help.html

<div class="helpPage" id="help_front">
<p>
    Welcome to <a href="https://github.com/hwatheod/retractor/blob/master/CHANGELOG.md" target="_blank">Retractor 2.3.5</a>! Retractor is a tool for working with retrograde analysis (retro) chess problems.
    <br>
    In a retro problem, you play chess backwards to learn about the history of a position.
        <a href="javascript:openHelpPage('help_tutorial_1')">Click here</a> for an introduction to retros.
    <br>
    The position above is a problem by Gerald Ettl.
    What were the last 30 single moves played?
    Source: <a href="https://www.janko.at/Retros/Schwalbe/N157.htm" target="_blank"><em>Die Schwalbe</em> Heft 157, Feb 1996, Problem 9129.</a>
    <br>
    <a href="javascript:openTutorialPosition('nBb2R1R/bqr5/kppp4/n3K2B/p1P1ppNN/rP2PPpp/P2P1QPP/8', 'b')">Click here</a> to set up the Ettl problem again.
    <a href="javascript:openHelpPage('help_ettl_solution')">Solution to Ettl problem.</a>
    </p>

    <p>
    Retractor has 2 modes: edit and play.<br>
    In edit mode, you set up the position on the chess board.<br>
    In play mode, you retract (take back) moves, and Retractor tells you when it detects an illegal position.<br>
    Retractor can also attempt to solve a position (find the last N moves).
    </p>

    <a href="javascript:openHelpPage('help_edit')">Edit mode controls</a>&nbsp;&nbsp;&nbsp;&nbsp;
    <a href="javascript:openHelpPage('help_play')">Play mode controls</a>&nbsp;&nbsp;&nbsp;&nbsp;
    <a href="javascript:openHelpPage('help_play_2')">Play mode details</a>&nbsp;&nbsp;&nbsp;&nbsp;
    <a href="javascript:openHelpPage('help_solve')">Solving a position</a><br>
    <a href="javascript:openHelpPage('help_piece_markings')">Frozen, promoted, original markings on pieces</a><br>
    <a href="javascript:openHelpPage('help_cage')">Cages</a><br>
    <a href="javascript:openHelpPage('help_config')">Config settings</a> (Advanced)<br>
    <a href="detectedByRetractor.html" target="_blank">What illegal positions are detected by Retractor 2? (new tab)</a><br>
    <a href="javascript:openHelpPage('help_about')">About Retractor 2</a>
</div>

<div class="helpPage" id="help_edit">
    <p>
    Edit mode controls:<br><br>
    Select a piece from the right panel, then left click on the board to add it.<br>
    Drag a piece around the board to move it.<br>
    Right click a piece to remove it. You can also remove pieces by selecting "None" from the right panel, then clicking on a square.<br>
    You can enter Forsythe notation in the box below the board and then click "Set" to set up the position.<br>
    <br>
    In the "Retract Next" section, you select which color will make the first retraction when you switch to Play mode.
    </p>
</div>

<div class="helpPage" id="help_play">
    <p>
    Play mode controls:<br><br>
    To retract a move, drag a piece from its square to an empty square.<br>
    To uncapture a piece, select it from the right panel, then perform the retraction. To uncapture en passant, select "e.p.". <br>
    To unpromote a piece, check the box "unpromote".<br>
    To uncastle, retract the king move, then the rook will automatically move (if legal).<br>
</p>
    <p>
    The &lt; button undoes a retraction.<br>
    The &lt;&lt; button undoes back to the initial position.<br>
    The &gt; button replays a retraction previously undone.<br>
    The &gt;&gt; button replays all retractions previously undone.<br>
    The <a href="javascript:openHelpPage('help_solve')">Solve</a> button attempts to solve the current position.<br>
    The Copy button displays all moves in a text box which you can then copy to the clipboard.<br>
    The Paste button allows you to paste a sequence of moves.<br>
    The <a href="javascript:openHelpPage('help_cage')">Cage</a> button allows you to verify, import, and export cages.
    </p>
</div>

<div class="helpPage" id="help_play_2">
    <p>
    Retractor attempts to detect illegal retractions. Simple illegalities are immediately rejected with a message
    in red below the board.  For more complex illegalities, the new position will show on the board, with a message
    in a popup box below the board.  This allows you to see the new position and why it is illegal. You can choose to
    undo the move with "Go Back", or play on by clicking "Continue anyway".  The purpose of "Continue anyway" is to
    let you play some more moves to see why it is illegal.  Some parts of Retractor may not function properly after
    you choose "Continue anyway" on an illegal position.
    </p>

    <p>
    In the "Captures" section, Retractor shows the number of <a href="javascript:openHelpPage('help_pawn_captures')">pawn captures</a>
    and number of total captures it could determine for White (W), Black (B), and Total (T).  The "Total" column may
    exceed the sum of "White" and "Black", because sometimes a capture can be detected without knowing which side made it
    (example: White pawn on e5, Black pawn on e4).  The "Total" row includes captures from non-pawn sources, such as an
    original bishop captured on its own square (example: White pawns on b2 and d2, empty square on c1, means that the
    White c1 bishop was captured on c1).
    </p>

    <p>
    In the "Promoted pieces" section, Retractor shows the number of promoted pieces of each color that it could
    detect. This includes excess pieces (for example, 2 queens or 3 rooks), pieces trapped in a cage (for example,
    White pawns on a2 and c2 with a black bishop on b1), and <a href="javascript:openHelpPage('help_piece_markings')">
    marked promoted</a> pieces.
    </p>

    <p>
    If the numbers in the "Captures" or "Promoted pieces" section are grey, that means that Retractor is still
    calculating their values. Most positions should calculate immediately on a modern computer, but positions with
    complicated pawn structures can take a long time. You can interrupt the calculation by playing a move on the
    board.  If you undo a move back to a position where you interrupted the calculation, the numbers will continue
    to show as grey as a reminder that they may not be correct.
    </p>
</div>

<div class="helpPage" id="help_pawn_captures">
    <p>If the number of pawn captures reported is too low, it may be because there are pawn promotions that cannot
        currently be detected by Retractor. Another possibility is when one side has reached its maximum number
        of pawn captures, then the number of pawn captures reported for the other side may be too low. In the
        latter case, you should try the config option <a href="javascript:openHelpPage('help_config')">separate capture tracking</a>.
    </p>

    <p>If the number of pawn captures reported is too high, it is because the number may include rooks captured
        in their home cage. Retractor does not attempt to determine whether they could actually have been captured by
        a pawn or not. However, the <b>total</b> number of captures reported will never be too high. When determining
        illegality, Retractor only uses the total number of captures. The pawn capture value is reported separately for
        the user's convenience only.
    </p>

</div>

<div class="helpPage" id="help_solve">
    <p>
    Solving a position in Retractor means to determine the possible sequences of last N moves in a position, for
    some value of N.
    </p>

    <p>
    When you click the "Solve" button in Play mode, these parameters are available:
    <ul>
        <li>Solve depth - the number of previous moves to solve for.  If you want to know the last 3 moves in a position,
            for example, you should set the "Solve depth" to be 3.</li>
        <li>Extra depth - the additional depth beyond the solve depth that Retractor should search, in order to confirm that
            a solution is legal. Sometimes, it is not obvious that a position is illegal until you search back a few
            more moves (beyond the solve depth) to see that one side has no possible last move. The default value 3
            is sufficient for most problems.
        </li>
        <li>Max solutions - the maximum number of solutions to report.</li>
        <li>No white/black uncaptures - If you check one of these boxes, then Retractor will not consider uncaptures for that side.</li>
    </ul>
    </p>

    <p>
        If Retractor finds one or more solutions, they will show as buttons in the upper right section of the
        page.  You can click on a button to navigate to that move in that solution.  "Copy" will display that solution
        in a text box which you can then copy to the clipboard. "Export Solutions" will export a text file with the
        final position of each solution (in Forsythe notation).
    </p>
    <p>
        If you make any move on the board, then all the solution buttons will be deactivated (because they may no
        longer apply to the new position). Using the navigation buttons is fine, though.  Even if the solution buttons
        are deactivated, the "Copy" button for each solution will still work.
    </p>
    <p>
        If Retractor finds no solutions, it will report that in an error message below the board. This means that
        the position is impossible.
    </p>
</div>

<div class="helpPage" id="help_piece_markings">
    <p>
    In Edit mode, you can mark pieces as either <em>frozen</em> or <em>promoted</em>.  By shift-clicking on a piece
    (not a pawn), the piece will cycle through the possibilities: frozen, promoted, neither.  The current markings,
    if any, for all pieces will show up as "Flags" in the upper right section of the page. If you do not see a Flags
    section, that means there are no markings for any pieces.
    </p>
    <p>
    A frozen piece is a piece on its original square which has never moved.  No retractions will be allowed with this
    piece. You can only mark a piece as frozen if it is on its original square (for example, a White king on e1, or a
    Black knight on g8).
    </p>
    <p>
    Marking a piece as promoted indicates to Retractor that this piece is promoted. This is useful if there is a
    promoted piece on the board that Retractor cannot detect, or if there is a condition "piece X is promoted"
    given in a problem.
    </p>
</div>

<div class="helpPage" id="help_cage">
    <p>
        We will explain cages via an example. Click to set up <a href="javascript:openTutorialPosition('8/8/8/8/8/1P6/1PkPP3/KR1b4', 'w')">this position</a>,
        a last move problem by Brandis. Have Retractor 2 try to solve it by clicking "Solve" and then "Solve" again.
        As it stands, Retractor 2 finds the correct answer Ka2-a1 but also several extraneous solutions a2xb3.
        Click one of the extraneous solutions a2xQb3 to see the position after that retraction is made. Why is it
        wrong? Because after a2xQb3, the arrangement of units in the lower left corner (the a1-e2 rectangle) is illegal,
        no matter how what other units are uncaptured from this point. We say that the units in the a1-e2
        rectangle form a <b>cage</b>.<br><br>
        Retractor knows about some cages, but this is not one of them. However, you can teach Retractor new cages. Make
        sure you are still on the position after retracting a2xQb3. Click on the "Cage" button, then "Select All", then click on
        the black queen on b3 to unselect it (because it is not part of the cage). Now click "Verify". Retractor says
        that it has verified that the selected squares do indeed form a cage.<br><br>
        Now go back to the original position (click <<), and have Retractor solve the problem again. This time, Retractor
        reports only the correct answer Ka2-a1, because it knows about this cage.<br><br>
        Retractor only learns cages that it can verify. So it is not possible to teach Retractor a wrong cage. However,
        there are some correct cages that Retractor cannot verify.<br><br>
        The Export button will download a text file of the new cages Retractor has learned, and the Import button can
        read these files. In ths way, new cages can be persisted between sessions, and shared with other people. On every
        import, Retractor re-verifies all the cages in the file before it learns them.<br>
        <a href="javascript:openHelpPage('help_cage_more')">Click here</a> for more examples of cages.<br>
        For a more formal description of the algorithm used by Retractor to verify cages, see <a href="https://github.com/hwatheod/retractor-python/blob/main/doc/cages.pdf" target="_blank">
        this document</a> (opens in a new tab).
    </p>
</div>
<div class="helpPage" id="help_cage_more">
    <p>
        <a href="javascript:openTutorialPosition('8/8/8/8/8/P2P4/P1kPP3/K1Bb4', 'w')">Problem by Fabel. Last move?</a><br>
        Similar to the previous example, we must rule out the move b2xa3. If <a href="javascript:openTutorialPosition('8/8/8/8/8/P2P4/P1kPP3/K1Bb4', 'w', 'b2xQa3')">
        b2xQa3 is retracted</a>, we have a cage in the lower left (excluding the black Queen), which Retractor can verify and then solve the original problem.<br>
        <a href="javascript:openTutorialPosition('4BQrk/3ppK1p/4p1p1/8/8/8/8/8', 'w')">Problem by Bartolovic, Gajdos, Maslar. Last move?</a><br>
        Here we must rule out the retractions Qh6-f8 or Qh6xNf8 followed by g7-g6.  <a href="javascript:openTutorialPosition('4BQrk/3ppK1p/4p1p1/8/8/8/8/8', 'w', 'Qh6-f8 g7-g6')">After this 2 move sequence</a>, we have a cage
        in the upper right, excluding the white Queen which has escaped. Retractor can verify this cage, then solve the original problem.
        <br>
        <a href="javascript:openTutorialPosition('8/8/8/8/1P6/kP6/2PP4/KBb5', 'w')">Problem by H&#xf8;eg. Last move?</a><br>
        Here we have two incorrect moves to rule out. First one is <a href="javascript:openTutorialPosition('8/8/8/8/1P6/kP6/2PP4/KBb5', 'w', 'c3xQb4')">c3xb4</a>.
        This produces a cage consisting of just the White bishop and pawns (note that both kings can escape via the bottom rank and then the Black bishop can escape too).
        Then we must rule out <a href="javascript:openTutorialPosition('8/8/8/8/1P6/kP6/2PP4/KBb5', 'w', 'Ba2xRb1')">Ba2xRb1</a>. The entire position would become an
        impossible cage. Retractor can verify both of these cages and then solve the original problem.
        <br><br>
        Hints on determining cages:<br>
        1. Visualize which units are actually trapped in a cage.<br>
        2. Do not include any pieces that have already escaped from the cage, or have an escape route.
    </p>
</div>
<div class="helpPage" id="help_config">
    <p>In most cases, users should not have to touch these settings. Config settings can only be changed in edit mode
        from the "Config" button on the left side.</p>
    <p>
    <b>Promotion search threshold:</b> When there are promoted pieces on the board, Retractor searches over all possible
       combinations of promotion squares for the promoted pieces to determine additional pawn captures. If the number of
       combinations exceeds this threshold, then Retractor will skip this search entirely. The default value 1000 is reasonable
       for most problems. I have not found any problems where it is necessary to set it higher. If Retractor is slow
       and you are working with a position with some promoted pieces on the board but the number of captures by promoted
       pawns is irrelevant, you can try setting it lower.
    </p>

    <p>
    <b>Separate capture tracking:</b> Checking this box is useful in positions where the number of pawn captures reported
       for one side is too low because the other side has already reached its maximum number of pawn captures.
        Consider the following problem by Dr. Niels H&#xf8;eg - <i>Retrograde Analysis</i>, 1915
        (<a href="javascript:openTutorialPosition('bN6/pPkR3p/PpPpPP2/8/2KP4/B6B/1q1P2PQ/br1R2Nr', 'w')">click here to set up</a>).
        If "separate capture tracking" is off (default), Retractor only reports 4 pawn captures for White, but
        because Black cannot make any pawn captures, White actually must make 6 pawn captures. If "separate capture tracking"
        is on, Retractor will report 6 pawn captures for White.
    </p>

    <p>
        In some positions, using "separate capture tracking" in combination with many promoted pieces can slow things down.
        In this case, you can try lowering the promotion search threshold.
    </p>

</div>
<div class="helpPage" id="help_ettl_solution">
    All 32 pieces are on the board, so there have been no captures. The White king on e5 is in check from the Black
    pawn on d6, so Black made the last move and it must have been d7-d6. Now all pieces on the left side of the board
    are locked in.
    <br><br>To unlock it, Black must retract Kb5-a6 and then White must retract c3-c4. However, we cannot
    do that immediately because then the configuration of White pawns forms a cage that the White rooks couldn't have
    escaped to get to their present positions.
    <br><br>
    So White must retract rook moves to bring them back into the cage before Kb5-a6 and c3-c4 can be retracted. In
    the meantime, Black has only pawn moves to retract, so there are only a limited number of moves for Black. So White
    must proceed as quickly as possible so that Black does not run out of moves to retract. White pieces must also
    move out of the way of the Black pawns at the right time, or Black will run out of moves even earlier.
    <br><br>
    The only
    <a href="javascript:openTutorialPosition('nBb2R1R/bqr5/kppp4/n3K2B/p1P1ppNN/rP2PPpp/P2P1QPP/8', 'b', 'd7-d6+ Kd6-e5 e5-e4 Rf5-f8 e6-e5 Rd5-f5 f5-f4 Rd3-d5 f6-f5 Rc3-d3 f7-f6 Nf6-g4 g4-g3 Rc1-c3 g5-g4 Bg4-h5 g6-g5 Rh5-h8 g7-g6 Ng6-h4 h4-h3 Rd5-h5 h5-h4 Rd3-d5 h6-h5 Rc3-d3 h7-h6 Rc2-c3 Kb5-a6 c3-c4+')">
    sequence of moves</a> that works is
    <b>d7-d6+ Kd6-e5 e5-e4 Rf5-f8 e6-e5 Rd5-f5 f5-f4 Rd3-d5 f6-f5 Rc3-d3 f7-f6 Nf6-g4 g4-g3 Rc1-c3 g5-g4 Bg4-h5 g6-g5 Rh5-h8
    g7-g6 Ng6-h4 h4-h3 Rd5-h5 h5-h4 Rd3-d5 h6-h5 Rc3-d3 h7-h6 Rc2-c3 Kb5-a6 c3-c4+.</b> Clicking the link will show the
    final position. You can use &lt;&lt; to go back to the beginning, then &gt; to view the moves one by one.
    <br>
</div>
<div class="helpPage" id="help_about">
    Retractor 2 is developed by Theodore Hwa. It is the successor to the original
    <a href="http://xenon.stanford.edu/~hwatheod/Retractor/" target="_blank">Retractor 1.0</a>, developed by Theodore Hwa and Chad Whipkey
    in 1998.<br><br>
    Retractor 2 Copyright (C) 2023 Theodore Hwa.<br>
    <a href="mailto:hwatheod@cs.stanford.edu">hwatheod@cs.stanford.edu</a>
    <br><br>
    Source code available at the <a href="https://github.com/hwatheod/retractor" target="_blank">Retractor 2 github repository</a>.
    <br>
</div>
<div class="helpPage" id="help_tutorial_1">
    Throughout this tutorial, you can navigate using the "Previous Page" and "Next Page" links at the top and bottom of each
    page of the tutorial. Be sure to scroll down if necessary to see all the text on each page.<br>
    <H3>What is Retrograde Analysis?</H3>
    Retrograde analysis is a type of chess problem in which you are asked to figure out something about
    the history of the game leading to a position. <a href="javascript:openTutorialPosition('8/8/8/8/1k6/P7/1K6/8', 'w')">Click here</a>
    to setup a very simple example of a retro problem on the board.
    <br><br>
    The problem is: what was the last move?  Try to answer this for yourself.  For the solution, turn to the next page.

</div>

<div class="helpPage" id="help_tutorial_2">
    The last move was made by White and it was <b>a3+</b>.
<br><br>
How do we solve this?  First, we notice that the black King is in check from the white pawn.
Therefore, the move must have been for White to deliver this check.
The pawn must have just moved to give this check.  The only possible such square is a2, since b2 is now occupied.
So the white pawn just advanced from a2 to a3.
<br><br>
Most retro problems are much more complicated than this.  However, there are several important principles to gather from
this problem:
<br><br>

1. If one side (such as Black) is in check, then the other side (White) must have made the last move.<br>
2. White's last move must have been to put Black in check.  There are two ways this can happen: the checking piece just moved,
    or some other piece moved to reveal a discovered check.  In this case, the check is by a pawn, so the pawn must have
    just moved.  We must now determine where this pawn moved from.<br>
3. The square that the pawn came from must now be empty.  A White pawn can move from a2 to a3 (without capturing a piece),
    or from b2 to a3 (capturing a Black piece). But in this case, b2 is occupied, so the second possibility is ruled out.<br>
<br>
To try another problem, turn to the next page.
</div>

<div class="helpPage" id="help_tutorial_3">
    <br>
    <a href="javascript:openTutorialPosition('k1K5/8/8/8/8/8/7P/6B1', 'b')">Click here</a> to setup the next problem
    by Raymond Smullyan, from the book <em>The Chess Mysteries of Sherlock Holmes</em>, 1979.<br><br>

    The problem is: Black made the last move.  What was it?<br><br>

    The solution is on the next page.
</div>

<div class="helpPage" id="help_tutorial_4">
    <br>
    <a href="javascript:openTutorialPosition('k1K5/8/8/8/8/8/7P/6B1', 'b')">Click here</a> to setup the problem again if necessary.<br><br>

    If you said that the last move was Ka7-a8, that is not correct. To see this, move the Black king from a8 to a7, and look at
    the resulting position.<br><br>
    Black is in check from the white Bishop.  How could White have delivered this check?  There is no way: the Bishop could
    only have come from squares further up the g1 to a7 diagonal, where it would already have been checking the black King.
    Try again before reading the correct solution on the next page.

</div>

<div class="helpPage" id="help_tutorial_5">
    <br>
    <a href="javascript:openTutorialPosition('k1K5/8/8/8/8/8/7P/6B1', 'b')">Click here</a> to setup the problem again if necessary.<br><br>
Black's last move must have been with the King (what else?) and it just moved from a7 (where else?).
However, the correct solution is that Black's last move was Ka7xNa8.  Black has just captured a knight!
<p>
To see the position before Ka7xNa8, click on the knight on the right panel, then move the Black king from a8 to a7. You
have just <em>uncaptured</em> a piece! This is the opposite from normal chess, where you <em>capture</em> pieces.
   </p>
<p>
Now again Black is in check from the white Bishop.  How did White deliver this check?  As before, the Bishop couldn't
have moved to deliver the check.  But now, the White Knight could have just moved from b6 to a8 to give a discovered check.
</p>

The following are important principles to gather from this problem:<br>
1. Always ask whether the position after taking back a move (or a sequence of moves) is still legal.
    Here, the problem only asked for the last move, but in order to determine the correct answer we had to look back
    to the move before the last move (to ask how White delivered the check).<br>
2. Always remember that the last move could have been a capture!  In order to completely solve a "last move(s)" problem,
    you must determine which piece, if any, was captured.  You must know exactly what the board looked like before the
    move(s) in question.<br>
</div>

<div class="helpPage" id="help_tutorial_6">
    <h3>Watching for special cases</h3>

    Next, we consider 3 problems that illustrate special cases that often come up in retro problems.<br><br>

    <a href="javascript:openTutorialPosition('7R/5R1k/5K2/8/8/8/8/8', 'w')">Click here</a> to set up problem 1.<br>
    Is this position legal? (Could it have arisen in a legal chess game?) <br><br>

    <a href="javascript:openTutorialPosition('8/8/4Pk2/8/8/7K/8/B7', 'w')">Click here</a> to set up problem 2.<br>
    Is this position legal? (Could it have arisen in a legal chess game?) <br><br>

    <a href="javascript:openTutorialPosition('r3k3/p1p5/Q3K3/8/8/8/8/8', 'b')">Click here</a> to set up problem 3.<br>
    Samuel Loyd, <em>Musical World</em>, 1859<br>
    White to play and mate in two <br><br>
    (Problem 3 might look like just an ordinary chess problem, but there is a retro component to it!)<br><br>

    The solutions are discussed in the next few pages.
</div>

<div class="helpPage" id="help_tutorial_7">
    <h3>Solution to special cases problem 1 </h3>
    <a href="javascript:openTutorialPosition('7R/5R1k/5K2/8/8/8/8/8', 'w')">Click here</a> to set up problem 1 again if necessary.<br><br>

At first sight, this position looks illegal because Black is in a double check by two rooks and it appears impossible
for one of the rooks to have revealed a check by the other rook.  However, this is possible by a pawn promotion!
The previous position had a White pawn on g7 and some other Black piece on h8.  White played gxh8=R, giving check with
the two rooks simultaneously.
<br><br>
To see this in Retractor, click the "unpromote" box, select one of the pieces (say a knight) to uncapture, then move
the White rook on h8 to g7.  You have <em>unpromoted</em> a rook back to a pawn! This is the opposite of the promotion
move in normal chess.
<br><br>
Whenever you see a White piece on the eighth rank, or a Black piece on the first rank, always remember that it could have
been created by promotion on the previous move.  Also, remember that unless stated or implied to the contrary, any piece
(except kings and pawns) on the board could been created by promotion earlier in the game!  It is entirely possible to have 2
queens or 3 rooks, etc., on the board.
<br><br>
Although in a normal, well-played game of chess, one generally promotes to a queen and there are only occasional
instances of promotions to other pieces, in retrograde analysis problems, because the game is only known to be legal
(not well-played), promotions to other pieces are often employed.
</div>

<div class="helpPage" id="help_tutorial_8">
    <h3>Solution to special cases problem 2 </h3>
     <a href="javascript:openTutorialPosition('8/8/4Pk2/8/8/7K/8/B7', 'w')">Click here</a> to set up problem 2 again if necessary.<br><br>

Just as in the previous problem, there appears to be an impossible check here.  White's bishop is giving check to the
Black king.  The bishop had no square to move from where it would not already be checking the king.  It might appear that
the White pawn could have moved from e5 to e6 to give the check, but this is impossible because the White pawn on e5 would
have already been checking the king.
<br><br>
The solution involves an en passant capture!  White's last move was actually an en passant capture: -1.d5xe6ep, taking a
Black pawn on e5 en passant, which was of course covering the bishop's diagonal.  Black's move before that must have been
e7-e5 (in order for the en passant capture to be legal), and White's move before that was d4-d5, discovering the check
from the bishop.
<br><br>
To play -1.d5xe6ep in Retractor, click the "e.p." button in the right panel, then move the e6 pawn back
to d5.  Then you can follow up with the retractions -1...e7-e5 -2. d4-d5.
<br><br>
Finally, note that the en passant capture must really have come from d5 rather than f5.  If, from the initial position,
we retract the alternative sequence -1. f5xe6ep?? e7-e5 then in the resulting position Black is again in check from the
White bishop, and now there really is no way of giving this check.
<br><br>
Remember that a White pawn on the sixth rank, or a Black pawn on the third rank, could just have made an en passant
capture.  Also, when you retract an en passant capture, you must immediately follow with the retraction of the double
step pawn move. Retractor will reject any other move.
</div>

<div class="helpPage" id="help_tutorial_9">
    <h3>Solution to special cases problem 3</h3>
     <a href="javascript:openTutorialPosition('r3k3/p1p5/Q3K3/8/8/8/8/8', 'b')">Click here</a> to set up problem 3 again if necessary.<br><br>

This problem looks like a normal mate in two problem.  But if you don't notice the hidden retro content, the problem may
appear to have no solution.  The retro-content revolves around Black's castling in the above position.<br><br>

The solution is to play 1. Qa1! followed by 2. Qh8 mate.  The only objection is to wonder why Black can't reply to
White's first move with 1... O-O-O, after which White has no mate, and therein lies the retro content.<br><br>

Since it is White to move in the above position, Black made the last move.  What was it?<br>
It could not have been either pawn, since they are on their original squares, hence it was with the king or rook.
Therefore, the king or rook has moved, and Black cannot castle.

</div>

<div class="helpPage" id="help_tutorial_10">
<h3>Cages and Captures</h3>

<a href="javascript:openTutorialPosition('B7/P1Ppp1p1/1k6/3Q4/1P6/5P1R/6PP/R3KB2', 'b')">Click here</a> for the next
    problem by Peter Schaefer.<br>
White to move.  Can White castle? <br>
(b) wNh3<br>
(c) Remove wRh3
<br><br>
There are 3 problems in one here.  The first problem is the diagram as shown;
in the second, we replace the White rook on h3 in the diagram by a White knight;
and in the third we remove the White rook in the diagram from h3.  In each case, we are asked whether
White castling is legal.  (Castling is always assumed to be legal, unless it can be proved to the contrary.)
So the question at hand is whether the White king or rook must have moved previously in the game.
<br><br>
For a start, try to figure out the last several moves played in this position.  Remember that it is White to move.  To start the solution, turn to the next page.
</div>

<div class="helpPage" id="help_tutorial_11">
<br>
<a href="javascript:openTutorialPosition('B7/P1Ppp1p1/1k6/3Q4/1P6/5P1R/6PP/R3KB2', 'b')">Click here</a> to set up the problem again if necessary.
<br><br>
Here Black has made the last move, obviously with his king.  All of the potential squares around the king look like they lead to impossible double checks, but the situation is explained by an en passant capture.  The last 3 single moves were
<a href="javascript:openTutorialPosition('B7/P1Ppp1p1/1k6/3Q4/1P6/5P1R/6PP/R3KB2', 'b', '0... Ka6xPb6 -1. a5xb6ep b7-b5')">0... Ka6xPb6 -1. a5xb6ep b7-b5</a>
<br><br>
Now Black is once again in check from the White bishop on f1.  How did White give this check?  There are two possibilities: the White king moved from e2 to e1, or the White pawn captured from e2 to f3.
In the former case, White cannot castle, but in the latter case there is no problem with the castling.
So we want to know if we can rule out e2xf3 as a possible last move.  Assume it was the last move, and we get
    <a href="javascript:openTutorialPosition('B7/P1Ppp1p1/1k6/3Q4/1P6/5P1R/6PP/R3KB2', 'b', '0... Ka6xPb6 -1. a5xb6ep b7-b5 -2. e2xRf3')">this position</a>
(we have arbitrarily uncaptured a rook on f3, but the choice of piece is not relevant):
<br><br>

To continue with the solution, turn to the next page.
</div>
<div class="helpPage" id="help_tutorial_12">
 <br>
    <a href="javascript:openTutorialPosition('B7/P1Ppp1p1/1k6/3Q4/1P6/5P1R/6PP/R3KB2', 'b', '0... Ka6xPb6 -1. a5xb6ep b7-b5 -2. e2xRf3')">Click here</a>
to set up the last position on the previous page if necessary.<br><br>

This is the only possible history of the game if White is assumed to be able to castle, except that the rook on f3
 was arbitrarily chosen as the uncaptured piece.  Now is this position possible?  To figure that out, we must draw more
conclusions about the history of the game.<br><br>

The first important fact is that the bishop on a8 must be a promoted pawn, since the Black pawn on b7 blocks the original
bishop from reaching a8.  We can also see this by noticing the original White bishop moving on light squares is still on
f1 on its original square (it is trapped in a cage).  But, assuming White can castle, the rook on h3 is also promoted!
Why?<br><br>

If White can castle, then the rook on a1 has not yet moved.  Could the rook on h3 be the rook from h1?  No!  Because the
White bishop on f1 is trapped on its original square, then the rook from h1 was also trapped in a cage consisting of
squares g1 and h1.  It could not leave those two squares, and was captured on one of those squares.  So the rook on h3
must also be promoted.  But since we have 7 White pawns on the board, we could have at most one promotion.  This is a
contradiction, so White cannot castle.<br><br>

On the next page, we discuss part (b) of the original problem, where the white rook on h3 is replaced by a white knight.
</div>

<div class="helpPage" id="help_tutorial_13">
<br>
<a href="javascript:openTutorialPosition('B7/P1Ppp1p1/1k6/3Q4/1P6/5P1N/6PP/R3KB2', 'b')">Click here</a> to set up part (b) of the problem.
<br><br>
By the same reasoning as before, we must have
<a href="javascript:openTutorialPosition('B7/P1Ppp1p1/1k6/3Q4/1P6/5P1N/6PP/R3KB2', 'b', '0... Ka6xPb6 -1. a5xb6ep b7-b5 -2. e2xRf3')">
    0... Ka6xPb6 -1. a5xb6ep b7-b5 -2. e2xRf3
</a> and as before, the White bishop on a8 must be promoted.  Now we introduce a very important technique in retro problems,
<em>counting captures</em>.<br><br>

First, we count pawn captures. There are 4 White pawns on the left side of the board, plus the promoted bishop on a8
which also came from a pawn. These 5 pawns collectively came from the a-, b-, c-, d-, f-files. We don't know for sure
which pawn came from which file, but we can say they must have made (at least) 8 captures total.<br><br>

Next, we have 2 cage captures to count: both original Black bishops were captured on their original squares c8 and f8,
since the releasing pawns have not moved.  This makes a total of 10 captures, and since Black has 6 units on the board,
that accounts for all missing Black units.<br><br>

    The solution continues on the next page.
</div>

<div class="helpPage" id="help_tutorial_14">
<a href="javascript:openTutorialPosition('B7/P1Ppp1p1/1k6/3Q4/1P6/5P1N/6PP/R3KB2', 'b', '0... Ka6xPb6 -1. a5xb6ep b7-b5 -2. e2xRf3')">
Click here
</a> to setup the position after part (b) 0... Ka6xPb6 -1. a5xb6ep b7-b5 -2. e2xRf3
<br><br>

On the previous page, we determined that the white pawns captured all the missing Black units except for the two original bishops.
Among these missing Black units is the Black pawn originally from h7.  How did it get captured?
<br><br>
Here we come to another important principle in retros: If a pawn is missing, it could have either been captured
<em>or it could have promoted</em>. (The promoted piece could have been captured later, or some original piece
could have been captured, and the promoted piece replaced it.) Suppose the Black pawn from h7 was captured by a White pawn.  The rightmost
capture by a White pawn was on the e-file, so the Black h-pawn would have to make 3 captures get to the e-file.
Now White has 13 units on the board, so there seems to be no problem with these 3 captures.<br><br>

But we must not forget about the cage in the lower right hand corner!  The White rook originally from h1 was captured
on either g1 or h1, and could not be one of the captures that the Black h-pawn used to get from the h-file to the e-file,
so that makes a fourth capture by Black, which is one too many.<br><br>

The remaining possibility is that the Black pawn on h7 promoted.   It takes at least 3 captures for this pawn to promote,
one of which had to be in the lower right cage (g1/h1).  Since only 3 captures are available, the Black h-pawn must have
captured f2xRg1 at some point in the game.  So a Black pawn occupied f2 at some point in the game.
The White king was not on e1 when Black played f2xRg1, since the pawn would have checked the king.  Therefore, the
White king has moved earlier in the game, and White cannot castle.<br><br>

To answer part (c), note that if we remove the White unit from h3, then White is missing 4 units so that there is no
problem with the h-pawn making 3 captures to get to the e-file to be captured.  The White rook on was captured on g1 or
h1 separately.  So in this case, White can castle.  (Technically, for completeness, we must give a legal game leading
to this position in which neither the king nor rook has moved.  We leave this to the reader.)<br><br>

This is the last problem in the tutorial. On the next page, we list some resources for finding more on retro problems.
</div>

<div class="helpPage" id="help_tutorial_15">
<h3>Conclusion</h3>
    There’s a lot more to the world of retros than was presented in this brief tutorial. An excellent starting point for more retro problems is
    the <a href="https://www.janko.at/Retros/" target="_blank">Retrograde Analysis Corner</a>, originally created by Philippe Schnoebelen
    and currently maintained jointly by Joost de Heer and Otto Janko. This collection of web pages contains an enormous collection
    of retro problems. <br><br>

There is also a mailing list for discussing retro problems. For instructions on subscribing to this
mailing list, see the Retrograde Analysis Corner.<br><br>

Finally, if you prefer books, there are two books by Raymond Smullyan that are
excellent introductions to retro problems: <em>The Chess Mysteries of Sherlock Holmes</em> and <em>
The Chess Mysteries of the Arabian Knights</em>. Additional information on books, journals, and articles related to
retrograde analysis can be found at the Retrograde Analysis Corner.<br><br>

This concludes the tutorial.
</div>