koushanejad74 wrote : LO-ABC => B and F Can take 2,3

The way I see it, in the most general case, I can't see, a priori, why F can't be 1 or 4 in the LO case.

If BDEF is LO its possible range is 12345. If ABC is LO it's 123, so DE = 45, a naked pair, so F obviously can't be 4 and it can't be 1 (out of range of the naked pair), but I see these last 2 deductions as follow on moves, specific to this situation, rather than as part of the general move. Remember, at this stage we haven't considered the HI case so we don't know what DE can be in totality.

As it turns out DE are both 456 at the conclusion of the move. My solver then says that BDEF can't contain 1, since 1 of DE must be at least 5 (whether BDEF turns out to be LO or HI), and then B can't be 2 (blocked by singleton 3 in BDEF if its LO or out of range if its HI) but I see these as follow on standard Str8ts moves, rather than as part of the main move.

So I see the main move as follows :

1. Identify a compartment that is contained in a single box (it will be of size 1, 2 or 3 but at this stage I can't see 1 working but it might). We know that there will be a grey cell in its row or column.

2. Check that the compartment has no clues or solved cells ( at this stage I don't want to deal with degenerate cases - these will almost certainly be handled by standard Str8ts moves).

3. Identify a cross compartment with a common cell (its B in this case) and which also has a grey cell in its column or row and the size of both compartments is < 8 (I'll now include that in the logic as per your post - another clever observation).

4. Consider the common LO and HI cases for the compartments and identify a list of different digits that can be in the second compartment, not in the first compartment, but in the same box as the first compartment.

5. Hopefully this will lead to some eliminations in these common box cells. Any other eliminations in these compartments can hopefully be covered by other moves.

BTW I'm fine with us struggling to see our different POVs when a new move is being considered - that's how the creative process works, it's nearly always a bit messy at the start.

Leren