diff --git a/Advanced/Retrograde Analysis/main.tex b/Advanced/Retrograde Analysis/main.tex index bfcbb5c..84cba44 100755 --- a/Advanced/Retrograde Analysis/main.tex +++ b/Advanced/Retrograde Analysis/main.tex @@ -13,34 +13,19 @@ \usepackage{afterpage} \usepackage[hang]{footmisc} -% A row of stars, for showing difficulty -% first arg: filled stars -% second arg: total stars -\def\liststars#1#2{% - \def\oncolor{\color{ogrape}}% - \def\offcolor{\color{white}}% - % - \count255=1% - \count254=#2% - \advance\count254 by -1% - \ifnum #1 > 0 - % The $$ are required around \bigstar. - % the special \odot chess piece breaks - % star sizing if they are ommited. - \loop - {\oncolor $\bigstar$}% - \ifnum\count255 < #1 - \advance\count255 by 1 - \repeat% - \else% - {\oncolor $\bigstar$}% - \fi% - % - \ifnum \count255 < #2% - \loop - {\offcolor $\bigstar$}% - \ifnum\count255 < \count254 - \advance\count255 by 1 +% Modify default tab positions for better stars +\TabPositions{1.2cm, 2cm, 3cm, 4cm, 5cm, 6cm, 7cm, 8cm} + + +\def\nstars#1#2{% + \ifnum #2 > 0% + \def\starcolor{\color{#1}}% + \count255=1% + \loop{% + \starcolor $\bigstar$% + }% + \ifnum \count255 < #2% + \advance\count255 by 1% \repeat% \fi% } @@ -102,16 +87,41 @@ $\odot$}} \fi } -\@makeORMCbox{hintlist} - {Available Hints} +\@makeORMCbox{@hintlist} + {Score Decomposition:} {black!12!white} {black!80!white} +\newenvironment{hintlist}{ + \begin{@hintlist} +}{ + % Remove vspace from the last \hintcontent + \if@solutions\vspace{-2mm}\fi + \end{@hintlist} +} + + +\def\threestars#1#2#3{ + \nstars{white}{#1}\nstars{ogrape}{#2}\nstars{white}{#3} +} + +\def\onestars#1{ + \nstars{ogrape}{#1} +} + +\long\def\hintcontentnew#1{ + \if@solutions + #1 \par + \vspace{2mm} + \fi +} + \long\def\hintcontent#1#2#3{ \if@solutions - \liststars{#1}{#2} \par #3 + \nstars{white}{#1}\nstars{ogrape}{#2} \par #3 + \vspace{2mm} \else - \liststars{#1}{#2} + \nstars{white}{#1}\nstars{ogrape}{#2} \fi\par } \makeatother diff --git a/Advanced/Retrograde Analysis/parts/00 rules.tex b/Advanced/Retrograde Analysis/parts/00 rules.tex index 48f2b17..42e50c3 100644 --- a/Advanced/Retrograde Analysis/parts/00 rules.tex +++ b/Advanced/Retrograde Analysis/parts/00 rules.tex @@ -1,51 +1,49 @@ \section{Rules} This handout contains a set of problems. \par -Each is marked with a few gold stars, which you collect by presenting a solution. - -\vspace{2mm} - -Below each problem is a list of hints, written next to their cost. \par -To get a hint, you must pay the marked number of stars. \par -Hints are usually provided in order, and are the same for all groups. \par - -\vspace{2mm} - -There is one exception: instructors may offer certain hints for a reduced fee, -judging by your explanation of what you have so far. - -\begin{instructornote} - This exception is for groups that are stuck on the last bit of a problem. \par - If they've solved most of it, give them the information they already know - for a steep discount (or even for free). -\end{instructornote} - - - -An example problem is below. +Each is marked with a few stars, which you collect by presenting solutions. \par +An example is below. \vspace{4mm} \generic{Problem $0$:} \starvalue{4} -This is a problem that's worth four points. \par -Two hints are available. The first costs two stars (of the four available). \par -The second costs one of the two stars available \textit{after} revealing the first hint. +This is a problem that has two parts. \par +If you solve the problem on your own, your team gets four points. \par + +\vspace{2mm} + +There are two ways you can ask for assistance: \par +\begin{itemize}[itemsep=1mm] + \item First, you may uncover a hint to a part for $\lceil 0.5 \times \text{that part's value} \rceil$ stars. \par + In this problem, the hints for both part 1 and 2 cost 1 star each. \par + These are always provided in order---you must solve or uncover part 1 to get a hint for part 2. + + \item You may also ask an instructor to check the work you have thus far. \par + By doing this, you will earn stars for all parts you no longer need a hint for. +\end{itemize} + \begin{hintlist} - Hint 1: - \hintcontent{2}{4}{This is a hint. Only instructors see this.} + Part 1: \tab\threestars{0}{1}{3} \par + \hintcontentnew{ + This is a hint. Only instructors see this. + } - Hint 2: - \hintcontent{1}{2}{This is another hint.} + Part 2: \tab\threestars{1}{2}{1} \par + \hintcontentnew{ + This is another hint. + } + + \vspace{2mm} + Done: \tab\threestars{3}{1}{0} \end{hintlist} -\vfill - -You may notice that hints often cost a significant fraction of their problem's score. \par -This is intentional---don't ask for hints unless you're very, very stuck. +\vspace{1cm} +Each \say{part} corresponds to one hint in the instructor's handout. \par +(\say{Done} is not a hint, it is simply a bonus for completing the problem). diff --git a/Advanced/Retrograde Analysis/parts/02 easy.tex b/Advanced/Retrograde Analysis/parts/02 easy.tex index e47d7f8..6031da7 100644 --- a/Advanced/Retrograde Analysis/parts/02 easy.tex +++ b/Advanced/Retrograde Analysis/parts/02 easy.tex @@ -17,11 +17,18 @@ What was Black's last move, and what was White's last move? \par } \begin{hintlist} - Hint 1: - \hintcontent{1}{3}{What was Black's last move? What White do to make this happen?} + Part 1: \tab\threestars{0}{1}{2} \par + \hintcontentnew{ + What was Black's last move? What White do to make this happen? + } - Hint 2: - \hintcontent{1}{2}{White uncovered a check. What piece did Black capture?} + Part 2: \tab\threestars{1}{1}{1} \par + \hintcontentnew{ + White uncovered a check. What piece did Black capture? + } + + \vspace{2mm} + Done: \tab\threestars{2}{1}{0} \end{hintlist} \begin{solution} @@ -55,13 +62,15 @@ What was Black's last move, and what was White's last move? \par + + % Sherlock, Which color? \problem{Which color?} %\difficulty{2}{5} \starvalue{4} In the game below, no pieces have moved from a black square to a white square, or from a white square to a black square. There is a pawn at G3. What color is it? \par -\hint{Again, White started on the bottom.} +As before, White started on the bottom of the board. \manyboards{ ke8, @@ -70,14 +79,20 @@ There is a pawn at G3. What color is it? \par Pd2,Pf2 } -\begin{hintlist} - Hint 1: - \hintcontent{2}{4}{How did the white king get off E1? It must have castled!} - Hint 2: - \hintcontent{1}{2}{ +\begin{hintlist} + Part 1: \tab\threestars{0}{1}{3} \par + \hintcontentnew{ + How did the white king get off E1? It must have castled! + } + + Part 2: \tab\threestars{1}{1}{2} \par + \hintcontentnew{ It castled kingside (how do we know?). Now, how did it get off G1? } + + \vspace{2mm} + Done: \tab\threestars{2}{2}{0} \end{hintlist} \begin{solution} @@ -121,11 +136,11 @@ Mate the king in one move. \par } \begin{hintlist} - Hint 1: - \hintcontent{1}{4}{Do you need to know \textit{exactly} where the black king is?} + Part 1: \tab\threestars{0}{1}{3} \par + \hintcontentnew{Don't forget about promotion.} - Hint 2: - \hintcontent{1}{3}{Don't forget about promotion.} + \vspace{2mm} + Done: \tab\threestars{1}{3}{0} \end{hintlist} \begin{solution} @@ -161,11 +176,16 @@ There is one more piece on the board, which isn't shown. What color square does Ke1 } + \begin{hintlist} - Hint 1: - \hintcontent{1}{4}{Which piece performed the last capture?} + Part 1: \tab\threestars{0}{1}{3} \par + \hintcontentnew{Which piece performed the last capture on a black square?} + + \vspace{2mm} + Done: \tab\threestars{1}{3}{0} \end{hintlist} + \begin{solution} Which piece performed the last capture on a black square? It couldn't have been a white pawn, which haven't moved. @@ -184,7 +204,7 @@ There is one more piece on the board, which isn't shown. What color square does % Sherlock, another monochromatic \problem{The knight's grave} %\difficulty{3}{5} -\starvalue{5} +\starvalue{4} In the game below, no pieces have moved from a black square to a white square, or from a white square to a black square. The white king has made less than fourteen moves. \par Use this information to show that a pawn was promoted. \par @@ -196,17 +216,12 @@ Use this information to show that a pawn was promoted. \par } \begin{hintlist} - Hint 1: - \hintcontent{1}{5}{ - \par + Part 1: \tab\threestars{0}{1}{3} \par + \hintcontentnew{ Who took the knights? Only one of them is interesting---most are easy to account for. - \vspace{2mm} } - - - Hint 2: - \hintcontent{2}{4}{We can easily account for the white knights and the - black knight on G8. Which white pieces can move to capture the black knight on B8?} + \vspace{2mm} + Done: \tab\threestars{1}{3}{0} \end{hintlist} \begin{solution} @@ -244,13 +259,17 @@ It is White's move. Have there been any promotions this game? \par } \begin{hintlist} - Hint 1: - \hintcontent{3}{6}{ + Part 1: \tab\threestars{0}{4}{2} \par + \hintcontentnew{ The black king must have moved from F1. (Why not G1?) \par This would be impossible if something hadn't blocked check from the white rook. } + + \vspace{2mm} + Done: \tab\threestars{4}{2}{0} \end{hintlist} + \begin{solution} Since it is White's move, Black has just moved his king. Where did he move it from? @@ -277,7 +296,7 @@ It is White's move. Have there been any promotions this game? \par % Sherlock Holmes, two bagatelles (1) \problem{Whodunit} %\difficulty{2}{5} -\starvalue{5} +\starvalue{6} It is Black's move. Can Black castle? \par \hint{Remember the rules of chess: you may not castle if you've moved your rook.} @@ -292,13 +311,17 @@ It is Black's move. Can Black castle? \par } \begin{hintlist} - Hint 1: - \hintcontent{1}{5}{ + Part 1: \tab\threestars{0}{4}{2} \par + \hintcontentnew{ Black captured a knight on his last move. \par Why do we know this, and how did he do it? } + + \vspace{2mm} + Done: \tab\threestars{4}{2}{0} \end{hintlist} + \begin{solution} White's last move was with the pawn. \par Black's last move must have been to capture the white piece which moved before that. @@ -324,6 +347,14 @@ It is Black's move. Can Black castle? \par \pagebreak + + + + + + + + % Sherlock Holmes, two bagatelles (2) \problem{Castle contradiction} %\difficulty{2}{5} @@ -341,12 +372,20 @@ It is Black's move. Can he castle? \par bd1,Rf1,Kg1 } + \begin{hintlist} - Hint 1: - \hintcontent{2}{7}{If White moved his king, Black cannot castle. Why? \par - That's the simple case. The other option: White castled. What did Black do before that?} + Part 1: \tab\threestars{0}{4}{3} \par + \hintcontentnew{ + If White moved his king, Black cannot castle. Why? \par + That's the simple case. The other option: White castled. What did Black do before that? + (Also, there was a promotion in this case.) + } + + \vspace{2mm} + Done: \tab\threestars{4}{3}{0} \end{hintlist} + \begin{solution} If White's last move was with the king, then the black rook moved to check him and Black can't castle. @@ -370,6 +409,15 @@ It is Black's move. Can he castle? \par + + + + + + + + + % Arabian Knights, intro (given with solution) \problem{A matter of order} %\difficulty{3}{5} @@ -392,33 +440,35 @@ Which bishop was it, and what did it capture? \par \begin{hintlist} - Hint 1: - \hintcontent{1}{8}{ + Part 1: \tab\threestars{0}{1}{7} \par + \hintcontentnew{ \begin{itemize} \item How many pieces are missing? Where were the missing ones captured? \item How did those pieces get to the place they were captured? \end{itemize} - \vspace{2mm} } - Hint 2: - \hintcontent{2}{7}{ + Part 2: \tab\threestars{1}{2}{5} \par + \hintcontentnew{ \begin{itemize} \item The pawn on C3 came from D2, capturing a black rook. \item The black rook it captured couldn't have moved there before... \end{itemize} - \vspace{2mm} } - Hint 3: - \hintcontent{1}{4}{ + Part 3: \tab\threestars{3}{2}{3} \par + \hintcontentnew{ \begin{itemize} \item ...the black pawn on G7 captured a white piece on H6. \item What else is missing? \end{itemize} } + + \vspace{2mm} + Done: \tab\threestars{5}{3}{0} \end{hintlist} + \begin{solution} First, notice that the pawn on C3 came from D2 by capturing a piece. \par This must have been a black rook, which is the only missing black piece. diff --git a/Advanced/Retrograde Analysis/parts/03 medium.tex b/Advanced/Retrograde Analysis/parts/03 medium.tex index 3a9b3dd..202a462 100644 --- a/Advanced/Retrograde Analysis/parts/03 medium.tex +++ b/Advanced/Retrograde Analysis/parts/03 medium.tex @@ -3,7 +3,7 @@ % Sherlock, A matter of direction \problem{A matter of direction} %\difficulty{3}{5} -\starvalue{5} +\starvalue{4} The results of a game of chess are shown below. \par Did White start on the north or south side of the board? \par @@ -17,8 +17,12 @@ Did White start on the north or south side of the board? \par } \begin{hintlist} - Hint 1: - \hintcontent{2}{5}{The bishop on H1 is important. How did White deliver this check?} + Part 1: \tab\threestars{0}{1}{3} \par + \hintcontentnew{ + The bishop on H1 is important. How did White deliver this check? + } + \vspace{2mm} + Done: \tab\threestars{1}{3}{0} \end{hintlist} \begin{solution} @@ -65,21 +69,23 @@ The white king has again become invisible. Find him. \par \begin{hintlist} - Hint 1: - \hintcontent{3}{8}{ + Part 1: \tab\threestars{0}{2}{6} \par + \hintcontentnew{ Either the white king is on B3, or Black is in check. \par First, show that the latter implies the former. - \vspace{2mm} } - Hint 2: - \hintcontent{2}{5}{ + Part 2: \tab\threestars{2}{2}{4} \par + \hintcontentnew{ Moving back in time, you'll need to add two pieces to the board (not counting the king). \par They have been captured! - \vspace{2mm} } + + \vspace{2mm} + Done: \tab\threestars{4}{4}{0} \end{hintlist} + \makeatletter \if@solutions \vfill @@ -158,12 +164,15 @@ White to move. Which side of the board did each color start on? \par } \begin{hintlist} - Hint 1: - \hintcontent{4}{10}{ + Part 1: \tab\threestars{0}{5}{5} \par + \hintcontentnew{ Double-checks make all positions seem impossible... \par Try E1 and F2 anyway. Can you add pieces to make it make sense? \par Don't forget about promotion. } + + \vspace{2mm} + Done: \tab\threestars{5}{5}{0} \end{hintlist} \begin{solution} @@ -223,68 +232,46 @@ What is it, and what is its color? \par Kc1,Rd1,nf1,Bh1 } + \begin{hintlist} - Hint 1: - \hintcontent{1}{20}{ + Part 1: \tab\threestars{0}{1}{19} \par + \hintcontentnew{ What color is the missing piece? Count captures.\par - Look at the region bounded by A1 and B3. How did the bishop get there? \par - \note[Note]{This is Part 1} - \vspace{2mm} + Look at the region bounded by A1 and B3. How did the bishop get there? } - - Hint 2: - \hintcontent{1}{19}{ + Part 2: \tab\threestars{1}{1}{18} \par + \hintcontentnew{ What was White's last move? \par - What does this tell us about White's king? \par - \note[Note]{This is Part 2} - \vspace{2mm} + What does this tell us about White's king? } - - Hint 3: - \hintcontent{1}{18}{ + + Part 3: \tab\threestars{2}{1}{17} \par + \hintcontentnew{ Now, look at the region bounded by G1 and H3. \par In Part 1, we found that all of White's pieces were captured---including the H1 rook. \par How did it get off its home square to be captured? \par - What does this tell us about the bishop on H1? \par - \note[Note]{This is Part 3} - \vspace{2mm} - } - - Hint 4: - \hintcontent{1}{17}{ - The black bishop on H2 must have been promoted on G1. \par - Which pawn was it, and how did it get there? (Remember, we counted captures in Part 1). \par - In what order did the cross capture by the G1 and H1 pawns occur? \par - \note[Note]{This is Part 4} - \vspace{2mm} + What does this tell us about the bishop on H1? } - Hint 5: - \hintcontent{5}{16}{ + Part 4: \tab\threestars{3}{2}{15} \par + \hintcontentnew{ + The black bishop on H2 must have been promoted on G1. \par + Which pawn was it, and how did it get there? (Remember, we counted captures in Part 1). \par + In what order did the cross capture by the G1 and H1 pawns occur? + } + + Part 5: \tab\threestars{5}{2}{13} \par + \hintcontentnew{ Which black pieces are still missing? \par Remember that White cannot castle through check. } - + \vspace{2mm} + Done: \tab\threestars{7}{13}{0} \end{hintlist} -%\begin{instructornote} -% \textbf{Hints to give:} (in this order) -% \begin{itemize} -% \item How did the black bishop on A2 get there? \note{(Part 1)} -% \item How many captures has Black made? \note{(Part 1)} -% \item What color is the missing piece? \note{(Part 1)} -% \item What was White's last move? What does this imply? \note{(Part 2)} -% \item Which white pieces were captured? \par -% How did they move from their starting positions? \note{(Part 3)} -% \item How did the bishop on H2 get to where it is now? \note{(Part 3)} -% \item Which pawn was promoted to the bishop now on H2? \note{(Part 4)} -% \item Which black pieces are still missing? \note{(Conclusion)} -% \item Remember that White cannot castle through check. \note{(Conclusion)} -% \end{itemize} -%\end{instructornote} \vfill \pagebreak