Analysis of xx-top500-187-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ...5..3.982.............1..76.....4....19....4..3.......1...5......2..8.......... initial

Autosolve

position: 1..5.832982.9134.5395.421.8763285941582194.3.4193..8522.183.59.95..21.83638.5921. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C1: 4,7 => CTR => C1: 6
* PRF # C1: 6 => SOL
* PRF # C1: 6,7 => SOL
* DIS # C1: 4 => CTR => C1: 6,7
* PRF # C1: 6,7 => SOL
* DIS # C1: 4 => CTR => C1: 6,7
* PRF # D8: 6,7 => SOL
* DIS # D8: 4 => CTR => D8: 6,7
* DIS # I7: 6,7 => CTR => I7: 4
* PRF # I7: 4 => SOL
* PRF # I7: 4,7 => SOL
* DIS # I7: 6 => CTR => I7: 4,7
* PRF # D8: 4,7 => SOL
* DIS # D8: 6 => CTR => D8: 4,7
* DIS # C1: 4,7 => CTR => C1: 6
* PRF # C1: 6 => SOL
* PRF # D8: 6,7 => SOL
* DIS # D8: 4 => CTR => D8: 6,7
* DIS # I7: 6,7 => CTR => I7: 4
* PRF # I7: 4 => SOL
* PRF # D8: 4,7 => SOL
* DIS # D8: 6 => CTR => D8: 4,7
* DIS # I7: 6,7 => CTR => I7: 4
* PRF # I7: 4 => SOL
* PRF # D8: 6,7 => SOL
* DIS # D8: 4 => CTR => D8: 6,7
* PRF # I7: 4,7 => SOL
* DIS # I7: 6 => CTR => I7: 4,7
* CNT  28 HDP CHAINS /  28 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 # C1: 4,7 => CTR => C1: 6
* PRF C1: 6 => SOL
* STA C1: 6
* CNT   2 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

...5..3.982.............1..76.....4....19....4..3.......1...5......2..8.......... initial
1..5.832982.9134.5395.421.8763285941582194.3.4193..8522.183.59.95..21.83638.5921. autosolve
146578329827913465395642178763285941582194736419367852271836594954721683638459217 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (16)
B1: 4,7
C2: 6,7
E1: 6,7
D3: 6,7
H2: 6,7
H3: 6,7
E6: 6,7
F6: 6,7
G5: 6,7
I5: 6,7
B7: 4,7
C8: 4,7
F7: 6,7
D9: 4,7
G8: 6,7
I9: 4,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B1,C1: 4.. / B1 = 4  =>  0 pairs (*) / C1 = 4  =>  0 pairs (X)
B7,C8: 4.. / B7 = 4  =>  0 pairs (X) / C8 = 4  =>  0 pairs (_)
D8,D9: 4.. / D8 = 4  =>  0 pairs (X) / D9 = 4  =>  0 pairs (_)
I7,I9: 4.. / I7 = 4  =>  0 pairs (*) / I9 = 4  =>  0 pairs (X)
B7,I7: 4.. / B7 = 4  =>  0 pairs (X) / I7 = 4  =>  0 pairs (_)
C8,D8: 4.. / C8 = 4  =>  0 pairs (*) / D8 = 4  =>  0 pairs (X)
D9,I9: 4.. / D9 = 4  =>  0 pairs (*) / I9 = 4  =>  0 pairs (X)
B1,B7: 4.. / B1 = 4  =>  0 pairs (*) / B7 = 4  =>  0 pairs (X)
C1,C8: 4.. / C1 = 4  =>  0 pairs (X) / C8 = 4  =>  0 pairs (_)
C1,C2: 6.. / C1 = 6  =>  0 pairs (*) / C2 = 6  =>  0 pairs (X)
E1,D3: 6.. / E1 = 6  =>  0 pairs (X) / D3 = 6  =>  0 pairs (_)
H2,H3: 6.. / H2 = 6  =>  0 pairs (*) / H3 = 6  =>  0 pairs (X)
E6,F6: 6.. / E6 = 6  =>  0 pairs (*) / F6 = 6  =>  0 pairs (X)
G5,I5: 6.. / G5 = 6  =>  0 pairs (X) / I5 = 6  =>  0 pairs (_)
F7,D8: 6.. / F7 = 6  =>  0 pairs (*) / D8 = 6  =>  0 pairs (X)
I7,G8: 6.. / I7 = 6  =>  0 pairs (X) / G8 = 6  =>  0 pairs (_)
C1,E1: 6.. / C1 = 6  =>  0 pairs (*) / E1 = 6  =>  0 pairs (X)
C2,H2: 6.. / C2 = 6  =>  0 pairs (X) / H2 = 6  =>  0 pairs (_)
D3,H3: 6.. / D3 = 6  =>  0 pairs (*) / H3 = 6  =>  0 pairs (X)
F7,I7: 6.. / F7 = 6  =>  0 pairs (*) / I7 = 6  =>  0 pairs (X)
D8,G8: 6.. / D8 = 6  =>  0 pairs (X) / G8 = 6  =>  0 pairs (_)
D3,D8: 6.. / D3 = 6  =>  0 pairs (*) / D8 = 6  =>  0 pairs (X)
E1,E6: 6.. / E1 = 6  =>  0 pairs (X) / E6 = 6  =>  0 pairs (_)
F6,F7: 6.. / F6 = 6  =>  0 pairs (X) / F7 = 6  =>  0 pairs (_)
G5,G8: 6.. / G5 = 6  =>  0 pairs (X) / G8 = 6  =>  0 pairs (_)
I5,I7: 6.. / I5 = 6  =>  0 pairs (*) / I7 = 6  =>  0 pairs (X)
E1,D3: 7.. / E1 = 7  =>  0 pairs (*) / D3 = 7  =>  0 pairs (X)
H2,H3: 7.. / H2 = 7  =>  0 pairs (X) / H3 = 7  =>  0 pairs (_)
E6,F6: 7.. / E6 = 7  =>  0 pairs (X) / F6 = 7  =>  0 pairs (_)
G5,I5: 7.. / G5 = 7  =>  0 pairs (*) / I5 = 7  =>  0 pairs (X)
B7,C8: 7.. / B7 = 7  =>  0 pairs (*) / C8 = 7  =>  0 pairs (X)
C2,H2: 7.. / C2 = 7  =>  0 pairs (*) / H2 = 7  =>  0 pairs (X)
D3,H3: 7.. / D3 = 7  =>  0 pairs (X) / H3 = 7  =>  0 pairs (_)
D9,I9: 7.. / D9 = 7  =>  0 pairs (X) / I9 = 7  =>  0 pairs (_)
B1,B7: 7.. / B1 = 7  =>  0 pairs (X) / B7 = 7  =>  0 pairs (_)
E1,E6: 7.. / E1 = 7  =>  0 pairs (*) / E6 = 7  =>  0 pairs (X)
F6,F7: 7.. / F6 = 7  =>  0 pairs (*) / F7 = 7  =>  0 pairs (X)
G5,G8: 7.. / G5 = 7  =>  0 pairs (*) / G8 = 7  =>  0 pairs (X)
* DURATION: 0:01:10.000915  START: 09:04:26.151253  END: 09:05:36.152168 2017-05-04
* CP COUNT: (38)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B7,C2,C8,D3,D9,E1,E6,F6,F7,G5,G8,H2,H3,I5,I9)
* 1..5.832982.9134.5395.421.8763285941582194.3.4193..8522.183.59.95..21.83638.5921.
* PAIR B1: 4,7 BLK 1
C1: 4,7,6                                # reduction candidate for 4,7
C1: 4,7 => CTR
* 1..568329826913475395742168763285941582194.3.4193768522.1837596957.21.83638.5921.
C1: 6 => SOLVED
* 146578329827913465395642178763285941582194736419367852271836594954721683638459217
* PAIR C2: 6,7 BLK 1
C1: 6,7,4                                # reduction candidate for 6,7
C1: 6,7 => SOLVED
* 146578329827913465395642178763285941582194736419367852271836594954721683638459217
C1: 4 => CTR
* 1.45683298269134753957421.8763285941582194.3.4193..8522.183.59.95..21.83638.5921.
* PAIR E1: 6,7 ROW 1
C1: 6,7,4                                # reduction candidate for 6,7
C1: 6,7 => SOLVED
* 146578329827913465395642178763285941582194736419367852271836594954721683638459217
C1: 4 => CTR
* 1.45683298269134753957421.8763285941582194.3.4193..8522.183.59.95..21.83638.5921.
* PAIR D3: 6,7 COL D
D8: 6,7,4                                # reduction candidate for 6,7
D8: 6,7 => SOLVED
* 146578329827913465395642178763285941582194736419367852271836594954721683638459217
D8: 4 => CTR
* 1..5.832982.9134.5395642178763285941582194.3.4193678522.183659.95.421683638759214
* PAIR I5: 6,7 COL I
I7: 6,7,4                                # reduction candidate for 6,7
I7: 6,7 => CTR
* 17456832982.9134.5395.421.8763285941582194.3.4193..85224183.59.957421683638759214
I7: 4 => SOLVED
* 146578329827913465395642178763285941582194736419367852271836594954721683638459217
* PAIR B7: 4,7 ROW 7
I7: 4,7,6                                # reduction candidate for 4,7
I7: 4,7 => SOLVED
* 146578329827913465395642178763285941582194736419367852271836594954721683638459217
I7: 6 => CTR
* 1..5.832982.9134.5395.421.8763285941582194.3.4193..85224183759695..21.83638.5921.
* PAIR C8: 4,7 ROW 8
D8: 4,7,6                                # reduction candidate for 4,7
D8: 4,7 => SOLVED
* 146578329827913465395642178763285941582194736419367852271836594954721683638459217
D8: 6 => CTR
* 1..5.832982.9134.5395.421.8763285941582194.3.4193..8522.183.59.954621783638.5921.
* PAIR C8: 4,7 COL C
C1: 4,7,6                                # reduction candidate for 4,7
C1: 4,7 => CTR
* 1..568329826913475395742168763285941582194.3.4193768522.1837596957.21.83638.5921.
C1: 6 => SOLVED
* 146578329827913465395642178763285941582194736419367852271836594954721683638459217
* PAIR F7: 6,7 BLK 8
D8: 6,7,4                                # reduction candidate for 6,7
D8: 6,7 => SOLVED
* 146578329827913465395642178763285941582194736419367852271836594954721683638459217
D8: 4 => CTR
* 1..5.832982.9134.5395642178763285941582194.3.4193678522.183659.95.421683638759214
* PAIR F7: 6,7 ROW 7
I7: 6,7,4                                # reduction candidate for 6,7
I7: 6,7 => CTR
* 17456832982.9134.5395.421.8763285941582194.3.4193..85224183.59.957421683638759214
I7: 4 => SOLVED
* 146578329827913465395642178763285941582194736419367852271836594954721683638459217
* PAIR D9: 4,7 BLK 8
D8: 4,7,6                                # reduction candidate for 4,7
D8: 4,7 => SOLVED
* 146578329827913465395642178763285941582194736419367852271836594954721683638459217
D8: 6 => CTR
* 1..5.832982.9134.5395.421.8763285941582194.3.4193..8522.183.59.954621783638.5921.
* PAIR G8: 6,7 BLK 9
I7: 6,7,4                                # reduction candidate for 6,7
I7: 6,7 => CTR
* 17456832982.9134.5395.421.8763285941582194.3.4193..85224183.59.957421683638759214
I7: 4 => SOLVED
* 146578329827913465395642178763285941582194736419367852271836594954721683638459217
* PAIR G8: 6,7 ROW 8
D8: 6,7,4                                # reduction candidate for 6,7
D8: 6,7 => SOLVED
* 146578329827913465395642178763285941582194736419367852271836594954721683638459217
D8: 4 => CTR
* 1..5.832982.9134.5395642178763285941582194.3.4193678522.183659.95.421683638759214
* PAIR I9: 4,7 BLK 9
I7: 4,7,6                                # reduction candidate for 4,7
I7: 4,7 => SOLVED
* 146578329827913465395642178763285941582194736419367852271836594954721683638459217
I7: 6 => CTR
* 1..5.832982.9134.5395.421.8763285941582194.3.4193..85224183759695..21.83638.5921.
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-187-base-pr-000.dot
* REASONING
* DIS # C1: 4,7 => CTR => C1: 6
* PRF # C1: 6 => SOL
* PRF # C1: 6,7 => SOL
* DIS # C1: 4 => CTR => C1: 6,7
* PRF # C1: 6,7 => SOL
* DIS # C1: 4 => CTR => C1: 6,7
* PRF # D8: 6,7 => SOL
* DIS # D8: 4 => CTR => D8: 6,7
* DIS # I7: 6,7 => CTR => I7: 4
* PRF # I7: 4 => SOL
* PRF # I7: 4,7 => SOL
* DIS # I7: 6 => CTR => I7: 4,7
* PRF # D8: 4,7 => SOL
* DIS # D8: 6 => CTR => D8: 4,7
* DIS # C1: 4,7 => CTR => C1: 6
* PRF # C1: 6 => SOL
* PRF # D8: 6,7 => SOL
* DIS # D8: 4 => CTR => D8: 6,7
* DIS # I7: 6,7 => CTR => I7: 4
* PRF # I7: 4 => SOL
* PRF # D8: 4,7 => SOL
* DIS # D8: 6 => CTR => D8: 4,7
* DIS # I7: 6,7 => CTR => I7: 4
* PRF # I7: 4 => SOL
* PRF # D8: 6,7 => SOL
* DIS # D8: 4 => CTR => D8: 6,7
* PRF # I7: 4,7 => SOL
* DIS # I7: 6 => CTR => I7: 4,7
* CNT  28 HDP CHAINS /  28 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B7,C2,C8,D3,D9,E1,E6,F6,F7,G5,G8,H2,H3,I5,I9)
* 1..5.832982.9134.5395.421.8763285941582194.3.4193..8522.183.59.95..21.83638.5921.
* PAIR B1: 4,7 BLK 1
C1: 4,7,6                                # reduction candidate for 4,7
C1: 4,7 => CTR
* 1..568329826913475395742168763285941582194.3.4193768522.1837596957.21.83638.5921.
C1: 6 => SOLVED
* 146578329827913465395642178763285941582194736419367852271836594954721683638459217
* DURATION: 0:00:03.093408  START: 09:06:12.778459  END: 09:06:15.871867 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-187-base-pr-001.dot
* REASONING
* DIS # C1: 4,7 => CTR => C1: 6
* PRF C1: 6 => SOL
* STA C1: 6
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 187

solution: 146578329827913465395642178763285941582194736419367852271836594954721683638459217
info: 1836     FNBTWY   S8.f     9830

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

Solution

position: 146578329827913465395642178763285941582194736419367852271836594954721683638459217 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 # C1: 4,7 => CTR => C1: 6
* PRF # C1: 6 => SOL
* PRF # C1: 6,7 => SOL
* DIS # C1: 4 => CTR => C1: 6,7
* PRF # C1: 6,7 => SOL
* DIS # C1: 4 => CTR => C1: 6,7
* PRF # D8: 6,7 => SOL
* DIS # D8: 4 => CTR => D8: 6,7
* DIS # I7: 6,7 => CTR => I7: 4
* PRF # I7: 4 => SOL
* PRF # I7: 4,7 => SOL
* DIS # I7: 6 => CTR => I7: 4,7
* PRF # D8: 4,7 => SOL
* DIS # D8: 6 => CTR => D8: 4,7
* DIS # C1: 4,7 => CTR => C1: 6
* PRF # C1: 6 => SOL
* PRF # D8: 6,7 => SOL
* DIS # D8: 4 => CTR => D8: 6,7
* DIS # I7: 6,7 => CTR => I7: 4
* PRF # I7: 4 => SOL
* PRF # D8: 4,7 => SOL
* DIS # D8: 6 => CTR => D8: 4,7
* DIS # I7: 6,7 => CTR => I7: 4
* PRF # I7: 4 => SOL
* PRF # D8: 6,7 => SOL
* DIS # D8: 4 => CTR => D8: 6,7
* PRF # I7: 4,7 => SOL
* DIS # I7: 6 => CTR => I7: 4,7
* CNT  28 HDP CHAINS /  28 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # C1: 4,7 => CTR => C1: 6
* PRF C1: 6 => SOL
* STA C1: 6
* CNT   2 HDP CHAINS /   1 HYP OPENED