Analysis of zz-www.sudokuwiki.org-0112-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=112

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=112

position: .5.........61.8....3.6.7..1.1....36.6.......9.48....2.7..9.1.8....2.54.........9. initial

Autosolve

position: .5.........61.8....3.6.7..1.1....36.6.......9.48....2.7..9.1.8....2.54.........9. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # E1: 3,4 => CTR => E1: 2,9
* DIS # F1: 3,4 => CTR => F1: 2,9
* DIS # I1: 3,4 => CTR => I1: 2,6,7,8
* DIS # D5: 3,4 => CTR => D5: 5,7,8
* DIS # D9: 3,4 => CTR => D9: 7,8
* DIS # I2: 4,5 => CTR => I2: 2,3,7
* DIS # E3: 2,9 => CTR => E3: 4,5
* DIS # H5: 4,5 => CTR => H5: 1,7
* DIS # C5: 2,7 => CTR => C5: 3,5
* PRF # E5: 2,7 => SOL
* PRF # B2: 2,7 => SOL
* DIS # B2: 9 => CTR => B2: 2,7
* DIS # I4: 5,7 => CTR => I4: 4,8
* DIS # G5: 5,7 => CTR => G5: 1,8
* DIS # H5: 5,7 => CTR => H5: 1,4
* DIS # D6: 5,7 => CTR => D6: 3
* DIS # B9: 2,6 => CTR => B9: 8
* CNT  17 HDP CHAINS /  41 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 # E1: 3,4 => CTR => E1: 2,9
* DIS E1: 2,9 # F1: 3,4 => CTR => F1: 2,9
* DIS E1: 2,9 + F1: 2,9 # E2: 5 => CTR => E2: 3,4
* DIS E1: 2,9 + F1: 2,9 + E2: 3,4 # D5: 3,4 => CTR => D5: 5,7
* DIS E1: 2,9 + F1: 2,9 + E2: 3,4 + D5: 5,7 # D9: 3,4 => CTR => D9: 7,8
* PRF E1: 2,9 + F1: 2,9 + E2: 3,4 + D5: 5,7 + D9: 7,8 => SOL
* STA E1: 2,9 + F1: 2,9 + E2: 3,4 + D5: 5,7 + D9: 7,8
* CNT   6 HDP CHAINS /   7 HYP OPENED

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

Details

Positions

.5.........61.8....3.6.7..1.1....36.6.......9.48....2.7..9.1.8....2.54.........9. initial
.5.........61.8....3.6.7..1.1....36.6.......9.48....2.7..9.1.8....2.54.........9. autosolve
157492638426138957839657241215879364673524819948316725762941583391285476584763192 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
D1: 3,4
H3: 4,5
B5: 2,7
I6: 5,7
B7: 2,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,C1: 1.. / A1 = 1  =>  8 pairs (_) / C1 = 1  =>  0 pairs (X)
E5,E6: 1.. / E5 = 1  =>  0 pairs (X) / E6 = 1  => 17 pairs (_)
H8,G9: 1.. / H8 = 1  =>  0 pairs (X) / G9 = 1  => 20 pairs (_)
E6,G6: 1.. / E6 = 1  => 17 pairs (_) / G6 = 1  =>  0 pairs (X)
H5,H8: 1.. / H5 = 1  => 20 pairs (_) / H8 = 1  =>  0 pairs (X)
C5,A6: 3.. / C5 = 3  =>  8 pairs (_) / A6 = 3  =>  0 pairs (X)
I4,H5: 4.. / I4 = 4  =>  7 pairs (_) / H5 = 4  =>  0 pairs (X)
C7,E7: 4.. / C7 = 4  =>  7 pairs (_) / E7 = 4  =>  7 pairs (_)
E2,E3: 5.. / E2 = 5  =>  6 pairs (_) / E3 = 5  =>  9 pairs (_)
G1,I1: 6.. / G1 = 6  =>  6 pairs (_) / I1 = 6  =>  0 pairs (X)
E6,F6: 6.. / E6 = 6  =>  0 pairs (X) / F6 = 6  =>  6 pairs (_)
F6,F9: 6.. / F6 = 6  =>  6 pairs (_) / F9 = 6  =>  0 pairs (X)
C1,B2: 7.. / C1 = 7  => 28 pairs (_) / B2 = 7  =>  0 pairs (X)
B2,B5: 7.. / B2 = 7  =>  0 pairs (X) / B5 = 7  => 28 pairs (_)
A1,A3: 8.. / A1 = 8  =>  0 pairs (X) / A3 = 8  =>  7 pairs (_)
I4,G5: 8.. / I4 = 8  =>  0 pairs (X) / G5 = 8  =>  6 pairs (_)
B8,B9: 8.. / B8 = 8  =>  0 pairs (X) / B9 = 8  =>  6 pairs (_)
A3,G3: 8.. / A3 = 8  =>  7 pairs (_) / G3 = 8  =>  0 pairs (X)
B8,E8: 8.. / B8 = 8  =>  0 pairs (X) / E8 = 8  =>  6 pairs (_)
I1,I4: 8.. / I1 = 8  =>  6 pairs (_) / I4 = 8  =>  0 pairs (X)
B2,B8: 9.. / B2 = 9  =>  0 pairs (X) / B8 = 9  =>  0 pairs (_)
* DURATION: 0:00:27.007991  START: 05:31:34.032934  END: 05:32:01.040925 2017-05-01
* CP COUNT: (21)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,B7,D1,H3,I6)
* .5.........61.8....3.6.7..1.1....36.6.......9.48....2.7..9.1.8....2.54.........9.
* PAIR D1: 3,4 BLK 2
E1: 3,4,2,9                              # reduction candidate for 3,4
E1: 3,4 => CTR
* .5.....7..761.8....3.6.7..1.1....36.62......9.48....2.76.9.1.8..9.2854.........9.
E1: 2,9                                  #  6 pairs
F1: 3,4,2,9                              # reduction candidate for 3,4
F1: 3,4 => CTR
* .5.....7..761.8....3.6.7..1.1....36.62......9.48....2.76.9.1.8..9.2854.........9.
F1: 2,9                                  #  6 pairs
E2: 3,4,2,5,9                            # reduction candidate for 3,4
E2: 3,4                                  # 15 pairs
* PAIR D1: 3,4 ROW 1
H1: 3,4,7                                # reduction candidate for 3,4
H1: 3,4                                  # 28 pairs
I1: 3,4,2,6,7,8                          # reduction candidate for 3,4
I1: 3,4 => CTR
* 851...67..761.8932.3.6.7851.1....36862...3.49348....2.76.9.1.8.98.2.541........9.
I1: 2,6,7,8                              #  5 pairs
* PAIR D1: 3,4 COL D
D5: 3,4,5,7,8                            # reduction candidate for 3,4
D5: 3,4 => CTR
* 157...638.96138.7.83.657941.1....36467.3148593485..1277.4961.839.32.541...1...79.
D5: 5,7,8                                #  5 pairs
D9: 3,4,7,8                              # reduction candidate for 3,4
D9: 3,4 => CTR
* 157....3..96138.7.83.657941.1....36467..14..9.48...12.7..9.1.8....2.541...1...79.
D9: 7,8                                  #  6 pairs
* PAIR H3: 4,5 BLK 3
H2: 4,5,3,7                              # reduction candidate for 4,5
H2: 4,5                                  # 13 pairs
I2: 4,5,2,3,7                            # reduction candidate for 4,5
I2: 4,5 => CTR
* 1574..63849613827583265794121.789364673...859.48...1277..9.1.83...275416..1...792
I2: 2,3,7                                #  8 pairs
* PAIR H3: 4,5 ROW 3
E3: 4,5,2,9                              # reduction candidate for 4,5
E3: 2,9 => CTR
* .5.....7..76158....3.6.7..1.1....36.62......9.48....2.76.9.1.8..9.2854.........9.
E3: 4,5                                  #  7 pairs
* PAIR H3: 4,5 COL H
H5: 4,5,1,7                              # reduction candidate for 4,5
H5: 4,5 => CTR
* 1574..638496138.7.83265794121.789364673...859.48...1277..9.1.83...275416..1...79.
H5: 1,7                                  # 11 pairs
* PAIR B5: 2,7 BLK 4
C4: 2,7,5,9                              # reduction candidate for 2,7
C4: 2,7                                  # 10 pairs
C5: 2,7,3,5                              # reduction candidate for 2,7
C5: 2,7 => CTR
* .57....3..96138.7..34657..1519...36.672.1...9348...12.7..9.1.8.9.32.541........9.
C5: 3,5                                  #  6 pairs
* PAIR B5: 2,7 ROW 5
E5: 2,7,1,3,4,8                          # reduction candidate for 2,7
E5: 2,7 => SOLVED
* 157492638426138957839657241215879364673524819948316725762941583391285476584763192
E5: 1,3,4,8                              #  5 pairs
* PAIR B5: 2,7 COL B
B2: 2,7,9                                # reduction candidate for 2,7
B2: 2,7 => SOLVED
* 157492638426138957839657241215879364673524819948316725762941583391285476584763192
B2: 9 => CTR
* 157.926.84961.8.7.8326.79.1215..9364673...8.9948....2.7..9.1.8.3.92.541.5.1....9.
* PAIR I6: 5,7 BLK 6
I4: 5,7,4,8                              # reduction candidate for 5,7
I4: 5,7 => CTR
* .5....678.76158.3483.6.7.51.1....36.62..13849348...12.76.9.1.8.98.2.541........9.
I4: 4,8                                  #  6 pairs
G5: 5,7,1,8                              # reduction candidate for 5,7
G5: 5,7 => CTR
* .5.....7..76158.3..3.6.7.51.1....36862.813.49348...12.76.9.1.8.98.2.541........9.
G5: 1,8                                  #  6 pairs
H5: 5,7,1,4                              # reduction candidate for 5,7
H5: 5,7 => CTR
* 157...638496138.7.83265794121578936467341.859.485..1277..9.1.8..8.275416..18..79.
H5: 1,4                                  #  6 pairs
G6: 5,7,1                                # reduction candidate for 5,7
G6: 5,7                                  # 17 pairs
* PAIR I6: 5,7 ROW 6
D6: 5,7,3                                # reduction candidate for 5,7
D6: 5,7 => CTR
* 1574..6384961382758326579412157..36467..1.859.485..1277.4961.83...275416561...792
D6: 3                                    # 10 pairs
* PAIR I6: 5,7 COL I
I2: 5,7,2,3,4                            # reduction candidate for 5,7
I2: 5,7                                  # 13 pairs
I9: 5,7,2,3,6                            # reduction candidate for 5,7
I9: 5,7                                  #  8 pairs
* PAIR B7: 2,6 BLK 7
B9: 2,6,8                                # reduction candidate for 2,6
B9: 2,6 => CTR
* 157.926.84961.8.7.8326.79.1215..9364673...8.9948....2.7..9.1.8.3892.541.5.1....9.
B9: 8                                    #  6 pairs
* PAIR B7: 2,6 ROW 7
G7: 2,6,5                                # reduction candidate for 2,6
G7: 2,6                                  #  8 pairs
I7: 2,6,3,5                              # reduction candidate for 2,6
I7: 2,6                                  #  9 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0112-base-pr-000.dot
* REASONING
* DIS # E1: 3,4 => CTR => E1: 2,9
* DIS # F1: 3,4 => CTR => F1: 2,9
* DIS # I1: 3,4 => CTR => I1: 2,6,7,8
* DIS # D5: 3,4 => CTR => D5: 5,7,8
* DIS # D9: 3,4 => CTR => D9: 7,8
* DIS # I2: 4,5 => CTR => I2: 2,3,7
* DIS # E3: 2,9 => CTR => E3: 4,5
* DIS # H5: 4,5 => CTR => H5: 1,7
* DIS # C5: 2,7 => CTR => C5: 3,5
* PRF # E5: 2,7 => SOL
* PRF # B2: 2,7 => SOL
* DIS # B2: 9 => CTR => B2: 2,7
* DIS # I4: 5,7 => CTR => I4: 4,8
* DIS # G5: 5,7 => CTR => G5: 1,8
* DIS # H5: 5,7 => CTR => H5: 1,4
* DIS # D6: 5,7 => CTR => D6: 3
* DIS # B9: 2,6 => CTR => B9: 8
* CNT  17 HDP CHAINS /  41 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,B7,D1,H3,I6)
* .5.........61.8....3.6.7..1.1....36.6.......9.48....2.7..9.1.8....2.54.........9.
* PAIR D1: 3,4 BLK 2
E1: 3,4,2,9                              # reduction candidate for 3,4
E1: 3,4 => CTR
* .5.....7..761.8....3.6.7..1.1....36.62......9.48....2.76.9.1.8..9.2854.........9.
F1: 3,4,2,9                              # reduction candidate for 3,4
F1: 3,4 => CTR
* .5.....7..761.8....3.6.7..1.1....36.62......9.48....2.76.9.1.8..9.2854.........9.
E2: 3,4,5                                # reduction candidate for 3,4
E2: 3,4                                  # 15 pairs
* RESTART
* PAIR D1: 3,4 BLK 2
E2: 3,4,5                                # reduction candidate for 3,4
E2: 5 => CTR
* .5.3......96158.3..3264795121....36.67..12.49.48...12.7.49.1.8....2.541.5.1....9.
* PAIR D1: 3,4 COL D
D5: 3,4,5,7                              # reduction candidate for 3,4
D5: 3,4 => CTR
* .5..296.8.961.8...83265794151...23646...1.8.9348.9612.7..9.1.8.9.32.541........9.
D9: 3,4,7,8                              # reduction candidate for 3,4
D9: 3,4 => CTR
* .5....678.761.89..8396572415178..3646237148599485..12776.9.158..9.2.54...8.....9.
D9: 7,8 => SOLVED
* 157492638426138957839657241215879364673524819948316725762941583391285476584763192
* DURATION: 0:00:06.994291  START: 05:32:29.207637  END: 05:32:36.201928 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0112-base-pr-001.dot
* REASONING
* DIS # E1: 3,4 => CTR => E1: 2,9
* DIS E1: 2,9 # F1: 3,4 => CTR => F1: 2,9
* DIS E1: 2,9 + F1: 2,9 # E2: 5 => CTR => E2: 3,4
* DIS E1: 2,9 + F1: 2,9 + E2: 3,4 # D5: 3,4 => CTR => D5: 5,7
* DIS E1: 2,9 + F1: 2,9 + E2: 3,4 + D5: 5,7 # D9: 3,4 => CTR => D9: 7,8
* PRF E1: 2,9 + F1: 2,9 + E2: 3,4 + D5: 5,7 + D9: 7,8 => SOL
* STA E1: 2,9 + F1: 2,9 + E2: 3,4 + D5: 5,7 + D9: 7,8
* CNT   6 HDP CHAINS /   7 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=112

Solution

position: 157492638426138957839657241215879364673524819948316725762941583391285476584763192 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 # E1: 3,4 => CTR => E1: 2,9
* INC # E1: 2,9 => UNS
* DIS # F1: 3,4 => CTR => F1: 2,9
* INC # F1: 2,9 => UNS
* INC # E2: 3,4 => UNS
* INC # H1: 3,4 => UNS
* DIS # I1: 3,4 => CTR => I1: 2,6,7,8
* INC # I1: 2,6,7,8 => UNS
* DIS # D5: 3,4 => CTR => D5: 5,7,8
* INC # D5: 5,7,8 => UNS
* DIS # D9: 3,4 => CTR => D9: 7,8
* INC # D9: 7,8 => UNS
* INC # H2: 4,5 => UNS
* DIS # I2: 4,5 => CTR => I2: 2,3,7
* INC # I2: 2,3,7 => UNS
* INC # E3: 4,5 => UNS
* DIS # E3: 2,9 => CTR => E3: 4,5
* DIS # H5: 4,5 => CTR => H5: 1,7
* INC # H5: 1,7 => UNS
* INC # C4: 2,7 => UNS
* DIS # C5: 2,7 => CTR => C5: 3,5
* INC # C5: 3,5 => UNS
* PRF # E5: 2,7 => SOL
* INC # E5: 1,3,4,8 => UNS
* PRF # B2: 2,7 => SOL
* DIS # B2: 9 => CTR => B2: 2,7
* DIS # I4: 5,7 => CTR => I4: 4,8
* INC # I4: 4,8 => UNS
* DIS # G5: 5,7 => CTR => G5: 1,8
* INC # G5: 1,8 => UNS
* DIS # H5: 5,7 => CTR => H5: 1,4
* INC # H5: 1,4 => UNS
* INC # G6: 5,7 => UNS
* DIS # D6: 5,7 => CTR => D6: 3
* INC # D6: 3 => UNS
* INC # I2: 5,7 => UNS
* INC # I9: 5,7 => UNS
* DIS # B9: 2,6 => CTR => B9: 8
* INC # B9: 8 => UNS
* INC # G7: 2,6 => UNS
* INC # I7: 2,6 => UNS
* CNT  41 HDP CHAINS /  41 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # E1: 3,4 => CTR => E1: 2,9
* DIS E1: 2,9 # F1: 3,4 => CTR => F1: 2,9
* INC E1: 2,9 + F1: 2,9 # E2: 3,4 => UNS
* INC E1: 2,9 + F1: 2,9 # E2: 3,4 => UNS
* DIS E1: 2,9 + F1: 2,9 # E2: 5 => CTR => E2: 3,4
* DIS E1: 2,9 + F1: 2,9 + E2: 3,4 # D5: 3,4 => CTR => D5: 5,7
* DIS E1: 2,9 + F1: 2,9 + E2: 3,4 + D5: 5,7 # D9: 3,4 => CTR => D9: 7,8
* PRF E1: 2,9 + F1: 2,9 + E2: 3,4 + D5: 5,7 + D9: 7,8 => SOL
* STA E1: 2,9 + F1: 2,9 + E2: 3,4 + D5: 5,7 + D9: 7,8
* CNT   8 HDP CHAINS /   7 HYP OPENED