%
%	gbb60166@gmail.com	https://unilab.gbb60166.jp/prekou/prekou.htm
%
% aspectratio= は 1610, 169, 149, 54, 32 の中から選べる（省略時は 43）
% C:\texlive\2024\texmf-dist\tex\latex\beamer\beamer.cls
%\documentclass[20pt,dvipdfmx,usepdftitle=false,hyperref={pdfpagemode=FullScreen},aspectratio=169]{beamer}
%\documentclass[20pt,dvipdfmx,usepdftitle=false,hyperref={pdfstartview={XYZ null null 8.00}},aspectratio=169]{beamer}
\documentclass[20pt,dvipdfmx,usepdftitle=false,aspectratio=169]{beamer}
% pdfの栞の字化けを防ぐ
%\AtBeginDvi{\special{pdf:tounicode EUC-UCS2}}
% テーマ
\usetheme{Copenhagen}
% navi. symbolsは目立たないが，dvipdfmxを使うと機能しないので非表示に
\setbeamertemplate{navigation symbols}{} 
\usepackage{bxdpx-beamer,pxjahyper,minijs}
%\usepackage{graphicx}
%\usepackage{tkokugo,furikana,tsayusen,shiika,sfkanbun,jdkintou,plext}
\usepackage{type1cm}
\usepackage[deluxe]{otf}
%\usepackage{tikzsymbols}
%\usepackage[dvipdfmx]{graphicx}%
\def\pgfsysdriver{pgfsys-dvipdfmx.def}%（graphicxパッケージを使用しない場合はこの行を有効に）
%\def\pgfsysdriver{pgfsys-dvips.def}%デフォルト
%\usepackage[e]{esvect}
\usepackage{tikz}%（これで、pgfとpgfforが読み込まれます。）
%\usepackage{tikz-3dplot}
\usetikzlibrary{calc,patterns}
%\usetikzlibrary{arrows.meta,angles,intersections,backgrounds}
%\usepackage{animate}
%\usepackage{pgfplots}
%\pgfplotsset{compat=newest}
%\pgfplotsset{compat=newest, every axis/.append style={line width=1pt}}
%\PassOptionsToPackage{dvipdfmx}{graphicx}
\nofiles

\hypersetup{% Jul 18 2023
	pdftitle={プレ高数学科（LaTeX Beamer で汎用PDFプレゼンを作る）},
	pdfauthor={gbb60166@gmail.com},
	pdfsubject={https://unilab.gbb60166.jp/prekou/prekou.htm}
	}

% フォントはお好みで
%\usepackage{txfonts}

\mathversion{bold}
\renewcommand{\familydefault}{\sfdefault}
\renewcommand{\seriesdefault}{bx}
\renewcommand{\kanjifamilydefault}{\gtdefault}
\renewcommand{\kanjiseriesdefault}{bx}
\setbeamerfont{title}{size=\normalsize,series=\bfseries}
\setbeamerfont{frametitle}{size=\normalsize,series=\bfseries}
\setbeamertemplate{frametitle}[default][center]
\usefonttheme{professionalfonts}

% 参考にしたURL
% http://windom.phys.hirosaki-u.ac.jp/fswiki/wiki.cgi?page=LaTeX+Beamer%A4%C7%A5%D7%A5%EC%A5%BC%A5%F3%A5%C6%A1%BC%A5%B7%A5%E7%A5%F3

\newcommand{\Slash}[1]{\ooalign{\hfil\kern-3pt／\hfil\crcr$#1$}}
\everymath{\displaystyle}

\def\maruwaku#1{\begin{tikzpicture}[scale=0.7, baseline={([yshift=-22pt] current bounding box.north)}]
\filldraw[color=CUDBlue, line width=1pt, rounded corners=2pt] (-0.1,0)--(2.1,0)--(2.1,1.1)--(-0.1,1.1)--cycle;
\draw(1,0.5) node[white]{#1};
\end{tikzpicture}
}

\setbeamersize{text margin left=3mm,text margin right=3mm}
\fboxrule=0.8pt

\makeatletter
\def\hooklen#1#2{\settowidth{\@tempdima}{\(#1\)}
%\advance\@tempdima by.3ex
% ↑ 数式モードで式の前後に入るスペースを制御したかったが、
%    難しいのでやめた。段々難解なコードになっているのでやめた方がよい？
\hbox to\@tempdima{\hfil \(#2\)\hfil}}
%■等号付き不等号 by 美文書作成入門
\newcommand{\myleqq}{\mathrel{\mathpalette\gl@align<}}
\newcommand{\mygeqq}{\mathrel{\mathpalette\gl@align>}}
\newcommand{\gl@align}[2]{\lower.6ex\vbox{\baselineskip\z@skip\lineskip\z@
	\ialign{$\m@th#1\hfil##\hfil$\crcr#2\crcr=\crcr}}}
\makeatother

% カラーユニバーサルデザインを調べたつもりだがあまり自信がありません
% http://www.fukushihoken.metro.tokyo.jp/kiban/machizukuri/kanren/color.files/colorudguideline.pdf
% http://jfly.iam.u-tokyo.ac.jp/colorset/

% ■ アクセントカラー小面積を目立たせる高彩度色
\definecolor{CUDRed}{RGB}{255,75,0}
\definecolor{CUDGreen}{RGB}{3,175,122}
\definecolor{CUDBlue}{RGB}{0,90,255}
\definecolor{CUDCyan}{RGB}{77,196,255}
\definecolor{CUDMagenta}{RGB}{153,0,153}
\definecolor{CUDYellow}{RGB}{255,241,0}
\definecolor{CUDBrown}{RGB}{128,64,0}

\definecolor{CUDOrange}{RGB}{246,170,0}

% ■ ベースカラー広い面積の塗り分けに用いる低・中彩度色
\definecolor{CUDPink}{RGB}{255,202,191}
\definecolor{CUDBrightGreen}{RGB}{119,217,168}
\definecolor{CUDLime}{RGB}{216,242,85}
\definecolor{CUDCream}{RGB}{255,255,128}
\definecolor{CUDBrightCyan}{RGB}{191,228,255}
%\definecolor{CUD}{RGB}{}%

\setbeamercolor{CUDBrightGreen}{fg=black,bg=CUDBrightGreen!50}
\setbeamercolor{CUDBrightCyan}{fg=black,bg=CUDBrightCyan}
\setbeamercolor{CUDCream}{fg=black,bg=CUDCream!75}



\begin{document}

\title{プレ高数学科}\author{gbb60166}

%■ 本文と数式モードの間に挿入される空白スペース
%\mathsurround=0pt
%■ \( \log\log \)でlogとlogの間に挿入される細スペース（省略形は \,）
%\thinmuskip=3mu%■default
%■ \( a+b \)で+の前後に挿入される中スペース（省略形は \>）
%\medmuskip=4mu plus 2mu minus 4mu%■default
\medmuskip=1mu plus 1mu minus 1mu
%■ \( x=5 \)で=の前後に挿入される太スペース（省略形は \;）
%\thickmuskip=5mu plus 5mu%■default
\thickmuskip=3mu plus 2mu minus 2mu
% mu は math units の省略で長さの単位

%■■■■■■■■■■■　実験エリア　■■■■■■■■■■■■■■■■


%\end{document}
%■■■■■■■■■■■　ここから本文　■■■■■■■■■■■■■■■■

\begin{frame}[t]
\frametitle{マス1グランプリ\quad 1st Round \quad 第１問}
\vspace*{-2ex}
\Large
\begin{center}
$1$から$15$までの\textcolor{CUDRed}{奇数}を\\
全部足すといくつ？
\end{center}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{マス1グランプリ\quad 1st Round \quad 第２問}
\vskip-2ex
\centerline{%
\begin{tikzpicture}[scale=2,very thick,
		baseline={( [yshift=-2ex] current bounding box.north)}]
\LARGE
\draw(1,2.4) node[left]{\(9\)}
	(1,1.8) node[left]{\(99\)}
	(1,1.2) node[left]{\(999\)}
	(1,0.6) node[left]{\(9999\)}
	(1,0) node[left]{\(+\ 99999\)};
\draw(-1.9,-0.3)--++(3,0);
\end{tikzpicture}
}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{マス1グランプリ\quad 1st Round \quad 第３問}
\centerline{%
\begin{tikzpicture}[scale=2,very thick,
		baseline={( [yshift=-2ex] current bounding box.north)}]
\LARGE
\draw(1,0.6) node[left]{\(27\)}
	(1,0) node[left]{\(\times\ 999\)};
\draw(-1.2,-0.3)--++(2.2,0);
\end{tikzpicture}
}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{マス1グランプリ\quad 1st Round \quad 第４問}
\vspace*{-3ex}
\Large
\[ 2^4\times5^5= \]
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{マス1グランプリ\quad 1st Round \quad 第５問}
\vspace*{-2ex}
\Large
\begin{center}
$4$を$4$回使って\\
四則演算\( (+-\times\div) \)で\\
$6$にしなさい\\
（カッコも使用可）
\end{center}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{マス1グランプリ\quad 1st Round \quad 第６問}
\vspace*{-3ex}
\Large
\[ 49^2-48^2= \]
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{マス1グランプリ\quad 1st Round \quad 第７問}
\( 2+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9=1022 \)\\
のとき\\[2ex]
	\( 2+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9+2^{10}= \)
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{マス1グランプリ\quad 1st Round \quad 第８問}
\vspace*{-1ex}
\Large
\begin{center}
\(\frac{364}{1365}\)を約分しなさい
\end{center}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{マス1グランプリ\quad 1st Round \quad 第９問}
\vspace*{-2ex}
\Large
\begin{center}
$2$進数\( 1111111 \)を\\
$10$進数で表しなさい
\end{center}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{マス1グランプリ\quad 1st Round \quad 第１\kern-.4zw０問}
\vspace*{-2ex}
\Large
\begin{center}
\( 3,6,8,9 \)を\\
四則演算\( (+-\times\div) \)で\\
$10$にしなさい\\
（順番を並べ替えてもよい\\
カッコも使用可）
\end{center}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{マス1グランプリ\quad 2nd Round}
\begin{minipage}[t]{0.6\textwidth}
\large
小さい正方形が$5$つ集まった紙を切り離し、
再度寄せ合わせて大きい正方形を作りなさい
\end{minipage}
%
\quad
%
\begin{tikzpicture}[scale=2,very thick,
		baseline={( [yshift=-2ex] current bounding box.north)}]
\draw(0,0) rectangle ++(1,1)
	(1,0) rectangle ++(1,1)
	(0,1) rectangle ++(1,1)
	(1,1) rectangle ++(1,1)
	(1,2) rectangle ++(1,1);
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{マス1グランプリ\quad Final Round}
\begin{minipage}[t]{0.48\textwidth}
\large
$1000$本の棒を使って正四面体を作り、積んでいくと何段になるでしょう？
\end{minipage}
%
%\quad
\pause
%
\begin{tikzpicture}[scale=0.6,very thick,
		baseline={( [yshift=-2ex] current bounding box.north)}]
\coordinate(T) at (5.5,10);
\coordinate(R1) at (0,2);
\coordinate(R4) at (7,0);
\coordinate(R7) at (11,3);

\coordinate(P1) at ($(T)!1/3!(R1)$);
\coordinate(P2) at ($(T)!1/3!(R4)$);
\coordinate(P3) at ($(T)!1/3!(R7)$);

\coordinate(Q1) at ($(T)!2/3!(R1)$);
\coordinate(Q3) at ($(T)!2/3!(R4)$);
\coordinate(Q5) at ($(T)!2/3!(R7)$);
\coordinate(Q2) at ($(Q1)!0.5!(Q3)$);
\coordinate(Q4) at ($(Q3)!0.5!(Q5)$);
\coordinate(Q6) at ($(Q1)!0.5!(Q5)$);

\coordinate(R2) at ($(R1)!1/3!(R4)$);
\coordinate(R3) at ($(R1)!2/3!(R4)$);
\coordinate(R5) at ($(R4)!1/3!(R7)$);
\coordinate(R6) at ($(R4)!2/3!(R7)$);
\coordinate(R8) at ($(R1)!2/3!(R7)$);
\coordinate(R9) at ($(R1)!1/3!(R7)$);
\coordinate(R10) at ($(R3)!0.5!(R8)$);

\draw(T)--(R1)--(R4)--(R7)--cycle
	(T)--(R4)
	(Q1)--(Q3)--(Q5)
	(P1)--(P2)--(P3)
	(P1)--(Q2)--(P2)--(Q4)--(P3);

\draw[line join=round](Q1)--(R2)--(Q2)--(R3)--(Q3)--(R5)--(Q4)--(R6)--(Q5);

\draw[dashed,thin](P1)--(P3)
	(Q1)--(Q5)
	(R1)--(R7)
	(P1)--(Q6)--(P3)
	(Q1)--(R9)--(Q6)--(R8)--(Q5)
	(Q2)--(Q4)--(Q6)--cycle
	(R2)--(R10)--(R3)--(R5)--(R10)
		--(R6)--(R8)--(R10)--(R9)--(R10)--(R9)--cycle
	(Q2)--(R10)--(Q4)
	(Q6)--(R10);

%■デバッグ用
%\foreach \z in {T,R1,R4,R7,P1,P2,P3,Q1,Q2,Q3,Q4,Q5,Q6,R2,R3,R5,R6,R8,R9,R10}
%	\draw[red](\z) node{\fontsize{5}{5}\selectfont\textrm{\z}};
\end{tikzpicture}
\end{frame}
%%%%%%%%%%■■■■■■■■■■■■%%%%%%%%%%

\begin{frame}[t]
\frametitle{マス1グランプリ\quad 解答}
\begin{center}
答えは

\href{https://unilab.gbb60166.jp/prekou/pdf/coma-M1GPans.pdf}
{\textcolor{CUDBlue}{\scriptsize https://unilab.gbb60166.jp/prekou/pdf/coma-M1GPans.pdf}\ \beamergotobutton{web}}
\end{center}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{1st Round \quad 第１問解答}
\vskip-3ex
\begin{minipage}{0.8\textwidth}
{\arrayrulewidth=1pt
	\begin{eqnarray*}
	S&=& \hooklen{15}{1}+\hooklen{13}{3}+\hooklen{11}{5}+\cdots+15\\
	+)\quad S&=& 15+13+11+\cdots+\hooklen{15}{1}\\[3pt]\hline\\
	2S&=& \underbrace{16+16+16+\cdots+16}_{8\text{個}}\\[-1ex]
	2S&=& 16\times8\\
	S&=& 8\times8\\
	S&=& 64 \ \text{\□答}\quad\text{\tiny 素直に足した方が早いかも}
	\end{eqnarray*}
	}
\end{minipage}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{1st Round \quad 第２問解答}
\vskip-4ex
\begin{eqnarray*}
& &(10-1)+(100-1)+(1000-1)\\
& & \hskip0.2\textwidth +(10000-1)+(100000-1)\\
&=& 111110-5 \\
&=& \quad 111105 \quad\text{\□答}
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{1st Round \quad 第３問解答}
\centerline{\□答\ \(26973\)}

\vskip3ex
そのまま計算

\bigskip
または\( 27\times999=27(1000-1)=27000-27 \)
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{1st Round \quad 第４問解答}
\centerline{\□答\ \(50000\)}

\[ 2^4\times5^5=2^4\times(5^4\times5)=(2\times5)^4\times5
	=10^4\times5 \]
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{1st Round \quad 第５問解答}
\centerline{\□答\ \( (4+4)\div4+4 \)\quad など}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{1st Round \quad 第６問解答}
\centerline{\□答\ \( 97 \)}

\[ 49^2-48^2=(49+48)(49-48)=97\times1 \]

\centerline{\colorbox{CUDCream}{\(
	\raisebox{0.7ex}{\fboxsep=1pt\framebox{\tiny 公式}}\quad
		A^2-B^2=(A+B)(A-B) \)}
	}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{1st Round \quad 第７問解答}
\centerline{\□答\ \(2046\)}
\begin{eqnarray*}
& & 2+2^2\!+2^3\!+2^4\!+2^5\!+2^6\!+2^7\!+2^8\!+2^9\!+2^{10}\\
&=& 2+2\!\times\!(2+2^2\!+2^3\!+2^4\!+2^5\!+2^6\!+2^7\!+2^8\!+2^9)\\
&=& 2+2\!\times\!1022\\
&=& 2+2044\\
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{1st Round \quad 第８問解答}
\centerline{\□答\ \(\frac{4}{15}\)\qquad ユークリッドの互除法を使う}
\vskip-3ex
\begin{eqnarray*}
1365 &=& \textcolor{CUDRed}{364}\times3+\textcolor{CUDBlue}{273} \\
\textcolor{CUDRed}{364} &=& \textcolor{CUDBlue}{273}\times1
	+\textcolor{CUDGreen}{91} \\
\textcolor{CUDBlue}{273} &=& \textcolor{CUDGreen}{91}\times3
\end{eqnarray*}

よって\(1365\)と\(364\)の
最小公倍数は\textcolor{CUDGreen}{\(91\)}なので、
\textcolor{CUDGreen}{\(91\)}で約分
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{1st Round \quad 第９問解答}
\centerline{\□答\ \(127\)}

\vskip-3ex
\small
\begin{eqnarray*}
& & 1111111_{(2)}\\
&=& 1\times64+1\times32+1\times16+1\times8+1\times4+1\times2+1\times1 \\
&=& \qquad 127 \quad\text{\□答}
\end{eqnarray*}

\bigskip
\( 1111111_{(2)}
	=10000000_{(2)}-1_{(2)}
	=128-1
	= 127 \ \text{\□答} \)
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{1st Round \quad 第１\kern-.4zw０問解答}
\centerline{\□答\ 
\begin{minipage}[t]{0.5\textwidth}
\( 6\div(9\div3)+8 \)

\bigskip
\( 3+6-8+9 \)

\bigskip
\( 8+6\times3\div9 \)

\bigskip
\( (9+3)\div6+8 \)\quad など
\end{minipage}
}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{2nd Round\quad 解答}
\begin{minipage}[t]{0.6\textwidth}
一辺を$1$とすると面積は$5$なので、\( \sqrt{5}\times\sqrt{5} \)の
正方形を作ればよい。\textcolor{CUDRed}{赤の長さが\( \sqrt{5} \)}に
なるので切って並べ替える。
\end{minipage}
%
\quad
%
\begin{tikzpicture}[scale=2,very thick,
		baseline={( [yshift=-2ex] current bounding box.north)}]
%\fill[CUDCream](0,0)--(0,2)--(1,0)--cycle;
%\fill[CUDBrightCyan](0,2)--(1,2)--(1,0)--cycle;
%\fill[CUDMagenta!25](1,0)--(1,2)--(2,0)--cycle;
%\fill[CUDBrightGreen](1,2)--(2,2)--(2,0)--cycle;
%視覚に障害がある人のことを考えると、色だけに頼らないのが正解だと思う
\visible<2->{\draw[pattern color=CUDRed,
			pattern=fivepointed stars,line join=round]
		(0,0)--(0,2)--(1,0)--cycle;
	\draw[pattern color=CUDBlue,pattern=bricks,line join=round]
		(0,2)--(1,2)--(1,0)--cycle;
	\draw[pattern color=CUDGreen,pattern=checkerboard,line join=round]
		(1,0)--(1,2)--(2,0)--cycle;
	\draw[pattern=crosshatch dots,line join=round]
		(1,2)--(2,2)--(2,0)--cycle;
	}
\draw(0,0) rectangle ++(1,1)
	(1,0) rectangle ++(1,1)
	(0,1) rectangle ++(1,1)
	(1,1) rectangle ++(1,1)
	(1,2) rectangle ++(1,1);
\draw[CUDRed,ultra thick](0,2)--(1,0)
	(1,2)--(2,0);
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{2nd Round\quad 解答
	{\footnotesize （他の切り方もあります）}
	}
\centerline{%
\begin{tikzpicture}[scale=2,very thick,
		baseline={( [yshift=-2ex] current bounding box.north)}]
\draw[pattern color=CUDRed,pattern=fivepointed stars,line join=round]
	(0,0)--(0,2)--(-1,2)--cycle;
\draw[pattern color=CUDBlue,pattern=bricks,line join=round]
	(0,0)--(0,1)--(2,1)--cycle;
\draw[pattern color=CUDGreen,pattern=checkerboard,line join=round]
	(1,1)--(1,3)--(2,1)--cycle;
\draw[pattern=crosshatch dots,line join=round]
	(1,2)--(1,3)--(-1,2)--cycle;

\begin{scope}
\clip(0,0)--(2,1)--(1,3)--(-1,2)--cycle;
\draw(0,0) rectangle ++(1,1)
	(1,0) rectangle ++(1,1)
	(0,1) rectangle ++(1,1)
	(1,1) rectangle ++(1,1)
	(1,2) rectangle ++(1,1)

	(-1,2) rectangle ++(1,1)
	(-1,1) rectangle ++(1,1)
	(0,2) rectangle ++(1,1);
\end{scope}
\draw(0,0)--(2,1)--(1,3)--(-1,2)--cycle;
\end{tikzpicture}
}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{Final Round\quad 解答\quad パスカルの三角形}
\vskip-1ex
\begin{tikzpicture}[scale=0.3,very thick,>=stealth,inner sep=1pt,
		baseline={( [yshift=-2ex] current bounding box.north)}]
\footnotesize
\draw(44,18) node[text width=12zw]{\textcolor{CUDRed}{$9$段}積むと
		正四面体の合計数が\colorbox{CUDBrightCyan}{\(165\)}になる};
\draw(46,13) node[text width=10zw]{正四面体$1$つの辺は$6$なので、辺の合計は};
\draw(47,9) node{\(
	\colorbox{CUDBrightCyan}{\(165\)}\times6=990 \)};
\draw(50,5) node{\normalsize
		\□答\ \textcolor{CUDRed}{$9$段}};
\tiny
\draw[->,CUDOrange](18,{9*sqrt(3)}) node[left]{四面体数の列}
	--(38,{-1*sqrt(3)});
\draw[->,CUDGreen](20,{10*sqrt(3)}) node[left]{三角数の列}
	--(42,{-sqrt(3)});
\draw[->,CUDBlue](22,{11*sqrt(3)}) node[left]{自然数の列}
	--(46,{-sqrt(3)});

%■ソースファイル改善の余地あり
\draw(26,{11*sqrt(3)}) node[circle,fill=white]{1};
\foreach \x/\n in {1/1,2/1}
		\draw(4*\x+20,{10*sqrt(3)}) node[circle,fill=white]{\(\n\)};
\foreach \x/\n in {1/1,2/2,3/1}
		\draw(4*\x+18,{9*sqrt(3)}) node[circle,fill=white]{\(\n\)};
\foreach \x/\n in {1/1,2/3,3/3,4/1}
		\draw(4*\x+16,{8*sqrt(3)}) node[circle,fill=white]{\(\n\)};
\foreach \x/\n in {1/1,2/4,3/6,4/4,5/1}
		\draw(4*\x+14,{7*sqrt(3)}) node[circle,fill=white]{\(\n\)};
\foreach \x/\n in {1/1,2/5,3/10,4/10,5/5,6/1}
		\draw(4*\x+12,{6*sqrt(3)}) node[circle,fill=white]{\(\n\)};
\foreach \x/\n in {1/1,2/6,3/15,4/20,5/15,6/6,7/1}
		\draw(4*\x+10,{5*sqrt(3)}) node[circle,fill=white]{\(\n\)};
\foreach \x/\n in {1/1,2/7,3/21,4/35,5/35,6/21,7/7,8/1}
		\draw(4*\x+8,{4*sqrt(3)}) node[circle,fill=white]{\(\n\)};
\foreach \x/\n in {1/1,2/8,3/28,4/56,5/70,6/56,7/28,8/8,9/1}
		\draw(4*\x+6,{3*sqrt(3)}) node[circle,fill=white]{\(\n\)};
\foreach \x/\n in {1/1,2/9,3/36,4/84,5/126,6/126,7/84,8/36,9/9,10/1}
		\draw(4*\x+4,{2*sqrt(3)}) node[circle,fill=white]{\(\n\)};
\foreach \x/\n in {1/1,2/10,3/45,4/120,5/210,6/252,
			7/210,8/120,9/45,10/10,11/1}
		\draw(4*\x+2,{sqrt(3)}) node[circle,fill=white]{\(\n\)};
\foreach \x/\n in {1/1,2/11,3/55,4/165,5/330,6/462,
			7/462,8/330,9/165,10/55,11/11,12/1}
		\draw(4*\x,0) node[circle,fill=white]{\(\n\)};

\draw(36,0) node[fill=CUDBrightCyan,inner sep=4pt]{\(165\)};
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




\end{document}

