## UR Type3

Post the puzzle or solving technique that's causing you trouble and someone will help

### UR Type3

UR3.png (40.48 KiB) Viewed 239 times

300000007000980503050000026231400685796851234000623791004000179003710450000000360
Can someone spot the Type 3 Unique Rectangle elimination which Hodoku says there is here?
There are a few Locked Pairs in Boxes, but I can’t see the other stuff that goes with them.
Yogi
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Joined: 05 December 2015
Location: New Zealand

### Re: UR Type3

Sukaku Explainer wrote:Unique Rectangle type 3 (with Naked Pair)
The cells r1c7,r3c7,r3c3,r1c3 form a Unique Rectangle with the values 8 and 9. There are exactly two ways of placing the values 8 and 9 in the cells of the Unique Rectangle, forming two possible configurations. In both configurations, each row, column or block touched by the Unique Rectangle contains each of the two values 8 and 9 exactly once. As a result, if one of these two configurations were part of the solution, it could then be replaced by the other one to get a second valid solution.
Because a valid sudoku cannot have more than one solution, none of the two configurations of the Unique Rectangle can be valid. This implies that either r3c3 or r1c3 contains one of the values 2 or 7. It follows that either r3c3 or r1c3 forms a Naked Pair with r2c3 on the values 2 and 7 in the block.

That is Block 1 (Box 1) but the same naked pair is in column 3
So r9c3<>2<>7 so are r12c2<>2<>7

tarek

Posts: 3745
Joined: 05 January 2006

### Re: UR Type3

Here is a picture of what has already been described.

Code: Select all
`*-------------------------------------------------*| 3    1468-2  #89+2   | 125 46  2456  |#89 14 7  || 146  146-27  *27     | 9   8   2467  | 5  14 3  || 1489 5       #89+7   | 13  347 47    |#89 2  6  ||----------------------+---------------+----------|| 2    3        1      | 4   79  79    | 6  8  5  || 7    9        6      | 8   5   1     | 2  3  4  || 458  48       58     | 6   2   3     | 7  9  1  ||----------------------+---------------+----------|| 568  268      4      | 235 36  2568  | 1  7  9  || 689  268      3      | 7   1   2689  | 4  5  28 || 1589 1278     589-27 | 25  49  24589 | 3  6  28 |*-------------------------------------------------*`

The UR is in the cells marked #. To avoid exposing the UR either r1c3 is 2 or r3c3 is 7. Together with r2c3 this forms an effective naked pair (27) in r123c3 and you can make the eliminations as shown (same as Tarek).

The Hodoku site is also pretty good with describing moves. You can read their writeup about UR Type 3's here.

Leren

<Edit>

Sorry Yogi - I didn't realise you were already using Hodoku. I put the puzzle into it and got the exact same diagram. All you have to do is paste the puzzle into Hodoku, go to View solution path and don't forget to double click on the entry that says Uniqueness test 3. The diagram will then come up.

Leren
Leren

Posts: 3927
Joined: 03 June 2012

### Re: UR Type3

Hopefully this doesn't confuse: With r13c3 needing to have either 2 or 7 to avoid the deadly pattern … You can think of these 2 cells as 1 virtual cell with 27. Now this virtual cell combines with r2c3 to form a naked pair. All the 2,7 candidates that can see the naked pair (the virtual cell r13c3 and r2c3) can be therefore eliminated

tarek

Posts: 3745
Joined: 05 January 2006

### UR Type3

Ok, lets see if I can get a hold on this. Hodoku said to regard all the extra candidates in the 2 potential UR cells (r13c3) as a virtual single cell, which can then form a 2-cell locked set in 2,7 with r2c3. This would tie up 2&7 for Block1 and eliminate those candidates from any other cell which can see them both, either within Block1 or in Column3.
The rationale is that we know that to avoid the multiple solutions both 2 & 7 must lie within Column3 of Block1, not just 2 or 7 at r2c3.
This case is different from one of the examples in Hodoku, which still works but involves cells beyond the blocks the UR cells are in, in the subset.
Complicated, but understandable. BUT!! We still have a puzzle to solve . . .
Yogi
2017 Supporter

Posts: 178
Joined: 05 December 2015
Location: New Zealand

### Re: UR Type3

Hi Yogi,

It just happens that all these cells (the virtual cell r13c3 & r2c3) that form the naked pair are all in Block 1 (Therefore are a naked pair in the block) but also are in column 3 (and therefore are a naked pair in column 3).

You can think about it as 2 separate UR type 3 steps which you have combined into one.

tarek

tarek

Posts: 3745
Joined: 05 January 2006

### Re: UR Type3

Hi Yogi, if you follow the Hodoku link I gave you , the example on the right is similar to the one here, you get both block and row eliminations.

For comparison you read Andrew Stuart's take on the same move here.

Leren
Leren

Posts: 3927
Joined: 03 June 2012

### UR Type3

Thanx, guys. The next one proved to be much more simple to work through and understand. And it went straight on to be solved in singles:
082735100075062308036400275309820000624501083807040002790600000260000800540200007
Here, with the 1,5 Locked Pair noted in Block4, the action takes place in Column8. The extra candidates 469 in the UR cells can be tied up in r1246c8.
This eliminates them from Column8 in Block9 => 6c7r9 => 9r8c9 => (1=3)r8c34 => 5r8c8. Row8 is now virtually complete and stte.
Yogi
2017 Supporter

Posts: 178
Joined: 05 December 2015
Location: New Zealand