Analysis of zz-www.sudokuoftheday.co.uk-20060701-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006

position: 17.59.2.8...3..5..59...8.........8..8....6.75...4.....6..........9..572...2.6..84 initial

Autosolve

position: 17.5942.82..3..5.959.628..7....5.8..82.9.6.75..548.6..6......5...9..5726.52.6..84 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # H3: 3,4 => CTR => H3: 1
* DIS # E7: 1,7 => CTR => E7: 3,4
* DIS # F4: 1,7 => CTR => F4: 2,3
* DIS # F7: 1,7 => CTR => F7: 2,3,9
* PRF # F9: 1,7 => SOL
* DIS # C2: 4,6 => CTR => C2: 8
* DIS # B4: 1,4 => CTR => B4: 3,6
* PRF # C4: 1,4 => SOL
* DIS # G5: 1,4 => CTR => G5: 3
* PRF # G5: 3 => SOL
* DIS # C7: 1,4 => CTR => C7: 7,8
* DIS # B4: 1,3 => CTR => B4: 4,6
* DIS # F6: 1,3 => CTR => F6: 2,7
* DIS # H6: 1,3 => CTR => H6: 9
* PRF # I6: 1,3 => SOL
* DIS # B7: 1,3 => CTR => B7: 4,8
* DIS # F6: 1,3 => CTR => F6: 2,7
* DIS # G5: 4 => CTR => G5: 1,3
* DIS # E7: 1,3 => CTR => E7: 4,7
* DIS # B7: 3,4 => CTR => B7: 1,8
* DIS # B8: 3,4 => CTR => B8: 1,8
* DIS # E8: 1 => CTR => E8: 3,4
* DIS # A4: 3,4 => CTR => A4: 7,9
* PRF # F9: 3,7 => SOL
* DIS # A4: 3,7 => CTR => A4: 4,9
* DIS # D7: 1,8 => CTR => D7: 2,7
* DIS # B8: 3,4 => CTR => B8: 1,8
* DIS # D7: 1,7 => CTR => D7: 2,8
* DIS # E7: 1,7 => CTR => E7: 3,4
* DIS # F7: 1,7 => CTR => F7: 2,3,9
* PRF # F9: 1,7 => SOL
* DIS # D4: 2 => CTR => D4: 1,7
* DIS # B7: 1,3 => CTR => B7: 4,8
* DIS # E7: 1,3 => CTR => E7: 4,7
* PRF # I6: 1,3 => SOL
* CNT  35 HDP CHAINS /  79 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 # H3: 3,4 => CTR => H3: 1
* DIS H3: 1 # E7: 1,7 => CTR => E7: 3,4
* DIS H3: 1 + E7: 3,4 # C2: 4,6 => CTR => C2: 8
* DIS H3: 1 + E7: 3,4 + C2: 8 # B4: 1,4 => CTR => B4: 3,6
* PRF H3: 1 + E7: 3,4 + C2: 8 + B4: 3,6 # C4: 1,4 => SOL
* STA H3: 1 + E7: 3,4 + C2: 8 + B4: 3,6 + C4: 1,4
* CNT   5 HDP CHAINS /   7 HYP OPENED

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

Details

Positions

17.59.2.8...3..5..59...8.........8..8....6.75...4.....6..........9..572...2.6..84 initial
17.5942.82..3..5.959.628..7....5.8..82.9.6.75..548.6..6......5...9..5726.52.6..84 autosolve
176594238248371569593628417961753842824916375735482691687249153419835726352167984 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
C1: 3,6
C3: 3,4
E2: 1,7
F2: 1,7
H1: 3,6
H2: 4,6
C5: 1,4
B6: 1,3
E5: 1,3
A8: 3,4
A9: 3,7
D8: 1,8
D9: 1,7
I7: 1,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E2,F2: 1.. / E2 = 1  =>  0 pairs (X) / F2 = 1  => 12 pairs (_)
G3,H3: 1.. / G3 = 1  =>  0 pairs (X) / H3 = 1  => 16 pairs (_)
I4,I6: 2.. / I4 = 2  =>  0 pairs (*) / I6 = 2  =>  0 pairs (X)
D7,F7: 2.. / D7 = 2  => 14 pairs (_) / F7 = 2  =>  0 pairs (X)
F6,I6: 2.. / F6 = 2  =>  0 pairs (*) / I6 = 2  =>  0 pairs (X)
D4,D7: 2.. / D4 = 2  =>  0 pairs (X) / D7 = 2  => 14 pairs (_)
C1,C3: 3.. / C1 = 3  =>  0 pairs (X) / C3 = 3  => 15 pairs (_)
C1,H1: 3.. / C1 = 3  =>  0 pairs (X) / H1 = 3  => 15 pairs (_)
E5,G5: 3.. / E5 = 3  =>  0 pairs (X) / G5 = 3  =>  0 pairs (_)
H4,G5: 4.. / H4 = 4  => 13 pairs (_) / G5 = 4  =>  0 pairs (X)
E7,E8: 4.. / E7 = 4  => 13 pairs (_) / E8 = 4  =>  0 pairs (X)
C5,G5: 4.. / C5 = 4  => 13 pairs (_) / G5 = 4  =>  0 pairs (X)
A4,A8: 4.. / A4 = 4  =>  0 pairs (X) / A8 = 4  => 15 pairs (_)
G3,G5: 4.. / G3 = 4  => 13 pairs (_) / G5 = 4  =>  0 pairs (X)
H1,H2: 6.. / H1 = 6  =>  0 pairs (X) / H2 = 6  => 15 pairs (_)
B4,C4: 6.. / B4 = 6  => 15 pairs (_) / C4 = 6  =>  0 pairs (X)
C1,H1: 6.. / C1 = 6  => 15 pairs (_) / H1 = 6  =>  0 pairs (X)
B2,B4: 6.. / B2 = 6  =>  0 pairs (X) / B4 = 6  => 15 pairs (_)
E2,F2: 7.. / E2 = 7  => 12 pairs (_) / F2 = 7  =>  0 pairs (X)
C7,A9: 7.. / C7 = 7  =>  0 pairs (*) / A9 = 7  =>  0 pairs (X)
A6,F6: 7.. / A6 = 7  =>  0 pairs (*) / F6 = 7  =>  0 pairs (X)
C4,C7: 7.. / C4 = 7  =>  0 pairs (X) / C7 = 7  =>  0 pairs (_)
E2,E7: 7.. / E2 = 7  => 12 pairs (_) / E7 = 7  =>  0 pairs (X)
B2,C2: 8.. / B2 = 8  =>  0 pairs (X) / C2 = 8  => 15 pairs (_)
D7,D8: 8.. / D7 = 8  =>  0 pairs (X) / D8 = 8  => 13 pairs (_)
B8,D8: 8.. / B8 = 8  =>  0 pairs (X) / D8 = 8  => 13 pairs (_)
C2,C7: 8.. / C2 = 8  => 15 pairs (_) / C7 = 8  =>  0 pairs (X)
A4,A6: 9.. / A4 = 9  => 18 pairs (_) / A6 = 9  =>  0 pairs (X)
H4,H6: 9.. / H4 = 9  =>  0 pairs (X) / H6 = 9  => 18 pairs (_)
F7,F9: 9.. / F7 = 9  => 21 pairs (_) / F9 = 9  => 15 pairs (_)
G7,G9: 9.. / G7 = 9  => 15 pairs (_) / G9 = 9  => 21 pairs (_)
A4,H4: 9.. / A4 = 9  => 18 pairs (_) / H4 = 9  =>  0 pairs (X)
A6,H6: 9.. / A6 = 9  =>  0 pairs (X) / H6 = 9  => 18 pairs (_)
F7,G7: 9.. / F7 = 9  => 21 pairs (_) / G7 = 9  => 15 pairs (_)
F9,G9: 9.. / F9 = 9  => 15 pairs (_) / G9 = 9  => 21 pairs (_)
* DURATION: 0:00:40.907059  START: 00:14:26.479064  END: 00:15:07.386123 2019-05-01
* CP COUNT: (35)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,B6,C1,C3,C5,D8,D9,E2,E5,F2,H1,H2,I7)
* 17.5942.82..3..5.959.628..7....5.8..82.9.6.75..548.6..6......5...9..5726.52.6..84
* PAIR C3: 3,4 ROW 3
G3: 3,4,1                                # reduction candidate for 3,4
G3: 3,4                                  # 16 pairs
H3: 3,4,1                                # reduction candidate for 3,4
H3: 3,4 => CTR
* 17.5942.82..3175.959.6281.74672518..821936475.3548.6.26......5131984572675216..84
H3: 1                                    # 16 pairs
* PAIR E2: 1,7 COL E
E7: 1,7,3,4                              # reduction candidate for 1,7
E7: 1,7 => CTR
* 17.5942.82..3..5.959.628..74...5.89.8219364759354876126......5131984572675216..84
E7: 3,4                                  # 13 pairs
* PAIR F2: 1,7 COL F
F4: 1,7,2,3                              # reduction candidate for 1,7
F4: 1,7 => CTR
* 17.5942382.83715695936284179...578..82.9163757.54836926.7.429534.9.35726352769184
F4: 2,3                                  # 15 pairs
F6: 1,7,2,3                              # reduction candidate for 1,7
F6: 1,7                                  # 18 pairs
F7: 1,7,2,3,9                            # reduction candidate for 1,7
F7: 1,7 => CTR
* 17.5942.82..3..5.959.628..7....5.8..82.916375..548.6..6..2..953.19835726352.69.84
F7: 2,3,9                                # 14 pairs
F9: 1,7,3,9                              # reduction candidate for 1,7
F9: 1,7 => SOLVED
* 176594238248371569593628417961753842824916375735482691687249153419835726352167984
F9: 3,9                                  # 15 pairs
* PAIR H2: 4,6 ROW 2
B2: 4,6,8                                # reduction candidate for 4,6
B2: 4,6                                  # 15 pairs
C2: 4,6,8                                # reduction candidate for 4,6
C2: 4,6 => CTR
* 17.5942.828.3..5.959.628..7.6725.8..821936475.354876.26.874..5...98.572675216..84
C2: 8                                    # 15 pairs
* PAIR C5: 1,4 BLK 4
B4: 1,4,3,6                              # reduction candidate for 1,4
B4: 1,4 => CTR
* 17.5942.82683..549594628..7..6.5.8..821936475.3548.6..6.7....5.3.9..5726.52.6..84
B4: 3,6                                  # 15 pairs
C4: 1,4,6,7                              # reduction candidate for 1,4
C4: 1,4 => SOLVED
* 176594238248371569593628417961753842824916375735482691687249153419835726352167984
C4: 6,7                                  # 15 pairs
* PAIR C5: 1,4 ROW 5
G5: 1,4,3                                # reduction candidate for 1,4
G5: 1,4 => CTR
* 17.5942.82..3175.959.628..7..72518..82.936.75..548.6..6......5...9..572675216..84
G5: 3 => SOLVED
* 176594238248371569593628417961753842824916375735482691687249153419835726352167984
* PAIR C5: 1,4 COL C
C7: 1,4,7,8                              # reduction candidate for 1,4
C7: 1,4 => CTR
* 176594238248371569593628..7.672538.182.916375.154876926.174295...9..572675216..84
C7: 7,8                                  # 18 pairs
* PAIR B6: 1,3 BLK 4
B4: 1,3,4,6                              # reduction candidate for 1,3
B4: 1,3 => CTR
* 17.5942.82683..549594628..74.6.5.89.8219.6.75..548.6..6......5...9..5726.52.6..84
B4: 4,6                                  # 15 pairs
* PAIR B6: 1,3 ROW 6
F6: 1,3,2,7                              # reduction candidate for 1,3
F6: 1,3 => CTR
* 17.5942.82.83715.959.628..79...5.8..82.9.6.757154836926.7....5.489..5726352.6..84
F6: 2,7                                  # 15 pairs
H6: 1,3,9                                # reduction candidate for 1,3
H6: 1,3 => CTR
* 17.5942.82..3715.959.628..7....5.89.8219364759354876126......51319845726.52.6..84
H6: 9                                    # 18 pairs
I6: 1,3,2                                # reduction candidate for 1,3
I6: 1,3 => SOLVED
* 176594238248371569593628417961753842824916375735482691687249153419835726352167984
I6: 2                                    # 15 pairs
* PAIR B6: 1,3 COL B
B7: 1,3,4,8                              # reduction candidate for 1,3
B7: 1,3 => CTR
* 17.5942.82..3715.959.628.179...5384.82491637573548.69.61....953..9.35726352769184
B7: 4,8                                  # 15 pairs
B8: 1,3,4,8                              # reduction candidate for 1,3
B8: 1,3                                  # 16 pairs
* PAIR E5: 1,3 BLK 5
F4: 1,3,2,7                              # reduction candidate for 1,3
F4: 1,3                                  # 19 pairs
F6: 1,3,2,7                              # reduction candidate for 1,3
F6: 1,3 => CTR
* 17.5942.82.83715.959.628..79...5.8..82.9.6.757154836926.7....5.489..5726352.6..84
F6: 2,7                                  # 15 pairs
* PAIR E5: 1,3 ROW 5
G5: 1,3,4                                # reduction candidate for 1,3
G5: 4 => CTR
* 17.5942.82..3175.959.628..74672518..821936475.3548.6..6......5.3.9..572675216..84
G5: 1,3                                  # 13 pairs
* PAIR E5: 1,3 COL E
E7: 1,3,4,7                              # reduction candidate for 1,3
E7: 1,3 => CTR
* 17.5942.82..3715.959.628..74...5.89.8219364759354876126...1..53..9.45726.52.6..84
E7: 4,7                                  # 15 pairs
E8: 1,3,4                                # reduction candidate for 1,3
E8: 1,3                                  # 13 pairs
* PAIR A8: 3,4 BLK 7
B7: 3,4,1,8                              # reduction candidate for 3,4
B7: 3,4 => CTR
* 17.5942.82..3715.959.628..7.672538.182.916375.1548769263.....5...9..572675216..84
B7: 1,8                                  # 15 pairs
B8: 3,4,1,8                              # reduction candidate for 3,4
B8: 3,4 => CTR
* 17.5942.82..3715.959.628.17...15.8..821936475.3548.69161.....5...9815726.5276.184
B8: 1,8                                  # 16 pairs
* PAIR A8: 3,4 ROW 8
E8: 3,4,1                                # reduction candidate for 3,4
E8: 1 => CTR
* 17.5942.82..3715.959.628.17...15.8..821936475.3548.691617.4..5...9.15726.5276.184
E8: 3,4                                  # 16 pairs
* PAIR A8: 3,4 COL A
A4: 3,4,7,9                              # reduction candidate for 3,4
A4: 3,4 => CTR
* 17.5942.82..3715.959.628..7..725.89.82.9.64759.54876.26......5...9..572675216..84
A4: 7,9                                  # 19 pairs
* PAIR A9: 3,7 ROW 9
F9: 3,7,1,9                              # reduction candidate for 3,7
F9: 3,7 => SOLVED
* 176594238248371569593628417961753842824916375735482691687249153419835726352167984
F9: 1,9                                  # 15 pairs
* PAIR A9: 3,7 COL A
A4: 3,7,4,9                              # reduction candidate for 3,7
A4: 3,7 => CTR
* 17.5942.82..3715.959.628..7....5.89.8219364759354876126...4..51419..5726.52.6..84
A4: 4,9                                  # 15 pairs
A6: 3,7,9                                # reduction candidate for 3,7
A6: 3,7                                  # 18 pairs
* PAIR D8: 1,8 BLK 8
D7: 1,8,2,7                              # reduction candidate for 1,8
D7: 1,8 => CTR
* 17.5942.82..3715.959.628.17...25.8.182.916375.1548.6926....295...9..5726.52769184
D7: 2,7                                  # 14 pairs
* PAIR D8: 1,8 ROW 8
B8: 1,8,3,4                              # reduction candidate for 1,8
B8: 3,4 => CTR
* 17.5942.82..3715.959.628.17...15.8..821936475.3548.69161.....5...9815726.5276.184
B8: 1,8                                  # 16 pairs
* PAIR D9: 1,7 BLK 8
D7: 1,7,2,8                              # reduction candidate for 1,7
D7: 1,7 => CTR
* 17.5942.82..3715.959.628417..125.8..82.916375..548.6.26....2953.19835726352769184
D7: 2,8                                  # 15 pairs
E7: 1,7,3,4                              # reduction candidate for 1,7
E7: 1,7 => CTR
* 17.5942.82..3..5.959.628..74...5.89.8219364759354876126......5131984572675216..84
E7: 3,4                                  # 13 pairs
F7: 1,7,2,3,9                            # reduction candidate for 1,7
F7: 1,7 => CTR
* 17.5942.82..3..5.959.628..7....5.8..82.916375..548.6..6..2..953.19835726352.69.84
F7: 2,3,9                                # 14 pairs
F9: 1,7,3,9                              # reduction candidate for 1,7
F9: 1,7 => SOLVED
* 176594238248371569593628417961753842824916375735482691687249153419835726352167984
F9: 3,9                                  # 15 pairs
* PAIR D9: 1,7 COL D
D4: 1,7,2                                # reduction candidate for 1,7
D4: 2 => CTR
* 17.5942.82..3715.959.628417...25.841824916375..548.6.26....2953..9.35726352769184
D4: 1,7                                  # 14 pairs
* PAIR I7: 1,3 BLK 9
G7: 1,3,9                                # reduction candidate for 1,3
G7: 1,3                                  # 21 pairs
G9: 1,3,9                                # reduction candidate for 1,3
G9: 1,3                                  # 15 pairs
* PAIR I7: 1,3 ROW 7
B7: 1,3,4,8                              # reduction candidate for 1,3
B7: 1,3 => CTR
* 17.5942.82..3715.959.628.179...5384.82491637573548.69.61....953..9.35726352769184
B7: 4,8                                  # 15 pairs
E7: 1,3,4,7                              # reduction candidate for 1,3
E7: 1,3 => CTR
* 17.5942.82..3715.959.628..74...5.89.8219364759354876126...1..53..9.45726.52.6..84
E7: 4,7                                  # 15 pairs
F7: 1,3,2,7,9                            # reduction candidate for 1,3
F7: 1,3                                  # 22 pairs
* PAIR I7: 1,3 COL I
I4: 1,3,2                                # reduction candidate for 1,3
I4: 1,3                                  # 15 pairs
I6: 1,3,2                                # reduction candidate for 1,3
I6: 1,3 => SOLVED
* 176594238248371569593628417961753842824916375735482691687249153419835726352167984
I6: 2                                    # 15 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060701-absurd-base-pr-000.dot
* REASONING
* DIS # H3: 3,4 => CTR => H3: 1
* DIS # E7: 1,7 => CTR => E7: 3,4
* DIS # F4: 1,7 => CTR => F4: 2,3
* DIS # F7: 1,7 => CTR => F7: 2,3,9
* PRF # F9: 1,7 => SOL
* DIS # C2: 4,6 => CTR => C2: 8
* DIS # B4: 1,4 => CTR => B4: 3,6
* PRF # C4: 1,4 => SOL
* DIS # G5: 1,4 => CTR => G5: 3
* PRF # G5: 3 => SOL
* DIS # C7: 1,4 => CTR => C7: 7,8
* DIS # B4: 1,3 => CTR => B4: 4,6
* DIS # F6: 1,3 => CTR => F6: 2,7
* DIS # H6: 1,3 => CTR => H6: 9
* PRF # I6: 1,3 => SOL
* DIS # B7: 1,3 => CTR => B7: 4,8
* DIS # F6: 1,3 => CTR => F6: 2,7
* DIS # G5: 4 => CTR => G5: 1,3
* DIS # E7: 1,3 => CTR => E7: 4,7
* DIS # B7: 3,4 => CTR => B7: 1,8
* DIS # B8: 3,4 => CTR => B8: 1,8
* DIS # E8: 1 => CTR => E8: 3,4
* DIS # A4: 3,4 => CTR => A4: 7,9
* PRF # F9: 3,7 => SOL
* DIS # A4: 3,7 => CTR => A4: 4,9
* DIS # D7: 1,8 => CTR => D7: 2,7
* DIS # B8: 3,4 => CTR => B8: 1,8
* DIS # D7: 1,7 => CTR => D7: 2,8
* DIS # E7: 1,7 => CTR => E7: 3,4
* DIS # F7: 1,7 => CTR => F7: 2,3,9
* PRF # F9: 1,7 => SOL
* DIS # D4: 2 => CTR => D4: 1,7
* DIS # B7: 1,3 => CTR => B7: 4,8
* DIS # E7: 1,3 => CTR => E7: 4,7
* PRF # I6: 1,3 => SOL
* CNT  35 HDP CHAINS /  79 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,B6,C1,C3,C5,D8,D9,E2,E5,F2,H1,H2,I7)
* 17.5942.82..3..5.959.628..7....5.8..82.9.6.75..548.6..6......5...9..5726.52.6..84
* PAIR C3: 3,4 ROW 3
G3: 3,4,1                                # reduction candidate for 3,4
G3: 3,4                                  # 16 pairs
H3: 3,4,1                                # reduction candidate for 3,4
H3: 3,4 => CTR
* 17.5942.82..3175.959.6281.74672518..821936475.3548.6.26......5131984572675216..84
* RESTART
* PAIR RESTART
* PAIR E2: 1,7 COL E
E7: 1,7,3,4                              # reduction candidate for 1,7
E7: 1,7 => CTR
* 17.5942.82..3..5.959.628.174...5.89.82193647593548.6..6......5...9.45726.52.6..84
* PAIR RESTART
* PAIR H2: 4,6 ROW 2
B2: 4,6,8                                # reduction candidate for 4,6
B2: 4,6                                  # 16 pairs
C2: 4,6,8                                # reduction candidate for 4,6
C2: 4,6 => CTR
* 17.5942.828.3715.959.628.17.672538.18219.6.75..548.6..6.8....5...98.572675216..84
* RESTART
* PAIR RESTART
* PAIR C5: 1,4 BLK 4
B4: 1,4,3,6                              # reduction candidate for 1,4
B4: 1,4 => CTR
* 17.5942.8268371549594628317..6.5.8..821936475.3548.6916.7.4..533.9..5726.52.6..84
C4: 1,4,6,7                              # reduction candidate for 1,4
C4: 1,4 => SOLVED
* 176594238248371569593628417961753842824916375735482691687249153419835726352167984
* DURATION: 0:00:06.436911  START: 00:15:58.117396  END: 00:16:04.554307 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060701-absurd-base-pr-001.dot
* REASONING
* DIS # H3: 3,4 => CTR => H3: 1
* DIS H3: 1 # E7: 1,7 => CTR => E7: 3,4
* DIS H3: 1 + E7: 3,4 # C2: 4,6 => CTR => C2: 8
* DIS H3: 1 + E7: 3,4 + C2: 8 # B4: 1,4 => CTR => B4: 3,6
* PRF H3: 1 + E7: 3,4 + C2: 8 + B4: 3,6 # C4: 1,4 => SOL
* STA H3: 1 + E7: 3,4 + C2: 8 + B4: 3,6 + C4: 1,4
* CNT   5 HDP CHAINS /   7 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060701, absurd

Solution

position: 176594238248371569593628417961753842824916375735482691687249153419835726352167984 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 # G3: 3,4 => UNS
* DIS # H3: 3,4 => CTR => H3: 1
* INC # H3: 1 => UNS
* DIS # E7: 1,7 => CTR => E7: 3,4
* INC # E7: 3,4 => UNS
* DIS # F4: 1,7 => CTR => F4: 2,3
* INC # F4: 2,3 => UNS
* INC # F6: 1,7 => UNS
* DIS # F7: 1,7 => CTR => F7: 2,3,9
* INC # F7: 2,3,9 => UNS
* PRF # F9: 1,7 => SOL
* INC # F9: 3,9 => UNS
* INC # B2: 4,6 => UNS
* DIS # C2: 4,6 => CTR => C2: 8
* INC # C2: 8 => UNS
* DIS # B4: 1,4 => CTR => B4: 3,6
* INC # B4: 3,6 => UNS
* PRF # C4: 1,4 => SOL
* INC # C4: 6,7 => UNS
* DIS # G5: 1,4 => CTR => G5: 3
* PRF # G5: 3 => SOL
* DIS # C7: 1,4 => CTR => C7: 7,8
* INC # C7: 7,8 => UNS
* DIS # B4: 1,3 => CTR => B4: 4,6
* INC # B4: 4,6 => UNS
* DIS # F6: 1,3 => CTR => F6: 2,7
* INC # F6: 2,7 => UNS
* DIS # H6: 1,3 => CTR => H6: 9
* INC # H6: 9 => UNS
* PRF # I6: 1,3 => SOL
* INC # I6: 2 => UNS
* DIS # B7: 1,3 => CTR => B7: 4,8
* INC # B7: 4,8 => UNS
* INC # B8: 1,3 => UNS
* INC # F4: 1,3 => UNS
* DIS # F6: 1,3 => CTR => F6: 2,7
* INC # F6: 2,7 => UNS
* INC # G5: 1,3 => UNS
* DIS # G5: 4 => CTR => G5: 1,3
* DIS # E7: 1,3 => CTR => E7: 4,7
* INC # E7: 4,7 => UNS
* INC # E8: 1,3 => UNS
* DIS # B7: 3,4 => CTR => B7: 1,8
* INC # B7: 1,8 => UNS
* DIS # B8: 3,4 => CTR => B8: 1,8
* INC # B8: 1,8 => UNS
* INC # E8: 3,4 => UNS
* DIS # E8: 1 => CTR => E8: 3,4
* DIS # A4: 3,4 => CTR => A4: 7,9
* INC # A4: 7,9 => UNS
* PRF # F9: 3,7 => SOL
* INC # F9: 1,9 => UNS
* DIS # A4: 3,7 => CTR => A4: 4,9
* INC # A4: 4,9 => UNS
* INC # A6: 3,7 => UNS
* DIS # D7: 1,8 => CTR => D7: 2,7
* INC # D7: 2,7 => UNS
* INC # B8: 1,8 => UNS
* DIS # B8: 3,4 => CTR => B8: 1,8
* DIS # D7: 1,7 => CTR => D7: 2,8
* INC # D7: 2,8 => UNS
* DIS # E7: 1,7 => CTR => E7: 3,4
* INC # E7: 3,4 => UNS
* DIS # F7: 1,7 => CTR => F7: 2,3,9
* INC # F7: 2,3,9 => UNS
* PRF # F9: 1,7 => SOL
* INC # F9: 3,9 => UNS
* INC # D4: 1,7 => UNS
* DIS # D4: 2 => CTR => D4: 1,7
* INC # G7: 1,3 => UNS
* INC # G9: 1,3 => UNS
* DIS # B7: 1,3 => CTR => B7: 4,8
* INC # B7: 4,8 => UNS
* DIS # E7: 1,3 => CTR => E7: 4,7
* INC # E7: 4,7 => UNS
* INC # F7: 1,3 => UNS
* INC # I4: 1,3 => UNS
* PRF # I6: 1,3 => SOL
* INC # I6: 2 => UNS
* CNT  79 HDP CHAINS /  79 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G3: 3,4 => UNS
* DIS # H3: 3,4 => CTR => H3: 1
* DIS H3: 1 # E7: 1,7 => CTR => E7: 3,4
* INC H3: 1 + E7: 3,4 # B2: 4,6 => UNS
* DIS H3: 1 + E7: 3,4 # C2: 4,6 => CTR => C2: 8
* DIS H3: 1 + E7: 3,4 + C2: 8 # B4: 1,4 => CTR => B4: 3,6
* PRF H3: 1 + E7: 3,4 + C2: 8 + B4: 3,6 # C4: 1,4 => SOL
* STA H3: 1 + E7: 3,4 + C2: 8 + B4: 3,6 + C4: 1,4
* CNT   7 HDP CHAINS /   7 HYP OPENED