I dont have a definition for UR type 1,2,3,4. Is there a link for it or can you explain it please?
Sure I'll try
The unique rectangle itself is defined by four cells forming a rectangle that satisfy these criteria:
1: all four cells must have the same two candidates in them
2: two parallell sides of the rectangle must share a box and a line(row or column), the other two sides need only to share the same line.
3: One pair of cells that shares one line (or box and line) must contain ONLY the two candidates, the other pair of cells can contain other candidates. (these "other" candidates is what defines the type of rectangle...
In other words you can't have the two cells with "other" candidates across from each other!
So lets use this puzzle as an example:
- Code: Select all
. . . | . . . | 2 9 .
9 . . | . . 8 | 4 7 .
. . 7 | . . 9 | . 1 5
------+-------+------
. 4 2 | 9 . 6 | . . .
. . . | . 3 . | . . .
. . . | 7 . 4 | 8 5 .
------+-------+------
7 9 . | 1 . . | 5 . .
1 2 8 | 4 . . | . . .
. . 5 | . . . | . 8 .
In this one there is both a Type 1 and Type 2. Now let's start with the Type 1 (though the type 2 comes first)
look at this:
As you can see, the UR is marked with the red lines, and has the candidates 2 and 4. Now in a Type 1 there is only ONE of the cells that has any other candidates then 2 and 4, and here that is the one with 6 and 9 marked with green. The logic goes that if that cell is either 4 or 2, then the puzzle has multiple solutions, hence we can eliminate them (marked in red).
now lets look at a Type 2:
Again the UR is marked with red, and here it has the candidates 1 and 7.
Now the definition of a Type 2 is that there are one extra candidate in two cells, and that those candidates are the same. Here a 9, marked in green. Now the logic goes: We don't know which one of them is a 9, but one of them HAS to be a nine to avoid the "multiple solution" dilemma. This means that we can kill of any other nines in the same sectors (sectors marked in blue, other nines marked in red)
and a Type 4:
using the sudoku from a previous post:
- Code: Select all
8 . . | 2 . 5 | . . 1
. . . | 1 . 3 | . . .
. . 3 | . 7 . | 8 . .
------+-------+------
6 3 . | . . . | . 7 5
. . 8 | . . . | 2 . .
9 1 . | . . . | . 4 8
------+-------+------
. . 5 | . 9 . | 1 . .
. . . | 7 . 6 | . . .
3 . . | 5 . 2 | . . 9
A type 4 is very handy, because unlike type 1-3 it does not matter how many extra candidates you have in your two cells.
Again the UR is marked with red lines, and is here 4 and 9.
Now if you look in column 4 (marked with blue) there are no other possible place for the number 9 than in our UR (marked with green). Hence ONE of those cells HAS to be a 9. Now say you pick one of them and assign a 9 to it... Then if the OTHER cell becomes a 4, you have a multiple solution sudoku... Now apply the same logic to the other cell. As you can see, the number 4 (marked in red) can not be in either of those cells, and you can eliminate them both! Notice also how the "other" candidates (in this case 6 and 3,6) does not play a part at all!
I have not separated between A and B types, but A is basically when your two cells with other candidates in them shares both a line and a box, and B types is when they only share a line.
Hope that is clear!
now give me a sudoku that requires type 3!
(and can not be solved with 1,2 and 4 instead)
havard
edit: typos...
