Analysis of xx-top500-237-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ...6..2.....23....1........4....8.536......7...........37.5.....2.7...........1.. initial

Autosolve

position: 3..6172..7..23.561162..573.47912865361...3.722.3.76.1..37.51.26.2176.3.55463.21.7 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # D3: 4,9 => SOL
* DIS # I1: 4,9 => CTR => I1: 8
* PRF # D3: 4,9 => SOL
* DIS # I6: 8 => CTR => I6: 4,9
* DIS # D5: 4,9 => CTR => D5: 5
* PRF # D5: 5 => SOL
* PRF # D6: 4,9 => SOL
* DIS # D6: 5 => CTR => D6: 4,9
* PRF # G5: 4,9 => SOL
* DIS # G5: 8 => CTR => G5: 4,9
* PRF # E3: 8 => SOL
* PRF # D7: 8,9 => SOL
* DIS # D7: 4 => CTR => D7: 8,9
* DIS # G7: 8,9 => CTR => G7: 4
* PRF # G7: 4 => SOL
* PRF # H8: 8,9 => SOL
* DIS # H8: 4 => CTR => H8: 8,9
* PRF # D7: 8 => SOL
* DIS # H8: 8 => CTR => H8: 4,9
* PRF # D7: 8,9 => SOL
* DIS # D7: 4 => CTR => D7: 8,9
* DIS # E3: 4 => CTR => E3: 8,9
* DIS # G7: 8,9 => CTR => G7: 4
* PRF # G7: 4 => SOL
* PRF # H8: 8,9 => SOL
* DIS # H8: 4 => CTR => H8: 8,9
* DIS # H1: 8,9 => CTR => H1: 4
* PRF # H1: 4 => SOL
* CNT  28 HDP CHAINS /  39 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 # D3: 4,9 => SOL
* STA D3: 4,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

...6..2.....23....1........4....8.536......7...........37.5.....2.7...........1.. initial
3..6172..7..23.561162..573.47912865361...3.722.3.76.1..37.51.26.2176.3.55463.21.7 autosolve
395617248784239561162485739479128653618543972253976814937851426821764395546392187 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
B1: 5,9
C1: 4,5
B2: 8,9
C2: 4,8
F2: 4,9
I3: 4,9
C5: 5,8
B6: 5,8
E5: 4,9
A7: 8,9
A8: 8,9
F8: 4,9
E9: 8,9
H9: 8,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C1,C2: 4.. / C1 = 4  =>  0 pairs (X) / C2 = 4  =>  0 pairs (_)
D7,F8: 4.. / D7 = 4  =>  0 pairs (X) / F8 = 4  =>  0 pairs (_)
G7,H8: 4.. / G7 = 4  =>  0 pairs (*) / H8 = 4  =>  0 pairs (X)
C2,F2: 4.. / C2 = 4  =>  0 pairs (*) / F2 = 4  =>  0 pairs (X)
D7,G7: 4.. / D7 = 4  =>  0 pairs (X) / G7 = 4  =>  0 pairs (_)
F8,H8: 4.. / F8 = 4  =>  0 pairs (*) / H8 = 4  =>  0 pairs (X)
E3,E5: 4.. / E3 = 4  =>  0 pairs (X) / E5 = 4  => 19 pairs (_)
F2,F8: 4.. / F2 = 4  =>  0 pairs (X) / F8 = 4  =>  0 pairs (_)
H1,H8: 4.. / H1 = 4  =>  0 pairs (*) / H8 = 4  =>  0 pairs (X)
B1,C1: 5.. / B1 = 5  =>  0 pairs (X) / C1 = 5  =>  0 pairs (_)
C5,B6: 5.. / C5 = 5  =>  0 pairs (X) / B6 = 5  =>  0 pairs (_)
D5,D6: 5.. / D5 = 5  =>  0 pairs (*) / D6 = 5  =>  0 pairs (X)
C5,D5: 5.. / C5 = 5  =>  0 pairs (X) / D5 = 5  =>  0 pairs (_)
B6,D6: 5.. / B6 = 5  =>  0 pairs (*) / D6 = 5  =>  0 pairs (X)
B1,B6: 5.. / B1 = 5  =>  0 pairs (X) / B6 = 5  =>  0 pairs (_)
C1,C5: 5.. / C1 = 5  =>  0 pairs (*) / C5 = 5  =>  0 pairs (X)
B2,C2: 8.. / B2 = 8  =>  0 pairs (*) / C2 = 8  =>  0 pairs (X)
D3,E3: 8.. / D3 = 8  => 18 pairs (_) / E3 = 8  =>  0 pairs (*)
H1,I1: 8.. / H1 = 8  =>  0 pairs (X) / I1 = 8  => 17 pairs (_)
C5,B6: 8.. / C5 = 8  =>  0 pairs (*) / B6 = 8  =>  0 pairs (X)
A7,A8: 8.. / A7 = 8  =>  0 pairs (X) / A8 = 8  => 17 pairs (_)
D7,E9: 8.. / D7 = 8  =>  0 pairs (*) / E9 = 8  =>  0 pairs (X)
C5,G5: 8.. / C5 = 8  =>  0 pairs (*) / G5 = 8  =>  0 pairs (X)
A8,H8: 8.. / A8 = 8  => 17 pairs (_) / H8 = 8  =>  0 pairs (X)
E9,H9: 8.. / E9 = 8  => 18 pairs (_) / H9 = 8  =>  0 pairs (*)
B2,B6: 8.. / B2 = 8  =>  0 pairs (*) / B6 = 8  =>  0 pairs (X)
C2,C5: 8.. / C2 = 8  =>  0 pairs (X) / C5 = 8  =>  0 pairs (_)
D3,D7: 8.. / D3 = 8  => 18 pairs (_) / D7 = 8  =>  0 pairs (*)
E3,E9: 8.. / E3 = 8  =>  0 pairs (*) / E9 = 8  =>  0 pairs (X)
I1,I6: 8.. / I1 = 8  => 17 pairs (_) / I6 = 8  =>  0 pairs (X)
B1,B2: 9.. / B1 = 9  =>  0 pairs (*) / B2 = 9  =>  0 pairs (X)
A7,A8: 9.. / A7 = 9  => 17 pairs (_) / A8 = 9  =>  0 pairs (X)
B2,F2: 9.. / B2 = 9  =>  0 pairs (X) / F2 = 9  =>  0 pairs (_)
E9,H9: 9.. / E9 = 9  =>  0 pairs (*) / H9 = 9  =>  0 pairs (X)
F2,F8: 9.. / F2 = 9  =>  0 pairs (*) / F8 = 9  =>  0 pairs (X)
* DURATION: 0:00:58.750667  START: 10:55:16.326998  END: 10:56:15.077665 2017-05-04
* CP COUNT: (35)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A8,B1,B2,B6,C1,C2,C5,E5,E9,F2,F8,H9,I3)
* 3..6172..7..23.561162..573.47912865361...3.722.3.76.1..37.51.26.2176.3.55463.21.7
* PAIR F2: 4,9 BLK 2
D3: 4,9,8                                # reduction candidate for 4,9
D3: 4,9 => SOLVED
* 395617248784239561162485739479128653618543972253976814937851426821764395546392187
D3: 8                                    # 18 pairs
E3: 4,9,8                                # reduction candidate for 4,9
E3: 4,9                                  # 18 pairs
* PAIR I3: 4,9 BLK 3
H1: 4,9,8                                # reduction candidate for 4,9
H1: 4,9                                  # 17 pairs
I1: 4,9,8                                # reduction candidate for 4,9
I1: 4,9 => CTR
* 3..61728.78423.561162..573.47912865361...3.722.3.76.18.37.5182682176.345546382197
I1: 8                                    # 17 pairs
* PAIR I3: 4,9 ROW 3
D3: 4,9,8                                # reduction candidate for 4,9
D3: 4,9 => SOLVED
* 395617248784239561162485739479128653618543972253976814937851426821764395546392187
D3: 8                                    # 18 pairs
E3: 4,9,8                                # reduction candidate for 4,9
E3: 4,9                                  # 18 pairs
* PAIR I3: 4,9 COL I
I6: 4,9,8                                # reduction candidate for 4,9
I6: 8 => CTR
* 3..61728.78423.561162..573.47912865361...3.722.3.76.18.37.5182682176.345546382197
I6: 4,9                                  # 17 pairs
* PAIR E5: 4,9 BLK 5
D5: 4,9,5                                # reduction candidate for 4,9
D5: 4,9 => CTR
* 3546172.8798234561162..5734479128653615.43872283576419.3745192692176.3.55463.21.7
D5: 5 => SOLVED
* 395617248784239561162485739479128653618543972253976814937851426821764395546392187
D6: 4,9,5                                # reduction candidate for 4,9
D6: 4,9 => SOLVED
* 395617248784239561162485739479128653618543972253976814937851426821764395546392187
D6: 5 => CTR
* 3546172..798234561162..5734479128653615.43872283576419.3745192692176.3.55463.21.7
* PAIR E5: 4,9 ROW 5
G5: 4,9,8                                # reduction candidate for 4,9
G5: 4,9 => SOLVED
* 395617248784239561162485739479128653618543972253976814937851426821764395546392187
G5: 8 => CTR
* 3546172.8798234561162..5734479128653615.43872283576419.3745192692176.3.55463.21.7
* PAIR E5: 4,9 COL E
E3: 4,9,8                                # reduction candidate for 4,9
E3: 8 => SOLVED
* 395617248784239561162485739479128653618543972253976814937851426821764395546392187
E3: 4,9                                  # 18 pairs
* PAIR A7: 8,9 ROW 7
D7: 8,9,4                                # reduction candidate for 8,9
D7: 8,9 => SOLVED
* 395617248784239561162485739479128653618543972253976814937851426821764395546392187
D7: 4 => CTR
* 3..61728.7982345611628957344791286536159438722.3.76.1..37451.26.21769345546382197
G7: 8,9,4                                # reduction candidate for 8,9
G7: 8,9 => CTR
* 3..61728.7982345611628957344791286536159438722.3.76.1..37451.26.21769345546382197
G7: 4 => SOLVED
* 395617248784239561162485739479128653618543972253976814937851426821764395546392187
* PAIR A8: 8,9 ROW 8
H8: 8,9,4                                # reduction candidate for 8,9
H8: 8,9 => SOLVED
* 395617248784239561162485739479128653618543972253976814937851426821764395546392187
H8: 4 => CTR
* 3..61728.798234561162895734479128653615.438722.3.76.1..37.51.26821769345546382197
* PAIR F8: 4,9 BLK 8
D7: 4,9,8                                # reduction candidate for 4,9
D7: 8 => SOLVED
* 395617248784239561162485739479128653618543972253976814937851426821764395546392187
D7: 4,9                                  # 18 pairs
* PAIR F8: 4,9 ROW 8
H8: 4,9,8                                # reduction candidate for 4,9
H8: 8 => CTR
* 3..6172487.4239561162..57394791286536185.3.72253.76814.37.51426921764385546382197
H8: 4,9                                  # 17 pairs
* PAIR E9: 8,9 BLK 8
D7: 8,9,4                                # reduction candidate for 8,9
D7: 8,9 => SOLVED
* 395617248784239561162485739479128653618543972253976814937851426821764395546392187
D7: 4 => CTR
* 3..61728.7982345611628957344791286536159438722.3.76.1..37451.26.21769345546382197
* PAIR E9: 8,9 COL E
E3: 8,9,4                                # reduction candidate for 8,9
E3: 4 => CTR
* 39561724878.23.56116284573947912865361..93.722.3.7691..37951426921764385546382197
E3: 8,9                                  # 19 pairs
* PAIR H9: 8,9 BLK 9
G7: 8,9,4                                # reduction candidate for 8,9
G7: 8,9 => CTR
* 3..61728.7982345611628957344791286536159438722.3.76.1..37451.26.21769345546382197
G7: 4 => SOLVED
* 395617248784239561162485739479128653618543972253976814937851426821764395546392187
H8: 8,9,4                                # reduction candidate for 8,9
H8: 8,9 => SOLVED
* 395617248784239561162485739479128653618543972253976814937851426821764395546392187
H8: 4 => CTR
* 3..61728.798234561162895734479128653615.438722.3.76.1..37.51.26821769345546382197
* PAIR H9: 8,9 COL H
H1: 8,9,4                                # reduction candidate for 8,9
H1: 8,9 => CTR
* 3.4617289798234561162895734479128653615.43.722.3.7641..37451.26821769345546382197
H1: 4 => SOLVED
* 395617248784239561162485739479128653618543972253976814937851426821764395546392187
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-237-base-pr-000.dot
* REASONING
* PRF # D3: 4,9 => SOL
* DIS # I1: 4,9 => CTR => I1: 8
* PRF # D3: 4,9 => SOL
* DIS # I6: 8 => CTR => I6: 4,9
* DIS # D5: 4,9 => CTR => D5: 5
* PRF # D5: 5 => SOL
* PRF # D6: 4,9 => SOL
* DIS # D6: 5 => CTR => D6: 4,9
* PRF # G5: 4,9 => SOL
* DIS # G5: 8 => CTR => G5: 4,9
* PRF # E3: 8 => SOL
* PRF # D7: 8,9 => SOL
* DIS # D7: 4 => CTR => D7: 8,9
* DIS # G7: 8,9 => CTR => G7: 4
* PRF # G7: 4 => SOL
* PRF # H8: 8,9 => SOL
* DIS # H8: 4 => CTR => H8: 8,9
* PRF # D7: 8 => SOL
* DIS # H8: 8 => CTR => H8: 4,9
* PRF # D7: 8,9 => SOL
* DIS # D7: 4 => CTR => D7: 8,9
* DIS # E3: 4 => CTR => E3: 8,9
* DIS # G7: 8,9 => CTR => G7: 4
* PRF # G7: 4 => SOL
* PRF # H8: 8,9 => SOL
* DIS # H8: 4 => CTR => H8: 8,9
* DIS # H1: 8,9 => CTR => H1: 4
* PRF # H1: 4 => SOL
* CNT  28 HDP CHAINS /  39 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A8,B1,B2,B6,C1,C2,C5,E5,E9,F2,F8,H9,I3)
* 3..6172..7..23.561162..573.47912865361...3.722.3.76.1..37.51.26.2176.3.55463.21.7
* PAIR F2: 4,9 BLK 2
D3: 4,9,8                                # reduction candidate for 4,9
D3: 4,9 => SOLVED
* 395617248784239561162485739479128653618543972253976814937851426821764395546392187
* DURATION: 0:00:02.095272  START: 10:56:57.892244  END: 10:56:59.987516 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-237-base-pr-001.dot
* REASONING
* PRF # D3: 4,9 => SOL
* STA D3: 4,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 237

solution: 395617248784239561162485739479128653618543972253976814937851426821764395546392187
info: 2068     FNBWXY   S8.f     46992

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

Solution

position: 395617248784239561162485739479128653618543972253976814937851426821764395546392187 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 # D3: 4,9 => SOL
* INC # D3: 8 => UNS
* INC # E3: 4,9 => UNS
* INC # H1: 4,9 => UNS
* DIS # I1: 4,9 => CTR => I1: 8
* INC # I1: 8 => UNS
* PRF # D3: 4,9 => SOL
* INC # D3: 8 => UNS
* INC # E3: 4,9 => UNS
* INC # I6: 4,9 => UNS
* DIS # I6: 8 => CTR => I6: 4,9
* DIS # D5: 4,9 => CTR => D5: 5
* PRF # D5: 5 => SOL
* PRF # D6: 4,9 => SOL
* DIS # D6: 5 => CTR => D6: 4,9
* PRF # G5: 4,9 => SOL
* DIS # G5: 8 => CTR => G5: 4,9
* INC # E3: 4,9 => UNS
* PRF # E3: 8 => SOL
* PRF # D7: 8,9 => SOL
* DIS # D7: 4 => CTR => D7: 8,9
* DIS # G7: 8,9 => CTR => G7: 4
* PRF # G7: 4 => SOL
* PRF # H8: 8,9 => SOL
* DIS # H8: 4 => CTR => H8: 8,9
* INC # D7: 4,9 => UNS
* PRF # D7: 8 => SOL
* INC # H8: 4,9 => UNS
* DIS # H8: 8 => CTR => H8: 4,9
* PRF # D7: 8,9 => SOL
* DIS # D7: 4 => CTR => D7: 8,9
* INC # E3: 8,9 => UNS
* DIS # E3: 4 => CTR => E3: 8,9
* DIS # G7: 8,9 => CTR => G7: 4
* PRF # G7: 4 => SOL
* PRF # H8: 8,9 => SOL
* DIS # H8: 4 => CTR => H8: 8,9
* DIS # H1: 8,9 => CTR => H1: 4
* PRF # H1: 4 => SOL
* CNT  39 HDP CHAINS /  39 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # D3: 4,9 => SOL
* STA D3: 4,9
* CNT   1 HDP CHAINS /   1 HYP OPENED