diff --git a/code/online-part-1/Roboterfahrt Aufgabe 1.ipynb b/code/online-part-1/Roboterfahrt Aufgabe 1.ipynb
index 30bd9f9..4ec81fd 100644
--- a/code/online-part-1/Roboterfahrt Aufgabe 1.ipynb	
+++ b/code/online-part-1/Roboterfahrt Aufgabe 1.ipynb	
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 2,
    "id": "00d20df1",
    "metadata": {},
    "outputs": [],
@@ -30,36 +30,33 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 24,
    "id": "bec0fab0",
    "metadata": {},
    "outputs": [],
    "source": [
     "start = np.array([3,5])\n",
-    "fahrt1 = ...\n",
-    "fahrt2 = ...\n",
-    "fahrt3 = ...\n",
-    "fahrt4 = ..."
+    "fahrt1 = np.array([+1, +2])\n",
+    "fahrt2 = np.array([+2, +1])\n",
+    "fahrt3 = np.array([+2, -1])\n",
+    "fahrt4 = np.array([-1, -3])"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 23,
    "id": "e55f20bc",
    "metadata": {},
    "outputs": [
     {
-     "ename": "ValueError",
-     "evalue": "all the input array dimensions except for the concatenation axis must match exactly, but along dimension 1, the array at index 0 has size 2 and the array at index 1 has size 1",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
-      "\u001b[31mValueError\u001b[39m                                Traceback (most recent call last)",
-      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[3]\u001b[39m\u001b[32m, line 8\u001b[39m\n\u001b[32m      5\u001b[39m     plt.xlim((\u001b[32m0\u001b[39m,\u001b[32m10\u001b[39m))\n\u001b[32m      6\u001b[39m     plt.ylim((\u001b[32m0\u001b[39m,\u001b[32m10\u001b[39m))\n\u001b[32m----> \u001b[39m\u001b[32m8\u001b[39m \u001b[43mplot_path\u001b[49m\u001b[43m(\u001b[49m\u001b[43mstart\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m[\u001b[49m\u001b[43mfahrt1\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfahrt2\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfahrt3\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfahrt4\u001b[49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n",
-      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[3]\u001b[39m\u001b[32m, line 3\u001b[39m, in \u001b[36mplot_path\u001b[39m\u001b[34m(start, moves)\u001b[39m\n\u001b[32m      2\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34mplot_path\u001b[39m(start, moves):\n\u001b[32m----> \u001b[39m\u001b[32m3\u001b[39m     path = \u001b[43mnp\u001b[49m\u001b[43m.\u001b[49m\u001b[43mvstack\u001b[49m\u001b[43m(\u001b[49m\u001b[43m[\u001b[49m\u001b[43mstart\u001b[49m\u001b[43m]\u001b[49m\u001b[43m \u001b[49m\u001b[43m+\u001b[49m\u001b[43m \u001b[49m\u001b[43mmoves\u001b[49m\u001b[43m)\u001b[49m.cumsum(axis=\u001b[32m0\u001b[39m)\n\u001b[32m      4\u001b[39m     plt.plot(path[:,\u001b[32m0\u001b[39m], path[:,\u001b[32m1\u001b[39m])\n\u001b[32m      5\u001b[39m     plt.xlim((\u001b[32m0\u001b[39m,\u001b[32m10\u001b[39m))\n",
-      "\u001b[36mFile \u001b[39m\u001b[32m~/Computational_and_Data_Science/FS25/CDS104-Databases-and-Data-Processing/code/.venv/lib/python3.13/site-packages/numpy/_core/shape_base.py:292\u001b[39m, in \u001b[36mvstack\u001b[39m\u001b[34m(tup, dtype, casting)\u001b[39m\n\u001b[32m    290\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(arrs, \u001b[38;5;28mtuple\u001b[39m):\n\u001b[32m    291\u001b[39m     arrs = (arrs,)\n\u001b[32m--> \u001b[39m\u001b[32m292\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43m_nx\u001b[49m\u001b[43m.\u001b[49m\u001b[43mconcatenate\u001b[49m\u001b[43m(\u001b[49m\u001b[43marrs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[32;43m0\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdtype\u001b[49m\u001b[43m=\u001b[49m\u001b[43mdtype\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcasting\u001b[49m\u001b[43m=\u001b[49m\u001b[43mcasting\u001b[49m\u001b[43m)\u001b[49m\n",
-      "\u001b[31mValueError\u001b[39m: all the input array dimensions except for the concatenation axis must match exactly, but along dimension 1, the array at index 0 has size 2 and the array at index 1 has size 1"
-     ]
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
     }
    ],
    "source": [
@@ -83,11 +80,23 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 22,
    "id": "90852486",
    "metadata": {},
-   "outputs": [],
-   "source": []
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Endposition: [7 4]\n"
+     ]
+    }
+   ],
+   "source": [
+    "fahrten = [fahrt1, fahrt2, fahrt3, fahrt4]\n",
+    "end = start + sum(fahrten)\n",
+    "print(\"Endposition:\", end)"
+   ]
   },
   {
    "cell_type": "markdown",
@@ -99,11 +108,22 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 21,
    "id": "6ee1ca50",
    "metadata": {},
-   "outputs": [],
-   "source": []
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Länge der Fahrt: 9.87048159266775\n"
+     ]
+    }
+   ],
+   "source": [
+    "lenght = sum([np.linalg.norm(f) for f in fahrten])\n",
+    "print(\"Länge der Fahrt:\", lenght)"
+   ]
   },
   {
    "cell_type": "markdown",
@@ -115,11 +135,22 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 20,
    "id": "04a2e60a",
    "metadata": {},
-   "outputs": [],
-   "source": []
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Direkte Länge: 4.123105625617661\n"
+     ]
+    }
+   ],
+   "source": [
+    "direct_length = np.linalg.norm(end - start)\n",
+    "print(\"Direkte Länge:\", direct_length)"
+   ]
   }
  ],
  "metadata": {