Mauricio wrote:Perhaps a reverse bug argument can be used to prove that this pattern is invalid, but I am no expert on the reverse bug. Would an expert care to give his/her opinion?

As an "expert" I must say that I can't see any direct explanation to why the pattern is invalid using reverse Bug arguments. However, Your pattern gave me one new idea about unavoidable sets. This is my conjecture:

Any group of N digits restricted to N+1 columns of the same band will contain at least one unavoidable set.So far I've quite easily proved this for N=2,3,5,6. N=2 is always an unavoidable set of size 6:

- Code: Select all
`1 | . | 2`

2 | 1 | .

. | 2 | 1

N=3 always contains at least one unavoidable set of size 6:

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`1 | 2 | XX`

2 | 3 | XX

3 | 1 | XX

N=5 requires a longer explanation, but it can be shown that it will always contain at least one simple unavoidable set (with "a simple" set I mean a set that is either confined to two rows or a set that uses only two different digits = easy to recognize for the human eye).

N=6 can give these two patterns that don't contain any simple unavoidable sets:

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`1 4 . | 6 5 . | . 2 3`

2 5 . | 1 3 . | 6 4 .

3 6 . | 2 4 . | 1 . 5

1 4 . | 5 3 . | . 2 6

2 5 . | 1 6 . | 4 3 .

3 6 . | 2 4 . | 1 . 5

but both of them contain several more complex unavoidable sets.

N=4 and N=7 are physically impossible, so all that remains is to prove the case of N=8, which is exactly the case of your pattern above.

RW