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