Analysis of xx-top500-015-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .358.........2.7...........4...7...17......6........5.28....4.....3.5......6..... initial

Autosolve

position: .35867.4.6..52.7838...345.6458.763.17...5386436.4.8.572867..435...3.56..5.36.2... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # G1: 1,9 => SOL
* DIS # G1: 2 => CTR => G1: 1,9
* PRF # D5: 1,9 => SOL
* DIS # D5: 2 => CTR => D5: 1,9
* PRF # G1: 2,9 => SOL
* DIS # G1: 1 => CTR => G1: 2,9
* PRF # I8: 8 => SOL
* PRF # G1: 1,9 => SOL
* DIS # G1: 2 => CTR => G1: 1,9
* DIS # H8: 1,9 => CTR => H8: 2,7
* DIS # H9: 1,9 => CTR => H9: 7
* DIS # D5: 2,9 => CTR => D5: 1
* PRF # D5: 1 => SOL
* PRF # D5: 1,9 => SOL
* DIS # D5: 2 => CTR => D5: 1,9
* PRF # C6: 1,9 => SOL
* DIS # C6: 2 => CTR => C6: 1,9
* PRF # H8: 2,9 => SOL
* DIS # H8: 1,7 => CTR => H8: 2,9
* DIS # C6: 2,9 => CTR => C6: 1
* PRF # C6: 1 => SOL
* PRF # G1: 2,9 => SOL
* DIS # G1: 1 => CTR => G1: 2,9
* DIS # H8: 1,9 => CTR => H8: 2,7
* DIS # H8: 1,9 => CTR => H8: 2,7
* DIS # H9: 1,9 => CTR => H9: 7
* PRF # G1: 1,9 => SOL
* DIS # G1: 2 => CTR => G1: 1,9
* PRF # I8: 8,9 => SOL
* DIS # I8: 2 => CTR => I8: 8,9
* CNT  30 HDP CHAINS /  45 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 # G1: 1,9 => SOL
* STA G1: 1,9
* CNT   1 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

.358.........2.7...........4...7...17......6........5.28....4.....3.5......6..... initial
.35867.4.6..52.7838...345.6458.763.17...5386436.4.8.572867..435...3.56..5.36.2... autosolve
135867942694521783872934516458276391729153864361498257286719435917345628543682179 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (18)
A1: 1,9
B3: 2,7
C3: 2,7
F2: 1,9
D3: 1,9
I1: 2,9
H3: 1,9
D4: 2,9
E6: 1,9
H4: 2,9
G6: 2,9
A8: 1,9
E7: 1,9
F7: 1,9
E8: 4,8
E9: 4,8
G9: 1,9
I9: 8,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F2,D3: 1.. / F2 = 1  =>  0 pairs (*) / D3 = 1  =>  0 pairs (X)
G1,H3: 1.. / G1 = 1  =>  0 pairs (X) / H3 = 1  =>  0 pairs (_)
D5,E6: 1.. / D5 = 1  =>  0 pairs (*) / E6 = 1  =>  0 pairs (X)
E7,F7: 1.. / E7 = 1  =>  0 pairs (*) / F7 = 1  =>  0 pairs (X)
A1,G1: 1.. / A1 = 1  =>  0 pairs (*) / G1 = 1  =>  0 pairs (X)
D3,H3: 1.. / D3 = 1  =>  0 pairs (X) / H3 = 1  =>  0 pairs (_)
C6,E6: 1.. / C6 = 1  =>  0 pairs (*) / E6 = 1  =>  0 pairs (X)
A1,A8: 1.. / A1 = 1  =>  0 pairs (*) / A8 = 1  =>  0 pairs (X)
D3,D5: 1.. / D3 = 1  =>  0 pairs (X) / D5 = 1  =>  0 pairs (_)
E6,E7: 1.. / E6 = 1  =>  0 pairs (X) / E7 = 1  =>  0 pairs (_)
F2,F7: 1.. / F2 = 1  =>  0 pairs (*) / F7 = 1  =>  0 pairs (X)
G1,G9: 1.. / G1 = 1  =>  0 pairs (X) / G9 = 1  =>  0 pairs (_)
B3,C3: 2.. / B3 = 2  => 17 pairs (_) / C3 = 2  =>  0 pairs (*)
G1,I1: 2.. / G1 = 2  =>  0 pairs (X) / I1 = 2  =>  0 pairs (_)
D4,D5: 2.. / D4 = 2  =>  0 pairs (*) / D5 = 2  =>  0 pairs (X)
H4,G6: 2.. / H4 = 2  =>  0 pairs (X) / G6 = 2  =>  0 pairs (_)
H8,I8: 2.. / H8 = 2  =>  0 pairs (*) / I8 = 2  =>  0 pairs (X)
D4,H4: 2.. / D4 = 2  =>  0 pairs (*) / H4 = 2  =>  0 pairs (X)
C6,G6: 2.. / C6 = 2  =>  0 pairs (X) / G6 = 2  =>  0 pairs (_)
B3,B5: 2.. / B3 = 2  => 17 pairs (_) / B5 = 2  =>  0 pairs (*)
G1,G6: 2.. / G1 = 2  =>  0 pairs (X) / G6 = 2  =>  0 pairs (_)
H4,H8: 2.. / H4 = 2  =>  0 pairs (X) / H8 = 2  =>  0 pairs (_)
I1,I8: 2.. / I1 = 2  =>  0 pairs (*) / I8 = 2  =>  0 pairs (X)
B2,C2: 4.. / B2 = 4  => 16 pairs (_) / C2 = 4  => 19 pairs (_)
E8,E9: 4.. / E8 = 4  =>  0 pairs (*) / E9 = 4  =>  0 pairs (X)
B9,E9: 4.. / B9 = 4  =>  0 pairs (*) / E9 = 4  =>  0 pairs (X)
C2,C8: 4.. / C2 = 4  => 19 pairs (_) / C8 = 4  => 16 pairs (_)
B3,C3: 7.. / B3 = 7  =>  0 pairs (*) / C3 = 7  =>  0 pairs (X)
H8,H9: 7.. / H8 = 7  =>  0 pairs (X) / H9 = 7  => 18 pairs (_)
B9,H9: 7.. / B9 = 7  =>  0 pairs (X) / H9 = 7  => 18 pairs (_)
C3,C8: 7.. / C3 = 7  => 17 pairs (_) / C8 = 7  =>  0 pairs (*)
E8,E9: 8.. / E8 = 8  => 16 pairs (_) / E9 = 8  =>  0 pairs (*)
I8,I9: 8.. / I8 = 8  =>  0 pairs (*) / I9 = 8  =>  0 pairs (X)
E8,I8: 8.. / E8 = 8  => 16 pairs (_) / I8 = 8  =>  0 pairs (*)
E9,I9: 8.. / E9 = 8  =>  0 pairs (*) / I9 = 8  =>  0 pairs (X)
F2,D3: 9.. / F2 = 9  =>  0 pairs (X) / D3 = 9  =>  0 pairs (_)
H4,G6: 9.. / H4 = 9  =>  0 pairs (*) / G6 = 9  =>  0 pairs (X)
E7,F7: 9.. / E7 = 9  =>  0 pairs (X) / F7 = 9  =>  0 pairs (_)
D3,H3: 9.. / D3 = 9  =>  0 pairs (*) / H3 = 9  =>  0 pairs (X)
D4,H4: 9.. / D4 = 9  =>  0 pairs (X) / H4 = 9  =>  0 pairs (_)
A1,A8: 9.. / A1 = 9  =>  0 pairs (X) / A8 = 9  =>  0 pairs (_)
E6,E7: 9.. / E6 = 9  =>  0 pairs (*) / E7 = 9  =>  0 pairs (X)
F2,F7: 9.. / F2 = 9  =>  0 pairs (X) / F7 = 9  =>  0 pairs (_)
* DURATION: 0:01:18.071924  START: 03:05:56.605297  END: 03:07:14.677221 2017-05-04
* CP COUNT: (43)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A8,B3,C3,D3,D4,E6,E7,E8,E9,F2,F7,G6,G9,H3,H4,I1,I9)
* .35867.4.6..52.7838...345.6458.763.17...5386436.4.8.572867..435...3.56..5.36.2...
* PAIR A1: 1,9 BLK 1
B2: 1,9,4                                # reduction candidate for 1,9
B2: 1,9                                  # 19 pairs
C2: 1,9,4                                # reduction candidate for 1,9
C2: 1,9                                  # 16 pairs
* PAIR A1: 1,9 ROW 1
G1: 1,9,2                                # reduction candidate for 1,9
G1: 1,9 => SOLVED
* 135867942694521783872934516458276391729153864361498257286719435917345628543682179
G1: 2 => CTR
* 1358672496..5217838..934516458.763.17...5386436.4.8.572867..435...3.56..5.36.2...
* PAIR F2: 1,9 ROW 2
B2: 1,9,4                                # reduction candidate for 1,9
B2: 1,9                                  # 19 pairs
C2: 1,9,4                                # reduction candidate for 1,9
C2: 1,9                                  # 16 pairs
* PAIR D3: 1,9 COL D
D5: 1,9,2                                # reduction candidate for 1,9
D5: 1,9 => SOLVED
* 135867942694521783872934516458276391729153864361498257286719435917345628543682179
D5: 2 => CTR
* .35867.4.6..52.7838..1345964589763217..2538643624189572867..435...3.56..5.36.2...
* PAIR I1: 2,9 BLK 3
G1: 2,9,1                                # reduction candidate for 2,9
G1: 2,9 => SOLVED
* 135867942694521783872934516458276391729153864361498257286719435917345628543682179
G1: 1 => CTR
* .358671426..52.7838..1345964589763217...5386436.4.8.572867..435...3.56..5.36.2...
* PAIR I1: 2,9 COL I
I8: 2,9,8                                # reduction candidate for 2,9
I8: 8 => SOLVED
* 135867942694521783872934516458276391729153864361498257286719435917345628543682179
I8: 2,9                                  # 16 pairs
* PAIR H3: 1,9 BLK 3
G1: 1,9,2                                # reduction candidate for 1,9
G1: 1,9 => SOLVED
* 135867942694521783872934516458276391729153864361498257286719435917345628543682179
G1: 2 => CTR
* 1358672496..5217838..934516458.763.17...5386436.4.8.572867..435...3.56..5.36.2...
* PAIR H3: 1,9 COL H
H8: 1,9,2,7                              # reduction candidate for 1,9
H8: 1,9 => CTR
* 1358672496..5297838...345.6458.763217..253864362418957286791435...3.56.25.36.2178
H8: 2,7                                  # 19 pairs
H9: 1,9,7                                # reduction candidate for 1,9
H9: 1,9 => CTR
* .358672496..52.783827934516458.763.17...5386436.4.8.572867..435...3.5672573642..8
H9: 7                                    # 18 pairs
* PAIR D4: 2,9 BLK 5
D5: 2,9,1                                # reduction candidate for 2,9
D5: 2,9 => CTR
* .35867.4.6..52.7838..1345964589763217..2538643624189572867..435...3.56..5.36.2...
D5: 1 => SOLVED
* 135867942694521783872934516458276391729153864361498257286719435917345628543682179
* PAIR E6: 1,9 BLK 5
D5: 1,9,2                                # reduction candidate for 1,9
D5: 1,9 => SOLVED
* 135867942694521783872934516458276391729153864361498257286719435917345628543682179
D5: 2 => CTR
* .35867.4.6..52.7838..1345964589763217..2538643624189572867..435...3.56..5.36.2...
* PAIR E6: 1,9 ROW 6
C6: 1,9,2                                # reduction candidate for 1,9
C6: 1,9 => SOLVED
* 135867942694521783872934516458276391729153864361498257286719435917345628543682179
C6: 2 => CTR
* 1358672496..5297838...345.6458.763.17...53864362418957286791435...3.56..5.36.21..
* PAIR H4: 2,9 COL H
H8: 2,9,1,7                              # reduction candidate for 2,9
H8: 2,9 => SOLVED
* 135867942694521783872934516458276391729153864361498257286719435917345628543682179
H8: 1,7 => CTR
* 1358672496..5297838...345.6458.763217..253864362418957286791435...3.56.25.36.21.8
* PAIR G6: 2,9 ROW 6
C6: 2,9,1                                # reduction candidate for 2,9
C6: 2,9 => CTR
* .35867.4.6..5297838..1345964589763217..253864362418957286791435...3.56..5.36.2...
C6: 1 => SOLVED
* 135867942694521783872934516458276391729153864361498257286719435917345628543682179
* PAIR G6: 2,9 COL G
G1: 2,9,1                                # reduction candidate for 2,9
G1: 2,9 => SOLVED
* 135867942694521783872934516458276391729153864361498257286719435917345628543682179
G1: 1 => CTR
* .358671426..52.7838..1345964589763217...5386436.4.8.572867..435...3.56..5.36.2...
* PAIR A8: 1,9 BLK 7
B8: 1,9,4,7                              # reduction candidate for 1,9
B8: 1,9                                  # 23 pairs
C8: 1,9,4,7                              # reduction candidate for 1,9
C8: 1,9                                  # 23 pairs
B9: 1,9,4,7                              # reduction candidate for 1,9
B9: 1,9                                  # 19 pairs
* PAIR A8: 1,9 ROW 8
H8: 1,9,2,7                              # reduction candidate for 1,9
H8: 1,9 => CTR
* 1358672496..5297838...345.6458.763217..253864362418957286791435...3.56.25.36.2178
H8: 2,7                                  # 19 pairs
* PAIR G9: 1,9 BLK 9
H8: 1,9,2,7                              # reduction candidate for 1,9
H8: 1,9 => CTR
* 1358672496..5297838...345.6458.763217..253864362418957286791435...3.56.25.36.2178
H8: 2,7                                  # 19 pairs
H9: 1,9,7                                # reduction candidate for 1,9
H9: 1,9 => CTR
* .358672496..52.783827934516458.763.17...5386436.4.8.572867..435...3.5672573642..8
H9: 7                                    # 18 pairs
* PAIR G9: 1,9 ROW 9
B9: 1,9,4,7                              # reduction candidate for 1,9
B9: 4,7                                  # 21 pairs
B9: 1,9                                  # 19 pairs
* PAIR G9: 1,9 COL G
G1: 1,9,2                                # reduction candidate for 1,9
G1: 1,9 => SOLVED
* 135867942694521783872934516458276391729153864361498257286719435917345628543682179
G1: 2 => CTR
* 1358672496..5217838..934516458.763.17...5386436.4.8.572867..435...3.56..5.36.2...
* PAIR I9: 8,9 BLK 9
I8: 8,9,2                                # reduction candidate for 8,9
I8: 8,9 => SOLVED
* 135867942694521783872934516458276391729153864361498257286719435917345628543682179
I8: 2 => CTR
* .358672496..52.7838..934516458.763.17...5386436.4.8.572867..435...3856.25.3642..8
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-015-base-pr-000.dot
* REASONING
* PRF # G1: 1,9 => SOL
* DIS # G1: 2 => CTR => G1: 1,9
* PRF # D5: 1,9 => SOL
* DIS # D5: 2 => CTR => D5: 1,9
* PRF # G1: 2,9 => SOL
* DIS # G1: 1 => CTR => G1: 2,9
* PRF # I8: 8 => SOL
* PRF # G1: 1,9 => SOL
* DIS # G1: 2 => CTR => G1: 1,9
* DIS # H8: 1,9 => CTR => H8: 2,7
* DIS # H9: 1,9 => CTR => H9: 7
* DIS # D5: 2,9 => CTR => D5: 1
* PRF # D5: 1 => SOL
* PRF # D5: 1,9 => SOL
* DIS # D5: 2 => CTR => D5: 1,9
* PRF # C6: 1,9 => SOL
* DIS # C6: 2 => CTR => C6: 1,9
* PRF # H8: 2,9 => SOL
* DIS # H8: 1,7 => CTR => H8: 2,9
* DIS # C6: 2,9 => CTR => C6: 1
* PRF # C6: 1 => SOL
* PRF # G1: 2,9 => SOL
* DIS # G1: 1 => CTR => G1: 2,9
* DIS # H8: 1,9 => CTR => H8: 2,7
* DIS # H8: 1,9 => CTR => H8: 2,7
* DIS # H9: 1,9 => CTR => H9: 7
* PRF # G1: 1,9 => SOL
* DIS # G1: 2 => CTR => G1: 1,9
* PRF # I8: 8,9 => SOL
* DIS # I8: 2 => CTR => I8: 8,9
* CNT  30 HDP CHAINS /  45 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A8,B3,C3,D3,D4,E6,E7,E8,E9,F2,F7,G6,G9,H3,H4,I1,I9)
* .35867.4.6..52.7838...345.6458.763.17...5386436.4.8.572867..435...3.56..5.36.2...
* PAIR A1: 1,9 BLK 1
B2: 1,9,4                                # reduction candidate for 1,9
B2: 1,9                                  # 19 pairs
C2: 1,9,4                                # reduction candidate for 1,9
C2: 1,9                                  # 16 pairs
* PAIR A1: 1,9 ROW 1
G1: 1,9,2                                # reduction candidate for 1,9
G1: 1,9 => SOLVED
* 135867942694521783872934516458276391729153864361498257286719435917345628543682179
* DURATION: 0:00:04.040147  START: 03:08:04.128757  END: 03:08:08.168904 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-015-base-pr-001.dot
* REASONING
* PRF # G1: 1,9 => SOL
* STA G1: 1,9
* CNT   1 HDP CHAINS /   3 HYP OPENED

Header Info

Top 500 Minimum 17 015

solution: 135867942694521783872934516458276391729153864361498257286719435917345628543682179
info: 1310     FNBTWXY  S8.f     18378

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

Solution

position: 135867942694521783872934516458276391729153864361498257286719435917345628543682179 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:

* INC # B2: 1,9 => UNS
* INC # C2: 1,9 => UNS
* PRF # G1: 1,9 => SOL
* DIS # G1: 2 => CTR => G1: 1,9
* INC # B2: 1,9 => UNS
* INC # C2: 1,9 => UNS
* PRF # D5: 1,9 => SOL
* DIS # D5: 2 => CTR => D5: 1,9
* PRF # G1: 2,9 => SOL
* DIS # G1: 1 => CTR => G1: 2,9
* INC # I8: 2,9 => UNS
* PRF # I8: 8 => SOL
* PRF # G1: 1,9 => SOL
* DIS # G1: 2 => CTR => G1: 1,9
* DIS # H8: 1,9 => CTR => H8: 2,7
* INC # H8: 2,7 => UNS
* DIS # H9: 1,9 => CTR => H9: 7
* INC # H9: 7 => UNS
* DIS # D5: 2,9 => CTR => D5: 1
* PRF # D5: 1 => SOL
* PRF # D5: 1,9 => SOL
* DIS # D5: 2 => CTR => D5: 1,9
* PRF # C6: 1,9 => SOL
* DIS # C6: 2 => CTR => C6: 1,9
* PRF # H8: 2,9 => SOL
* DIS # H8: 1,7 => CTR => H8: 2,9
* DIS # C6: 2,9 => CTR => C6: 1
* PRF # C6: 1 => SOL
* PRF # G1: 2,9 => SOL
* DIS # G1: 1 => CTR => G1: 2,9
* INC # B8: 1,9 => UNS
* INC # C8: 1,9 => UNS
* INC # B9: 1,9 => UNS
* DIS # H8: 1,9 => CTR => H8: 2,7
* INC # H8: 2,7 => UNS
* DIS # H8: 1,9 => CTR => H8: 2,7
* INC # H8: 2,7 => UNS
* DIS # H9: 1,9 => CTR => H9: 7
* INC # H9: 7 => UNS
* INC # B9: 1,9 => UNS
* INC # B9: 4,7 => UNS
* PRF # G1: 1,9 => SOL
* DIS # G1: 2 => CTR => G1: 1,9
* PRF # I8: 8,9 => SOL
* DIS # I8: 2 => CTR => I8: 8,9
* CNT  45 HDP CHAINS /  45 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B2: 1,9 => UNS
* INC # C2: 1,9 => UNS
* PRF # G1: 1,9 => SOL
* STA G1: 1,9
* CNT   3 HDP CHAINS /   3 HYP OPENED