dailysudoku.com

[keith]

[arkietech]

[keith]

[arkietech]

[Clement]

Also Type 4 UR 38; r46c4<>3 and
a kite on 9 originating from BOX 9; r5c5<>9 which opens a skyscraper originating from r5c59; r7c8<>4.

[Luke451]

Just in the pursuit of MUG fun, here's a bigun.

[tlanglet]

[Marty R.]

If there's a longer way, I can usually find it.

Type 4 UR (38); r46c4<>3
Skyscraper, c57; r8c4, r9c8<>9
Finned X-Wing, c49; r5c5<>4

[ronk]

[Luke451]

[aran]

Luke, always nice to have something like that to look at and think about.
From replies, I cannot tell whether it is accepted and proven that this is a MUG.
If so, then I'll have to go back to the drawing board, and think a little better, because I don't see it as such.
Firstly I've converted from the digits in the specific case to abcde, so the starting position is

[ronk]

[Luke451]

aran, are you trying to say I'm wrongly convinced??

Very interesting breakdown of that particular pattern. I got out a pencil and paper and broke it down with consideration of the potential UR. My results were exactly the same as yours.

1 and 4 were mirrors, as were 2 and 3, and the latter is different from the former. I still trying to wrap my head around how it's a legal pattern when either way results in two solutions.

The 4 candidate single band pattern seems to be proven and accepted as a MUG:

[aran]

Luke
We're agreed about the results. All that remains is the interpretation.
As I see it :
in a UP setting (MUG BUG UR), ignoring the UP breaking candidate(s) which must exist, there can be no latitude, everything is forced, and the UP candidates are hermetically sealed inside the UP.
Here I don't...yet...see that this is the case because AUR(cd) does not force r1c4, it forces something over r12c4 but there is enough latitude there for non-UP.
At the moment there are four viable solutions.
1 is viable, so is 3 and they are different.
The fact that 1 is viable, and so is 4, and that they are the same...is unfortunate...but I think (for the time being...) irrelevant !

A tricky area though.

[Luke451]

aran, I think I heard what I wanted to hear from the replies to my question at Players'.

When ronk said "gsf's program shows that placements for this pattern produce only two essentially-different unavoidable sets corresponding to BUG-Lites," perhaps the program just found the two different sets that you did. Just guessing here.

I took that to mean that the pattern reduced to BUG-Lites and was therefore deadly, but that's not what was said.

Also, though I'm not up on "Reverse Bug-Lites," now I'm wondering if that stategy produces any different results for this pattern. RW seemed to imply that was the case in his quote above.

[ronk]

[Luke451]

Gentlemen, thank you for taking the time to parse out this pattern.

Here's what one of my so-called "empirical approaches" looks like.
It's enough to make one's eyes glaze over...

[ronk]

[aran]

Luke
Just back from that parallel MUG-free universe.
Yes that MUG of yours was a very nice find

Having had to think about it, here are some thoughts (already expressed by many others, notably RW, all I'm merely doing is re-discovering for myself and saying things in my own way) :
- let there be a locked set of N candidates in N cells in a row
- in another row on the same floor, let there be the same N candidates locked in the same N relative cells.
For shorthand call that configuration the N-pattern.
Then N-pattern is MUG/impossible.
Whether N be 2 or 9, N-pattern => MUG/impossible
Simple explanation :
let S be any solution to those 2N cells
then W is also a solution, where W= xx the relative partners (xx having no external effect on columns, rows, boxes).

Concerning cases beyond N=4.
N=9 : => absence of givens in such a configuration is impossible =>in a sudoku with a unique solution, there cannot be two rows in same floor without any givens.
N=8 : impossible =>implies same remaining candidate occurs in both relative cells
N=7,6,5 : there must be a reverse MUG/impossible pattern in the "other" cells.
This means that one can look for this reverse pattern as an alternative to examination of the other.
In particular it means that this reverse pattern can include givens as well as assigned. This notion always comes as a surprise because of the tendency to think of givens as barriers to uniqueness (eg UR).
I think this could be formulated as :
if all the givens and assigned would generate an N-pattern, then those givens and assigneds cannot exist.

To take an example for N=5 ie your example

[Luke451]

I looked into the Reverse BUG-Lite perspective. This may be the way to go when the MUG gets big