7  =>  0 pairs (X) / I3 = 7  =>  0 pairs (_)
C8,B9: 7.. / C8 = 7  =>  0 pairs (X) / B9 = 7  =>  0 pairs (_)
E7,D9: 7.. / E7 = 7  =>  0 pairs (*) / D9 = 7  =>  0 pairs (X)
G7,G8: 7.. / G7 = 7  =>  0 pairs (X) / G8 = 7  =>  0 pairs (_)
C1,E1: 7.. / C1 = 7  =>  0 pairs (*) / E1 = 7  =>  0 pairs (X)
B3,I3: 7.. / B3 = 7  =>  0 pairs (X) / I3 = 7  =>  0 pairs (_)
E7,G7: 7.. / E7 = 7  =>  0 pairs (*) / G7 = 7  =>  0 pairs (X)
C8,G8: 7.. / C8 = 7  =>  0 pairs (X) / G8 = 7  =>  0 pairs (_)
B9,D9: 7.. / B9 = 7  =>  0 pairs (*) / D9 = 7  =>  0 pairs (X)
B3,B9: 7.. / B3 = 7  =>  0 pairs (X) / B9 = 7  =>  0 pairs (_)
C1,C8: 7.. / C1 = 7  =>  0 pairs (*) / C8 = 7  =>  0 pairs (X)
D6,D9: 7.. / D6 = 7  =>  0 pairs (*) / D9 = 7  =>  0 pairs (X)
H2,H5: 7.. / H2 = 7  =>  0 pairs (X) / H5 = 7  =>  0 pairs (_)
F5,F6: 8.. / F5 = 8  =>  0 pairs (*) / F6 = 8  =>  0 pairs (X)
I5,I6: 8.. / I5 = 8  => 18 pairs (_) / I6 = 8  =>  0 pairs (*)
F5,I5: 8.. / F5 = 8  =>  0 pairs (*) / I5 = 8  =>  0 pairs (X)
F6,I6: 8.. / F6 = 8  => 18 pairs (_) / I6 = 8  =>  0 pairs (*)
E2,F2: 9.. / E2 = 9  =>  0 pairs (*) / F2 = 9  =>  0 pairs (X)
B5,C6: 9.. / B5 = 9  =>  0 pairs (*) / C6 = 9  =>  0 pairs (X)
C8,B9: 9.. / C8 = 9  =>  0 pairs (*) / B9 = 9  =>  0 pairs (X)
E7,D9: 9.. / E7 = 9  =>  0 pairs (X) / D9 = 9  =>  0 pairs (_)
G7,G8: 9.. / G7 = 9  =>  0 pairs (*) / G8 = 9  =>  0 pairs (X)
B5,F5: 9.. / B5 = 9  =>  0 pairs (*) / F5 = 9  =>  0 pairs (X)
E7,G7: 9.. / E7 = 9  =>  0 pairs (X) / G7 = 9  =>  0 pairs (_)
C8,G8: 9.. / C8 = 9  =>  0 pairs (*) / G8 = 9  =>  0 pairs (X)
B9,D9: 9.. / B9 = 9  =>  0 pairs (X) / D9 = 9  =>  0 pairs (_)
B5,B9: 9.. / B5 = 9  =>  0 pairs (*) / B9 = 9  =>  0 pairs (X)
C6,C8: 9.. / C6 = 9  =>  0 pairs (X) / C8 = 9  =>  0 pairs (_)
D6,D9: 9.. / D6 = 9  =>  0 pairs (X) / D9 = 9  =>  0 pairs (_)
E2,E7: 9.. / E2 = 9  =>  0 pairs (*) / E7 = 9  =>  0 pairs (X)
* DURATION: 0:01:28.600128  START: 09:22:30.593779  END: 09:23:59.193907 2017-05-04
* CP COUNT: (42)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B5,B9,C1,C6,C8,D6,D9,E1,E7,F2,G7,G8,H2,H5,I3)
* 94.3.28166281..4.33.148629.7845613291.324.6..26..3.14.5168.4.3243.625.818.2.13564
* PAIR E1: 5,7 BLK 2
E2: 5,7,9                                # reduction candidate for 5,7
E2: 5,7 => CTR
* 94.3.28166281.94.33.148629.78456132919324.6..26593.14.51689473243.625.818.2.13564
E2: 9 => SOLVED
* 947352816628197453351486297784561329193248675265739148516874932439625781872913564
* PAIR F2: 7,9 BLK 2
E2: 7,9,5                                # reduction candidate for 7,9
E2: 7,9 => SOLVED
* 947352816628197453351486297784561329193248675265739148516874932439625781872913564
E2: 5 => CTR
* 94.3.28166281594733714862957845613291.324.6..26..3.14.5168.4.3243.625.818.2.13564
* PAIR F2: 7,9 COL F
F5: 7,9,8                                # reduction candidate for 7,9
F5: 7,9                                  # 18 pairs
F6: 7,9,8                                # reduction candidate for 7,9
F6: 7,9 => SOLVED
* 947352816628197453351486297784561329193248675265739148516874932439625781872913564
F6: 8                                    # 18 pairs
* PAIR H2: 5,7 ROW 2
E2: 5,7,9                                # reduction candidate for 5,7
E2: 5,7 => CTR
* 94.3.28166281.94.33.148629.78456132919324.6..26593.14.51689473243.625.818.2.13564
E2: 9 => SOLVED
* 947352816628197453351486297784561329193248675265739148516874932439625781872913564
* PAIR I3: 5,7 COL I
I5: 5,7,8                                # reduction candidate for 5,7
I5: 5,7 => SOLVED
* 947352816628197453351486297784561329193248675265739148516874932439625781872913564
I5: 8                                    # 18 pairs
I6: 5,7,8                                # reduction candidate for 5,7
I6: 5,7                                  # 18 pairs
* PAIR D6: 7,9 BLK 5
F5: 7,9,8                                # reduction candidate for 7,9
F5: 7,9                                  # 18 pairs
F6: 7,9,8                                # reduction candidate for 7,9
F6: 7,9 => SOLVED
* 947352816628197453351486297784561329193248675265739148516874932439625781872913564
F6: 8                                    # 18 pairs
* PAIR H5: 5,7 BLK 6
I5: 5,7,8                                # reduction candidate for 5,7
I5: 5,7 => SOLVED
* 947352816628197453351486297784561329193248675265739148516874932439625781872913564
I5: 8                                    # 18 pairs
I6: 5,7,8                                # reduction candidate for 5,7
I6: 5,7                                  # 18 pairs
* PAIR E7: 7,9 COL E
E2: 7,9,5                                # reduction candidate for 7,9
E2: 7,9 => SOLVED
* 947352816628197453351486297784561329193248675265739148516874932439625781872913564
E2: 5 => CTR
* 94.3.28166281594733714862957845613291.324.6..26..3.14.5168.4.3243.625.818.2.13564
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-194-base-pr-000.dot
* REASONING
* DIS # E2: 5,7 => CTR => E2: 9
* PRF # E2: 9 => SOL
* PRF # E2: 7,9 => SOL
* DIS # E2: 5 => CTR => E2: 7,9
* PRF # F6: 7,9 => SOL
* DIS # E2: 5,7 => CTR => E2: 9
* PRF # E2: 9 => SOL
* PRF # I5: 5,7 => SOL
* PRF # F6: 7,9 => SOL
* PRF # I5: 5,7 => SOL
* PRF # E2: 7,9 => SOL
* DIS # E2: 5 => CTR => E2: 7,9
* CNT  12 HDP CHAINS /  20 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B5,B9,C1,C6,C8,D6,D9,E1,E7,F2,G7,G8,H2,H5,I3)
* 94.3.28166281..4.33.148629.7845613291.324.6..26..3.14.5168.4.3243.625.818.2.13564
* PAIR E1: 5,7 BLK 2
E2: 5,7,9                                # reduction candidate for 5,7
E2: 5,7 => CTR
* 94.3.28166281.94.33.148629.78456132919324.6..26593.14.51689473243.625.818.2.13564
E2: 9 => SOLVED
* 947352816628197453351486297784561329193248675265739148516874932439625781872913564
* DURATION: 0:00:03.501297  START: 09:24:28.463768  END: 09:24:31.965065 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-194-base-pr-001.dot
* REASONING
* DIS # E2: 5,7 => CTR => E2: 9
* PRF E2: 9 => SOL
* STA E2: 9
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 194

solution: 947352816628197453351486297784561329193248675265739148516874932439625781872913564
info: 1849     FNBTWX   S8.f     47765

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

Solution

position: 947352816628197453351486297784561329193248675265739148516874932439625781872913564 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:

* DIS # E2: 5,7 => CTR => E2: 9
* PRF # E2: 9 => SOL
* PRF # E2: 7,9 => SOL
* DIS # E2: 5 => CTR => E2: 7,9
* INC # F5: 7,9 => UNS
* PRF # F6: 7,9 => SOL
* INC # F6: 8 => UNS
* DIS # E2: 5,7 => CTR => E2: 9
* PRF # E2: 9 => SOL
* PRF # I5: 5,7 => SOL
* INC # I5: 8 => UNS
* INC # I6: 5,7 => UNS
* INC # F5: 7,9 => UNS
* PRF # F6: 7,9 => SOL
* INC # F6: 8 => UNS
* PRF # I5: 5,7 => SOL
* INC # I5: 8 => UNS
* INC # I6: 5,7 => UNS
* PRF # E2: 7,9 => SOL
* DIS # E2: 5 => CTR => E2: 7,9
* CNT  20 HDP CHAINS /  20 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # E2: 5,7 => CTR => E2: 9
* PRF E2: 9 => SOL
* STA E2: 9
* CNT   2 HDP CHAINS /   1 HYP OPENED