daj95376 wrote:It sure sounds to me like a Naked/Hidden Single qualifies as a Subset.
the
subset terminology
is based on cells which are a sub-set of some
"set" (unit, sector, house) --
- a "naked" subset of size j means that, within a specific unit,
we've identified j cells for which only j possible digits remain;
therefore, we must reserve these digits for these cells
-- exclude these digits elsewhere in this unit.
- a "hidden" subset of size j means that, for a specific unit,
we've identified j digits for which only j possible cells remain;
therefore, we must reserve these cells for these digits
-- exclude any other possibilities in these cells.
so -- yes,
daj95376, you are right, every
"single" does also qualify as a
subset of size 1this keeps the subset definitions beautifully simple
(i.e. a subset can be of any size, no need to require size > 1)
it has, however, only theoretical interest -- as you said, in practice we alwasys use a
"single" rather than a
subset of size 1 --
- a "naked" subset of size 1
would merely give us the exclusion of this digit in the other cells of that unit --
thus, for this one cell
we'd have to recognize 3 "naked" subsets of size 1 (one in each unit)
- a "hidden" subset of size 1
would merely give us the exclusion of all other digits in that cell --
we would then have to wait for the next "step"
to recognize this cell as 3 "naked" subsets of size 1 (one in each unit)---
-- we each discovered
"singles" long before learning about
subsets,
and whenever we notice a
"single", we do all this in just one "step" --
- "naked single" means that we've identified a cell in which only one possible digit can be placed.
(that's a property of the cell, never involving any unit whatsoever.)
this allows us to solve the cell (often called "making a placement", as we're placing this digit in this cell).
which is immediately followed by the Basic Exclusions --
excluding this digit in all the peer cells (yes, in 3 different units).
and all of this is considered part of one "step" in solving the puzzle.
- "hidden single" means that, within a specific unit, we've identified a digit for which only one possible cell is available.
this allows us to solve the cell (incidentally removing all other possibilities in this cell).
which is immediately followed by the Basic Exclusions --
excluding this digit in all the peer cells.
and all of this is considered part of one "step" in solving the puzzle.
thus,
daj95376, it seems we do agree about
"singles" -- but still differ about the larger subsets.
consider your earlier example -- "naked" duo
r3c13=35 --
as i said in my earlier post,
r3c13 is a "naked" duo in r3 and also (at the very same time) a "naked" duo in b1.
when counting "steps" of solving, these 2 duos obviously belong in the same "step";
but when counting the subsets i've used, i'd have to count them as 2 different duos.
this is my opportunity to thank
Jean-Christophe and
tarekfor the discussion in the
Superior Variants Topic (2008.Jul.31),
where i first bumped into this new type of "naked" beast
(and an extra thank-you to
tarek for bringing it to our attention in the present Topic!)
while Jean-Christophe calls this beast a "Generalized Naked Subset",
and while i agree that it is indeed stronger than the "naked" subset,
i still think it needs a better name
as it is not a sub-set of any "set" (unit, sector, house)
so
daj95376, getting back to those 2-"naked"-duos-in-the-same-cells,
obviously you
do have a valid reason to consider these 2 as
just one instance of some beast,
and this beast is the so-called "Generalized Naked Subset".
(which is -- let me repeat -- not a subset.
it provides the desired exclusions,
but the logic is not based on the theory of subsets.)
