Generalized hidden conjugates

Generalized hidden conjugates (+ Fireworks)

This is a generalization of hidden pairs, triples, and quads.

Basically, you look for $n$ cells where $n$ digits must appear. Any remaining digits can then be removed.

12345678. | 12345678. | ...45678.
12345678. | ........9 | ...45678.
...45678. | ...45678. | ...45678.

Here, the usual strategy applies. 1, 2, and 3 each must appear once in cells R1C1, R1C2, and R2C1. So 45678 can be removed.

       column 1:         column 9:
row 1: 123456789 | ... | 123456789
row 9: 123456789 | ... | 123456789

Given the nature of the hidden strats, they are not obvious with the usual pencilmarking.

Instead, given some selected cells, I will only leave candidates that must appear at least once in those cells:

       column 1:         column 9:
row 1: 12....... | ... | .23......
row 9: 1..4..... | ... | ..34.....

And now the elimination is obvious.

(So this is also a generalization of a strategy where you eliminate based on a strong-link-loop.)

When a candidate goes like this:

A n n | . . . | . . C
n
n
------
.
.
.
------
.
.
B

We know that the candidate must appear in {A, B, C} at least once.

This is a very convenient addition to this strategy. Observe that if 3 fireworks coincide, then A B C becomes a hidden triple.