Analysis of zz-sudoku-de-777320-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 1.3.7.8.9............3..521...91...59..6.8..72...54...687..2............4.2.8.7.6 initial

Autosolve

position: 1.32758.952.8.1.73...3.6521...9132.59..628.172.1754.986871329543..467182412589736 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C2: 9 => CTR => C2: 4,6
* PRF # B4: 4,6 => SOL
* DIS # C2: 4,9 => CTR => C2: 6
* PRF # C2: 6 => SOL
* PRF # C3: 4,9 => SOL
* DIS # C2: 9 => CTR => C2: 4,6
* PRF # B5: 4,5 => SOL
* DIS # B5: 3 => CTR => B5: 4,5
* PRF # B4: 4,6 => SOL
* PRF # B5: 5 => SOL
* CNT  10 HDP CHAINS /  18 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 # C2: 9 => CTR => C2: 4,6
* PRF C2: 4,6 # B4: 4,6 => SOL
* STA C2: 4,6 + B4: 4,6
* CNT   2 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

1.3.7.8.9............3..521...91...59..6.8..72...54...687..2............4.2.8.7.6 initial
1.32758.952.8.1.73...3.6521...9132.59..628.172.1754.986871329543..467182412589736 autosolve
143275869526891473879346521768913245954628317231754698687132954395467182412589736 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
B1: 4,6
A3: 7,8
E2: 4,9
E3: 4,9
H1: 4,6
G2: 4,6
A4: 7,8
C5: 4,5
B6: 3,6
H4: 4,6
G5: 3,4
G6: 3,6
B8: 5,9
C8: 5,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B5,B6: 3.. / B5 = 3  =>  0 pairs (X) / B6 = 3  =>  0 pairs (_)
G5,G6: 3.. / G5 = 3  =>  0 pairs (*) / G6 = 3  =>  0 pairs (X)
B5,G5: 3.. / B5 = 3  =>  0 pairs (X) / G5 = 3  =>  0 pairs (_)
B6,G6: 3.. / B6 = 3  =>  0 pairs (*) / G6 = 3  =>  0 pairs (X)
E2,E3: 4.. / E2 = 4  =>  0 pairs (X) / E3 = 4  => 15 pairs (_)
H1,G2: 4.. / H1 = 4  =>  0 pairs (X) / G2 = 4  =>  0 pairs (_)
H4,G5: 4.. / H4 = 4  =>  0 pairs (*) / G5 = 4  =>  0 pairs (X)
B1,H1: 4.. / B1 = 4  =>  0 pairs (*) / H1 = 4  =>  0 pairs (X)
G2,G5: 4.. / G2 = 4  =>  0 pairs (*) / G5 = 4  =>  0 pairs (X)
H1,H4: 4.. / H1 = 4  =>  0 pairs (X) / H4 = 4  =>  0 pairs (_)
B5,C5: 5.. / B5 = 5  =>  0 pairs (*) / C5 = 5  =>  0 pairs (X)
B8,C8: 5.. / B8 = 5  => 10 pairs (_) / C8 = 5  =>  0 pairs (*)
B5,B8: 5.. / B5 = 5  =>  0 pairs (*) / B8 = 5  =>  0 pairs (X)
C5,C8: 5.. / C5 = 5  => 10 pairs (_) / C8 = 5  =>  0 pairs (*)
B1,C2: 6.. / B1 = 6  =>  0 pairs (X) / C2 = 6  =>  0 pairs (_)
H1,G2: 6.. / H1 = 6  =>  0 pairs (*) / G2 = 6  =>  0 pairs (X)
H4,G6: 6.. / H4 = 6  =>  0 pairs (X) / G6 = 6  =>  0 pairs (_)
B1,H1: 6.. / B1 = 6  =>  0 pairs (X) / H1 = 6  =>  0 pairs (_)
C2,G2: 6.. / C2 = 6  =>  0 pairs (*) / G2 = 6  =>  0 pairs (X)
B6,G6: 6.. / B6 = 6  =>  0 pairs (X) / G6 = 6  =>  0 pairs (_)
C2,C4: 6.. / C2 = 6  =>  0 pairs (*) / C4 = 6  =>  0 pairs (X)
G2,G6: 6.. / G2 = 6  =>  0 pairs (X) / G6 = 6  =>  0 pairs (_)
H1,H4: 6.. / H1 = 6  =>  0 pairs (*) / H4 = 6  =>  0 pairs (X)
A3,B3: 7.. / A3 = 7  => 14 pairs (_) / B3 = 7  =>  0 pairs (*)
A4,B4: 7.. / A4 = 7  =>  0 pairs (*) / B4 = 7  =>  0 pairs (X)
A3,A4: 7.. / A3 = 7  => 14 pairs (_) / A4 = 7  =>  0 pairs (*)
B3,B4: 7.. / B3 = 7  =>  0 pairs (*) / B4 = 7  =>  0 pairs (X)
A3,C3: 8.. / A3 = 8  =>  0 pairs (*) / C3 = 8  =>  0 pairs (X)
A4,C4: 8.. / A4 = 8  => 14 pairs (_) / C4 = 8  =>  0 pairs (*)
A3,A4: 8.. / A3 = 8  =>  0 pairs (*) / A4 = 8  =>  0 pairs (X)
C3,C4: 8.. / C3 = 8  => 14 pairs (_) / C4 = 8  =>  0 pairs (*)
E2,E3: 9.. / E2 = 9  => 15 pairs (_) / E3 = 9  =>  0 pairs (X)
B8,C8: 9.. / B8 = 9  =>  0 pairs (*) / C8 = 9  =>  0 pairs (X)
C2,E2: 9.. / C2 = 9  =>  0 pairs (X) / E2 = 9  => 15 pairs (_)
B3,B8: 9.. / B3 = 9  => 10 pairs (_) / B8 = 9  =>  0 pairs (*)
* DURATION: 0:00:57.584393  START: 08:46:46.094411  END: 08:47:43.678804 2017-05-01
* CP COUNT: (35)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B1,B6,B8,C5,C8,E2,E3,G2,G5,G6,H1,H4)
* 1.32758.952.8.1.73...3.6521...9132.59..628.172.1754.986871329543..467182412589736
* PAIR B1: 4,6 BLK 1
C2: 4,6,9                                # reduction candidate for 4,6
C2: 9 => CTR
* 163275849529841673...396521..69132.59..628.172.1754.986871329543..467182412589736
C2: 4,6                                  # 15 pairs
* PAIR B1: 4,6 COL B
B4: 4,6,7                                # reduction candidate for 4,6
B4: 4,6 => SOLVED
* 143275869526891473879346521768913245954628317231754698687132954395467182412589736
B4: 7                                    # 14 pairs
* PAIR E2: 4,9 ROW 2
C2: 4,9,6                                # reduction candidate for 4,9
C2: 4,9 => CTR
* 16327584952.8.1673...3.6521..69132.59..628.172.1754.986871329543..467182412589736
C2: 6 => SOLVED
* 143275869526891473879346521768913245954628317231754698687132954395467182412589736
* PAIR E3: 4,9 ROW 3
B3: 4,9,7                                # reduction candidate for 4,9
B3: 4,9                                  # 14 pairs
C3: 4,9,8                                # reduction candidate for 4,9
C3: 4,9 => SOLVED
* 143275869526891473879346521768913245954628317231754698687132954395467182412589736
C3: 8                                    # 14 pairs
* PAIR G2: 4,6 ROW 2
C2: 4,6,9                                # reduction candidate for 4,6
C2: 9 => CTR
* 163275849529841673...396521..69132.59..628.172.1754.986871329543..467182412589736
C2: 4,6                                  # 15 pairs
* PAIR C5: 4,5 BLK 4
B5: 4,5,3                                # reduction candidate for 4,5
B5: 4,5 => SOLVED
* 143275869526891473879346521768913245954628317231754698687132954395467182412589736
B5: 3 => CTR
* 1.32758.952.8.1.73...3.6521...9132.5935628417261754398687132954359467182412589736
* PAIR H4: 4,6 ROW 4
B4: 4,6,7                                # reduction candidate for 4,6
B4: 4,6 => SOLVED
* 143275869526891473879346521768913245954628317231754698687132954395467182412589736
B4: 7                                    # 14 pairs
C4: 4,6,8                                # reduction candidate for 4,6
C4: 4,6                                  # 14 pairs
* PAIR G5: 3,4 ROW 5
B5: 3,4,5                                # reduction candidate for 3,4
B5: 5 => SOLVED
* 143275869526891473879346521768913245954628317231754698687132954395467182412589736
B5: 3,4                                  # 10 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-sudoku-de-777320-base-pr-000.dot
* REASONING
* DIS # C2: 9 => CTR => C2: 4,6
* PRF # B4: 4,6 => SOL
* DIS # C2: 4,9 => CTR => C2: 6
* PRF # C2: 6 => SOL
* PRF # C3: 4,9 => SOL
* DIS # C2: 9 => CTR => C2: 4,6
* PRF # B5: 4,5 => SOL
* DIS # B5: 3 => CTR => B5: 4,5
* PRF # B4: 4,6 => SOL
* PRF # B5: 5 => SOL
* CNT  10 HDP CHAINS /  18 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B1,B6,B8,C5,C8,E2,E3,G2,G5,G6,H1,H4)
* 1.32758.952.8.1.73...3.6521...9132.59..628.172.1754.986871329543..467182412589736
* PAIR B1: 4,6 BLK 1
C2: 4,6,9                                # reduction candidate for 4,6
C2: 9 => CTR
* 163275849529841673...396521..69132.59..628.172.1754.986871329543..467182412589736
* PAIR B1: 4,6 COL B
B4: 4,6,7                                # reduction candidate for 4,6
B4: 4,6 => SOLVED
* 143275869526891473879346521768913245954628317231754698687132954395467182412589736
* DURATION: 0:00:03.793796  START: 08:48:03.510579  END: 08:48:07.304375 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-sudoku-de-777320-base-pr-001.dot
* REASONING
* DIS # C2: 9 => CTR => C2: 4,6
* PRF C2: 4,6 # B4: 4,6 => SOL
* STA C2: 4,6 + B4: 4,6
* CNT   2 HDP CHAINS /   3 HYP OPENED

Header Info

http://www.sudokus.de/777320.html
sehr schwierig

* STABLE PAIRS (10p + 71s = 81c) # zz-sudoku-de-777320-base.sdk
position: I25vdGU6IFBhaXIgUmVkdWN0aW9uIEFuYWx5c2lzICogU1RBQkxFIFBBSVJTICgxMHAgKyA3MXMgPSA4MWMpCgojZGlhZ29uYWxzOiAwCgojZGlzYWJsZWQ6IEIvNS81CjEuMzI3NTguOTUyLjg5MS43Mzc5ODM0NjUyMTg3LjkxMzIuNTkuNTYyOC4xNzIuMTc1NC45ODY4NzEzMjk1NDM1OTQ2NzE4MjQxMjU4OTczNg==

--------------------------------------------------
level: medium

* PAIR REDUCTION ..
* ROUND 1: 1.32758.952.8.1.73...3.6521...9132.59..628.172.1754.986871329543..467182412589736
B1: 4,6
C2: 4,6,9                                # reduction candidate for 4,6
C2: 9 => CTR
* 163275849529841673...396521..69132.59..628.172.1754.986871329543..467182412589736
B4: 4,6,7                                # reduction candidate for 4,6
B4: 4,6 => SOLVED
* 143275869526891473879346521768913245954628317231754698687132954395467182412589736
* SOLVED!
--------------------------------------------------

|:step:| 00
--------------------------------------------------

* DISABLE VALUE:: B5 != 3

|:step:| 01
--------------------------------------------------

Solution

position: 143275869526891473879346521768913245954628317231754698687132954395467182412589736 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 # C2: 4,6 => UNS
* DIS # C2: 9 => CTR => C2: 4,6
* PRF # B4: 4,6 => SOL
* INC # B4: 7 => UNS
* DIS # C2: 4,9 => CTR => C2: 6
* PRF # C2: 6 => SOL
* INC # B3: 4,9 => UNS
* PRF # C3: 4,9 => SOL
* INC # C3: 8 => UNS
* INC # C2: 4,6 => UNS
* DIS # C2: 9 => CTR => C2: 4,6
* PRF # B5: 4,5 => SOL
* DIS # B5: 3 => CTR => B5: 4,5
* PRF # B4: 4,6 => SOL
* INC # B4: 7 => UNS
* INC # C4: 4,6 => UNS
* INC # B5: 3,4 => UNS
* PRF # B5: 5 => SOL
* CNT  18 HDP CHAINS /  18 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C2: 4,6 => UNS
* DIS # C2: 9 => CTR => C2: 4,6
* PRF C2: 4,6 # B4: 4,6 => SOL
* STA C2: 4,6 + B4: 4,6
* CNT   3 HDP CHAINS /   3 HYP OPENED