ronk wrote:Your BUG-Lite is indeed an outlier, but for a different reason I think. The correct MUG for it is ...

- Code: Select all
` . ab . | . bc . | . ac . . abcd . | . abcd . | . abcd .`

. ad . | . . . | . ad . ==> . abcd . | . abcd . | . abcd .

. bd . | . bc . | . cd . . abcd . | . abcd . | . abcd .

-----------|-----------|----------- ----------------|----------------|----------------

. . . | . . . | . . . . . . | . . . | . . .

BUG-Lite MUG

Note the MUG candidates in r2c5 where the BUG-Lite has none.

This confuses me as I don't understand how r2c5 becomes part of the pattern when the digits are pemutated.

Last week I thought your resultant pattern of quads wasn't a MUG, but today I investigated derivatives assuming that no pattern cell contains any other digit and consequently that no containing house could hold more than one external member digit:

- Code: Select all
` . abc . | . abd . | . acd . d abc . | . ab . | . ac . `

. abc . | . abd . | . acd . ==> . ab . | c abd . | . ad .

. abc . | . abd . | . acd . . ac . | . ad . | b acd .

-----------|-----------|------------- ---------|----------|-----------

. (d) . | . (c) . | . (b) . . . . | . . . | . . .

This derivative is definitely a MUG because (d)box1 (c)box2 and (b)box3 must all be true in external cells on different rows to leave a version of the MUG pattern I made a hash of last week.

- Code: Select all
` (d) abc . | . abc . | . abc . `

. abc . | (d) abc . | . abc .

. abc . | . abc . | . abcd .

-------------|--------------|-------------

. . . | . . . | . . .

This derivative leaves just r3c79 capable of holding a member digit. If it's (d) we get a 9-cell MUG and if it's anything else naked pairs force (d)r3c8 to leave an 8-cell MUG.

If these two examples essentially cover all the cases I was wrong before. If so, that's good news for your conjecture with respect to one band of boxes.

What I was saying before, that it should be impossible to reduce any member digit to a single cell, therefore doesn't feature as although this may make one cell solvable, what remains isn't.

ronk wrote:We should probably first look at all three-digit and four-digit patterns. Is there an exhaustive catalog of these in unavoidable-set ("UA") form somewhere? In any form?

Thatâ€™s sensible. The

<Sudopedia Entry> is the only catalogue of deadly patterns that I'm aware of.