Refactor retrograde
This commit is contained in:
parent
e3baa4f86e
commit
11bd085595
GPG Key ID:
C6D63995FE72FD80
@ -13,6 +13,47 @@
|
||||
\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
|
||||
\repeat%
|
||||
\fi%
|
||||
}
|
||||
|
||||
|
||||
\def\startimes#1{
|
||||
{\color{ogrape} $\bigstar \times #1$}
|
||||
}
|
||||
|
||||
\def\starvalue#1{
|
||||
\stars{#1}{#1} \par
|
||||
\vspace{1mm}
|
||||
}
|
||||
|
||||
\def\difficulty#1#2{
|
||||
\textbf{Difficulty:} \stars{#1}{#2} \par
|
||||
@ -60,8 +101,20 @@ $\odot$}}
|
||||
\chessboard[setpieces = {#1}]
|
||||
\fi
|
||||
}
|
||||
\makeatother
|
||||
|
||||
\@makeORMCbox{hintlist}
|
||||
{Available Hints}
|
||||
{black!12!white}
|
||||
{black!80!white}
|
||||
|
||||
\long\def\hintcontent#1#2#3{
|
||||
\if@solutions
|
||||
\liststars{#1}{#2} \par #3
|
||||
\else
|
||||
\liststars{#1}{#2}
|
||||
\fi\par
|
||||
}
|
||||
\makeatother
|
||||
|
||||
|
||||
|
||||
@ -83,18 +136,71 @@ $\odot$}}
|
||||
}
|
||||
|
||||
|
||||
\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.
|
||||
|
||||
\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.
|
||||
|
||||
\begin{hintlist}
|
||||
Hint 1:
|
||||
\hintcontent{2}{4}{This is a hint. Only instructors see this.}
|
||||
|
||||
Hint 2:
|
||||
\hintcontent{1}{2}{This is another hint.}
|
||||
\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.
|
||||
|
||||
|
||||
|
||||
|
||||
\vfill
|
||||
\pagebreak
|
||||
|
||||
\input{parts/intro}
|
||||
|
||||
|
||||
\section{Simple problems}
|
||||
\input{parts/easy}
|
||||
|
||||
|
||||
\section{Harder problems}
|
||||
\section{Slightly harder problems}
|
||||
\input{parts/medium}
|
||||
|
||||
\section{Very difficult problems}
|
||||
\input{parts/hard}
|
||||
%\section{Very difficult problems}
|
||||
%\input{parts/hard}
|
||||
|
||||
\chessboard \hfill \chessboard \par
|
||||
\chessboard \hfill \chessboard \par
|
||||
|
||||
@ -1,6 +1,7 @@
|
||||
% Sherlock, A little exercise
|
||||
\problem{A little exercise}
|
||||
\difficulty{1}{5}
|
||||
%\difficulty{1}{5}
|
||||
\starvalue{3}
|
||||
|
||||
Black has just moved in the game below. White started on the south side of the board.\par
|
||||
What was Black's last move, and what was White's last move? \par
|
||||
@ -11,6 +12,14 @@ What was Black's last move, and what was White's last move? \par
|
||||
Bg1
|
||||
}
|
||||
|
||||
\begin{hintlist}
|
||||
Hint 1:
|
||||
\hintcontent{1}{3}{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?}
|
||||
\end{hintlist}
|
||||
|
||||
\begin{solution}
|
||||
It's pretty clear that Black just moved out of check from A7.
|
||||
|
||||
@ -37,9 +46,15 @@ What was Black's last move, and what was White's last move? \par
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
% Sherlock, Which color?
|
||||
\problem{Which color?}
|
||||
\difficulty{2}{5}
|
||||
%\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.}
|
||||
@ -51,6 +66,16 @@ 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}{
|
||||
It castled kingside (how do we know?). Now, how did it get off G1?
|
||||
}
|
||||
\end{hintlist}
|
||||
|
||||
\begin{solution}
|
||||
The white king is the key to this solution. How did it get off of E1? \par
|
||||
It must have castled kingside---castling queenside would move a rook from black to white.
|
||||
@ -67,13 +92,23 @@ There is a pawn at G3. What color is it? \par
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
% Arabian Knights 2
|
||||
\problem{Invisible, but not invincible}
|
||||
\difficulty{2}{5}
|
||||
%\difficulty{2}{5}
|
||||
\starvalue{4}
|
||||
|
||||
Seeing that this battle was lost, the black king has turned himself invisible. \par
|
||||
Unfortunately, his position is hopeless. Mate the king in one move. \par
|
||||
\hint{You don't need to find the king, you only need a checkmate.} \par
|
||||
The black king has turned himself invisible. Unfortunately, his position is hopeless. \par
|
||||
Mate the king in one move. \par
|
||||
|
||||
\manyboards{
|
||||
Ra8,rb8,Kf8,
|
||||
@ -81,6 +116,14 @@ Unfortunately, his position is hopeless. Mate the king in one move. \par
|
||||
Pa6,Rc6
|
||||
}
|
||||
|
||||
\begin{hintlist}
|
||||
Hint 1:
|
||||
\hintcontent{1}{4}{Do you need to know \textit{exactly} where the black king is?}
|
||||
|
||||
Hint 2:
|
||||
\hintcontent{1}{3}{Don't forget about promotion.}
|
||||
\end{hintlist}
|
||||
|
||||
\begin{solution}
|
||||
Since it is White's move, Black cannot be in check. \par
|
||||
So, either White is in check or the black king is on C8. \par
|
||||
@ -97,9 +140,14 @@ Unfortunately, his position is hopeless. Mate the king in one move. \par
|
||||
\pagebreak
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
% Sherlock, a question of survival
|
||||
\problem{An empty board}
|
||||
\difficulty{2}{5}
|
||||
%\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 one more piece on the board, which isn't shown. What color square does it stand on? \par
|
||||
|
||||
@ -109,6 +157,11 @@ 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?}
|
||||
\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.
|
||||
@ -126,7 +179,8 @@ 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}
|
||||
%\difficulty{3}{5}
|
||||
\starvalue{5}
|
||||
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
|
||||
@ -137,6 +191,20 @@ Use this information to show that a pawn was promoted. \par
|
||||
Ke1
|
||||
}
|
||||
|
||||
\begin{hintlist}
|
||||
Hint 1:
|
||||
\hintcontent{1}{5}{
|
||||
\par
|
||||
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?}
|
||||
\end{hintlist}
|
||||
|
||||
\begin{solution}
|
||||
Knights always move to a different colored square, so all four missing knights must have been captured on their home square.
|
||||
What pieces captured them?
|
||||
@ -156,9 +224,13 @@ Use this information to show that a pawn was promoted. \par
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
% Arabian Knights, intro (given with solution)
|
||||
\problem{Promotion?}
|
||||
\difficulty{2}{5}
|
||||
%\difficulty{2}{5}
|
||||
\starvalue{6}
|
||||
|
||||
It is White's move. Have there been any promotions this game? \par
|
||||
|
||||
@ -167,6 +239,14 @@ It is White's move. Have there been any promotions this game? \par
|
||||
Bc1,Kd1,Rh1
|
||||
}
|
||||
|
||||
\begin{hintlist}
|
||||
Hint 1:
|
||||
\hintcontent{3}{6}{
|
||||
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.
|
||||
}
|
||||
\end{hintlist}
|
||||
|
||||
\begin{solution}
|
||||
|
||||
Since it is White's move, Black has just moved his king. Where did he move it from?
|
||||
@ -192,9 +272,11 @@ It is White's move. Have there been any promotions this game? \par
|
||||
|
||||
% Sherlock Holmes, two bagatelles (1)
|
||||
\problem{Whodunit}
|
||||
\difficulty{2}{5}
|
||||
%\difficulty{2}{5}
|
||||
\starvalue{5}
|
||||
|
||||
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.}
|
||||
|
||||
\manyboards{
|
||||
ra8,bc8,ke8,rh8,
|
||||
@ -205,6 +287,14 @@ It is Black's move. Can Black castle? \par
|
||||
Bc1,Qd1,Ke1,Bf1
|
||||
}
|
||||
|
||||
\begin{hintlist}
|
||||
Hint 1:
|
||||
\hintcontent{1}{5}{
|
||||
Black captured a knight on his last move. \par
|
||||
Why do we know this, and how did he do it?
|
||||
}
|
||||
\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.
|
||||
@ -232,10 +322,12 @@ It is Black's move. Can Black castle? \par
|
||||
|
||||
% Sherlock Holmes, two bagatelles (2)
|
||||
\problem{Castle contradiction}
|
||||
\difficulty{2}{5}
|
||||
%\difficulty{2}{5}
|
||||
\startimes{7}
|
||||
|
||||
Neither Black nor White captured a piece on their last move. \par
|
||||
It is Black's move. Can he castle? \par
|
||||
\hint{What was White's last move? Check the cases.}
|
||||
|
||||
\manyboards{
|
||||
ke8,rh8,
|
||||
@ -245,6 +337,12 @@ 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?}
|
||||
\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.
|
||||
|
||||
@ -270,10 +368,12 @@ It is Black's move. Can he castle? \par
|
||||
|
||||
% Arabian Knights, intro (given with solution)
|
||||
\problem{A matter of order}
|
||||
\difficulty{3}{5}
|
||||
%\difficulty{3}{5}
|
||||
\startimes{8}
|
||||
|
||||
A black bishop captured a White piece earlier in this game. \par
|
||||
Which bishop was it, and what did it capture? \par
|
||||
\hint{Black and White start with 16 pieces each.}
|
||||
|
||||
\manyboards{
|
||||
ra8,qd8,ke8,
|
||||
@ -286,16 +386,34 @@ Which bishop was it, and what did it capture? \par
|
||||
Kc1,Rd1,Rh1
|
||||
}
|
||||
|
||||
\begin{instructornote}
|
||||
|
||||
\textbf{Hints to give:} (these should be answered in order)
|
||||
\begin{hintlist}
|
||||
Hint 1:
|
||||
\hintcontent{1}{8}{
|
||||
\begin{itemize}
|
||||
\item How many pieces does Black have? Where were the missing ones captured?
|
||||
\item Which pieces is White missing? Where could they have been captured?
|
||||
\item How did those white pieces get to the place they were captured?
|
||||
\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}
|
||||
}
|
||||
|
||||
\end{instructornote}
|
||||
Hint 2:
|
||||
\hintcontent{2}{7}{
|
||||
\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}{
|
||||
\begin{itemize}
|
||||
\item ...the black pawn on G7 captured a white piece on H6.
|
||||
\item What else is missing?
|
||||
\end{itemize}
|
||||
}
|
||||
\end{hintlist}
|
||||
|
||||
\begin{solution}
|
||||
First, notice that the pawn on C3 came from D2 by capturing a piece. \par
|
||||
|
||||
@ -136,5 +136,18 @@ A king and rook can \textit{castle} under the following conditions:
|
||||
\end{minipage}
|
||||
\par
|
||||
|
||||
\vfill
|
||||
|
||||
\generic{General Strategies:}
|
||||
Below is a list of questions you'll want to ask yourself if you get stuck. \par
|
||||
\note[Note]{Yes, I know you don't have the problems yet. Patience.}
|
||||
|
||||
\begin{itemize}
|
||||
\item What was the last move? (By black or white)
|
||||
\item Were there any promotions? This may be indirect:\par
|
||||
if White needs a third bishop, there was a promotion.\par
|
||||
\note{Promotions often resolve seemingly impossible situations.}
|
||||
\end{itemize}
|
||||
|
||||
\vfill
|
||||
\pagebreak
|
||||
@ -1,7 +1,8 @@
|
||||
|
||||
% Sherlock, A matter of direction
|
||||
\problem{A matter of direction}
|
||||
\difficulty{3}{5}
|
||||
%\difficulty{3}{5}
|
||||
\starvalue{5}
|
||||
|
||||
The results of a game of chess are shown below. \par
|
||||
Did White start on the north or south side of the board? \par
|
||||
@ -14,6 +15,11 @@ Did White start on the north or south side of the board? \par
|
||||
Bh1
|
||||
}
|
||||
|
||||
\begin{hintlist}
|
||||
Hint 1:
|
||||
\hintcontent{2}{5}{The bishop on H1 is important. How did White deliver this check?}
|
||||
\end{hintlist}
|
||||
|
||||
\begin{solution}
|
||||
Let us first find White's last move. It wasn't with the pawns on D4 and E5, since Black wouldn't have a move before that.
|
||||
(Note the double-check on A7).
|
||||
@ -29,11 +35,15 @@ Did White start on the north or south side of the board? \par
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
% Arabian Knights 1
|
||||
\problem{Where is the king?}
|
||||
\difficulty{3}{5}
|
||||
%\difficulty{3}{5}
|
||||
\startimes{8}
|
||||
|
||||
The white king has turned himself invisible. Find him. \par
|
||||
The white king has again become invisible. Find him. \par
|
||||
\hint{White started on the bottom. En passant.} \par
|
||||
|
||||
\manyboards{
|
||||
@ -42,6 +52,30 @@ The white king has turned himself invisible. Find him. \par
|
||||
kd1
|
||||
}
|
||||
|
||||
|
||||
\begin{hintlist}
|
||||
Hint 1:
|
||||
\hintcontent{3}{8}{
|
||||
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}{
|
||||
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}
|
||||
}
|
||||
\end{hintlist}
|
||||
|
||||
\makeatletter
|
||||
\if@solutions
|
||||
\vfill
|
||||
\pagebreak
|
||||
\fi
|
||||
\makeatother
|
||||
|
||||
\begin{solution}
|
||||
Looking at the board, we see that the white king is on B3 or Black is in check.
|
||||
|
||||
@ -86,9 +120,22 @@ The white king has turned himself invisible. Find him. \par
|
||||
\pagebreak
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
% Arabian Knights, intro (given with solution)
|
||||
\problem{Double-checks}
|
||||
\difficulty{3}{5}
|
||||
%\difficulty{3}{5}
|
||||
\startimes{10}
|
||||
|
||||
White to move. Which side of the board did each color start on? \par
|
||||
\hint{What was Black's last move? }
|
||||
@ -99,12 +146,14 @@ White to move. Which side of the board did each color start on? \par
|
||||
Nd1,kf1,Kh1
|
||||
}
|
||||
|
||||
\begin{instructornote}
|
||||
\textbf{Hints to give:}\par
|
||||
Clearly, Black just moved his king. From where? \par
|
||||
All possible positions may seem impossible (thanks to double-checks), but E1 and F2 are a bit more reasonable than others.
|
||||
Move the king to both and try to add (or un-promote) pieces to make the position make sense.
|
||||
\end{instructornote}
|
||||
\begin{hintlist}
|
||||
Hint 1:
|
||||
\hintcontent{4}{10}{
|
||||
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.
|
||||
}
|
||||
\end{hintlist}
|
||||
|
||||
\begin{solution}
|
||||
Black's last move was from F2, where his king was in double-check from both a rook and a knight.
|
||||
@ -133,6 +182,17 @@ White to move. Which side of the board did each color start on? \par
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
% Arabian Knights 4
|
||||
\problem{A missing piece}
|
||||
\difficulty{4}{5}
|
||||
@ -151,6 +211,16 @@ What is it, and what is its color? \par
|
||||
Kc1,Rd1,nf1,Bh1
|
||||
}
|
||||
|
||||
\begin{hintlist}
|
||||
Hint 1:
|
||||
\hintcontent{4}{10}{
|
||||
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.
|
||||
}
|
||||
\end{hintlist}
|
||||
|
||||
|
||||
\begin{instructornote}
|
||||
\textbf{Hints to give:} (in this order)
|
||||
\begin{itemize}
|
||||
@ -173,7 +243,7 @@ What is it, and what is its color? \par
|
||||
\begin{solution}
|
||||
\textbf{Part 1:}
|
||||
|
||||
The black bishop on A2 cannot be original, since the white pawn on B3 would have prevented its getting there.
|
||||
The black bishop on A2 cannot be original, since the white pawn on B3 would have prevented it from getting there.
|
||||
That bishop is a promoted bishop. \par
|
||||
|
||||
The black pawn it was promoted from must have come from E7,
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user