Analysis of xx-top500-429-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ..3.....7...5...1..8..........8..3...6.4.....1........5...37.......2.6....2...8.. initial

Autosolve

position: ..32...877.658..13.8.37......78..3..86.4.37..13.7.2..85986371..3..9286756721..839 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A3: 2 => CTR => A3: 4,9
* DIS # E1: 4,9 => CTR => E1: 1,6
* PRF # F1: 4,9 => SOL
* PRF # B4: 5 => SOL
* DIS # E1: 4,9 => CTR => E1: 1,6
* PRF # F1: 4,9 => SOL
* DIS # G2: 2 => CTR => G2: 4,9
* DIS # H3: 4,6 => CTR => H3: 5,9
* PRF # B4: 5 => SOL
* PRF # C6: 4 => SOL
* CNT  10 HDP CHAINS /  32 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 # A3: 2 => CTR => A3: 4,9
* DIS A3: 4,9 # E1: 4,9 => CTR => E1: 1,6
* PRF A3: 4,9 + E1: 1,6 # F1: 4,9 => SOL
* STA A3: 4,9 + E1: 1,6 + F1: 4,9
* CNT   3 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

..3.....7...5...1..8..........8..3...6.4.....1........5...37.......2.6....2...8.. initial
..32...877.658..13.8.37......78..3..86.4.37..13.7.2..85986371..3..9286756721..839 autosolve
913264587726589413485371296257896341869413752134752968598637124341928675672145839 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (15)
A1: 4,9
B1: 1,5
B2: 2,4
C3: 1,5
F2: 4,9
I3: 4,6
A4: 2,4
C5: 5,9
I5: 1,2
B8: 1,4
C8: 1,4
E9: 4,5
F9: 4,5
H7: 2,4
I7: 2,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B1,C3: 1.. / B1 = 1  =>  0 pairs (*) / C3 = 1  =>  0 pairs (X)
I4,I5: 1.. / I4 = 1  => 12 pairs (_) / I5 = 1  => 14 pairs (_)
B8,C8: 1.. / B8 = 1  => 19 pairs (_) / C8 = 1  =>  0 pairs (*)
C3,F3: 1.. / C3 = 1  => 19 pairs (_) / F3 = 1  =>  0 pairs (*)
E5,I5: 1.. / E5 = 1  => 12 pairs (_) / I5 = 1  => 14 pairs (_)
B1,B8: 1.. / B1 = 1  =>  0 pairs (*) / B8 = 1  =>  0 pairs (X)
C3,C8: 1.. / C3 = 1  => 19 pairs (_) / C8 = 1  =>  0 pairs (*)
B2,A3: 2.. / B2 = 2  => 16 pairs (_) / A3 = 2  =>  0 pairs (X)
G2,G3: 2.. / G2 = 2  =>  0 pairs (X) / G3 = 2  => 16 pairs (_)
A4,B4: 2.. / A4 = 2  => 16 pairs (_) / B4 = 2  =>  0 pairs (X)
H5,I5: 2.. / H5 = 2  => 14 pairs (_) / I5 = 2  => 12 pairs (_)
H7,I7: 2.. / H7 = 2  => 12 pairs (_) / I7 = 2  => 14 pairs (_)
B2,G2: 2.. / B2 = 2  => 16 pairs (_) / G2 = 2  =>  0 pairs (X)
A3,G3: 2.. / A3 = 2  =>  0 pairs (X) / G3 = 2  => 16 pairs (_)
A3,A4: 2.. / A3 = 2  =>  0 pairs (X) / A4 = 2  => 16 pairs (_)
B2,B4: 2.. / B2 = 2  => 16 pairs (_) / B4 = 2  =>  0 pairs (X)
H5,H7: 2.. / H5 = 2  => 14 pairs (_) / H7 = 2  => 12 pairs (_)
I5,I7: 2.. / I5 = 2  => 12 pairs (_) / I7 = 2  => 14 pairs (_)
B8,C8: 4.. / B8 = 4  =>  0 pairs (*) / C8 = 4  =>  0 pairs (X)
E9,F9: 4.. / E9 = 4  => 13 pairs (_) / F9 = 4  =>  0 pairs (X)
H7,I7: 4.. / H7 = 4  => 14 pairs (_) / I7 = 4  => 12 pairs (_)
C6,C8: 4.. / C6 = 4  =>  0 pairs (*) / C8 = 4  =>  0 pairs (X)
E1,E9: 4.. / E1 = 4  =>  0 pairs (X) / E9 = 4  => 13 pairs (_)
B1,C3: 5.. / B1 = 5  => 19 pairs (_) / C3 = 5  =>  0 pairs (*)
E9,F9: 5.. / E9 = 5  =>  0 pairs (X) / F9 = 5  => 13 pairs (_)
B1,G1: 5.. / B1 = 5  => 19 pairs (_) / G1 = 5  =>  0 pairs (*)
B1,B4: 5.. / B1 = 5  => 19 pairs (_) / B4 = 5  =>  0 pairs (*)
F4,F9: 5.. / F4 = 5  =>  0 pairs (X) / F9 = 5  => 13 pairs (_)
E1,F1: 6.. / E1 = 6  => 14 pairs (_) / F1 = 6  => 15 pairs (_)
H3,I3: 6.. / H3 = 6  =>  0 pairs (X) / I3 = 6  => 15 pairs (_)
E6,H6: 6.. / E6 = 6  => 15 pairs (_) / H6 = 6  => 16 pairs (_)
F1,F4: 6.. / F1 = 6  => 15 pairs (_) / F4 = 6  => 14 pairs (_)
I3,I4: 6.. / I3 = 6  => 15 pairs (_) / I4 = 6  =>  0 pairs (X)
A1,A3: 9.. / A1 = 9  => 16 pairs (_) / A3 = 9  => 15 pairs (_)
C5,C6: 9.. / C5 = 9  => 17 pairs (_) / C6 = 9  => 21 pairs (_)
F2,G2: 9.. / F2 = 9  => 16 pairs (_) / G2 = 9  => 15 pairs (_)
* DURATION: 0:01:09.539315  START: 17:26:25.440454  END: 17:27:34.979769 2017-05-04
* CP COUNT: (36)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B1,B2,B8,C3,C5,C8,E9,F2,F9,H7,I3,I5,I7)
* ..32...877.658..13.8.37......78..3..86.4.37..13.7.2..85986371..3..9286756721..839
* PAIR A1: 4,9 BLK 1
A3: 4,9,2                                # reduction candidate for 4,9
A3: 2 => CTR
* 953261487746589213281374..64278.63.186.4137.213.7.2.48598637124314928675672145839
A3: 4,9                                  # 16 pairs
* PAIR A1: 4,9 ROW 1
E1: 4,9,1,6                              # reduction candidate for 4,9
E1: 4,9 => CTR
* .132.65877.658..13.85371....578.93..8694.37..1347.29.85986371..3419286756721.5839
E1: 1,6                                  # 15 pairs
F1: 4,9,1,6                              # reduction candidate for 4,9
F1: 4,9 => SOLVED
* 913264587726589413485371296257896341869413752134752968598637124341928675672145839
F1: 1,6                                  # 16 pairs
G1: 4,9,5                                # reduction candidate for 4,9
G1: 4,9                                  # 19 pairs
* PAIR B2: 2,4 BLK 1
A3: 2,4,9                                # reduction candidate for 2,4
A3: 2,4                                  # 16 pairs
A3: 9                                    # 15 pairs
* PAIR B2: 2,4 ROW 2
G2: 2,4,9                                # reduction candidate for 2,4
G2: 2,4                                  # 16 pairs
G2: 9                                    # 15 pairs
* PAIR B2: 2,4 COL B
B4: 2,4,5                                # reduction candidate for 2,4
B4: 5 => SOLVED
* 913264587726589413485371296257896341869413752134752968598637124341928675672145839
B4: 2,4                                  # 19 pairs
* PAIR F2: 4,9 BLK 2
E1: 4,9,1,6                              # reduction candidate for 4,9
E1: 4,9 => CTR
* .132.65877.658..13.85371....578.93..8694.37..1347.29.85986371..3419286756721.5839
E1: 1,6                                  # 15 pairs
F1: 4,9,1,6                              # reduction candidate for 4,9
F1: 4,9 => SOLVED
* 913264587726589413485371296257896341869413752134752968598637124341928675672145839
F1: 1,6                                  # 16 pairs
F3: 4,9,1                                # reduction candidate for 4,9
F3: 4,9                                  # 19 pairs
* PAIR F2: 4,9 ROW 2
G2: 4,9,2                                # reduction candidate for 4,9
G2: 2 => CTR
* 953261487746589213281374..64278.63.186.4137.213.7.2.48598637124314928675672145839
G2: 4,9                                  # 16 pairs
* PAIR I3: 4,6 BLK 3
H3: 4,6,5,9                              # reduction candidate for 4,6
H3: 4,6 => CTR
* .532..9877.6589213.8137.5....78..3..86.4.37..13.7.24.85986371..3149286756721..839
H3: 5,9                                  # 17 pairs
* PAIR I3: 4,6 COL I
I4: 4,6,1                                # reduction candidate for 4,6
I4: 4,6                                  # 14 pairs
I4: 1                                    # 12 pairs
* PAIR A4: 2,4 BLK 4
B4: 2,4,5                                # reduction candidate for 2,4
B4: 5 => SOLVED
* 913264587726589413485371296257896341869413752134752968598637124341928675672145839
B4: 2,4                                  # 19 pairs
* PAIR A4: 2,4 COL A
A3: 2,4,9                                # reduction candidate for 2,4
A3: 2,4                                  # 16 pairs
A3: 9                                    # 15 pairs
* PAIR C5: 5,9 BLK 4
C6: 5,9,4                                # reduction candidate for 5,9
C6: 4 => SOLVED
* 913264587726589413485371296257896341869413752134752968598637124341928675672145839
C6: 5,9                                  # 19 pairs
* PAIR C5: 5,9 ROW 5
E5: 5,9,1                                # reduction candidate for 5,9
E5: 5,9                                  # 14 pairs
H5: 5,9,2                                # reduction candidate for 5,9
H5: 5,9                                  # 12 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-429-base-pr-000.dot
* REASONING
* DIS # A3: 2 => CTR => A3: 4,9
* DIS # E1: 4,9 => CTR => E1: 1,6
* PRF # F1: 4,9 => SOL
* PRF # B4: 5 => SOL
* DIS # E1: 4,9 => CTR => E1: 1,6
* PRF # F1: 4,9 => SOL
* DIS # G2: 2 => CTR => G2: 4,9
* DIS # H3: 4,6 => CTR => H3: 5,9
* PRF # B4: 5 => SOL
* PRF # C6: 4 => SOL
* CNT  10 HDP CHAINS /  32 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B1,B2,B8,C3,C5,C8,E9,F2,F9,H7,I3,I5,I7)
* ..32...877.658..13.8.37......78..3..86.4.37..13.7.2..85986371..3..9286756721..839
* PAIR A1: 4,9 BLK 1
A3: 4,9,2                                # reduction candidate for 4,9
A3: 2 => CTR
* 953261487746589213281374..64278.63.186.4137.213.7.2.48598637124314928675672145839
* PAIR A1: 4,9 ROW 1
E1: 4,9,1,6                              # reduction candidate for 4,9
E1: 4,9 => CTR
* .132.658772658..13.853712..2578.93..8694.37..1347.29.85986371..3.19286756721..839
F1: 4,9,1,6                              # reduction candidate for 4,9
F1: 4,9 => SOLVED
* 913264587726589413485371296257896341869413752134752968598637124341928675672145839
* DURATION: 0:00:05.798031  START: 17:28:10.628032  END: 17:28:16.426063 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-429-base-pr-001.dot
* REASONING
* DIS # A3: 2 => CTR => A3: 4,9
* DIS A3: 4,9 # E1: 4,9 => CTR => E1: 1,6
* PRF A3: 4,9 + E1: 1,6 # F1: 4,9 => SOL
* STA A3: 4,9 + E1: 1,6 + F1: 4,9
* CNT   3 HDP CHAINS /   4 HYP OPENED

Header Info

Top 500 Minimum 17 429

solution: 913264587726589413485371296257896341869413752134752968598637124341928675672145839
info: 95185    FNBHWXYK S8.f     39923

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

Solution

position: 913264587726589413485371296257896341869413752134752968598637124341928675672145839 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 # A3: 4,9 => UNS
* DIS # A3: 2 => CTR => A3: 4,9
* DIS # E1: 4,9 => CTR => E1: 1,6
* INC # E1: 1,6 => UNS
* PRF # F1: 4,9 => SOL
* INC # F1: 1,6 => UNS
* INC # G1: 4,9 => UNS
* INC # A3: 2,4 => UNS
* INC # A3: 9 => UNS
* INC # G2: 2,4 => UNS
* INC # G2: 9 => UNS
* INC # B4: 2,4 => UNS
* PRF # B4: 5 => SOL
* DIS # E1: 4,9 => CTR => E1: 1,6
* INC # E1: 1,6 => UNS
* PRF # F1: 4,9 => SOL
* INC # F1: 1,6 => UNS
* INC # F3: 4,9 => UNS
* INC # G2: 4,9 => UNS
* DIS # G2: 2 => CTR => G2: 4,9
* DIS # H3: 4,6 => CTR => H3: 5,9
* INC # H3: 5,9 => UNS
* INC # I4: 4,6 => UNS
* INC # I4: 1 => UNS
* INC # B4: 2,4 => UNS
* PRF # B4: 5 => SOL
* INC # A3: 2,4 => UNS
* INC # A3: 9 => UNS
* INC # C6: 5,9 => UNS
* PRF # C6: 4 => SOL
* INC # E5: 5,9 => UNS
* INC # H5: 5,9 => UNS
* CNT  32 HDP CHAINS /  32 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A3: 4,9 => UNS
* DIS # A3: 2 => CTR => A3: 4,9
* DIS A3: 4,9 # E1: 4,9 => CTR => E1: 1,6
* PRF A3: 4,9 + E1: 1,6 # F1: 4,9 => SOL
* STA A3: 4,9 + E1: 1,6 + F1: 4,9
* CNT   4 HDP CHAINS /   4 HYP OPENED