{VERSION 3 0 "IBM INTEL NT" "3.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }
{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 
"" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 1 18 0 0 0 0 0 
1 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 1 24 0 0 0 0 0 1 0 0 0 0 0 0 0 }
{CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 
"" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 1 
0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }
{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 266 
"" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 0 
1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 
12 0 0 0 1 2 2 2 2 2 2 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "He
ading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 
1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE 
"" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 
-1 0 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 
2 1 2 2 2 2 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "" 3 257 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 
0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 
0 0 0 0 -1 0 }{PSTYLE "" 0 260 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 19 
"Matem\341tica Discreta" }{TEXT 259 0 "" }{TEXT -1 0 "" }}{PARA 258 "
" 0 "" {TEXT 260 32 "Soluciones del examen de Maple B" }}{PARA 259 "" 
0 "" {TEXT -1 66 "Ingenier\355a T\351cnica en Inform\341tica de Sistem
as (tarde) y de Gesti\363n" }}{PARA 260 "" 0 "" {TEXT -1 19 " Septiemb
re de 2004" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }{TEXT 256 13 "Ejercicio 1. " }{TEXT -1 28 "Encuentra el n\372
mero natural " }{TEXT 262 1 "n" }{TEXT -1 1 " " }{TEXT 264 6 "m\355nim
o" }{TEXT -1 32 " tal que 123 divide a  468 + 88 " }{TEXT 263 2 "n." }
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "restart;with
(numtheory):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "i:=1:\nwhil
e (468 + 88*i) mod 123<>0 do i:=i+1: od:\ni+1;" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT 258 1 " " }{TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT 257 12 "Ejercicio 2." }{TEXT -1 60 " Tene
mos 4 trajes de verano, 8 de primavera y 3 de invierno." }}{PARA 0 "" 
0 "" {TEXT -1 111 "\277De cu\341ntas maneras distintas podemos dispone
rlos en un armario? \277Y si ponemos juntos los de la misma estaci\363
n?" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "restart; with(combinat
):" }}}{PARA 0 "" 0 "" {TEXT -1 98 "Para contestar a la primera pregun
ta tenemos que calcular las permutaciones de 4+8+3=15 elementos:" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "numbperm(15);factorial(15);
" }}}{PARA 0 "" 0 "" {TEXT -1 179 "Para contestar a la segunda pregunt
a observamos que hay 3! maneras de ordenar les tres estaciones, 4! los
 trajes de verano, 8! los trajes de primavera y 3! los trajes de invie
rno:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "numbperm(3)*numbperm
(4)*numbperm(8)*numbperm(3);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 261 12 "Ejercicio 3." }{TEXT -1 
5 "  Sea" }{TEXT 266 1 " " }{TEXT -1 51 "G el cubo Q3.  Responde a las
 siguientes preguntas:" }}{PARA 0 "" 0 "" {TEXT -1 73 "a)  \277Cu\341l
 es el n\372mero de caminos de longitud 3 entre los v\351rtices 1 y 3?
" }}{PARA 0 "" 0 "" {TEXT -1 44 "b) \277Es G Euleriano?  Justifica tu \+
respuesta." }}{PARA 0 "" 0 "" {TEXT -1 44 "c) \277Es G un \341rbol?  J
ustifica tu respuesta. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "r
estart; with(networks):" }}}{PARA 0 "" 0 "" {TEXT -1 46 "Comenzamos po
r hacer la matriz de adyacencias," }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "M:= adjacency(cube(3));" }}}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 66 "a) El n\372mero de caminos de long
itud 3 entre los v\351rtices 1 y 3 es:" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "evalm(M^3)[1,3];" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 57 "b) Veamos si es euleriano utilizando el t
eorema de Euler:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "degreese
q(cube(3)); " }}}{PARA 0 "" 0 "" {TEXT -1 68 "al ser todos sus v\351rt
ices de grado impar, el grafo no es Euleriano. " }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 68 "c) Para ver si es un \341
rbol, hemos de comprobar si tiene o no ciclos:" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 17 "evalm(M^4)[1,1]; " }}}{PARA 0 "" 0 "" {TEXT -1 
73 "Al tener caminos de longitud 4 de 1 a 1, no es un \341rbol (no es \+
ac\355clico)." }}{PARA 11 "" 1 "" {TEXT -1 0 "" }{TEXT 265 0 "" }}
{PARA 0 "" 0 "" {TEXT 267 13 "Ejercicio 4. " }{TEXT -1 82 " Dado el ci
clo C24, calcula el n\372mero de entradas nulas de su matriz de adyace
ncia" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(networks):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "L:=adjacency(cycle(24)):" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "with(linalg): rowdim(L);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "c:=0; for i from 1 to 24 d
o for j from 1 to 24 do\nc:=c + L[i,j] od; od; c; " }}}{PARA 0 "" 0 "
" {TEXT -1 26 "As\355, la respuesta ser\341:   " }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 9 "24*24-48;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{MARK "46" 0 }{VIEWOPTS 1 1 0 1 1 1803 }