Checkmating the bare king with 3 knights – can the mate be forced on any edge square? In the case where White has King and 3 Knights, and Black has just the bare King, it is known that White can force checkmate. But can White in fact pick any edge square in advance, and force the checkmate to occur with the black King on that square? For example, can White guarantee checkmating on e8, if he so chooses?

There's an answer to a related 3 Knights post


mentioning "side mate" as opposed to "corner mate", without going further into it.
In the given example the bare king is not obliged to go to the non-corner edge square where the mate occurs.


Edit after answer accepting
The question is answered in the positive: Any edge square can be chosen to become the mate square.
Here's how to forcibly checkmate the bare King on f8 or e8
(added later: or on g8 or h8) once it's been cornered on h8.
First put Kg6 and Nd7, so the other Knights can roam freely
as long as they don't accidentally checkmate or stalemate
the cornered King; then:

[Title "h8 to f8 (or g8 or h8)"]
[Fen "7k/3N4/2N3K1/4N3/8/8/8/8 w - - 0 0"]

1. Nf7+
(1. Kh6 Kg8 2. Ne7+ Kh8 3. Nf7#) Kg8
2. Nde5 (2. Ne7#) Kf8
3. Kh7 Ke8
4. Nd6+ Kf8
5. Nd7#
(5. Ng6#)


and likewise:

[Title "h8 to e8"]
[Fen "7k/3N4/2N3K1/4N3/8/8/8/8 w - - 0 0"]

1. Nf7+ Kg8
2. Nde5 Kf8
3. Nh6 Ke8
4. Nf5 Kf8
5. Nfe7 Ke8
6. Nd5 Kf8
7. Nce7 Ke8
8. Kg7 Kd8
9. Kg8 Ke8
10. Nc8 Kd8
11. Ncb6 Ke8
12. Kg7 Kd8
13. Nc6+ Ke8
14. Nc7# (14. Nf6#)


To answer the question Glorfindel asks in a comment:
White can start the same way, then set up the Knights on c5/d5/e5
to form a gauntlet and use the wK to push bK to the a8 corner:

[Title "h8 to a8"]
[Fen "7k/3N4/2N3K1/4N3/8/8/8/8 w - - 0 0"]

1. Nf7+ Kg8
2. Nde5 Kf8
3. Nh6 Ke8
4. Nf5 Kf8
5. Nfe7 Ke8
6. Nd5 Kf8
7. Kh7 Ke8
8. Nd4 Kd8
9. Ne6+ Ke8 (9... Kc8 10. Nc5)
10. Nc5 Kf8
11. Kh8 Ke8
12. Kg8 Kd8
13. Kf8 Kc8
14. Ke8 Kb8
15. Kd8 Ka7
16. Kc7 Ka8
17. Nb4 (17. Kb6 Kb8 18. Ne7)


and then use the previous analysis to force mate on any of a5/a6/a7/a8
(or b8/c8/d8), or push the King further to a1, etc.  So once the lone King
has been securely cornered it can be checkmated on any prescribed square
on the board's edge.