user3664: A friend and I yesterday asked ourselves what the highest number of possible mates in a (legal) position is. We were able to come up with the following position which has a total of 76 unique mates in 1, but we then failed to improve upon this one.
Q3Q3/4K2Q/6R1/3R4/QB2k3/5R1N/2R5/QQ1Q1N1B w - - 0 1

Do you know if this problem ever has been solved and what the highest possible number is? It was hard for us to come up with a reasonably low upper bound so that I have no idea whether this solution is close to the maximum.

user18786: The following version has 99 threats none of which is a discovered check. It is possibly the best under that additional requirement.
I made it as an answer to the same question asked on Puzzling SE.


user10380: Anthony Stewart Mackay Dickens found another solution, also with 105 mating moves, but with only 17 units in the diagram (16 white and the black king):
[title "Anthony Stewart Mackay Dickens, The Problemist, Jan 1970. 105 mates"]
[fen "2Q1Q3/2Q4Q/Q4Q2/3k4/Q5Q1/1R6/B1NBQ3/K2R1N2 w - - 0 1"]

This may be found here on PDB.
Black's last move must have been ...Kc5-d5 following Qxc7+.

user2299: [FEN "1B1Q1Q2/2R5/pQ4QN/RB2k3/1Q5Q/N4Q2/K2Q4/6Q1 w - - 0 1 "]

105 mates — Nenad Petrovic, Sahovski Vjesnika 1947 (Chess Problem Database)
In this position any check is mate. There are 3 knight mates (c4, g4, f7), 23 discovered mates (14 moves for the rook on c7, 9 for the bishop on b5), and 79 queen mates: 1 on a1, 2 on b2, 3 on c3, 4 on c5, 6 on d4, 3 on d5, 6 on d6, 3 on e1, 2 on e2, 4 on e3, 4 on e4, 2 on e6, 4 on e7, 3 on e8, 5 on f4, 3  on f5, 6 on f6, 4 on g3, 5 on g5, 2 on g7, 3 on h2, 3 on h5, and 1 on h8, for a total of 105 mates.

3664: <p>A friend and I yesterday asked ourselves what the highest number of possible mates in a (legal) position is. We were able to come up with the following position which has a total of <strong>76 unique mates in 1</strong>, but we then failed to improve upon this one.</p>

<pre><code>Q3Q3/4K2Q/6R1/3R4/QB2k3/5R1N/2R5/QQ1Q1N1B w - - 0 1
</code></pre>

<p>Do you know if this problem ever has been solved and what the highest possible number is? It was hard for us to come up with a reasonably low upper bound so that I have no idea whether this solution is close to the maximum.</p>
 18786: <p>The following version has 99 threats <strong>none of which is a discovered check</strong>. It is possibly the best under that additional requirement.</p>

<p>I made it as an answer to <a href="https://puzzling.stackexchange.com/questions/81096/how-many-total-checkmates-can-you-possibly-make-against-the-enemy-king/81097#81097">the same question asked on Puzzling SE</a>.</p>

<p><a href="https://i.stack.imgur.com/PIZBS.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/PIZBS.jpg" alt="enter image description here"></a></p>
 10380: <p>Anthony Stewart Mackay Dickens found another solution, also with 105 mating moves, but with only 17 units in the diagram (16 white and the black king):</p>

<pre><code>[title "Anthony Stewart Mackay Dickens, The Problemist, Jan 1970. 105 mates"]
[fen "2Q1Q3/2Q4Q/Q4Q2/3k4/Q5Q1/1R6/B1NBQ3/K2R1N2 w - - 0 1"]
</code></pre>

<p>This may be found <a href="http://pdb.dieschwalbe.de/search.jsp?expression=PROBID=%27P1180418%27">here on PDB</a>.</p>

<p>Black's last move must have been <code>...Kc5-d5</code> following <code>Qxc7+</code>.</p>
 2299: <pre><code>[FEN "1B1Q1Q2/2R5/pQ4QN/RB2k3/1Q5Q/N4Q2/K2Q4/6Q1 w - - 0 1 "]
</code></pre>

<p>105 mates — Nenad Petrovic, <em>Sahovski Vjesnika</em> 1947 (<a href="http://pdb.dieschwalbe.de/search.jsp?expression=probid=%27P0004129%27" rel="noreferrer">Chess Problem Database</a>)</p>

<p>In this position any check is mate. There are 3 knight mates (c4, g4, f7), 23 discovered mates (14 moves for the rook on c7, 9 for the bishop on b5), and 79 queen mates: 1 on a1, 2 on b2, 3 on c3, 4 on c5, 6 on d4, 3 on d5, 6 on d6, 3 on e1, 2 on e2, 4 on e3, 4 on e4, 2 on e6, 4 on e7, 3 on e8, 5 on f4, 3  on f5, 6 on f6, 4 on g3, 5 on g5, 2 on g7, 3 on h2, 3 on h5, and 1 on h8, for a total of 105 mates.</p>
