Analysis of xx-top500-134-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ..72..5...4......6.......1.62....3......47.......6....1..8...5.........49........ initial

Autosolve

position: .672145...41...72629.7.641.62.1..347.1..4726.47..62...1348796527.26....49.642..7. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # A2: 3,8 => SOL
* DIS # A2: 5 => CTR => A2: 3,8
* DIS # C3: 3,8 => CTR => C3: 5
* PRF # C3: 5 => SOL
* PRF # I1: 3,8 => SOL
* DIS # A5: 3,8 => CTR => A5: 5
* PRF # A5: 5 => SOL
* PRF # E2: 5,9 => SOL
* DIS # E2: 3,8 => CTR => E2: 5,9
* PRF # I1: 3,8 => SOL
* DIS # C3: 3,8 => CTR => C3: 5
* PRF # C3: 5 => SOL
* PRF # E3: 3,8 => SOL
* DIS # E3: 5 => CTR => E3: 3,8
* DIS # I9: 3,8 => CTR => I9: 1
* PRF # I9: 1 => SOL
* DIS # C5: 5,9 => CTR => C5: 3,8
* DIS # C6: 5,9 => CTR => C6: 3,8
* PRF # E4: 8 => SOL
* PRF # E4: 5,8 => SOL
* DIS # E4: 9 => CTR => E4: 5,8
* PRF # F2: 5,8 => SOL
* DIS # F2: 3 => CTR => F2: 5,8
* PRF # I5: 8,9 => SOL
* DIS # I5: 5 => CTR => I5: 8,9
* DIS # G6: 8,9 => CTR => G6: 1
* PRF # G6: 1 => SOL
* DIS # I6: 8,9 => CTR => I6: 1,5
* DIS # C6: 8,9 => CTR => C6: 3,5
* PRF # H1: 8,9 => SOL
* DIS # H1: 3 => CTR => H1: 8,9
* DIS # H8: 8,9 => CTR => H8: 3
* PRF # H8: 3 => SOL
* DIS # F8: 3,5 => CTR => F8: 1
* DIS # E2: 3,5 => CTR => E2: 8,9
* DIS # G8: 1,8 => CTR => G8: 9
* PRF # I9: 1,8 => SOL
* DIS # I9: 3 => CTR => I9: 1,8
* DIS # G6: 9 => CTR => G6: 1,8
* CNT  39 HDP CHAINS /  56 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 # A2: 3,8 => SOL
* STA A2: 3,8
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

..72..5...4......6.......1.62....3......47.......6....1..8...5.........49........ initial
.672145...41...72629.7.641.62.1..347.1..4726.47..62...1348796527.26....49.642..7. autosolve
867214593341598726295736418629185347518347269473962185134879652782651934956423871 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
A1: 3,8
D2: 5,9
I3: 3,8
C4: 5,9
F4: 5,8
H6: 8,9
B8: 5,8
B9: 5,8
E8: 3,5
G9: 1,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G6,I6: 1.. / G6 = 1  =>  0 pairs (*) / I6 = 1  =>  0 pairs (X)
F8,F9: 1.. / F8 = 1  => 12 pairs (_) / F9 = 1  =>  0 pairs (X)
F8,G8: 1.. / F8 = 1  => 12 pairs (_) / G8 = 1  =>  0 pairs (X)
I6,I9: 1.. / I6 = 1  =>  0 pairs (X) / I9 = 1  =>  0 pairs (_)
D5,D6: 3.. / D5 = 3  => 14 pairs (_) / D6 = 3  => 11 pairs (_)
H8,I9: 3.. / H8 = 3  =>  0 pairs (*) / I9 = 3  =>  0 pairs (X)
C6,D6: 3.. / C6 = 3  => 14 pairs (_) / D6 = 3  => 11 pairs (_)
F9,I9: 3.. / F9 = 3  =>  0 pairs (*) / I9 = 3  =>  0 pairs (X)
H1,H8: 3.. / H1 = 3  =>  0 pairs (X) / H8 = 3  =>  0 pairs (_)
A2,C3: 5.. / A2 = 5  =>  0 pairs (X) / C3 = 5  =>  0 pairs (_)
I5,I6: 5.. / I5 = 5  =>  0 pairs (X) / I6 = 5  =>  0 pairs (_)
B8,B9: 5.. / B8 = 5  =>  0 pairs (X) / B9 = 5  => 11 pairs (_)
C3,E3: 5.. / C3 = 5  =>  0 pairs (*) / E3 = 5  =>  0 pairs (X)
B9,F9: 5.. / B9 = 5  => 11 pairs (_) / F9 = 5  =>  0 pairs (X)
A2,A5: 5.. / A2 = 5  =>  0 pairs (X) / A5 = 5  =>  0 pairs (_)
E4,F4: 8.. / E4 = 8  =>  0 pairs (*) / F4 = 8  =>  0 pairs (X)
B8,B9: 8.. / B8 = 8  => 11 pairs (_) / B9 = 8  =>  0 pairs (X)
F2,F4: 8.. / F2 = 8  =>  0 pairs (*) / F4 = 8  =>  0 pairs (X)
D2,E2: 9.. / D2 = 9  =>  0 pairs (X) / E2 = 9  =>  0 pairs (_)
H1,I1: 9.. / H1 = 9  =>  0 pairs (*) / I1 = 9  =>  0 pairs (X)
G8,H8: 9.. / G8 = 9  => 13 pairs (_) / H8 = 9  =>  0 pairs (X)
C4,E4: 9.. / C4 = 9  =>  0 pairs (*) / E4 = 9  =>  0 pairs (X)
E2,E4: 9.. / E2 = 9  =>  0 pairs (*) / E4 = 9  =>  0 pairs (X)
G6,G8: 9.. / G6 = 9  =>  0 pairs (X) / G8 = 9  => 13 pairs (_)
* DURATION: 0:00:43.434591  START: 07:19:36.795413  END: 07:20:20.230004 2017-05-04
* CP COUNT: (24)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B8,B9,C4,D2,E8,F4,G9,H6,I3)
* .672145...41...72629.7.641.62.1..347.1..4726.47..62...1348796527.26....49.642..7.
* PAIR A1: 3,8 BLK 1
A2: 3,8,5                                # reduction candidate for 3,8
A2: 3,8 => SOLVED
* 867214593341598726295736418629185347518347269473962185134879652782651934956423871
A2: 5 => CTR
* .6721453954198372629375641862519834731..4726.47..62...1348796527.263...49.642..73
C3: 3,8,5                                # reduction candidate for 3,8
C3: 3,8 => CTR
* .6721453954198372629375641862519834731..4726.47..62...1348796527.263...49.642..73
C3: 5 => SOLVED
* 867214593341598726295736418629185347518347269473962185134879652782651934956423871
* PAIR A1: 3,8 ROW 1
H1: 3,8,9                                # reduction candidate for 3,8
H1: 3,8                                  # 13 pairs
I1: 3,8,9                                # reduction candidate for 3,8
I1: 3,8 => SOLVED
* 867214593341598726295736418629185347518347269473962185134879652782651934956423871
I1: 9                                    # 13 pairs
* PAIR A1: 3,8 COL A
A5: 3,8,5                                # reduction candidate for 3,8
A5: 3,8 => CTR
* .6721453954198372629375641862519834731..4726.47..62...1348796527.263...49.642..73
A5: 5 => SOLVED
* 867214593341598726295736418629185347518347269473962185134879652782651934956423871
* PAIR D2: 5,9 BLK 2
E2: 5,9,3,8                              # reduction candidate for 5,9
E2: 5,9 => SOLVED
* 867214593341598726295736418629185347518347269473962185134879652782651934956423871
E2: 3,8 => CTR
* .6721453954198372629375641862519834731..4726.47..62...1348796527.263...49.642..73
* PAIR D2: 5,9 COL D
D5: 5,9,3                                # reduction candidate for 5,9
D5: 5,9                                  # 11 pairs
D6: 5,9,3                                # reduction candidate for 5,9
D6: 5,9                                  # 14 pairs
* PAIR I3: 3,8 BLK 3
H1: 3,8,9                                # reduction candidate for 3,8
H1: 3,8                                  # 13 pairs
I1: 3,8,9                                # reduction candidate for 3,8
I1: 3,8 => SOLVED
* 867214593341598726295736418629185347518347269473962185134879652782651934956423871
I1: 9                                    # 13 pairs
* PAIR I3: 3,8 ROW 3
C3: 3,8,5                                # reduction candidate for 3,8
C3: 3,8 => CTR
* .6721453954198372629375641862519834731..4726.47..62...1348796527.263...49.642..73
C3: 5 => SOLVED
* 867214593341598726295736418629185347518347269473962185134879652782651934956423871
E3: 3,8,5                                # reduction candidate for 3,8
E3: 3,8 => SOLVED
* 867214593341598726295736418629185347518347269473962185134879652782651934956423871
E3: 5 => CTR
* .6721453954198372629375641862.19834731..4726.47..62...1348796527.263...49.642..73
* PAIR I3: 3,8 COL I
I9: 3,8,1                                # reduction candidate for 3,8
I9: 3,8 => CTR
* .672145.95419..72629.75641.62.198347.19347265473562..11348796527.263...49.642..73
I9: 1 => SOLVED
* 867214593341598726295736418629185347518347269473962185134879652782651934956423871
* PAIR C4: 5,9 BLK 4
C5: 5,9,3,8                              # reduction candidate for 5,9
C5: 5,9 => CTR
* .67214539541983726293756418625198347.19.4726.47..62...1348796527.263...49.642..73
C5: 3,8                                  # 11 pairs
C6: 5,9,3,8                              # reduction candidate for 5,9
C6: 5,9 => CTR
* .672145..5419..72629.75641.62.198347.1.547269479362.851348796527.263.9.49.642..7.
C6: 3,8                                  # 11 pairs
* PAIR C4: 5,9 ROW 4
E4: 5,9,8                                # reduction candidate for 5,9
E4: 8 => SOLVED
* 867214593341598726295736418629185347518347269473962185134879652782651934956423871
E4: 5,9                                  # 11 pairs
* PAIR F4: 5,8 BLK 5
E4: 5,8,9                                # reduction candidate for 5,8
E4: 5,8 => SOLVED
* 867214593341598726295736418629185347518347269473962185134879652782651934956423871
E4: 9 => CTR
* .6721453954198372629375641862519834731..4726.47..62...1348796527.263...49.642..73
* PAIR F4: 5,8 COL F
F2: 5,8,3                                # reduction candidate for 5,8
F2: 5,8 => SOLVED
* 867214593341598726295736418629185347518347269473962185134879652782651934956423871
F2: 3 => CTR
* .67214539.41..372629375641862519834731..4726.47..62...1348796527.263...49.642..73
* PAIR H6: 8,9 BLK 6
I5: 8,9,5                                # reduction candidate for 8,9
I5: 8,9 => SOLVED
* 867214593341598726295736418629185347518347269473962185134879652782651934956423871
I5: 5 => CTR
* .672145..5419..72629.75641.62.198347.19347265473562...1348796527.263...49.642..73
G6: 8,9,1                                # reduction candidate for 8,9
G6: 8,9 => CTR
* .672145.95419..72629.75641.62.198347.19347265473562..11348796527.263...49.642..73
G6: 1 => SOLVED
* 867214593341598726295736418629185347518347269473962185134879652782651934956423871
I6: 8,9,1,5                              # reduction candidate for 8,9
I6: 8,9 => CTR
* .672145..5419..72629.75641.62.198347.1..4726547..621..1348796527.26.19.49.642.871
I6: 1,5                                  # 11 pairs
* PAIR H6: 8,9 ROW 6
C6: 8,9,3,5                              # reduction candidate for 8,9
C6: 8,9 => CTR
* .672145...41...7262957.641.629185347513947268478362195134879652782651934956423871
C6: 3,5                                  # 12 pairs
* PAIR H6: 8,9 COL H
H1: 8,9,3                                # reduction candidate for 8,9
H1: 8,9 => SOLVED
* 867214593341598726295736418629185347518347269473962185134879652782651934956423871
H1: 3 => CTR
* 8672145395419..7262937.641862.1..347.1..4726547..62..11348796527.26....49.642..73
H8: 8,9,3                                # reduction candidate for 8,9
H8: 8,9 => CTR
* 8672145395419..7262937.641862.1..347.1..4726547..62..11348796527.26....49.642..73
H8: 3 => SOLVED
* 867214593341598726295736418629185347518347269473962185134879652782651934956423871
* PAIR E8: 3,5 BLK 8
F8: 3,5,1                                # reduction candidate for 3,5
F8: 3,5 => CTR
* 8672145395419..7262937.641862.1..347.1..4726547..629811348796527826..194956421873
F8: 1                                    # 12 pairs
F9: 3,5,1                                # reduction candidate for 3,5
F9: 3,5                                  # 12 pairs
* PAIR E8: 3,5 COL E
E2: 3,5,8,9                              # reduction candidate for 3,5
E2: 3,5 => CTR
* .672145..8419..7262957.641.62.198347.1..4726.47..62...1348796527.26....49.642..7.
E2: 8,9                                  # 11 pairs
E3: 3,5,8                                # reduction candidate for 3,5
E3: 3,5                                  # 14 pairs
* PAIR G9: 1,8 BLK 9
G8: 1,8,9                                # reduction candidate for 1,8
G8: 1,8 => CTR
* 867214539541...72629.7.641862.1..347.1894726547.3629811348796527.26...949.642..73
G8: 9                                    # 13 pairs
I9: 1,8,3                                # reduction candidate for 1,8
I9: 1,8 => SOLVED
* 867214593341598726295736418629185347518347269473962185134879652782651934956423871
I9: 3 => CTR
* 8672145395419..7262937.641862.1..347.1..4726547..62..11348796527.26....49.642..73
* PAIR G9: 1,8 COL G
G6: 1,8,9                                # reduction candidate for 1,8
G6: 9 => CTR
* 867214539541...72629.7.641862.1..347.1894726547.3629811348796527.26...949.642..73
G6: 1,8                                  # 13 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-134-base-pr-000.dot
* REASONING
* PRF # A2: 3,8 => SOL
* DIS # A2: 5 => CTR => A2: 3,8
* DIS # C3: 3,8 => CTR => C3: 5
* PRF # C3: 5 => SOL
* PRF # I1: 3,8 => SOL
* DIS # A5: 3,8 => CTR => A5: 5
* PRF # A5: 5 => SOL
* PRF # E2: 5,9 => SOL
* DIS # E2: 3,8 => CTR => E2: 5,9
* PRF # I1: 3,8 => SOL
* DIS # C3: 3,8 => CTR => C3: 5
* PRF # C3: 5 => SOL
* PRF # E3: 3,8 => SOL
* DIS # E3: 5 => CTR => E3: 3,8
* DIS # I9: 3,8 => CTR => I9: 1
* PRF # I9: 1 => SOL
* DIS # C5: 5,9 => CTR => C5: 3,8
* DIS # C6: 5,9 => CTR => C6: 3,8
* PRF # E4: 8 => SOL
* PRF # E4: 5,8 => SOL
* DIS # E4: 9 => CTR => E4: 5,8
* PRF # F2: 5,8 => SOL
* DIS # F2: 3 => CTR => F2: 5,8
* PRF # I5: 8,9 => SOL
* DIS # I5: 5 => CTR => I5: 8,9
* DIS # G6: 8,9 => CTR => G6: 1
* PRF # G6: 1 => SOL
* DIS # I6: 8,9 => CTR => I6: 1,5
* DIS # C6: 8,9 => CTR => C6: 3,5
* PRF # H1: 8,9 => SOL
* DIS # H1: 3 => CTR => H1: 8,9
* DIS # H8: 8,9 => CTR => H8: 3
* PRF # H8: 3 => SOL
* DIS # F8: 3,5 => CTR => F8: 1
* DIS # E2: 3,5 => CTR => E2: 8,9
* DIS # G8: 1,8 => CTR => G8: 9
* PRF # I9: 1,8 => SOL
* DIS # I9: 3 => CTR => I9: 1,8
* DIS # G6: 9 => CTR => G6: 1,8
* CNT  39 HDP CHAINS /  56 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B8,B9,C4,D2,E8,F4,G9,H6,I3)
* .672145...41...72629.7.641.62.1..347.1..4726.47..62...1348796527.26....49.642..7.
* PAIR A1: 3,8 BLK 1
A2: 3,8,5                                # reduction candidate for 3,8
A2: 3,8 => SOLVED
* 867214593341598726295736418629185347518347269473962185134879652782651934956423871
* DURATION: 0:00:02.178265  START: 07:21:24.123510  END: 07:21:26.301775 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-134-base-pr-001.dot
* REASONING
* PRF # A2: 3,8 => SOL
* STA A2: 3,8
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 134

solution: 867214593341598726295736418629185347518347269473962185134879652782651934956423871
info: 1811     FNBWY    S8.f     45892

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

Solution

position: 867214593341598726295736418629185347518347269473962185134879652782651934956423871 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 # A2: 3,8 => SOL
* DIS # A2: 5 => CTR => A2: 3,8
* DIS # C3: 3,8 => CTR => C3: 5
* PRF # C3: 5 => SOL
* INC # H1: 3,8 => UNS
* PRF # I1: 3,8 => SOL
* INC # I1: 9 => UNS
* DIS # A5: 3,8 => CTR => A5: 5
* PRF # A5: 5 => SOL
* PRF # E2: 5,9 => SOL
* DIS # E2: 3,8 => CTR => E2: 5,9
* INC # D5: 5,9 => UNS
* INC # D6: 5,9 => UNS
* INC # H1: 3,8 => UNS
* PRF # I1: 3,8 => SOL
* INC # I1: 9 => UNS
* DIS # C3: 3,8 => CTR => C3: 5
* PRF # C3: 5 => SOL
* PRF # E3: 3,8 => SOL
* DIS # E3: 5 => CTR => E3: 3,8
* DIS # I9: 3,8 => CTR => I9: 1
* PRF # I9: 1 => SOL
* DIS # C5: 5,9 => CTR => C5: 3,8
* INC # C5: 3,8 => UNS
* DIS # C6: 5,9 => CTR => C6: 3,8
* INC # C6: 3,8 => UNS
* INC # E4: 5,9 => UNS
* PRF # E4: 8 => SOL
* PRF # E4: 5,8 => SOL
* DIS # E4: 9 => CTR => E4: 5,8
* PRF # F2: 5,8 => SOL
* DIS # F2: 3 => CTR => F2: 5,8
* PRF # I5: 8,9 => SOL
* DIS # I5: 5 => CTR => I5: 8,9
* DIS # G6: 8,9 => CTR => G6: 1
* PRF # G6: 1 => SOL
* DIS # I6: 8,9 => CTR => I6: 1,5
* INC # I6: 1,5 => UNS
* DIS # C6: 8,9 => CTR => C6: 3,5
* INC # C6: 3,5 => UNS
* PRF # H1: 8,9 => SOL
* DIS # H1: 3 => CTR => H1: 8,9
* DIS # H8: 8,9 => CTR => H8: 3
* PRF # H8: 3 => SOL
* DIS # F8: 3,5 => CTR => F8: 1
* INC # F8: 1 => UNS
* INC # F9: 3,5 => UNS
* DIS # E2: 3,5 => CTR => E2: 8,9
* INC # E2: 8,9 => UNS
* INC # E3: 3,5 => UNS
* DIS # G8: 1,8 => CTR => G8: 9
* INC # G8: 9 => UNS
* PRF # I9: 1,8 => SOL
* DIS # I9: 3 => CTR => I9: 1,8
* INC # G6: 1,8 => UNS
* DIS # G6: 9 => CTR => G6: 1,8
* CNT  56 HDP CHAINS /  56 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # A2: 3,8 => SOL
* STA A2: 3,8
* CNT   1 HDP CHAINS /   1 HYP OPENED