Analysis of xx-top95-041-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ...5.1....9....8...6.......4.1..........7..9........3.8.....1.5...2..4.....36.... initial

Autosolve

position: .485913.6.9....8...6..8.5.94.1....58....7..9.....5..3.8...4.1.5...21.4.3.1436.9.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A2: 2,7 => CTR => A2: 1,3,5
* DIS # C2: 2,7 => CTR => C2: 3,5
* PRF # A3: 2,7 => SOL
* DIS # A6: 2,7 => CTR => A6: 6,9
* PRF # F2: 2,3 => SOL
* DIS # A2: 2,3 => CTR => A2: 1,5,7
* DIS # C2: 2,3 => CTR => C2: 5,7
* PRF # H9: 2,7 => SOL
* DIS # A2: 2,7 => CTR => A2: 1,3,5
* DIS # C2: 2,7 => CTR => C2: 3,5
* DIS # A5: 2,6 => CTR => A5: 3,5
* DIS # C7: 6 => CTR => C7: 2,3
* DIS # A8: 5,7 => CTR => A8: 6,9
* DIS # C8: 5,7 => CTR => C8: 6,9
* DIS # C7: 3 => CTR => C7: 2,6
* PRF # H9: 2,7 => SOL
* PRF # A9: 5 => SOL
* CNT  17 HDP CHAINS /  53 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 # A2: 2,7 => CTR => A2: 1,3,5
* DIS A2: 1,3,5 # C2: 2,7 => CTR => C2: 3,5
* PRF A2: 1,3,5 + C2: 3,5 # A3: 2,7 => SOL
* STA A2: 1,3,5 + C2: 3,5 + A3: 2,7
* CNT   3 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

...5.1....9....8...6.......4.1..........7..9........3.8.....1.5...2..4.....36.... initial
.485913.6.9....8...6..8.5.94.1....58....7..9.....5..3.8...4.1.5...21.4.3.1436.9.. autosolve
748591326195623847263487519421936758356874291987152634832749165679215483514368972 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (22)
A1: 2,7
E2: 2,3
D3: 4,7
H1: 2,7
H2: 1,4
I2: 2,7
H3: 1,4
D4: 6,9
E4: 2,3
D5: 1,8
D6: 1,8
G5: 2,6
I5: 1,4
I6: 1,4
B7: 2,3
B8: 5,7
D7: 7,9
F7: 7,9
F8: 5,8
F9: 5,8
H7: 2,6
I9: 2,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A2,A3: 1.. / A2 = 1  => 21 pairs (_) / A3 = 1  => 20 pairs (_)
H2,H3: 1.. / H2 = 1  => 20 pairs (_) / H3 = 1  => 21 pairs (_)
D5,D6: 1.. / D5 = 1  => 22 pairs (_) / D6 = 1  => 20 pairs (_)
I5,I6: 1.. / I5 = 1  => 20 pairs (_) / I6 = 1  => 22 pairs (_)
A2,H2: 1.. / A2 = 1  => 21 pairs (_) / H2 = 1  => 20 pairs (_)
A3,H3: 1.. / A3 = 1  => 20 pairs (_) / H3 = 1  => 21 pairs (_)
D5,I5: 1.. / D5 = 1  => 22 pairs (_) / I5 = 1  => 20 pairs (_)
D6,I6: 1.. / D6 = 1  => 20 pairs (_) / I6 = 1  => 22 pairs (_)
H1,I2: 2.. / H1 = 2  =>  0 pairs (*) / I2 = 2  =>  0 pairs (X)
A1,H1: 2.. / A1 = 2  =>  0 pairs (X) / H1 = 2  =>  0 pairs (_)
E2,E4: 2.. / E2 = 2  =>  0 pairs (*) / E4 = 2  =>  0 pairs (X)
I2,I9: 2.. / I2 = 2  =>  0 pairs (X) / I9 = 2  =>  0 pairs (_)
B7,C7: 3.. / B7 = 3  => 23 pairs (_) / C7 = 3  =>  0 pairs (X)
E2,E4: 3.. / E2 = 3  => 24 pairs (_) / E4 = 3  =>  0 pairs (*)
D2,D3: 4.. / D2 = 4  => 20 pairs (_) / D3 = 4  => 21 pairs (_)
H2,H3: 4.. / H2 = 4  => 21 pairs (_) / H3 = 4  => 20 pairs (_)
F5,F6: 4.. / F5 = 4  => 20 pairs (_) / F6 = 4  => 22 pairs (_)
I5,I6: 4.. / I5 = 4  => 22 pairs (_) / I6 = 4  => 20 pairs (_)
D2,H2: 4.. / D2 = 4  => 20 pairs (_) / H2 = 4  => 21 pairs (_)
D3,H3: 4.. / D3 = 4  => 21 pairs (_) / H3 = 4  => 20 pairs (_)
F5,I5: 4.. / F5 = 4  => 20 pairs (_) / I5 = 4  => 22 pairs (_)
F6,I6: 4.. / F6 = 4  => 22 pairs (_) / I6 = 4  => 20 pairs (_)
A2,C2: 5.. / A2 = 5  =>  0 pairs (X) / C2 = 5  => 22 pairs (_)
F8,F9: 5.. / F8 = 5  =>  0 pairs (*) / F9 = 5  =>  0 pairs (X)
A9,F9: 5.. / A9 = 5  =>  0 pairs (*) / F9 = 5  =>  0 pairs (X)
B5,B8: 5.. / B5 = 5  =>  0 pairs (*) / B8 = 5  =>  0 pairs (X)
D2,F2: 6.. / D2 = 6  => 17 pairs (_) / F2 = 6  => 23 pairs (_)
H7,H8: 6.. / H7 = 6  => 26 pairs (_) / H8 = 6  =>  0 pairs (X)
C7,H7: 6.. / C7 = 6  =>  0 pairs (X) / H7 = 6  => 26 pairs (_)
D2,D4: 6.. / D2 = 6  => 17 pairs (_) / D4 = 6  => 23 pairs (_)
H1,I2: 7.. / H1 = 7  =>  0 pairs (X) / I2 = 7  =>  0 pairs (_)
G4,G6: 7.. / G4 = 7  => 28 pairs (_) / G6 = 7  => 27 pairs (_)
D7,F7: 7.. / D7 = 7  => 17 pairs (_) / F7 = 7  => 23 pairs (_)
A1,H1: 7.. / A1 = 7  =>  0 pairs (*) / H1 = 7  =>  0 pairs (X)
B4,G4: 7.. / B4 = 7  => 27 pairs (_) / G4 = 7  => 28 pairs (_)
I2,I9: 7.. / I2 = 7  =>  0 pairs (*) / I9 = 7  =>  0 pairs (X)
B5,B6: 8.. / B5 = 8  => 22 pairs (_) / B6 = 8  => 20 pairs (_)
D5,D6: 8.. / D5 = 8  => 20 pairs (_) / D6 = 8  => 22 pairs (_)
F8,F9: 8.. / F8 = 8  => 24 pairs (_) / F9 = 8  =>  0 pairs (*)
H8,H9: 8.. / H8 = 8  =>  0 pairs (*) / H9 = 8  =>  0 pairs (X)
B5,D5: 8.. / B5 = 8  => 22 pairs (_) / D5 = 8  => 20 pairs (_)
B6,D6: 8.. / B6 = 8  => 20 pairs (_) / D6 = 8  => 22 pairs (_)
F8,H8: 8.. / F8 = 8  => 24 pairs (_) / H8 = 8  =>  0 pairs (*)
F9,H9: 8.. / F9 = 8  =>  0 pairs (*) / H9 = 8  =>  0 pairs (X)
A6,C6: 9.. / A6 = 9  => 22 pairs (_) / C6 = 9  => 22 pairs (_)
D4,F4: 9.. / D4 = 9  => 17 pairs (_) / F4 = 9  => 23 pairs (_)
A8,C8: 9.. / A8 = 9  => 22 pairs (_) / C8 = 9  => 22 pairs (_)
D7,F7: 9.. / D7 = 9  => 23 pairs (_) / F7 = 9  => 17 pairs (_)
A6,A8: 9.. / A6 = 9  => 22 pairs (_) / A8 = 9  => 22 pairs (_)
C6,C8: 9.. / C6 = 9  => 22 pairs (_) / C8 = 9  => 22 pairs (_)
D4,D7: 9.. / D4 = 9  => 17 pairs (_) / D7 = 9  => 23 pairs (_)
F4,F7: 9.. / F4 = 9  => 23 pairs (_) / F7 = 9  => 17 pairs (_)
* DURATION: 0:02:11.724745  START: 23:38:18.248230  END: 23:40:29.972975 2017-05-03
* CP COUNT: (52)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B7,B8,D3,D4,D5,D6,D7,E2,E4,F7,F8,F9,G5,H1,H2,H3,H7,I2,I5,I6,I9)
* .485913.6.9....8...6..8.5.94.1....58....7..9.....5..3.8...4.1.5...21.4.3.1436.9..
* PAIR A1: 2,7 BLK 1
A2: 2,7,1,3,5                            # reduction candidate for 2,7
A2: 2,7 => CTR
* .485913.6.95...81.163.825494.1.2..5835.87..91.8.15..348...4.1.5...21.4.3.1436.9..
A2: 1,3,5                                # 22 pairs
C2: 2,7,3,5                              # reduction candidate for 2,7
C2: 2,7 => CTR
* .485913.659.43681.16378254947162..583...7..9.....5..3.83..4.1.5...21.4.3.1436598.
C2: 3,5                                  # 23 pairs
A3: 2,7,1,3                              # reduction candidate for 2,7
A3: 2,7 => SOLVED
* 748591326195623847263487519421936758356874291987152634832749165679215483514368972
A3: 1,3                                  # 23 pairs
C3: 2,7,3                                # reduction candidate for 2,7
C3: 2,7                                  # 25 pairs
* PAIR A1: 2,7 COL A
A6: 2,7,6,9                              # reduction candidate for 2,7
A6: 2,7 => CTR
* 248591376.95...8.2.67482519421.3..58653874291.8915..34832.4.1659762154835143689..
A6: 6,9                                  # 23 pairs
A9: 2,7,5                                # reduction candidate for 2,7
A9: 2,7                                  # 24 pairs
* PAIR E2: 2,3 BLK 2
F2: 2,3,6,7                              # reduction candidate for 2,3
F2: 2,3 => SOLVED
* 748591326195623847263487519421936758356874291987152634832749165679215483514368972
F2: 6,7                                  # 24 pairs
F3: 2,3,7                                # reduction candidate for 2,3
F3: 2,3                                  # 24 pairs
* PAIR E2: 2,3 ROW 2
A2: 2,3,1,5,7                            # reduction candidate for 2,3
A2: 2,3 => CTR
* 748591326.95426817162783549421639758.5687429198715263483.947165.79215483514368972
A2: 1,5,7                                # 22 pairs
C2: 2,3,5,7                              # reduction candidate for 2,3
C2: 2,3 => CTR
* .485913.659.4.681716.78.5494.16.9.583...7..9.....5..3.83.9471.5...218473714365982
C2: 5,7                                  # 23 pairs
* PAIR D3: 4,7 BLK 2
D2: 4,7,6                                # reduction candidate for 4,7
D2: 4,7                                  # 23 pairs
D2: 6                                    # 17 pairs
* PAIR H1: 2,7 COL H
H9: 2,7,8                                # reduction candidate for 2,7
H9: 2,7 => SOLVED
* 748591326195623847263487519421936758356874291987152634832749165679215483514368972
H9: 8                                    # 24 pairs
* PAIR I2: 2,7 ROW 2
A2: 2,7,1,3,5                            # reduction candidate for 2,7
A2: 2,7 => CTR
* .485913.6.95...81.163.825494.1.2..5835.87..91.8.15..348...4.1.5...21.4.3.1436.9..
A2: 1,3,5                                # 22 pairs
C2: 2,7,3,5                              # reduction candidate for 2,7
C2: 2,7 => CTR
* .485913.659.43681.16378254947162..583...7..9.....5..3.83..4.1.5...21.4.3.1436598.
C2: 3,5                                  # 23 pairs
F2: 2,7,3,6                              # reduction candidate for 2,7
F2: 2,7                                  # 20 pairs
* PAIR D4: 6,9 BLK 5
F4: 6,9,2,3                              # reduction candidate for 6,9
F4: 6,9                                  # 25 pairs
F4: 2,3                                  # 24 pairs
* PAIR E4: 2,3 BLK 5
F4: 2,3,6,9                              # reduction candidate for 2,3
F4: 2,3                                  # 24 pairs
F5: 2,3,4,6                              # reduction candidate for 2,3
F5: 2,3                                  # 25 pairs
* PAIR E4: 2,3 ROW 4
B4: 2,3,7                                # reduction candidate for 2,3
B4: 2,3                                  # 28 pairs
B4: 7                                    # 27 pairs
* PAIR G5: 2,6 BLK 6
G4: 2,6,7                                # reduction candidate for 2,6
G4: 2,6                                  # 27 pairs
G6: 2,6,7                                # reduction candidate for 2,6
G6: 2,6                                  # 28 pairs
* PAIR G5: 2,6 ROW 5
A5: 2,6,3,5                              # reduction candidate for 2,6
A5: 2,6 => CTR
* .485913.6.95.2.8.7.62.8.5.9421.3.758653874291.87152634836.4.125.7.21.4.3.1436.9..
A5: 3,5                                  # 25 pairs
C5: 2,6,3,5                              # reduction candidate for 2,6
C5: 2,6                                  # 27 pairs
F5: 2,6,3,4                              # reduction candidate for 2,6
F5: 2,6                                  # 27 pairs
* PAIR B7: 2,3 BLK 7
C7: 2,3,6                                # reduction candidate for 2,3
C7: 6 => CTR
* .485913.6.9....8...6..8.5.94.1....58....7..9.....5..3.836.4.125...21.463214365987
C7: 2,3                                  # 26 pairs
* PAIR B7: 2,3 COL B
B4: 2,3,7                                # reduction candidate for 2,3
B4: 2,3                                  # 28 pairs
B5: 2,3,5,8                              # reduction candidate for 2,3
B5: 2,3                                  # 24 pairs
* PAIR B8: 5,7 BLK 7
A8: 5,7,6,9                              # reduction candidate for 5,7
A8: 5,7 => CTR
* .48591376.9....8.2.6..825.94.1.2..586...7.29.9...5..3.8.6.4.125..921846321436.987
A8: 6,9                                  # 23 pairs
C8: 5,7,6,9                              # reduction candidate for 5,7
C8: 5,7 => CTR
* .48591376.9....8.2.6..825.94.1.2..58....7..9...9.5..3.8.6.4.1259..21846321436.987
C8: 6,9                                  # 23 pairs
A9: 5,7,2                                # reduction candidate for 5,7
A9: 5,7                                  # 26 pairs
* PAIR H7: 2,6 ROW 7
C7: 2,6,3                                # reduction candidate for 2,6
C7: 3 => CTR
* 248591376.95...8.2.674825194.1.2..585...7..9.....5..3.823.4.165...21.4.3.1436.9..
C7: 2,6                                  # 23 pairs
* PAIR I9: 2,7 BLK 9
H9: 2,7,8                                # reduction candidate for 2,7
H9: 2,7 => SOLVED
* 748591326195623847263487519421936758356874291987152634832749165679215483514368972
H9: 8                                    # 24 pairs
* PAIR I9: 2,7 ROW 9
A9: 2,7,5                                # reduction candidate for 2,7
A9: 5 => SOLVED
* 748591326195623847263487519421936758356874291987152634832749165679215483514368972
A9: 2,7                                  # 24 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top95-041-base-pr-000.dot
* REASONING
* DIS # A2: 2,7 => CTR => A2: 1,3,5
* DIS # C2: 2,7 => CTR => C2: 3,5
* PRF # A3: 2,7 => SOL
* DIS # A6: 2,7 => CTR => A6: 6,9
* PRF # F2: 2,3 => SOL
* DIS # A2: 2,3 => CTR => A2: 1,5,7
* DIS # C2: 2,3 => CTR => C2: 5,7
* PRF # H9: 2,7 => SOL
* DIS # A2: 2,7 => CTR => A2: 1,3,5
* DIS # C2: 2,7 => CTR => C2: 3,5
* DIS # A5: 2,6 => CTR => A5: 3,5
* DIS # C7: 6 => CTR => C7: 2,3
* DIS # A8: 5,7 => CTR => A8: 6,9
* DIS # C8: 5,7 => CTR => C8: 6,9
* DIS # C7: 3 => CTR => C7: 2,6
* PRF # H9: 2,7 => SOL
* PRF # A9: 5 => SOL
* CNT  17 HDP CHAINS /  53 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B7,B8,D3,D4,D5,D6,D7,E2,E4,F7,F8,F9,G5,H1,H2,H3,H7,I2,I5,I6,I9)
* .485913.6.9....8...6..8.5.94.1....58....7..9.....5..3.8...4.1.5...21.4.3.1436.9..
* PAIR A1: 2,7 BLK 1
A2: 2,7,1,3,5                            # reduction candidate for 2,7
A2: 2,7 => CTR
* .485913.6.95...81.163.825494.1.2..5835.87..91.8.15..348...4.1.5...21.4.3.1436.9..
C2: 2,7,3,5                              # reduction candidate for 2,7
C2: 2,7 => CTR
* .485913.659.43681.16378254947162..583...7..9.....5..3.83..4.1.5...21.4.3.1436598.
A3: 2,7,1,3                              # reduction candidate for 2,7
A3: 2,7 => SOLVED
* 748591326195623847263487519421936758356874291987152634832749165679215483514368972
* DURATION: 0:00:05.797417  START: 23:41:44.442739  END: 23:41:50.240156 2017-05-03
* SOLUTION FOUND
* SAVE PR GRAPH xx-top95-041-base-pr-001.dot
* REASONING
* DIS # A2: 2,7 => CTR => A2: 1,3,5
* DIS A2: 1,3,5 # C2: 2,7 => CTR => C2: 3,5
* PRF A2: 1,3,5 + C2: 3,5 # A3: 2,7 => SOL
* STA A2: 1,3,5 + C2: 3,5 + A3: 2,7
* CNT   3 HDP CHAINS /   3 HYP OPENED

Header Info

Top 95 Sudokus 041
[sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt

Solution

position: 748591326195623847263487519421936758356874291987152634832749165679215483514368972 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 # A2: 2,7 => CTR => A2: 1,3,5
* INC # A2: 1,3,5 => UNS
* DIS # C2: 2,7 => CTR => C2: 3,5
* INC # C2: 3,5 => UNS
* PRF # A3: 2,7 => SOL
* INC # A3: 1,3 => UNS
* INC # C3: 2,7 => UNS
* DIS # A6: 2,7 => CTR => A6: 6,9
* INC # A6: 6,9 => UNS
* INC # A9: 2,7 => UNS
* PRF # F2: 2,3 => SOL
* INC # F2: 6,7 => UNS
* INC # F3: 2,3 => UNS
* DIS # A2: 2,3 => CTR => A2: 1,5,7
* INC # A2: 1,5,7 => UNS
* DIS # C2: 2,3 => CTR => C2: 5,7
* INC # C2: 5,7 => UNS
* INC # D2: 4,7 => UNS
* INC # D2: 6 => UNS
* PRF # H9: 2,7 => SOL
* INC # H9: 8 => UNS
* DIS # A2: 2,7 => CTR => A2: 1,3,5
* INC # A2: 1,3,5 => UNS
* DIS # C2: 2,7 => CTR => C2: 3,5
* INC # C2: 3,5 => UNS
* INC # F2: 2,7 => UNS
* INC # F4: 6,9 => UNS
* INC # F4: 2,3 => UNS
* INC # F4: 2,3 => UNS
* INC # F5: 2,3 => UNS
* INC # B4: 2,3 => UNS
* INC # B4: 7 => UNS
* INC # G4: 2,6 => UNS
* INC # G6: 2,6 => UNS
* DIS # A5: 2,6 => CTR => A5: 3,5
* INC # A5: 3,5 => UNS
* INC # C5: 2,6 => UNS
* INC # F5: 2,6 => UNS
* INC # C7: 2,3 => UNS
* DIS # C7: 6 => CTR => C7: 2,3
* INC # B4: 2,3 => UNS
* INC # B5: 2,3 => UNS
* DIS # A8: 5,7 => CTR => A8: 6,9
* INC # A8: 6,9 => UNS
* DIS # C8: 5,7 => CTR => C8: 6,9
* INC # C8: 6,9 => UNS
* INC # A9: 5,7 => UNS
* INC # C7: 2,6 => UNS
* DIS # C7: 3 => CTR => C7: 2,6
* PRF # H9: 2,7 => SOL
* INC # H9: 8 => UNS
* INC # A9: 2,7 => UNS
* PRF # A9: 5 => SOL
* CNT  53 HDP CHAINS /  53 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A2: 2,7 => CTR => A2: 1,3,5
* DIS A2: 1,3,5 # C2: 2,7 => CTR => C2: 3,5
* PRF A2: 1,3,5 + C2: 3,5 # A3: 2,7 => SOL
* STA A2: 1,3,5 + C2: 3,5 + A3: 2,7
* CNT   3 HDP CHAINS /   3 HYP OPENED