Difference Between Type 2 & Type 3 Unique Rectangle

Advanced methods and approaches for solving Sudoku puzzles

Difference Between Type 2 & Type 3 Unique Rectangle

Postby jeanboucher » Sun Aug 27, 2006 3:16 am

Can someone explain the difference between a Type 2 & Type 3 Unique Rectangle please!

Thanks
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Postby keith » Sun Aug 27, 2006 3:27 am

You can find an explanation of Unique Rectangles here:

http://forum.enjoysudoku.com/viewtopic.php?t=4204

Best wishes,

Keith
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Postby jeanboucher » Sun Aug 27, 2006 1:41 pm

Hi Keith, I am Cartesian,
After reading your post Unique Rectangles: The Essentials

I was even more confuse...

After reading this: http://www.scanraid.com/AdvanStrategies.htm#UR

And This: http://www.brainbashers.com/sudokuuniquerectangles.asp

confused again!


Summary

Type 1
One or More Extra Candidates in ONE Corner.
Possibility: You can remove the pair from THE cell containing the Extra Candidates

Type 2
ONE 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 & Block

Type 2B
ONE 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 Blocks


Type 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 situation

Type 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 5
One 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)
Last edited by jeanboucher on Mon Sep 04, 2006 10:21 pm, edited 12 times in total.
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Postby ravel » Sun Aug 27, 2006 2:32 pm

In a type 3 UR the extra candidates form a pair, triple or quad in a unit with candidates outside the UR. Then those numbers can be eliminated in the rest of this unit. To take Keith's sample:

Code: Select all
+-------------+
|  -   -   #  |
| 12   -  123 |
|  -   -   #  |
+-------------+
| 12   -  124 |
|  -   -   #  |
|  -   -  345 |
+-------------+
|  -   -   #  |
|  -   -  45  |
|  -   -   #  |
+-------------+

The extra candidates are 34, they form a triple with 345 and 45 in rows 6 and 8. (Since 3 or 4 have to go to one of the UR corners, they are bound to them like you would have 34 in a single cell.) Therefore you can eliminate 345 from the rest of the column (cells marked with #).
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Postby jeanboucher » Sun Aug 27, 2006 3:43 pm

Example:

Image

So, for a Type 3, you merge the Outside UR Candidates (from the Roof) & treat them as one (i.e. 269).

Then, do the reductions (if it form a naked pair or triple - in this case)?
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Postby ravel » Sun Aug 27, 2006 3:59 pm

Yep, nice sample and graphics:)
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Another Guide

Postby keith » Sun Aug 27, 2006 4:13 pm

If you look in this thread

http://forum.enjoysudoku.com/viewtopic.php?t=2000

you will find another guide to Unique Rectangles by "MadOverlord" (Robert Woodhead, author of Sudoku Susser).

Keith
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Postby jeanboucher » Sun Aug 27, 2006 7:57 pm

Thank you Keith,

This huge Thread seems promissing...
I have made some editing to the Original SUMMARY, to save space & for clarity...
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