Thanks manu and Afmob for interesting discussion about killer subsets.
There are two main ways to use killer subsets, the traditional way and the wider way used by
Afmob and some others.
The traditional way, the one that
udosuk refers to as naked killers, uses killer values in
two or more cages/cells in a row, column or nonet (also diagonal if the puzzle is a Killer-X) to eliminate those values from
all other cells in that row, ...
In addition to using the traditional way,
Afmob also uses another version where killer subsets in
one cage are used to eliminate combination(s) from
another cage in the same row, ... This use seems to me to be a form of hidden killer subset.
Both ways can be correctly described as killers although I stick to the traditional way, preferring to describe the other type as clashes with, or blocked by, without using the phrase "killer".
A186 provides examples of both ways and also prompted me to make this post.
First, here are some examples from
Afmob's walkthrough for A186.
The traditional type of killer is used in step 4d
d) ! Killer pair (49) locked in Outies R789 + R6C4 for R6
and the blocking type of killer in step 1c
c) Innies D/ = 13(3) <> 9 since {139} blocked by Killer pair (13) of 8(2) @ D/
Afmob suggested to me that step 8 of
my walkthrough for A186 used a killer triple.
8. 45 rule on N7 3 innies R7C23 + R8C3 = 15 = {249/258/348} (cannot be {159/357} which clash with 8(2) cage, cannot be {168/267} which clash with R78C1, cannot be {456} which clashes with R9C23), no 1,7
While this step can be seen as a blocking type of killer, I don't see it that way. To me it's a simple clash, the sort of thing that someone solving a newspaper killer sudoku would easily spot.
In this case R9C23 contains 123456. Any combination in a 3 cell cage in N7 that clashes with either
123456 or 123
456 is a simple clash.
At one stage, I was looking at a similar but slightly harder clash for 45 rule on N1, 3 innies R2C3 + R3C23 = 14 where I could eliminate {257} because it clashed with R1C23. In this case any combination in a 3 cell cage in N1 that clashes with either
12
35
67 or 1
23
56
7 can be eliminated. In each of these cases the clash is with alternating candidates in a cage. However by the time I was ready to use these innies in step 17, I was able to use a simpler clash with R23C1.
Both of the above are, in my opinion, much simpler when seen as clashes rather than as killer subsets.