user2698: For the following position to occur in legal play, with Black on move, what would White's second-to-last move need to have been?  Note that Black is checked by two pieces on the h1-h8 file and two more on the c1-h6 diagonal, and both the d2 bishop nor the h2 must have been at their present locations when check was given.
b/7P/6Pk/5P/4P/2PP/3B2KR/2Q1N2R w K - 0 1

This is my first effort at a retrograde analysis problem: I think the position shown is reachable via legal moves, but that there's only one possible way the last three half-moves could have transpired.  Did I formulate the puzzle "correctly"?  Could/should it be improved?  Would it be better with fewer pieces?
8/8/4Pk/3P/8/8/5QK/B w K - 0 1

In the latter formulation, I like the way the White queen is placed so that it could have moved from b2 or d4, unblocking the bishop, but for the fact that it would have been giving check if it had been in either of those places.
EDIT
Here's yet another formulation, perhaps a bit more subtle, but I think the solution is still unique.  Note that in this revision, White's last move is not certain, but the second-to-last move is.
[FEN "8/8/4Pk/8/8/8/8/B6K w - - 0 1"]


user10179: The simplest version of the problem is 'cooked' - there are three distinct solutions:
a) setup - White king on B2, White pawn on F5, Black pawn on E7
   --> 1) B2-B1+ E7-E5  2) F5xE5ep
b) setup - White king on B2, White pawn on D5, Black pawn on E7
   --> 1) B2-B1+ E7-E5  2) D5xE5ep
c) setup - White pawn on D4, Black pawn on E7
   --> 1) D4-D5+ E7-E5  2) D5xE5ep

user2429: White's second to last move must be f5+.
So, this is what the position looked like before White's second to last move - 
   [FEN "b7/6pP/7k/7P/4PP2/2PP4/3B2KR/2Q1N2R w - - 0 1"]

   1. f5+ g5 2. hxg6+ 

How to arrive at the solution - 
In this position, it is Black to play and the Black king is checked by a double-battery of the two rooks and the bishop and queen. What was White's last move? 
        [FEN "b7/7P/6Pk/5P2/4P3/2PP4/3B2KR/2Q1N2R w - - 0 1"]

Since it is a double check, it must be some form of discovered check. However, since we have a double-battery, it cannot be possible that the discovered check was caused by a move of one of the pieces involved in the battery, because the other piece in the same battery would have already been checking the Black king if such were the case. Thus, it has to be some other "piece". But no such piece can uncover two attacks. Thus, it must be a very specific case of a pawn capture, an en passant, where two lines are opened at the same time. 
     [FEN "b7/6pP/7k/5P1P/4P3/2PP4/3B2KR/2Q1N2R b - - 0 1"]

     1... g5 2. hxg6+

In the above, position, we see that the Black king is checked by a battery of queen and bishop. The only way that could have occurred in this position is if White played f4-f5. 
Thus, White's second to last move is f4-f5. 

2698: <p>For the following position to occur in legal play, with Black on move, what would White's second-to-last move need to have been?  Note that Black is checked by two pieces on the h1-h8 file and two more on the c1-h6 diagonal, and both the d2 bishop nor the h2 must have been at their present locations when check was given.</p>
<pre><code>b/7P/6Pk/5P/4P/2PP/3B2KR/2Q1N2R w K - 0 1
</code></pre>
<p>This is my first effort at a retrograde analysis problem: I think the position shown is reachable via legal moves, but that there's only one possible way the last three half-moves could have transpired.  Did I formulate the puzzle &quot;correctly&quot;?  Could/should it be improved?  Would it be better with fewer pieces?</p>
<pre><code>8/8/4Pk/3P/8/8/5QK/B w K - 0 1
</code></pre>
<p>In the latter formulation, I like the way the White queen is placed so that it could have moved from b2 or d4, unblocking the bishop, but for the fact that it would have been giving check if it had been in either of those places.</p>
<p>EDIT</p>
<p>Here's yet another formulation, perhaps a bit more subtle, but I think the solution is still unique.  Note that in this revision, White's last move is not certain, but the second-to-last move is.</p>
<pre><code>[FEN &quot;8/8/4Pk/8/8/8/8/B6K w - - 0 1&quot;]
</code></pre>
 10179: <p>The simplest version of the problem is 'cooked' - there are three distinct solutions:</p>

<p>a) <em>setup - White king on B2, White pawn on F5, Black pawn on E7</em>
   --> <strong><em>1)</em> B2-B1+ E7-E5  <em>2)</em> F5xE5ep</strong></p>

<p>b) <em>setup - White king on B2, White pawn on D5, Black pawn on E7</em>
   --> <strong><em>1)</em> B2-B1+ E7-E5  <em>2)</em> D5xE5ep</strong></p>

<p>c) <em>setup - White pawn on D4, Black pawn on E7</em>
   --> <strong><em>1)</em> D4-D5+ E7-E5  <em>2)</em> D5xE5ep</strong></p>
 2429: <p>White's second to last move must be <strong>f5+</strong>.</p>

<p>So, this is what the position looked like before White's second to last move - </p>

<pre><code>   [FEN "b7/6pP/7k/7P/4PP2/2PP4/3B2KR/2Q1N2R w - - 0 1"]

   1. f5+ g5 2. hxg6+ 
</code></pre>

<p><strong>How to arrive at the solution -</strong> </p>

<p>In this position, it is Black to play and the Black king is checked by a <strong>double-battery</strong> of the two rooks and the bishop and queen. What was White's last move? </p>

<pre><code>        [FEN "b7/7P/6Pk/5P2/4P3/2PP4/3B2KR/2Q1N2R w - - 0 1"]
</code></pre>

<p>Since it is a double check, it must be some form of <strong>discovered check</strong>. However, since we have a double-battery, it cannot be possible that the discovered check was caused by a move of one of the pieces involved in the battery, because the other piece in the same battery would have already been checking the Black king if such were the case. Thus, it has to be some other "piece". But no such piece can uncover two attacks. Thus, it must be a very specific case of a pawn capture, an en passant, where two lines are opened at the same time. </p>

<pre><code>     [FEN "b7/6pP/7k/5P1P/4P3/2PP4/3B2KR/2Q1N2R b - - 0 1"]

     1... g5 2. hxg6+
</code></pre>

<p>In the above, position, we see that the Black king is checked by a battery of queen and bishop. The only way that could have occurred in this position is if White played <strong>f4-f5</strong>. </p>

<p>Thus, White's second to last move is <strong>f4-f5</strong>. </p>
