However, there are certain patterns where some of the cells have more than 2 candidates, but which are just as deadly. These patterns exist when multiple bivalue patterns, which by themselves are deadly, are intertwined because they share a candidate.
Here is an example, which has 3 solutions:
- Code: Select all
.-------------.-------------.
| ab . . | ab . . |
| ab . . | abc ac . |
| . . . | . . . |
:-------------+-------------+
| . . . | ac ac . |
| . . . | . . . |
| . . . | . . . |
:-------------+-------------+
The r12c14 UR can be avoided by placing c in r2c4.
The r24c45 UR can be avoided by placing b in r2c4.
Avoiding one of the UR's would result in the other UR. This pattern should be avoided at all times.
In the following diagram, an extra candidate z is present in both of the intertwined UR's. One of them must be true, so we can eliminate z from all cells that can see both these cells.
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.-------------.-------------.
| abz . . | ab -z . |
| ab . . | abc ac . |
| . . . | . . . |
:-------------+-------------+
|-z . . | ac acz . |
| . . . | . . . |
| . . . | . . . |
:-------------+-------------+
Finally, a more complex example. Two intertwined UR's and a BUG-Lite intertwined with one of them.
- Code: Select all
.-------------.-------------.-------------.
| abz . . | ab . . | . . . |
| abz . . | abc ac . | . . . |
| . . . | . . . | . . . |
:-------------+-------------+-------------:
| . . . | ac acd . | cd . . |
| . . . | . . . | . . . |
| . . . | . . cd | cd . . |
:-------------+-------------+-------------:
|-z . . | . cdz cdz | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
'-------------'-------------'-------------'
I could not find any reference to these patterns in the existing BUG & BUG-Lite threads, but if they have been discussed before, a pointer would be appreciated.
I haven't found any real life examples, but they should not be hard to find.
Ruud
