🚀 go-pugleaf

RetroBBS NetNews Server

Inspired by RockSolid Light RIP Retro Guy

Article View: fj.sci.math
Article #14274

Math. Olympiad 1993 Domestic first round

#14274
From: MARUYAMA Naomasa
Date: Fri, 15 Jan 1993 07:15
171 lines
6434 bytes
$@E}?t8&$N4];3$G$9!#(J

$@#1#9#9#3G/?t3X%*%j%s%T%C%/9qFbBh0l<!M=A*$O$?$C(J$@$?:#=*$j$^$7$?!#LdBj$N(J 
amsjlatex $@%=!<%9$rN.$7$^$9!#Cx:n8"$O?t3X%*%j%s%T%C%/:bCD$K5"B0$7$^$9$,!"(J
$@%3%T(J$@!<%U%j!<$G$9!#$?$@$71DMxE*MxMQ$K4X$7$F$O%*%j%s%T%C%/:bCD$N5v2D$rF@(J
$@$F$/$@$5$$!#(J

$@?7J9!";(;o$J$I$KJsF;(J$@$9$k>l9g$K$O!"?t3X%*%j%s%T%C%/:bCD$NL>A0$rF~$l$FD:(J
$@$1$l$P!"8DJL$K:bCD$N5v2D$rF@$k<j4V$O>J$$$FD:$$$F7k(J$@9=$G$9!#(J

%\documentstyle{article}
\documentstyle[amstex,amssymb,12pt]{jarticle}
\setlength{\topmargin}{-30mm}
%\addtolength{\textheight}{+30mm}
%\addtolength{\oddsidemargin}{-6mm}
%\addtolength{\evensidemargin}{-6mm}
\addtolength{\textwidth}{-12mm}
%\pagestyle{empty}
\newcommand{\spl}{\\[5mm]}

\title{1993$@G/F|K\?t3X%*%j%s%T%C%/M=A*(J}
\author{$@9q:]?t3X%*%j%s%T%C%/F|K\0Q0w2q(J}
\date{}
\begin{document}
\maketitle

\setlength{\baselineskip}{13pt}

\vspace*{0.5em}
\centerline{\bf \Large $@Ld(J \ \ $@Bj(J\footnote{Copyright \copyright 1993
 by Mathematical Olympiad Foundation of Japan \\
$@Cx:n8"$O?t3X%*%j%s%T%C%/:bCD(J$@$K5"B0$7$^$9(J.}}
\vspace{1em}
\noindent $\dagger$ 1993$@G/(J 1$@7n(J 15$@F|(J $@;n83;~4V(J 3$@;~4V(J 12$@Ld(J

\begin{description}
%
\item[1.]  \makebox[2 em]{}
$n^2$ $@$r(J 120 $@$G3d$k$H(J1$@M>$k$h$&$J!"(J 120 $@0J2<$N@5@0?t(J
$n$ $@$O$$$/$D$"(J$@$k$+!#(J
\spl


\item[2.] \makebox[2 em]{}
$@0lNs$K(J12$@6h2h$K6h@Z$i$l$?Cs<V>l$,$"$j!">hMQ<V$O(J1$@6h2h!"%H(J
$@%i%C(J$@%/$OO"B3$7$?(J2$@6h2h$rI,MW$H$9$k!#(J6$@Bf$N>hMQ<V$H(J2$@Bf$N%H(J
$@%i%C%/$,Cs<V$7$F$$$F!"$5$i$K%H%i%C%/(J1$@Bf$,Cs<V$G$-(J$@$k6u$-(J
$@6h2h$,$"$k!#$3$N$h$&$K>hMQ<V$H%H%i%C%/$rCs<V6h2h$KCs<V$9$k(J
$@%Q%?!<%s$O2?DL$j$"$k$+!#$?$@$73F>hMQ(J$@<V!"3F%H%i%C%/$O6hJL(J
$@$7$J$$!#(J
\spl

\item[3.]  \makebox[2 em]{}
$@BN@Q(J1$@$N@5(J4$@LLBN$K$*$$$F!"3FLL$H!"3FJU$N(J$@?bD>FsEyJ,J?LL$G0O$^$l$k(J
$@:G$b>.$5$$ItJ,$NBN@Q$r5a$a$h!#(J
\spl


\item[4.]  \makebox[2 em]{}
$@:BI8J?LL>e(J$@$N(J3$@E@(J$(0,0)$, $(276,153)$, $(a,b)$ 
$@$rD:E@$H$9$k;03Q7A$NLL@Q$,(J2$@0J2<$K$J$k$h$&$K!"(J
$@@5@0?t(J $a,b$ $@$rA*$V(J$@!#(J
$@$3$N$h$&$JE@(J$(a,b)$$@$N$&$A!"(J
$@86E@$K:G$b6a$$$b$N$r5a$a$h!#(J
\spl

\item[5.]  {\makebox[2 em]{}
$@0lJU$N(J$@D9$5$,(J1$@$N@5J}7A(JABCD$@Fb$NG$0U$NE@$r(JP,Q$@$H$9$k$H$-!"(J\par
\hskip15mm$\displaystyle{\mathrm{ AP}+\mathrm{ BP}+\mathrm{ PQ}+\mathrm{ CQ}+\mathrm{ DQ}}$\par
\noindent $@$N:G>.CM$r5a$a$h!#(J}
\spl


\item[6.]  \makebox[2 em]{}
$@=89g(J$ A=\{1,2,3,4,5,6,7\}$ $@$+$i(J $A$ $@$X$N<LA|(J $f$ $@$G!"(J
$@<!$N>r7o(J (1),(2) $@$r$_$?$9$b$N$O!"$$(J$@$/$D$"$k$+!#(J
\begin{description}
\item[ ]  (1) \ $@3F(J$j \in { A}$ $@$KBP$7$F!"(J
  $j=f(k)$ $@$H$J$k(J $k \in { A}$ $@$,M#0l$D$"$j!"(J
$@$7$+$b(J $k \neq j$ $@$G$"$k!#(J
\item[ ]  (2) \ $A$$@$+$i(J$A$$@$X$N<LA|(J$g$$@$,$"$j!"3F(J$j \in
{ A}$ $@$KBP$7$F!"(J\ $f(j)=g(g(j))$ $@$H$J$k!#(J
\end{description}

\vfill\eject


\vspace*{30mm}
\item[7.]  \makebox[2 em]{}
$@0lJ}$,(J 3 $@%2!<%`>!1[$7$?$H$-M%>!<T$,7h$^$k$H$$$&%k!<%k$G!"(J A,B $@$N(J2$@?M(J
$@$,6%5;$r9T$J$C$?(J$@!#$A$g$&$I(J 9 $@%2!<%`L\$G(J A $@$,(J 6$@>!(J3$@GT$H$J$j!"(J 
3 $@%2!<%`>!1[$7$FM%>!$7$?!#(J
$@$3$N$H$-9M$($i$l$k(J 9 $@%2!<%`$N(J$@>!GT%Q%?!<%s$O2?DL$j$"$k$+!#(J
\\[2mm]

%\eject
\item[8.] {\makebox[2 em]{}
$@:BI86u4V$K$*$$$F!"(J
$@6u4V?^7A(J$A$$@$r(J\par
\hskip7mm$\displaystyle{A = \{\;(x,y,z) \; | \; 2xy \geqq z^2,
\ x + y \leqq 1,\ x \geqq 0,\ y \geqq 0\;\}}$\par
\noindent $@$K$h$jDj$a$k!#(J
$@$^$?!"(J
$@6u4V?^7A(J$B$$@$r(J \par
\hskip7mm$\displaystyle{
  B = \{\;(u,v,w) \; | \; A \mbox{ $@$N$9$Y$F$NE@(J } (x,y,z)
\mbox{ $@$KBP$7$F!"(J } 0 \leqq ux + vy + wz \leqq 1\;\}}$\par
\noindent $@$K$h$jDj$a$k!#(J
$@$3$N$H$-!"(J
$@6u4V?^7A(J$B$$@$NBN@Q$r5a$a$h!#(J}\par\relax
\vskip9mm


\item[9.]  \makebox[2 em]{}
$S = \{1, 11, 31, 51, 71\}$ $@$H$7$F!"(J$\{a_n\}$ $@$O<!$N(J 
$@>r7o(J (1),(2),(3) $@$r$_(J$@$?$9?tNs$H$9$k!#(J
%{\parindent=20mm
\begin{description}
   \item[] (1) $a_1 \in { S}$
   \item[] (2) $\displaystyle{\frac{{a_{n+1} -1}}{a_n +1} \in { S}}$
   \item[] (3) 10 $@0J2<$N$"$k@5@0?t(J $n$ $@$KBP$7$F(J $a_n = 1993$
\end{description}

$@$3$N$h$&$J$9$Y$F$N?tNs(J $\{a_n\}$ $@$K$D$$$F!"(J $a_4$ $@$NCM$rNs5s$;$h!#(J
\\[2mm]

\item[10.]  \makebox[2 em]{}
$\displaystyle{\frac{1}{1 + \sqrt[5]{64} - \sqrt[5]{4}}}$ 
$@$rM-M}(J$@2=$7$?$H$-$NJ,Jl$N:G>.CM$r5a$a$h!#(J
\\[2mm]
$@$3$3$GM-M}2=$H$O!"(J
$@J,Jl$r@5$N@0?t$G!"(J
$@J,;R$r@0?t$H@0?t$NN_(J$@>h:,$$$/$D$+$NOB!":9$*$h$S@Q$GI=$9$3$H$G(J
$@$"$k!#(J
\\[2mm]


\item[11.]  \makebox[2 em]{}
$@<!$N?^7A$r0lI.(J$@=q$-$G=q$/$H$-!"=q$-J}$O(J
$@2?DL$j$"$k$+!#(J{
\setlength{\unitlength}{1mm}
\begin{center}
\begin{picture}(120,30)
  \put(15,25){\line(1,0){90}}
  \put(105,25){\line(-3,-5){15}}
  \put(90,0){\line(-1,0){90}}
  \put(0,0){\line(3,5){15}}
  \put(15,25){\line(3,-5){15}}
  \put(30,0){\line(3,5){15}}
  \put(45,25){\line(3,-5){15}}
  \put(60,0){\line(3,5){15}}
  \put(75,25){\line(3,-5){15}}
\end{picture}
\end{center}}
\vskip5mm


\item[12.]  \makebox[2 em]{}
4$@$D$NAj0[$J$k(J3$@7e$N@5@0?t$,$"$j!"I4$N0L$O$9$Y$FEy$7$$!#(J
$@$3$N$&$A(J3$@$D$N?t$O!"(J4$@?t$NOB$NLs?t$K$J$C$F$$$k!#(J
$@$3$N$h$&$J(J4$@$D$N?t$NAH$r$9$Y$F5a$a$h!#(J
\\[2mm]


\end{description}
\end{document}
--
1993$@G/(J01$@7n(J15$@F|(J($@6b(J)
--------
$@4];3D>>;!wE}7W?tM}8&5f=j(J
maruyama@ism.ac.jp
Technical Details
Message-ID: <MARUYAMA.93Jan15161522@sunnm.ism.ac.jp>
Path: arc1-ca.pugleaf.net!sparky!uunet!spool.mu.edu!sdd.hp.com!sgiblab!nec-gw!nec-tyo!wnoc-tyo-news!news.u-tokyo.ac.jp!ccut!s.u-tokyo!ismspc6!maruyama

Show Full Headers
Complete Article Headers
X-Google-Language: Japanese,JIS
X-Google-Thread: 10160c,428a89ca08d95bf,start
X-Google-Attributes: gid10160c,public
X-Google-Thread: f4956,428a89ca08d95bf,start
X-Google-Attributes: gidf4956,public
X-Google-ArrivalTime: 1993-01-14 23:15:22 PST
Newsgroups: fj.sci.math,fj.sources
Path: arc1-ca.pugleaf.net!sparky!uunet!spool.mu.edu!sdd.hp.com!sgiblab!nec-gw!nec-tyo!wnoc-tyo-news!news.u-tokyo.ac.jp!ccut!s.u-tokyo!ismspc6!maruyama
From: maruyama@sunnm.ism.ac.jp (MARUYAMA Naomasa)
Subject: Math. Olympiad 1993 Domestic first round
Date: Fri, 15 Jan 1993 07:15:22 GMT
Nntp-Posting-Host: sunnm
Distribution: fj
Reply-To: maruyama@ism.ac.jp
Organization: The Inst. of Statistical Mathematics, Tokyo Japan
Sender: news@ism.ac.jp
Message-ID: <MARUYAMA.93Jan15161522@sunnm.ism.ac.jp>
Lines: 171