Hi Keith, I am Cartesian,
After reading your post
Unique Rectangles: The EssentialsI was even more confuse...
After reading this:
http://www.scanraid.com/AdvanStrategies.htm#URAnd This:
http://www.brainbashers.com/sudokuuniquerectangles.aspconfused again!
SummaryType 1One or More Extra Candidates in ONE Corner.
Possibility: You can remove the pair from THE cell containing the Extra CandidatesType 2ONE Extra Candidates on TWO Corners (Line OR Column) with a roof & Floor. (Either the Roof or Floor, MUST BE INCLUDED INSIDE the same Block)
Possibility: You can remove a Buddy of the Extra Candidate, from the Line, Column & BlockType 2BONE Extra Candidates on TWO Corners (Line OR Column) with a roof & Floor. (Either the Roof or Floor, MUST BE INCLUDED INSIDE TWO DIFFERENTS Blocks)
Possibility: You can remove a Buddy of the Extra Candidate, from the Line or Column => CANNOT reduce the BlocksType 3 (Type 2 with a Lock Set)Two or more Extra Candidates on TWO Corners (Line OR Column) with a roof & Floor.
You merge the Outside UR Candidates (from the Roof) & treat them as one square. (you can treat the roof squares as a single quantum-square containing all the possibilities that are not in the floor squares!) Source: Robert Woodhead
Possibility: You can do the reductions (if it form a Lock set), accordingly to the situationType 4 (Destructive)Two or more Extra Candidates on TWO Corners (Line OR Column) with a roof & Floor, floor cells must be contained in the same box.
Possibility: to remove ONE CANDIDATE of the original pair of possibilities from the roof squares.Type 4b (Destructive)Two or more Extra Candidates on TWO Corners (Line OR Column) with a roof & Floor, floor cells are
NOT contained in the same box.
Possibility: to remove ONE CANDIDATE of the original pair of possibilities from the roof squares.Type 5One Extra Candidates on TWO DIAGONAL corners
Note:
The difference between the Regular Type & the Variant is this:
In the "regular" UR, the cells with the extra values are in the same box. They have two sets of shared buddies: One is their line (row or column), and a second is their box.
In the "Type B" UR, the cells with the extra values are not in the same box. They have one set of shared buddies in their line.I am using this thread to gather my reflexions about UR (hopefully it will make sense at the end)