user16477: 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.

user14079: EDIT: This answer in incorrect, Noam solved the problem in the accepted answer.
I'm leaving it as an example of an unsuccessful attempt. My mistake was to try to keep the wK on the 6th rank, where it cannot make tempo moves, and push the bK with the knights. Noam proved that the reverse strategy is the correct one: knights guard the bK, the wK pushes it sideways, and thus the wK has tempo moves between the 7th and the 8th rank.

After the question has been edited, I will try and demonstrate how White fail to mate on e8 starting from the same random position I used before (conveniently, it is not too far from e8).
The main point is that if you use a knight to block one escape square along the edge (say, d8), then you are basically reduced to mate in the hence created 'artificial corner' (here, e8) using a king and two knights. And just as in the KNNK ending, due to impossibility to attack the last black square (f8) and the last light square (e8) with the same knight, White fails and stalemates.
[FEN "6kN/8/4NK2/8/6N1/8/8/8 w - - 0 1"]

1.Nf7 Kh7 2. Nfg5 Kh8 3.Kg6 Kg8 4.Ne5 Kh8 5.Nd8 Kg8 6.Ndc6 Kh8 7.Ngf7 Kg8 8.Kh6 Kf8 (8.Kf6 {the other plan: the king blocks in front and the two knights try to attack g8, then f8, then e8.} Kf8 9.Ng6 Kg8 10.Nge7 Kf8 11.Nfe5 Ke8 12.Ke6 Kf8 {and you cannot force the king to e8 and deliver mate.} 13.N7g6 Ke8 (13...Kg7 {escapes}) 14.Ng4 {and if it was White's turn the next move would be Nf6#, but this is stalemate.}) 9.Kh7 Ke8 10.Nd6 Kf8 11.Nf5 (11.Ng6 {mates on the wrong square}) Ke8 12.Nfd4 (12.Kg7 {stalemate}) Kf8 13.Ne6 Ke8 14.Nc7 {The knight can control either f8 or e8, but not both.} 

Of course, if the square you have picked is in a corner, White succeeds. I feel like he would fail on g8, but I leave it for someone else to check.


user8860: 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.

16477: <p>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 <code>e8</code>, if he so chooses?</p>

<p>There's an <a href="https://chess.stackexchange.com/a/15696/16477">answer to a related 3 Knights post</a></p>

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

<p><em>Edit after answer accepting</em><br>
The question is answered in the positive: Any edge square can be chosen to become the mate square.</p>
 14079: <p><strong>EDIT: This answer in incorrect, Noam solved the problem in the accepted answer.</strong></p>
<p>I'm leaving it as an example of an unsuccessful attempt. My mistake was to try to keep the wK on the 6th rank, where it cannot make tempo moves, and push the bK with the knights. Noam proved that the reverse strategy is the correct one: knights guard the bK, the wK pushes it sideways, and thus the wK has tempo moves between the 7th and the 8th rank.</p>
<hr />
<p>After the question has been edited, I will try and demonstrate how White fail to mate on e8 starting from the same random position I used before (conveniently, it is not too far from e8).</p>
<p>The main point is that if you use a knight to block one escape square along the edge (say, d8), then you are basically reduced to mate in the hence created 'artificial corner' (here, e8) using a king and two knights. And just as in the KNNK ending, due to impossibility to attack the last black square (f8) and the last light square (e8) with the same knight, White fails and stalemates.</p>
<pre><code>[FEN &quot;6kN/8/4NK2/8/6N1/8/8/8 w - - 0 1&quot;]

1.Nf7 Kh7 2. Nfg5 Kh8 3.Kg6 Kg8 4.Ne5 Kh8 5.Nd8 Kg8 6.Ndc6 Kh8 7.Ngf7 Kg8 8.Kh6 Kf8 (8.Kf6 {the other plan: the king blocks in front and the two knights try to attack g8, then f8, then e8.} Kf8 9.Ng6 Kg8 10.Nge7 Kf8 11.Nfe5 Ke8 12.Ke6 Kf8 {and you cannot force the king to e8 and deliver mate.} 13.N7g6 Ke8 (13...Kg7 {escapes}) 14.Ng4 {and if it was White's turn the next move would be Nf6#, but this is stalemate.}) 9.Kh7 Ke8 10.Nd6 Kf8 11.Nf5 (11.Ng6 {mates on the wrong square}) Ke8 12.Nfd4 (12.Kg7 {stalemate}) Kf8 13.Ne6 Ke8 14.Nc7 {The knight can control either f8 or e8, but not both.} 
</code></pre>
<p>Of course, if the square you have picked is in a corner, White succeeds. I feel like he would fail on g8, but I leave it for someone else to check.</p>
<hr />
 8860: <p>Here's how to forcibly checkmate the bare King on f8 or e8
(<em>added later</em>: 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:</p>

<pre><code>[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#)
</code></pre>

<p>and likewise:</p>

<pre><code>[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#)
</code></pre>

<p>To answer the question <strong>Glorfindel</strong> 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:</p>

<pre><code>[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)
</code></pre>

<p>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.</p>
