These posts were prompted by two recent Human Solvables posted by HATMAN.
However I'll start with a simple example first, Afmob's
Assassin 122 Note the ring of cages around the outside edges of the cage pattern. Their cage total = 170. Each of the edges totals 45, however each of the corner cells count toward both a row and a column -> R19C19 must total 180 - 170 = 10. And since this is a Killer-X, each of the corner cells "sees" the other three corner cells so the four corner cells must have different values -> R19C19 = {1234}. And since R19C19 also "see" R5C5 then there's no 1,2,3,4 in R5C5.
I think there may be a similar posted puzzle for which the outside edges total 150 -> R19C19 must total 180 - 150 = 30 -> R19C19 = {6789}.
Edge totals of 151 and 169 also give immediate combinations for R19C19 of {5789} and {1235}. For other edge totals between 152 and 168 there will still be a disjoint cage R19C19.
Note that a continuous ring of cages around the outside edge, without the puzzle being a Killer-X, may also lead to immediate results in a few cases. When the edge total is 146 the corner cells will total 34 so R1C19 = {89} and R9C19 = {89}. Similarly when the edge total is 174 the corner cells will total 6 so R1C19 = {12} and R9C19 = {12}.
My
Outies posts in this Killer Techniques forum was an example of a technique which isn't programmed into SudokuSolver. The technique covered by the posts in this thread seems to be another one not programmed into SudokuSolver, and possibly other software solvers.