{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "336da017-8148-4cdc-aa8f-da7479904ad1",
   "metadata": {},
   "source": [
    "# Sudoku"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db2f4bc6-3df0-450e-9565-3834fa4218fd",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d01887c-a1c4-4b7f-aa83-6c6e90793a62",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-danger\">\n",
    "<b>Ziel des Notebooks:</b>\n",
    "\n",
    "- Wie kann man das Konzept von Sudokus mathematisch sinnvoll modellieren?\n",
    "- Wieviele verschiedene Sudokus gibt es?\n",
    "- (Wie) kann man Sudokus klassifizieren oder vergleichen?\n",
    "\n",
    "<br>\n",
    "    \n",
    "<b>Mathematische Tools:<b>\n",
    "- Kombinatorik\n",
    "- Gruppen, Gruppenoperationen und $G$-Mengen\n",
    "- Burnsidesches Lemma\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a66a211-9294-4943-b781-770914688710",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "attachments": {
    "e02f1141-72ec-45ff-8f76-8864a2300c92.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "35ae266a-5d8d-4397-baba-35bc11e053fd",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Definition des Sudoku\n",
    "\n",
    "Ein <b>klassisches Sudoku</b> ist ein Zahlenfeld der Größe $9\\times9$, also bestehend aus $9$ <b>Zeilen</b> und $9$ <b>Spalten</b>, mit Zahleneinträgen aus der Menge $\\{1,\\dots,9\\}$. Dieses Feld teilt man auf in $9$ sogenannte <b>Blöcke</b> der Größe $3\\times3$. Deswegen sprechen wir in diesem Fall von einem $3\\times 3$-Sudoku.\n",
    "\n",
    "<div>\n",
    "<img src=\"attachment:e02f1141-72ec-45ff-8f76-8864a2300c92.png\" width=\"300\"/>\n",
    "</div>\n",
    "\n",
    "\n",
    "Die Anordnung der Zahlen müssen folgende Regeln erfüllen:\n",
    "- jede Zeile muss jede Zahl $k\\in\\{1,\\dots,9\\}$ genau einmal enthalten\n",
    "- jede Spalte muss jede Zahl $k\\in\\{1,\\dots,9\\}$ genau einmal enthalten\n",
    "- jeder Block muss jede Zahl $k\\in\\{1,\\dots,9\\}$ genau einmal enthalten\n",
    "\n",
    "Ein <b>Sudoku-Puzzle</b> ist ein nur teilweise ausgefülltes Zahlenfeld derselben Größe, welches sich durch Eintragen von Zahlen in den leeren Feldern zu einem Sudoku vervollständigen lässt. Das <b>Sudoku-Spiel</b> besteht gerade darin, das Sudoku-Puzzle zu einem Sudoku zu vervollständigen.\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29048ba9-c434-49ea-b2fd-1ee1f60fe233",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Recherche-Aufgabe\n",
    "***\n",
    "- Wie ist ein Lateinisches Quadrat definiert?\n",
    "- In welchem Zusammenhang steht dieses zum $9\\times9$-Sudoku, wie Sie es kennen?\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bdbff649-f176-45f4-ae8b-e2482d89342c",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "attachments": {
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"
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"
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    }
   },
   "cell_type": "markdown",
   "id": "153aaa76-a2aa-4710-8c3e-779135505af6",
   "metadata": {},
   "source": [
    "Beginnend werden ein paar Bezeichnungen eingeführt, um besser über ein Sudoku sprechen und dieses analysieren zu können.\n",
    "\n",
    "Die Struktur eines $9 \\times 9$-Sudokus entspricht offenbar einer $9 \\times 9$-Matrix mit bestimmten Zahleneinträgen aus $\\{1,\\dots,9\\}$. Wir übernehmen hier die Begriffe, die Sie in der Linearen Algebra für allgemeine Matrizen gelernt haben.\n",
    "Somit besitzt ein Sudoku jeweils $9$ <b>Zeilen</b> und <b>Spalten</b>, die wir mit $r_{j}$ bzw. $c_{i}$ für $i,j\\in\\{1,\\dots,9\\}$ bezeichnen.\n",
    "\n",
    "\n",
    "<div>\n",
    "<img src=\"attachment:dfaab7c8-29d5-4945-85fe-b64238017cae.png\" width=\"250\"/>\n",
    "</div>\n",
    "\n",
    "\n",
    "Eine Gliederung des Sudokus ist auch anhand seiner <b>Blöcke</b> $q_{k,l}$ mit  $k,l\\in\\{1,2,3\\}$ möglich.\n",
    "\n",
    "<div>\n",
    "<img src=\"attachment:1c6102a9-5c4f-49b9-979b-cb7893c61f4e.png\" width=\"250\"/>\n",
    "</div>\n",
    "\n",
    "Ein Sudoku kann man auch als $3 \\times 3$-Matrix auffassen, deren Einträge $3 \\times 3$-Zahlenblöcke sind. Einen bestimmten Block referieren wir mit $q_{i,j}$. <br>\n",
    "Die Zeilen und Spalten der $3 \\times 3$-Matrix entsprechen in unserem Sudoku den <b>Bändern</b> $b_{j}$  und <b>Stapeln</b> $s_{i}$. Zum Beispiel stellt in der folgenden Abbildung $b_2$ die markierte Zeile und $s_2$ die markierte Spalte dar.\n",
    "\n",
    "<div>\n",
    "<img src=\"attachment:4dc6008d-a144-4baa-88ab-ed6843c759a7.png\" width=\"250\"/>\n",
    "<img src=\"attachment:0d23dd85-28b4-4051-bf91-0edfda592258.png\" width=\"250\"/>\n",
    "</div>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52f36be1-3bf2-4c5c-a52a-7b8581e61782",
   "metadata": {},
   "source": [
    "Als nächstes wollen wir uns Gedanken darüber machen, welche Vertauschungen der Einträge man auf einem Sudoku ausführen kann, ohne seine Gültigkeit zu verletzen. Das sind genau die folgenden Operationen:\n",
    "\n",
    "- Permutation der Zahlen $1,\\dots,9$ in der gesamten Matrix\n",
    "- Permutation der drei Bänder\n",
    "- Permutation der drei Stapel\n",
    "- Permutation der drei Zeilen innerhalb eines Bands\n",
    "- Permutation der drei Spalten innerhalb eines Stapels\n",
    "- alle Spiegelungen oder Rotationen\n",
    "\n",
    "Machen Sie Sich anschaulich klar, warum das so ist und warum man nach beliebiger Hintereinanderausführung der Operationen wieder ein Sudoku erhält."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc8391b1-cae9-4091-ab52-1c1a23c95825",
   "metadata": {},
   "source": [
    "In der Vorlesung haben Sie bereits die <b>Symmetriegruppe der Rotationen und Spiegelungen</b> $D_4=\\{s_0,s_1,s_2,s_3,r_0,r_1,r_2,r_3\\}$ mit der Gruppenoperation der Hintereinanderausführung kennengelernt. Die Gruppenelemente sind Selbstabbildungen verschiedener geometrischer Objekte, wie z.B. von Quadraten:\n",
    "\n",
    "- $r_0$: Drehung um $0°$ im Uhrzeigersinn\n",
    "- $r_1$: Drehung um $90°$ im Uhrzeigersinn\n",
    "- $r_2$: Drehung um $180°$ im Uhrzeigersinn\n",
    "- $r_3$: Drehung um $270°$ im Uhrzeigersinn\n",
    "- $s_0$: Spiegelung an der x-Achse/horizontalen Achse\n",
    "- $s_1$: Spiegelung an der 1. Winkelhalbierenden\n",
    "- $s_2$: Spiegelung an der y-Achse/vertikalen Achse\n",
    "- $s_3$: Spiegelung an der 2. Winkelhalbierenden\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1405a47-0689-4fff-8d5c-fd71a6be23cf",
   "metadata": {},
   "source": [
    "$G_s$ bezeichnet die Gruppe, die durch die gesamten oben aufgezählten Operationen (Permutationen, Drehungen und Spiegelungen) erzeugt wird. Diese enthält offenbar die echte Untergruppe $D_4$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fbc75c1a-2bc1-49be-80db-65bd238f79a8",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "\n",
    "Sei $G$ eine Gruppe, $g\\in G$. Wir definieren die Ornung von $g$ durch \n",
    "    $$\\text{ord}(G)=\\min\\{n\\in\\mathbb{N} \\mid g^n=g\\cdot g \\cdot \\dots \\cdot g = 1_G\\}$$\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07b80165-e668-4657-a9a2-9db8fba81169",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe\n",
    "***\n",
    "Finden Sie eine nichttriviale Untergruppe der Symmetriegruppe $D_4$ und erstellen Sie für diese eine Verknüpfungstafel.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7482a80c-3087-4c7a-84a9-0e312d4eed89",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe\n",
    "***\n",
    "Finden Sie drei nichttiviale Relationen der oben angegebenen Erzeuger von $D_4$ und geben Sie Ihre jeweilige Ordnung an.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2af7042b-38bd-47e6-bf48-59798a73c86c",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f86cfa8b-7257-486e-ac86-0517b9996291",
   "metadata": {},
   "source": [
    "### Gruppentheorie des Sudokus\n",
    "\n",
    "In der Vorlesung haben Sie die Gruppe $D_4$ mit der Gruppenoperation der Hintereinanderausführung kennengelernt. \n",
    "Wir wollen hier die Rotationen und Spiegelungen nicht nur als Gruppe für sich betrachten, sondern sie auf ein beliebiges Sudoku anwenden, also sie auf einer anderen Menge <b>operieren</b> lassen. In der Gruppentheorie gibt es ein passendes Konzept, um diese Idee zu formalisieren:\n",
    "\n",
    "\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "\n",
    "Sei $G$ eine Gruppe und $M$ eine Menge. Eine Abbildung $$M\\times G \\to M: (m,g)\\mapsto m^g$$ mit\n",
    "    \n",
    "- $m^{g_1 g_2} = (m^{g_1})^{g_2}$ für alle $m\\in M,\\ g_1,g_1\\in G$ (Assoziativgesetz)\n",
    "- $m^1=m$ für alle $m\\in M$ (Existenz der Eins)\n",
    "    \n",
    "heißt <b>Operation</b> (genauer Rechtsoperation) von $G$ auf $M$. Man sagt auch $G$ operiert (von rechts) auf $M$. Die Menge $M$ ausgestattet mit der Operation der Gruppe $G$ nennt man auch <b>$G$-Menge</b>.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bbb7f214-d016-430e-930c-bad9d26b4787",
   "metadata": {},
   "source": [
    "Wir nennen zwei Sudokus <b>essentiell gleich</b>, wenn sie durch Operationen von Gruppenelementen aus $G_s$ ineinander überführbar sind. Also sind die Sudokus $S_1$ und $S_2$ gleich genau dann, wenn ein $g\\in G_s$ existiert, sodass $S_1=S_2^g$. Wenn zwei Sudokus nicht essentiell gleich sind, nennen wir sie <b>essentiell verschieden</b>. <br>\n",
    "Eine wichtige Frage, die man sich in diesem Zusammenhang stellen kann, ist: Wie viele essentiell verschiedene Sudokus gibt es überhaupt?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1699d07f-8eb5-4834-8707-f245a78a8e34",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "Sei $G$ eine Gruppe, die auf der Menge $M$ operiert. Die <b>Bahn</b> (oder auch <b>Orbit</b>) von $m\\in M$ unter $G$ ist definiert als\n",
    "    $$m^G:= \\{m^g \\mid g\\in G\\} \\ .$$\n",
    "    \n",
    "Die Menge aller Bahnen auf $M$ unter $G$ bildet eine Partition von $M$. Die Menge dieser Bahnen wird auch mit $M/G$ bezeichnet.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59524539-1217-440a-91cc-78815e08b6db",
   "metadata": {},
   "source": [
    "Man kann die essentiell verschiedenen Sudokus durch eine Menge an Vertretern für jede Bahn angeben. Die Anzahl der essentiell verschiedenen Sudokus entspricht also gerade der Anzahl der verschiedenen Bahnen bzw. der Kardinalität eines Vertretersystems. <br>\n",
    "Wollten wir diese berechnen, würde man durch Ausprobieren in diesem Fall nicht weit kommen, da sich jetzt schon vermuten lässt, dass es sich bei der Anzahl der Sudokus um eine sehr große Zahl handeln wird. Gibt es eine andere Möglichkeit, die Anzahl der essentiell verschiedenen Sudokus effizient zu berechnen?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e404ac1d-4a44-4a63-b8f4-fdabf18b17ed",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "\n",
    "Sei $G$ eine Gruppe, die auf der Menge $M$ operiert. Der Stabilisator von $m\\in M$ in $G$ ist definiert als\n",
    "    $$G_m := \\text{Stab}_G(m) := \\{g\\in G \\mid m^g=m\\}$$\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4b42659-4cff-4a3c-b6f5-8c0eea8a8a31",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Burnsidesches Lemma</b>\n",
    "    \n",
    "Sei $G$ eine endliche Gruppe, die auf einer endlichen Menge $M$ operiert. Für $g\\in G$ definiere die Fixpunkte \n",
    "    $$\\text{fix}(g):=\\{m\\in M \\mid m^g = m\\} \\ .$$\n",
    "Dann lässt sich die Anzahl der Bahnen von $G$ auf $M$ berechnen durch\n",
    "$$|M/G| = \\frac{1}{|G|} \\cdot \\sum_{g\\in G} |\\text{fix}(g)| \\ .$$\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e0bc3d3-8a3d-4ebe-acde-b12e487aee6c",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe\n",
    "***\n",
    "Wir betrachten wieder unser Beispiel der Symmetriegruppe $G_s$, die auf der Menge der $3\\times 3$-Sudokus operiert.\n",
    "\n",
    "- Warum ist die Symmetriegrupperuppe $G_s$ endlich?\n",
    "- Warum ist jede Bahn endlich?\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a75decc-3ef3-4161-bba1-a8de40a8a440",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70ed9faa-d6c0-41e3-ad76-f4287b14684d",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "Betrachten wir als Beispiel die Menge $Q$ aller Quadrate aus $2\\times 2$ Kästchen mit möglichen Farben rosa, grün, gelb und blau. Insgesamt gibt es $3^4 =81$ mögliche Färbungen der Kästchen, also $|Q|=81$.\n",
    "\n",
    "Betrachten wir $Q$ als $G$-Menge, wobei $G:=<s_0, s_1, s_2, s_3, r_0, r_2>$ eine Untergruppe der obigen Symmetriegruppe $D_4$ sei. Wir wollen den Orbit des Elements $q\\in Q$ berechnen, wobei q folgendermaßen aussieht:"
   ]
  },
  {
   "attachments": {
    "48c31a3f-c98f-4436-aa55-201f547294f2.png": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAAADIAAAAyCAIAAACRXR/mAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAABxSURBVFhH7dGxDYAwDAVRhwmYkQUoKFmBbWmQkAiNB+BkihT3Gv/yJLej3/GTbT1zlU15B2MWYRZhFmEWYRZhFmEWYRZhFmEWYRYxaFbr156zbHnmXGU+kTCLMIswizCLMIswizCLMIswizCLMOu7iBeMGwigCu4LrwAAAABJRU5ErkJggg=="
    }
   },
   "cell_type": "markdown",
   "id": "6f3204bb-df78-4f60-bcb7-a9e8ea5191f6",
   "metadata": {},
   "source": [
    "![quadrat.png](attachment:48c31a3f-c98f-4436-aa55-201f547294f2.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ef93229-8f88-4718-90dd-8e429967a1f1",
   "metadata": {},
   "source": [
    "Den Orbit von $q$ berechnen wir mit der Berechnungsvorschrift:"
   ]
  },
  {
   "attachments": {
    "a7601943-f177-4c1b-921f-3be1e2376133.png": {
     "image/png": 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"
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   },
   "cell_type": "markdown",
   "id": "ed80bfdf-42ed-4339-9d5f-08c86b77374b",
   "metadata": {},
   "source": [
    "![Pseudocode.png](attachment:a7601943-f177-4c1b-921f-3be1e2376133.png)"
   ]
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   "id": "862f1c3a-ac06-4d08-b607-9b4be564cd71",
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   "source": [
    "Nach Ausführung des Algorithmus erhalten wir die Bahn von $q$:"
   ]
  },
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    "![r.png](attachment:36eca70d-7536-4634-ab9b-86719abe7e77.png)\n",
    "![rr.png](attachment:fb132e7d-4985-4f3d-9e48-949f409fd5a6.png)\n",
    "![rrr.png](attachment:d097bd41-bc55-46ad-93cc-2b737287c34e.png)\n",
    "![x.png](attachment:06bc1468-8830-485e-a839-b9182e376628.png)\n",
    "![y.png](attachment:c0fe2cad-5b46-4182-95ac-b93fbcadec02.png)\n",
    "![rx.png](attachment:9d7def90-054d-4c84-a10a-12a390405dff.png)\n",
    "![ry.png](attachment:a2e70ee5-4df5-4411-8f62-23330e0cf014.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f14adcc9-1254-457c-a508-a89ff96e2169",
   "metadata": {},
   "source": [
    "Sie werden nun ein paar konkrete Rechnungen für $4\\times 4$-Sudokus ausführen."
   ]
  },
  {
   "attachments": {
    "bccebc35-2282-48fa-b2ac-0e3b8dd94bbd.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "d1869288-ddc9-4389-af1c-627a9c023187",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe\n",
    "***\n",
    "Benutze den Bahnenalgorithmus, um den Orbit unter $D_4$ des folgenden Sudokus zu berechnen. Visualisiere die Ergebnisse anschaulich.\n",
    "   \n",
    "<div>\n",
    "<img src=\"attachment:bccebc35-2282-48fa-b2ac-0e3b8dd94bbd.png\" width=\"100\"/>\n",
    "</div>\n",
    "    \n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21ced9e4-29a6-4a99-aaa6-397ed2b69528",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Freiwillige Aufgabe\n",
    "***\n",
    "Benutze den Bahnenalgorithmus, um die Kardinalität des Orbit unter $G_s$ des obigen Sudokus zu berechnen.\n",
    "    \n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54ee9055-e145-460d-ab33-eea429101097",
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   "source": [
    "Die folgenden Aufgaben sollen auf jeden Fall bearbeitet werden, aber eine vollständige Lösung ist nicht erforderlich. Ein Ansatz ist in vielen Fällen auch ausreichend. Ziel ist es zu zeigen, dass Sie Sich mit den Aufgaben und einem möglichen Lösungsweg auseinandergesetzt haben."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ab07e5d-b325-434d-8fe6-d421925668b8",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Weiterführende Aufgabe\n",
    "***\n",
    "1. 1. Wieviele unterschiedliche $2\\times 2$-Sudokus bis auf Permutation der Zahlen $1,\\dots,9$ gibt es? (<i>Hinweis:</i> Hier ist wirklich die Verschiedenheit im Sinne von Ungleichheit mindestens eines Felds gemeint, <i>nicht</i> essentiell unterschiedlich!)\n",
    "    2. Wieviele Felder müssen in einem $2\\times 2$-Sudoku-Puzzle mindestens belegt sein, damit es eine eindeutige Lösung gibt? Wie sieht ein entsprechendes Sudoku und seine Lösung aus?\n",
    "    3. Wieviele Felder eines $2\\times 2$-Sudoku-Rätsels dürfen maximal belegt sein, ohne dass es eine eindeutige Lösung gibt?\n",
    "\n",
    "    \n",
    "2. 1. Wieviele unterschiedliche $3\\times 3$-Sudokus bis auf Permutation der Zahlen $1,\\dots,9$ gibt es? (<i>Hinweis:</i> Hier ist wirklich die Verschiedenheit im Sinne von Ungleichheit mindestens eines Felds gemeint, <i>nicht</i> essentiell unterschiedlich!)\n",
    "    2. Wieviele Felder müssen in einem $3\\times 3$-Sudoku-Puzzle mindestens belegt sein, damit es eine eindeutige Lösung gibt? Wie sieht ein entsprechendes Sudoku und seine Lösung aus?\n",
    "    3. Wieviele Felder eines $3\\times 3$-Sudoku-Rätsels dürfen maximal belegt sein, ohne dass es eine eindeutige Lösung gibt?\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9454f7dc-69aa-46ad-9e35-bea6537e549a",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Weiterführende Aufgabe\n",
    "***\n",
    "Berechne mit dem Lemma von Burnside, wieviele essentiell verschiedene $2\\times 2$- und $3\\times 3$-Sudokus es gibt.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c76af87-487d-48e8-8edf-a4375efba3fd",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9f0d69b-24a5-4fb6-b61e-99a2584e2603",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-danger\">\n",
    "    \n",
    "### Rückblick-Aufgabe\n",
    "***\n",
    "Das Ziel dieses Projekts war es, einen Weg zu finden um die Anzahl aller essentiell verschiedener Sudokus zu berechnen.\n",
    "    \n",
    "Schildern Sie das Vorgehen für Sudokus der Größe $n\\times n$ für $n\\in\\mathbb{N}$ und erklären Sie die Funktionsweise der einzelnen Schritte im Lösungsweg.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab8a8fbf-70bd-4fd0-bf53-a774c044e83e",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "278d5820-b659-4183-9796-ce91eca88d5a",
   "metadata": {},
   "source": [
    "### Literaturhinweise\n",
    "- Sudoku. (2023). In <i>Wikipedia, The Free Encyclopedia.</i> https://en.wikipedia.org/wiki/Sudoku\n"
   ]
  }
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