Weitere Aufgabe Kombinatorik

21_22_B/6MG19t_pr2_Kombinatorik/Pruefung.tex

@@ -31,6 +31,8 @@
 \input{P_GESO/stoch/kombinatorik/Variation_Ohne_Wiederholung_Theater_v1}
 \input{P_GESO/stoch/kombinatorik/Variation_mit_Wiederholung_Zelte_v1}
 
+\input{P_GESO/stoch/kombinatorik/Wegnetz_v1}
+
 \input{P_GESO/stoch/kombinatorik/Permutation_der_Permutation_v1}
 
 \end{document}

aufgaben/P_GESO/stoch/kombinatorik/Permutation_der_Permutation_v1.tex

@@ -1,6 +1,6 @@
 \begin{frage}[3]%% Anzahl Punkte für diese Aufgabe
 
-Pascal richtet sein Dessert auf einer langen Platte in einer Reihen
+Pascal richtet sein Dessert auf einer langen Platte in einer Reihe
 an. Es gibt sechs verschiedene Pralinen, vier verschiedene Donuts und
 fünf verschiedene Biskuits.
 

aufgaben/P_GESO/stoch/kombinatorik/Wegnetz_v1.tex

@@ -0,0 +1,14 @@
+\begin{frage}[3]%% Anzahl Punkte für diese Aufgab
+
+  \bbwCenterGraphic{8cm}{P_GESO/stoch/kombinatorik/img/Wegnetz.png}
+
+  Eine Laufstrecke führt von $A$ nach $E$. Dabei führt sie optional
+  auch über $B$, $C$ oder $D$.
+
+  Auf wie viele Arten kann Kim von $A$ nach $E$ laufen, wenn
+  ausschließlich Nordwest- nach Südoststrecken sinnvoll sind. Es soll
+  also nie zurück in Richtung $A$ gelaufen werden. 
+
+  Total stehen \LoesungsRaum{15} Varianten zur Auswahl.
+  \platzFuerBerechnungen{4.4}
+\end{frage}

aufgaben/P_GESO/stoch/kombinatorik/img_src/Wegnetz.svg

@@ -0,0 +1,238 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   xmlns:dc="http://purl.org/dc/elements/1.1/"
+   xmlns:cc="http://creativecommons.org/ns#"
+   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
+   xmlns:svg="http://www.w3.org/2000/svg"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   width="115.38426mm"
+   height="133.97153mm"
+   viewBox="0 0 115.38426 133.97153"
+   version="1.1"
+   id="svg8"
+   sodipodi:docname="Wegnetz.svg"
+   inkscape:version="0.92.4 (5da689c313, 2019-01-14)">
+  <defs
+     id="defs2" />
+  <sodipodi:namedview
+     id="base"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:pageopacity="0.0"
+     inkscape:pageshadow="2"
+     inkscape:zoom="1.979899"
+     inkscape:cx="194.92987"
+     inkscape:cy="111.21921"
+     inkscape:document-units="mm"
+     inkscape:current-layer="g1139"
+     showgrid="false"
+     inkscape:window-width="3840"
+     inkscape:window-height="2135"
+     inkscape:window-x="1920"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     fit-margin-top="0"
+     fit-margin-left="0"
+     fit-margin-right="0"
+     fit-margin-bottom="0" />
+  <metadata
+     id="metadata5">
+    <rdf:RDF>
+      <cc:Work
+         rdf:about="">
+        <dc:format>image/svg+xml</dc:format>
+        <dc:type
+           rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
+        <dc:title></dc:title>
+      </cc:Work>
+    </rdf:RDF>
+  </metadata>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1"
+     transform="translate(-12.975445,-13.632762)">
+    <g
+       id="g1010">
+      <g
+         id="g1061">
+        <g
+           id="g1035">
+          <g
+             id="g1196">
+            <g
+               id="g1167">
+              <g
+                 id="g1139">
+                <path
+                   style="opacity:1;fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:0.46899223"
+                   d="M 33.406175,27.608 C 22.692789,32.521845 9.8633669,43.940953 14.029213,56.922599 c 3.889682,10.217772 23.906284,9.229646 18.282523,23.334209 -6.154912,10.341263 -6.469511,24.871032 5.382813,31.385412 13.562693,3.71836 15.49724,17.94575 23.786994,26.8864 11.291938,7.79735 25.703333,11.48975 38.972557,6.65681 7.48369,-1.08864 11.95818,-7.87735 16.86277,-12.87801"
+                   id="path852"
+                   inkscape:connector-curvature="0" />
+                <path
+                   style="opacity:1;fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:0.46899223"
+                   d="m 33.409622,27.607429 c -0.496033,-2.48174 1.84449,-4.867917 4.358842,-3.94283 4.66684,0.131869 9.343206,0.02012 14.014275,0.05861 3.315312,0.986266 7.262314,-0.568291 10.087471,2.038958 2.124807,1.615153 1.762439,4.403233 2.436687,6.567638 0.0797,1.726042 -3.231116,3.740929 0.03701,3.652737 0.520373,1.57491 0.785472,3.400574 3.000678,2.491824 2.304984,-0.790969 5.858281,0.660653 4.146727,3.522902 -1.565619,2.252103 -3.362147,4.435403 -5.489851,6.185895 -3.080403,1.321668 -6.947695,3.217864 -7.922525,6.594106 0.212081,1.247147 1.138276,2.218864 1.407583,3.446807"
+                   id="path854"
+                   inkscape:connector-curvature="0" />
+                <path
+                   style="opacity:1;fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.493;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:0.46899223"
+                   d="M 58.078327,56.397685 C 57.485599,50.861587 97.57147,42.659888 101.61432,40.820093 c 9.08097,3.660265 3.00288,8.695558 10.70615,13.945862 1.88388,4.922324 6.4733,7.034775 9.99081,10.621856 -0.0218,3.84723 2.1487,5.8068 3.72452,8.947176 -1.08,5.493628 -2.65511,10.937223 -2.87329,16.616797 -2.72206,4.658598 4.88685,8.622403 4.9507,14.936826 -0.80969,4.66393 -2.49664,5.0073 -2.96441,12.28673 -1.94878,4.78575 -2.64297,7.51071 -7.89489,10.70919 0.18949,0.65644 -0.0112,-0.71052 0,0"
+                   id="path856"
+                   inkscape:connector-curvature="0"
+                   sodipodi:nodetypes="cccccccccc" />
+                <path
+                   style="opacity:1;fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.52380884;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:0.46899223"
+                   d="m 33.406175,27.608 c -3.924208,9.433864 5.403448,16.548542 11.230102,22.23561 4.934318,4.0019 17.267366,2.433985 14.405721,12.072052 -3.918154,7.783682 -3.465123,18.436245 3.842877,24.040088 6.890696,4.338249 12.347214,11.979066 20.797395,13.110837 3.974269,0.09441 6.068669,-8.36953 8.389122,-3.385079"
+                   id="path860"
+                   inkscape:connector-curvature="0"
+                   sodipodi:nodetypes="cccccc" />
+                <path
+                   style="opacity:1;fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:0.46899223"
+                   d="m 59.489964,58.223512 c 0.435716,-1.811919 2.56296,-2.51083 4.186033,-1.898418 1.373801,0.804533 2.944276,0.935851 4.483026,1.215433 1.912911,0.306748 2.673796,2.129172 3.978459,3.266677 0.787286,1.372783 0.63418,3.385663 -0.648231,4.409517 0.875249,2.218716 -2.346172,4.013472 -1.451514,5.926151 1.876813,2.159621 5.282248,1.152998 7.288422,3.081182 0.600563,1.549645 0.671514,3.402022 -0.987828,4.251335 -0.679213,1.835645 1.429745,3.074467 2.755564,3.880416 1.643343,0.514072 2.27338,2.467033 4.15805,2.667298 1.648175,0.301572 3.227381,1.181106 4.161157,2.465405 2.523904,0.200645 1.560213,4.047292 2.017945,4.721052 1.148563,-0.122761 -0.471718,2.821352 0.324524,1.863921 0.617864,0.111841 1.133655,0.496206 1.714667,0.709256"
+                   id="path862"
+                   inkscape:connector-curvature="0" />
+                <path
+                   style="opacity:1;fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:0.46899223"
+                   d="m 57.452381,54.717261 c 2.914048,1.549493 5.409788,1.380386 7.068123,-0.826541 4.184151,-0.675483 8.513264,-0.132058 12.765665,-0.304965 2.80106,0.170068 8.390276,-0.550901 9.099137,0.748289 2.370398,1.345729 4.850307,2.371296 4.779886,5.281784 0.235044,2.975259 1.538342,4.728475 2.558673,7.238641 0.513289,2.965728 4.245218,3.976727 5.320435,6.841095 1.47407,2.656754 3.59662,7.009378 0.866405,9.041666 -1.00029,3.208435 -3.557293,5.792579 -4.711877,9.285894 -2.292637,-0.231506 -1.434669,3.659243 -3.72859,2.759617"
+                   id="path864"
+                   inkscape:connector-curvature="0" />
+                <text
+                   xml:space="preserve"
+                   style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10.58333302px;line-height:1.25;font-family:Grey;-inkscape-font-specification:Grey;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.26458332"
+                   x="18.898809"
+                   y="20.321428"
+                   id="text868"><tspan
+                     sodipodi:role="line"
+                     id="tspan866"
+                     x="18.898809"
+                     y="20.321428"
+                     style="stroke-width:0.26458332">A</tspan></text>
+                <text
+                   xml:space="preserve"
+                   style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10.58333302px;line-height:1.25;font-family:Grey;-inkscape-font-specification:Grey;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.26458332"
+                   x="49.5369"
+                   y="66.742477"
+                   id="text872"><tspan
+                     sodipodi:role="line"
+                     id="tspan870"
+                     x="49.5369"
+                     y="66.742477"
+                     style="stroke-width:0.26458332">B</tspan></text>
+                <text
+                   xml:space="preserve"
+                   style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10.58333302px;line-height:1.25;font-family:Grey;-inkscape-font-specification:Grey;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.26458332"
+                   x="74.143105"
+                   y="69.822006"
+                   id="text876"><tspan
+                     sodipodi:role="line"
+                     id="tspan874"
+                     x="74.143105"
+                     y="69.822006"
+                     style="stroke-width:0.26458332">C</tspan></text>
+                <text
+                   xml:space="preserve"
+                   style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:11.9911108px;line-height:1.25;font-family:Grey;-inkscape-font-specification:Grey;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.29977778"
+                   x="112.46525"
+                   y="81.965569"
+                   id="text880"
+                   transform="scale(0.88259819,1.1330184)"><tspan
+                     sodipodi:role="line"
+                     id="tspan878"
+                     x="112.46525"
+                     y="81.965569"
+                     style="stroke-width:0.29977778">D</tspan></text>
+                <path
+                   style="opacity:1;fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:0.64980541"
+                   d="m 91.659225,97.286827 c -1.224267,2.072397 -2.644308,6.264503 0.884275,6.845643 3.785682,-0.19772 3.61938,3.81162 1.084578,5.55522 -2.641388,2.3017 -0.345996,4.37262 1.072036,6.44282 2.113432,1.07968 4.617094,1.84172 4.915548,4.80285 0.835588,2.9613 3.874608,4.1139 5.406818,6.53121 1.14879,3.01584 4.92056,3.81232 7.76128,2.99824 0.89059,-0.21858 1.75654,-0.52404 2.64103,-0.7645"
+                   id="path959"
+                   inkscape:connector-curvature="0" />
+                <path
+                   style="opacity:1;fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:0.64980541"
+                   d="m 93.832589,95.680431 c 2.720908,-1.024632 5.757828,-0.01476 8.602101,0.05663 3.44959,0.01522 3.97352,3.204339 4.32726,5.894149 1.55323,3.42787 -2.33949,3.47778 -0.13817,6.23619 1.73543,2.26778 7.92404,-0.0684 7.09822,3.18066 -0.24241,1.79189 -1.26105,8.02714 1.65618,8.50681 0.61762,2.94555 3.60553,5.2001 1.32594,7.34023 -0.67456,0.91465 -1.09868,3.45979 0.89359,2.61446"
+                   id="path961"
+                   inkscape:connector-curvature="0"
+                   sodipodi:nodetypes="cccccccc" />
+                <path
+                   style="opacity:1;vector-effect:none;fill:#00a105;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:0.5;stroke-linecap:square;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+                   id="path815"
+                   sodipodi:type="arc"
+                   sodipodi:cx="32.883945"
+                   sodipodi:cy="25.235107"
+                   sodipodi:rx="2.793129"
+                   sodipodi:ry="2.415488"
+                   sodipodi:start="1.3827196"
+                   sodipodi:end="1.381463"
+                   sodipodi:open="true"
+                   d="m 33.406176,27.608 a 2.793129,2.415488 0 0 1 -3.26594,-1.920524 2.793129,2.415488 0 0 1 2.219755,-2.824977 2.793129,2.415488 0 0 1 3.267335,1.918749 2.793129,2.415488 0 0 1 -2.217702,2.826182" />
+                <path
+                   style="opacity:1;vector-effect:none;fill:#00a105;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:0.5;stroke-linecap:square;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+                   id="path815-3"
+                   sodipodi:type="arc"
+                   sodipodi:cx="116.79464"
+                   sodipodi:cy="129.93452"
+                   sodipodi:rx="2.793129"
+                   sodipodi:ry="2.415488"
+                   sodipodi:start="1.3827196"
+                   sodipodi:end="1.381463"
+                   sodipodi:open="true"
+                   d="m 117.31687,132.30742 a 2.793129,2.415488 0 0 1 -3.26594,-1.92053 2.793129,2.415488 0 0 1 2.21975,-2.82497 2.793129,2.415488 0 0 1 3.26734,1.91874 2.793129,2.415488 0 0 1 -2.2177,2.82619" />
+                <path
+                   style="opacity:1;vector-effect:none;fill:#00a105;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:0.5;stroke-linecap:square;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+                   id="path815-6"
+                   sodipodi:type="arc"
+                   sodipodi:cx="58.964287"
+                   sodipodi:cy="55.851189"
+                   sodipodi:rx="2.793129"
+                   sodipodi:ry="2.415488"
+                   sodipodi:start="1.3827196"
+                   sodipodi:end="1.381463"
+                   sodipodi:open="true"
+                   d="m 59.486518,58.224081 a 2.793129,2.415488 0 0 1 -3.265941,-1.920523 2.793129,2.415488 0 0 1 2.219755,-2.824978 2.793129,2.415488 0 0 1 3.267335,1.918749 2.793129,2.415488 0 0 1 -2.217702,2.826183" />
+                <path
+                   style="opacity:1;vector-effect:none;fill:#00a105;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:0.5;stroke-linecap:square;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+                   id="path815-7"
+                   sodipodi:type="arc"
+                   sodipodi:cx="78.254356"
+                   sodipodi:cy="74.389984"
+                   sodipodi:rx="2.793129"
+                   sodipodi:ry="2.415488"
+                   sodipodi:start="1.3827196"
+                   sodipodi:end="1.381463"
+                   sodipodi:open="true"
+                   d="m 78.776587,76.762877 a 2.793129,2.415488 0 0 1 -3.26594,-1.920524 2.793129,2.415488 0 0 1 2.219755,-2.824977 2.793129,2.415488 0 0 1 3.267335,1.918748 2.793129,2.415488 0 0 1 -2.217702,2.826183" />
+                <path
+                   style="opacity:1;vector-effect:none;fill:#00a105;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:0.5;stroke-linecap:square;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+                   id="path815-5"
+                   sodipodi:type="arc"
+                   sodipodi:cx="92.604164"
+                   sodipodi:cy="95.160713"
+                   sodipodi:rx="2.793129"
+                   sodipodi:ry="2.415488"
+                   sodipodi:start="1.3827196"
+                   sodipodi:end="1.381463"
+                   sodipodi:open="true"
+                   d="m 93.126395,97.533606 a 2.793129,2.415488 0 0 1 -3.265941,-1.920524 2.793129,2.415488 0 0 1 2.219755,-2.824977 2.793129,2.415488 0 0 1 3.267336,1.918749 2.793129,2.415488 0 0 1 -2.217702,2.826182" />
+                <text
+                   xml:space="preserve"
+                   style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10.58333302px;line-height:1.25;font-family:Grey;-inkscape-font-specification:Grey;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.26458332"
+                   x="121.73512"
+                   y="133.25327"
+                   id="text872-3"><tspan
+                     sodipodi:role="line"
+                     id="tspan870-5"
+                     x="121.73512"
+                     y="133.25327"
+                     style="stroke-width:0.26458332">E</tspan></text>
+              </g>
+            </g>
+          </g>
+        </g>
+      </g>
+    </g>
+  </g>
+</svg>