My two trouble on Unique Rectangle or loop and BUG

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My two trouble on Unique Rectangle or loop and BUG

Postby Eioru » Sat Aug 19, 2006 8:17 am

I read that :
The theoretical maximum length of Unique loop is 16.
Unique Rectangle type has 1, 2, 3 and 4.
BUG type also has 1, 2, 3 and 4,
BUG type 3 nearly always occurs with a BUG type 4,
it is frequent enough to find Sudoku requiring both a BUG type 4 and a BUG type 1.

So I have these questions:
Why the maximum length of Unique loop can't over 16?
Are there puzzles have to require all of BUG types ( from 1 to 4 ) ?
Are there puzzles have to require all of Unique Rectangle types ( from 1 to 4 ) ?


I find one has Unique Rectangle types 1 and Unique Rectangle types 4
........4..716..2...12.9....8..1...26.....3.1...69..8.......9.545..268......3....
Eioru
 
Posts: 182
Joined: 16 August 2006

Postby Mike Barker » Sun Aug 27, 2006 2:05 am

Here's a puzzle with UR Types 1, 2, 3, and 4. Note I look for Type 3 before Type 4 and all may not be necessary, but I think the idea here is to have some fun and not be necessarily to be to strict. It also contains an 7-cell XY-chain.
Code: Select all
 7 . . | . . 6 | . . .
 . . . | 7 . . | 9 . .
 . . 6 | . 5 . | . . 7
 ------+-------+------
 . . 9 | . . 3 | . . 2
 . 1 4 | . . 9 | . . 3
 2 . . | . . . | . 1 .
 ------+-------+------
 4 . . | . 6 1 | . 2 .
 . . . | . 3 . | 5 . .
 . . 3 | 4 . 2 | . . .
Mike Barker
 
Posts: 458
Joined: 22 January 2006

Postby Eioru » Sun Aug 27, 2006 9:40 am

Mike Barker wrote:Here's a puzzle with UR Types 1, 2, 3, and 4. Note I look for Type 3 before Type 4 and all may not be necessary, but I think the idea here is to have some fun and not be necessarily to be to strict. It also contains an 7-cell XY-chain.
Code: Select all
 7 . . | . . 6 | . . .
 . . . | 7 . . | 9 . .
 . . 6 | . 5 . | . . 7
 ------+-------+------
 . . 9 | . . 3 | . . 2
 . 1 4 | . . 9 | . . 3
 2 . . | . . . | . 1 .
 ------+-------+------
 4 . . | . 6 1 | . 2 .
 . . . | . 3 . | 5 . .
 . . 3 | 4 . 2 | . . .


by SE
It has UR1,2,4 and a BUG1
Eioru
 
Posts: 182
Joined: 16 August 2006

Postby Mike Barker » Sun Aug 27, 2006 1:21 pm

Often times a Type 4 UR will distroy a Type 3 UR. Most solvers, including SE, put Type 4 before Type 3 so in this puzzle the Type 3 is distroyed by SE. It's still there, SE just didn't use it:
Code: Select all
+--------------+----------------+-------------------+
|   7   48 *15 |  1239  129   6 | -1248  #348  *145 |
|   3  248 *15 |     7   12  48 |     9  #468 *1456 |
|   9  248   6 |   123    5  48 | -1248  #348     7 |
+--------------+----------------+-------------------+
|  56    7   9 |    18  148   3 |   468  4568     2 |
|  56    1   4 |    28  278   9 |   678  5678     3 |
|   2    3   8 |     6   47   5 |    47     1     9 |
+--------------+----------------+-------------------+
|   4    9   7 |     5    6   1 |     3     2     8 |
|  18    6   2 |    89    3   7 |     5    49    14 |
|  18    5   3 |     4   89   2 |   167   679    16 |
+--------------+----------------+-------------------+
Mike Barker
 
Posts: 458
Joined: 22 January 2006


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