user5784: What is the longest way to checkmate with 1 queen against 4 queens, with no other pieces on the board?
Since there are 13 moves long games with a queen vs two queens, I conjecture this should be possible also for this certain endgame, but I am not sure. The maximum position I know has the disadvantage that the first move is a capture. It would be nice if the first move is not a capture.

user15296: The best I could come up with is 7 moves, I don't believe it could take much longer, because with 4 queens there's not as much freedom as with 2, I cannot put black king in the middle of the board when capturing black queens while keeping king in check:
3q4/q7/q7/q7/8/8/8/k1K4Q w - - 0 1

And I made it nice as you asked -- the first move it not a capture! =)

user3122: This max-DTZ position is mate in 8, but probably also a dead-end because it seems hard to improve starting here.
[FEN "7q/4q1q1/8/8/3q2Q1/1K6/8/1k6 w - - 0 1"]

1. Qf5+ Qde4 2. Qf1+ Qe1 3. Qd3+ Ka1 4. Qa6+ Qa5
5. Qxa5+ Qa3+ 6. Qxa3+ Kb1 7. Qa2+ Kc1 8. Qc2#


5784: <p>What is the longest way to checkmate with 1 queen against 4 queens, with no other pieces on the board?</p>

<p>Since there are 13 moves long games with a queen vs two queens, I conjecture this should be possible also for this certain endgame, but I am not sure. The maximum position I know has the disadvantage that the first move is a capture. It would be nice if the first move is not a capture.</p>
 15296: <p>The best I could come up with is 7 moves, I don't believe it could take much longer, because with 4 queens there's not as much freedom as with 2, I cannot put black king in the middle of the board when capturing black queens while keeping king in check:</p>

<pre><code>3q4/q7/q7/q7/8/8/8/k1K4Q w - - 0 1
</code></pre>

<p>And I made it nice as you asked -- the first move it not a capture! =)</p>
 3122: <p>This max-DTZ position is mate in 8, but probably also a dead-end because it seems hard to improve starting here.</p>

<pre><code>[FEN "7q/4q1q1/8/8/3q2Q1/1K6/8/1k6 w - - 0 1"]

1. Qf5+ Qde4 2. Qf1+ Qe1 3. Qd3+ Ka1 4. Qa6+ Qa5
5. Qxa5+ Qa3+ 6. Qxa3+ Kb1 7. Qa2+ Kc1 8. Qc2#
</code></pre>
