I have long been interested in whether these 3 different elimination methods can be worked together in a single process, since they all depend on the same type of data, involving the interaction of boxes with one or two columns or rows that have conjugate pairs (just two possible instances of a given candidate) in separate boxes. Clearly they overlap anyway. Numerous times I have found that the same elimination I made with a Kite was found by a solver with an ER. In fact I notice that some solvers often find ERs but never mention Kites of Skyscrapers. Also, since they are relatively simple to work with, I think they are the logical first line of attack for Pen & Paper Solvers after the Basics.
In this puzzle the Kite Map shows:
There were no Skyscrapers, but the 8Kite r6c378 / r15c7 => r1c3<>8. This expands the list of 8 Conjugate Pairs to 8C137, 8R145
but there are no more Kites or Skyscrapers, so we can move on to try for Empty Rectangles. The ER Map is the same except that Box3 has no 9ER and 5s are now included.
However, none of the 5CPs combine with the ERs in Boxes 129 to eliminate anything, so it’s back to looking for eliminations in 8 or 9.
8ER in Box3 + c1 => r9c9<>8, which further expands the list of 8CPs to 8C1379, 8R1456.
Now we have 8ER in Box4 + c9 => r2c2<>8 => 8r1c1 stte.
It is true that the puzzle as shown can be solved more simply with the Contradiction Chain 8r4c2 => 8r2c2 Not Possible! So 8r6c3, but that was not the purpose of this exercise.
BTW, what’s the standard hieroglyph for ‘Not Possible,’?
Here’s another example: .47.8..61.6..........6..7..62..1357......5..6.1..6....28..4.....9.1...4.....2.69.
2-String Kite (5)r1c14 / r238 => r8c1<>5 OR Empty Rectangle (5)Box8(r8->c4) - r1c4=r1c1 Remove candidate 5 from r8c1