Problem with Unique Rectangle Type II

NewUrbanBlues

Here is a board after a few steps ...

+----------------+----------------+----------------+
| 2 56 69 | 7 59 3 | 4 8 1 |
| 1 8 7 | 29 4 259 | 359 6 39 |
| 59 3 4 | 1 6 8 | 259 2579 279 |
+----------------+----------------+----------------+
| 8 27 3 | 4 279 1 | 6 279 5 |
| 6 2457 29 | 8 23579 259 | 1 23479 23479|
| 59 2457 1 | 6 23579 259 | 8 23479 23479|
+----------------+----------------+----------------+
| 4 1 5 | 3 29 6 | 7 29 8 |
| 37 9 26 | 25 8 47 | 235 1 2346 |
| 37 26 8 | 259 1 47 | 2359 23459 23469 |
+----------------+----------------+----------------+

There looks to be a Unique Rect type II at R4C5, R4C8, R7C5 and R7C8

+----------------+----------------+----------------+
| 2 56 69 | 7 59 3 | 4 8 1 |
| 1 8 7 | 29 4 259 | 359 6 39 |
| 59 3 4 | 1 6 8 | 259 2579 279 |
+----------------+----------------+----------------+
| 8 27 3 | 4 *279 1 | 6 *279 5 |
| 6 2457 29 | 8 23579 259 | 1 23479 23479|
| 59 2457 1 | 6 23579 259 | 8 23479 23479|
+----------------+----------------+----------------+
| 4 1 5 | 3 *29 6 | 7 *29 8 |
| 37 9 26 | 25 8 47 | 235 1 2346 |
| 37 26 8 | 259 1 47 | 2359 23459 23469 |
+----------------+----------------+----------------+

If I understand UR Type II, the additional candidate is 7. It can be removed in the cell R4C2, leaving a cell with only the candidate 2.

Solving this board using brute-force algorythm shows that the cell R4C2 contains the value 7 !!! Oops ...

What is the rule here that must avoid removing the candidate 7 in the cell R4C2 ?

Thanks for your help

NewUrbanBlues · Posted: Wed Oct 10, 2007 9:07 pm Post subject: Problem with UR - Solved

Ok .. Classical error ... UR spans over 4 blocks ...

wapati · Posted: Thu Oct 11, 2007 11:18 am Post subject:

It is interesting that you were looking at the key cells for solving this puzzle.

The marked cells form an x-wing on nines and that knocks the puzzle down to simple stuff.

NewUrbanBlues · Posted: Thu Oct 11, 2007 6:50 pm Post subject:

Well, I'm not really looking ... this is the order I run the different techniques in my solver. And you'll see that the UR is checked before the XWings technique.

There it is:

Single in a Box, a Row or a Column
Hidden Single in a Box, a Row or a Column
Naked Single
Pointing Pair Reduction in a Row and in a Column
BoxLine Reduction in a Row and in a Column
Naked Pair in a Box, a Row or a Column
Hidden Pair in a Box, a Row or a Column
NakedTriple in a Box, a Row or a Column
Hidden Triple in a Box, a Row or a Column
Naked Quad in a Box, a Row or a Column
UniqueRectangleType 1 & 2
XWings
YWings
SingleColours
ForcedChains
BruteForceGuess

Thanks for your comment