All Chains are not Equal

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All Chains are not Equal

Postby civiliza » Tue Jun 18, 2013 4:09 pm

I have been adding a new (to me) type of chain to my generator which doesn't seem to be recognised by Sudoku Explainer.

Anyway, SE uses a total of four chains to solve the following puzzle, but it was generated with a single chain:

Code: Select all
010002000
067000080
009603005
900080500
000100070
002004060
004009000
700050930
000000020


What is this mystery chain?
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Re: All Chains are not Equal

Postby ArkieTech » Tue Jun 18, 2013 5:13 pm

There are many chains but two ur's and a bug will solve it. :D
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Re: All Chains are not Equal

Postby daj95376 » Tue Jun 18, 2013 5:46 pm

Your post lacks much. Still, let's see where it goes.

Code: Select all
 +-----------------------+
 | . 1 . | . . 2 | . . . |
 | . 6 7 | . . . | . 8 . |
 | . . 9 | 6 . 3 | . . 5 |
 |-------+-------+-------|
 | 9 . . | . 8 . | 5 . . |
 | . . . | 1 . . | . 7 . |
 | . . 2 | . . 4 | . 6 . |
 |-------+-------+-------|
 | . . 4 | . . 9 | . . . |
 | 7 . . | . 5 . | 9 3 . |
 | . . . | . . . | . 2 . |
 +-----------------------+

   c4    Hidden Pair                     =  59   r26c4

   c5b2  Locked Candidate 1              <> 4    r9c5
 r2  b2  Locked Candidate 1              <> 5    r2c1
   c5b2  Locked Candidate 1              <> 7    r679c5

   c6b8  Naked  Pair                     <> 18   r79c5

 r5  b4  Locked Candidate 1              <> 8    r5c79

 r7  b9  Locked Candidate 2              <> 1    r9c79

   c28   X-Wing                          <> 4    r3c157,r4c9

 <17+4>  XY-Wing  r3c5/r1c5+r3c8         <> 4    r1c9

 r89c36  <18> UR Type 1.2224             <> 18   r9c3

 <45+3>  XYZ-Wing r1c1/r1c3+r5c1         <> 3    r2c1

 r1  b1  Hidden Pair                     =  35   r1c13

 r19c13  <35> UR Type 1.2224             <> 35   r9c1

 r7  b7  Locked Candidate 1              <> 3    r7c45

 +--------------------------------------------------------------+
 |  5     1     3     |  8     4     2     |  6     9     7     |
 |  24    6     7     |  9     1     5     |  234   8     234   |
 |  28    48    9     |  6     7     3     |  12    14    5     |
 |--------------------+--------------------+--------------------|
 |  9     34    6     |  23    8     7     |  5     14    123   |
 |  34    5     8     |  1     239   6     |  234   7     2349  |
 |  1     7     2     |  5     39    4     |  38    6     389   |
 |--------------------+--------------------+--------------------|
 |  368   38    4     |  27    26    9     |  178   5     18    |
 |  7     2     1     |  4     5     8     |  9     3     6     |
 |  68    9     5     |  37    36    1     |  478   2     48    |
 +--------------------------------------------------------------+
 # 40 eliminations remain

 4-SI S-Wing: (3)r5c1 = r4c2 - r4c4 = r9c4 - (3=6)r9c5 - r7c5 = (6)r7c1  =>  r7c1<>3

   c9    Naked  Pair                     <> 23   r56c9

         BUG+1                           =  8    r9c7

So, a simple chain is all that's needed besided non-chain solving techniques.
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