## Not seeing hidden unique rectangle

HowardBrazee
Rookie
Posts: 7
Joined: Wed Mar 07, 2007 8:36 pm

### Not seeing hidden unique rectangle

I used a web site to help solve a square that I was stuck with:
609240007
002076090
173090624
806430079
090000060
000069005
918000746
000687912
267914358

When it got to where I was stuck, it found:
HIDDEN UNIQUE RECTANGLE Type 2: removing 5 at E4 because of CE46 and one strong link between C6 and E6

Trouble is - I still don't see it.

Could someone explain this in more detail for me to understand it?

Thanks
enxio27
Master
Posts: 165
Joined: Sat Mar 17, 2007 1:20 am
Howard, almost no one visits these forums anymore. I suggest you repost your question at the forums that were set up to replace these:

http://www.rcbroughton.co.uk/sudoku/forum/index.php
zoltag
Expert
Posts: 126
Joined: Sat Apr 01, 2006 10:57 pm

### Re: Not seeing hidden unique rectangle

HowardBrazee wrote:I used a web site to help solve a square that I was stuck with:
609240007
002076090
173090624
806430079
090000060
000069005
918000746
000687912
267914358

When it got to where I was stuck, it found:
HIDDEN UNIQUE RECTANGLE Type 2: removing 5 at E4 because of CE46 and one strong link between C6 and E6

Trouble is - I still don't see it.

Could someone explain this in more detail for me to understand it?

Thanks
Sure, I can possibly explain but the suggestion wasn't great as that removal doesn't help much.

There are 2 valid hidden rectangles on 5 in this position. The one you ask about is this.

Code: Select all

.------------------.------------------.------------------.
| 6     58    9    | 2     4     13   | 158   38    7    |
| 45    458   2    | 13    7     6    | 58    9     13   |
| 1     7     3    |*58    9    *58   | 6     2     4    |
&#58;------------------+------------------+------------------&#58;
| 8     25    6    | 4     3     125  | 12    7     9    |
| 3457  9     145  |*178-5 25   *1258 | 1248  6     13   |
| 347   234   14   | 178   6     9    | 1248  38    5    |
&#58;------------------+------------------+------------------&#58;
| 9     1     8    | 35    25    235  | 7     4     6    |
| 345   345   45   | 6     8     7    | 9     1     2    |
| 2     6     7    | 9     1     4    | 3     5     8    |
'------------------'------------------'------------------'
There is a strong link on 8s in row 3 and in column 6.
If r5c4 is 5 then you get this deadly pattern:

Code: Select all

.------------------.------------------.------------------.
| 6     58    9    | 2     4     13   | 158   38    7    |
| 45    458   2    | 13    7     6    | 58    9     13   |
| 1     7     3    |*8    9     *5    | 6     2     4    |
&#58;------------------+------------------+------------------&#58;
| 8     25    6    | 4     3     125  | 12    7     9    |
| 3457  9     145  |*5     25   *8    | 1248  6     13   |
| 347   234   14   | 178   6     9    | 1248  38    5    |
&#58;------------------+------------------+------------------&#58;
| 9     1     8    | 35    25    235  | 7     4     6    |
| 345   345   45   | 6     8     7    | 9     1     2    |
| 2     6     7    | 9     1     4    | 3     5     8    |
'------------------'------------------'------------------'
Why is that bad? Well, if you could complete the puzzle you could then swap (in that pattern) the 5 for the 8 and the 8 for the 5 and still have a valid solution, that is there would be 2 valid solutions to this puzzle and that means the original was not a valid puzzle.

Here is the other hidden rectangle, this one on 25 rather than 58.

Code: Select all

.------------------.------------------.------------------.
| 6     58    9    | 2     4     13   | 158   38    7    |
| 45    458   2    | 13    7     6    | 58    9     13   |
| 1     7     3    | 58    9     58   | 6     2     4    |
&#58;------------------+------------------+------------------&#58;
| 8     25    6    | 4     3     125  | 12    7     9    |
| 3457  9     145  | 1578 *25   *128-5| 1248  6     13   |
| 347   234   14   | 178   6     9    | 1248  38    5    |
&#58;------------------+------------------+------------------&#58;
| 9     1     8    | 35   *25   *235  | 7     4     6    |
| 345   345   45   | 6     8     7    | 9     1     2    |
| 2     6     7    | 9     1     4    | 3     5     8    |
'------------------'------------------'------------------'

Code: Select all

To actually solve the puzzle I suggest these 2 steps rather than the hidden URs.

First an x-wing on 1s.
.------------------.------------------.------------------.
| 6     58    9    | 2     4    *13   |*158   38    7    |
| 45    458   2    | 13    7     6    | 58    9     13   |
| 1     7     3    | 58    9     58   | 6     2     4    |
&#58;------------------+------------------+------------------&#58;
| 8     25    6    | 4     3    *125  |*12    7     9    |
| 3457  9     145  | 1578  25    258-1| 248-1 6     13   |
| 347   234   14   | 178   6     9    | 248-1 38    5    |
&#58;------------------+------------------+------------------&#58;
| 9     1     8    | 35    25    235  | 7     4     6    |
| 345   345   45   | 6     8     7    | 9     1     2    |
| 2     6     7    | 9     1     4    | 3     5     8    |
'------------------'------------------'------------------'

Then an xyz-wing on 258.
.------------------.------------------.------------------.
| 6     58    9    | 2     4     13   | 158   38    7    |
| 45    458   2    | 13    7     6    | 58    9     13   |
| 1     7     3    | 58    9    *58   | 6     2     4    |
&#58;------------------+------------------+------------------&#58;
| 8     25    6    | 4     3     12-5 | 12    7     9    |
| 3457  9     145  | 1578 *25   *258  | 248   6     13   |
| 347   234   14   | 178   6     9    | 248   38    5    |
&#58;------------------+------------------+------------------&#58;
| 9     1     8    | 35    25    235  | 7     4     6    |
| 345   345   45   | 6     8     7    | 9     1     2    |
| 2     6     7    | 9     1     4    | 3     5     8    |
'------------------'------------------'------------------'
The rest is clean-up!