user15027: Is it possible that the king can move to a square, and the opponent can move, but no matter where it is a stalemate? If it is impossible, how do you prove that?

user4050: It might also be worth pointing out that if you make a move after which any move by your opponent would lead to stalemate, the game finishes immediately. See FIDE's Laws of Chess, Article 9.6:

The game is drawn when a position is reached from which a checkmate
cannot occur by any possible series of legal moves. This immediately
ends the game, provided that the move producing this position was
legal.

Thus, from a technical point of view, some of the answers to this questions are slightly wrong. The game is not ended by stalemate (article 5.2) but by the article above.
The only (admittedly, very conceived) practical relevance that I can think of is that without the rule above, after playing Ka3 in Rewan Demontay's example, you could resign and hence lose the game. But you cannot resign as the game has already finished. (Note that even without Article 9.6, you still would not be able to lose on time, that is covered (redundantly?) by Article 6.9.)

user-1: [Title "Black to move and draw"]
[FEN "6k1/7P/7K/6PP/8/8/8/8 b - - 0 1"]
[startflipped ""]

1... Kh8 {Kf8 and Kf7 would be blunders.} 2. Kg6 {Pawn to g6 is also legal, but both result in a stalemate.}

This position is only possible if the foremost pawn has just captured a piece (say, black's pawn).

user15543: On a similar beat to Ian Bush's answer, here is a chess problem that takes this idea to wacky proportions!
[Title "Christopher Jeremy Morse, EG 1984, White Stalemates Themselves In 4 Moves"]
[FEN "8/pp2r1q1/1p6/1pkr4/2p5/1pp5/nK6/1b6 w - - 0 1"]

   1. Ka3 b4+ 2. Ka4 b5+ 3. Ka5 b6+ 4. Ka6 Nc1 {Any move by Black is fine anyway, as all result in stalemating White!}

Source: The Die Schwalbe Chess Problem Databse

user7726: If I understand what you are asking how about this
[Event ""]
[Site ""]
[Date "????.??.??"]
[Round ""]
[White ""]
[Black ""]
[Result "*"]
[FEN "6k1/8/3p4/2bPp3/1p1bP3/1Pp3p1/2P3P1/6Kn w - - 0 1"]

1.Kxh1 *

Black's last move was Nf2-h1+

user26601: Here is a variation on the answer of Ian Bush that I could see occuring in an actual game between (low-rated) human players. Of course, realistically White should have resigned long ago, but he plays on in hopes of a draw. Black has a mate in two, but because of time pressure decides to just push a pawn instead of looking for mating attacks...
[Event "?"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "*"]
[SetUp "1"]
[FEN "8/q4k2/8/p1b5/P2p4/6p1/6P1/6K1 b - - 0 1"]

1... d3+?? 2. Kh1! 


15027: <p>Is it possible that the king can move to a square, and the opponent can move, but no matter where it is a stalemate? If it is impossible, how do you prove that?</p>
 4050: <p>It might also be worth pointing out that if you make a move after which any move by your opponent would lead to stalemate, the game finishes immediately. See <a href="https://www.fide.com/FIDE/handbook/LawsOfChess.pdf" rel="nofollow noreferrer">FIDE's Laws of Chess</a>, Article 9.6:</p>
<blockquote>
<p>The game is drawn when a position is reached from which a checkmate
cannot occur by any possible series of legal moves. This immediately
ends the game, provided that the move producing this position was
legal.</p>
</blockquote>
<p>Thus, from a technical point of view, some of the answers to this questions are slightly wrong. The game is not ended by stalemate (article 5.2) but by the article above.</p>
<p>The only (admittedly, very conceived) practical relevance that I can think of is that without the rule above, after playing Ka3 in Rewan Demontay's example, you could resign and hence lose the game. But you cannot resign as the game has already finished. (Note that even without Article 9.6, you still would not be able to lose on time, that is covered (redundantly?) by Article 6.9.)</p>
 -1: <pre><code>[Title &quot;Black to move and draw&quot;]
[FEN &quot;6k1/7P/7K/6PP/8/8/8/8 b - - 0 1&quot;]
[startflipped &quot;&quot;]

1... Kh8 {Kf8 and Kf7 would be blunders.} 2. Kg6 {Pawn to g6 is also legal, but both result in a stalemate.}
</code></pre>
<p>This position is only possible if the foremost pawn has just captured a piece (say, black's pawn).</p>
 15543: <p>On a similar beat to Ian Bush's answer, here is a chess problem that takes this idea to wacky proportions!</p>
<pre><code>[Title &quot;Christopher Jeremy Morse, EG 1984, White Stalemates Themselves In 4 Moves&quot;]
[FEN &quot;8/pp2r1q1/1p6/1pkr4/2p5/1pp5/nK6/1b6 w - - 0 1&quot;]

   1. Ka3 b4+ 2. Ka4 b5+ 3. Ka5 b6+ 4. Ka6 Nc1 {Any move by Black is fine anyway, as all result in stalemating White!}
</code></pre>
<p>Source: <a href="https://pdb.dieschwalbe.de/P0501027" rel="noreferrer">The Die Schwalbe Chess Problem Databse</a></p>
 7726: <p>If I understand what you are asking how about this</p>
<pre><code>[Event &quot;&quot;]
[Site &quot;&quot;]
[Date &quot;????.??.??&quot;]
[Round &quot;&quot;]
[White &quot;&quot;]
[Black &quot;&quot;]
[Result &quot;*&quot;]
[FEN &quot;6k1/8/3p4/2bPp3/1p1bP3/1Pp3p1/2P3P1/6Kn w - - 0 1&quot;]

1.Kxh1 *
</code></pre>
<p>Black's last move was Nf2-h1+</p>
 26601: <p>Here is a variation on the answer of Ian Bush that I could see occuring in an actual game between (low-rated) human players. Of course, realistically White should have resigned long ago, but he plays on in hopes of a draw. Black has a mate in two, but because of time pressure decides to just push a pawn instead of looking for mating attacks...</p>
<pre><code>[Event &quot;?&quot;]
[Site &quot;?&quot;]
[Date &quot;????.??.??&quot;]
[Round &quot;?&quot;]
[White &quot;?&quot;]
[Black &quot;?&quot;]
[Result &quot;*&quot;]
[SetUp &quot;1&quot;]
[FEN &quot;8/q4k2/8/p1b5/P2p4/6p1/6P1/6K1 b - - 0 1&quot;]

1... d3+?? 2. Kh1! 
</code></pre>
