From 62779ec260266f80c57084f5b08c86ab135207a9 Mon Sep 17 00:00:00 2001
From: udlbook <110402648+udlbook@users.noreply.github.com>
Date: Sun, 20 Apr 2025 10:23:27 -0400
Subject: [PATCH] Created using Colab

---
 Trees/SAT_Sudoku_Answers.ipynb | 24 +++++++++++-------------
 1 file changed, 11 insertions(+), 13 deletions(-)

diff --git a/Trees/SAT_Sudoku_Answers.ipynb b/Trees/SAT_Sudoku_Answers.ipynb
index fa2d6f5..81eee4a 100644
--- a/Trees/SAT_Sudoku_Answers.ipynb
+++ b/Trees/SAT_Sudoku_Answers.ipynb
@@ -4,7 +4,7 @@
   "metadata": {
     "colab": {
       "provenance": [],
-      "authorship_tag": "ABX9TyOLnEFh9BVTdtSWc9zHSjyA",
+      "authorship_tag": "ABX9TyPtj9hlWODaIsW0bHgGf3Hg",
       "include_colab_link": true
     },
     "kernelspec": {
@@ -58,16 +58,14 @@
         "# Install relevant packages\n",
         "!pip install z3-solver\n",
         "from z3 import *\n",
-        "import numpy as np\n",
-        "import geopandas as gpd\n",
-        "import matplotlib.pyplot as plt"
+        "import numpy as np"
       ],
       "metadata": {
         "id": "mF6ngqCses3n",
         "colab": {
           "base_uri": "https://localhost:8080/"
         },
-        "outputId": "fad1115b-b146-46bc-b298-7c0885fe75ac"
+        "outputId": "f3748d40-b6bd-4e8e-f082-f8668ac33720"
       },
       "execution_count": 1,
       "outputs": [
@@ -78,7 +76,7 @@
             "Collecting z3-solver\n",
             "  Downloading z3_solver-4.14.1.0-py3-none-manylinux_2_17_x86_64.manylinux2014_x86_64.whl.metadata (602 bytes)\n",
             "Downloading z3_solver-4.14.1.0-py3-none-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (29.5 MB)\n",
-            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m29.5/29.5 MB\u001b[0m \u001b[31m17.6 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m29.5/29.5 MB\u001b[0m \u001b[31m19.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
             "\u001b[?25hInstalling collected packages: z3-solver\n",
             "Successfully installed z3-solver-4.14.1.0\n"
           ]
@@ -110,7 +108,7 @@
       "metadata": {
         "id": "cvGNbKkf-Qix"
       },
-      "execution_count": 2,
+      "execution_count": null,
       "outputs": []
     },
     {
@@ -136,7 +134,7 @@
       "metadata": {
         "id": "0EkPFukj_-qc"
       },
-      "execution_count": 3,
+      "execution_count": null,
       "outputs": []
     },
     {
@@ -151,7 +149,7 @@
         "id": "CB0QFnLODWTu",
         "outputId": "3698caa2-e0a2-466a-a542-5e141d7b6bce"
       },
-      "execution_count": 4,
+      "execution_count": null,
       "outputs": [
         {
           "output_type": "stream",
@@ -243,7 +241,7 @@
       "metadata": {
         "id": "dRmdNKGdZRks"
       },
-      "execution_count": 23,
+      "execution_count": null,
       "outputs": []
     },
     {
@@ -259,7 +257,7 @@
         },
         "outputId": "8840695c-8ce0-4ce1-93ef-d68d1c7098ed"
       },
-      "execution_count": 24,
+      "execution_count": null,
       "outputs": [
         {
           "output_type": "stream",
@@ -320,7 +318,7 @@
         "id": "3SWS2QUqtlNI",
         "outputId": "8c7419ff-70b2-4322-81c0-2f8d8727de72"
       },
-      "execution_count": 32,
+      "execution_count": null,
       "outputs": [
         {
           "output_type": "stream",
@@ -400,7 +398,7 @@
         "id": "0lfUKX66ubj0",
         "outputId": "e74941c8-addd-46fd-d908-34b0d975fd71"
       },
-      "execution_count": 34,
+      "execution_count": null,
       "outputs": [
         {
           "output_type": "stream",