From 0f6df37aec9fc73aab2e52c533f481b2ee0f1db7 Mon Sep 17 00:00:00 2001
From: Manish <manish@radii.dev>
Date: Thu, 27 Jul 2023 18:19:40 +1000
Subject: [PATCH] Solution

---
 Three Math Games.ipynb | 354 +++++++++++++++++++++++++++++++++++++++++
 Three Math Games.md    | 231 +++++++++++++++++++++++++++
 output_5_0.png         | Bin 0 -> 20041 bytes
 output_9_0.png         | Bin 0 -> 6597 bytes
 4 files changed, 585 insertions(+)
 create mode 100644 Three Math Games.ipynb
 create mode 100644 Three Math Games.md
 create mode 100644 output_5_0.png
 create mode 100644 output_9_0.png

diff --git a/Three Math Games.ipynb b/Three Math Games.ipynb
new file mode 100644
index 0000000..6f03c00
--- /dev/null
+++ b/Three Math Games.ipynb	
@@ -0,0 +1,354 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 128,
+   "id": "e4365f4a-71af-4b54-8000-e549c34df127",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%matplotlib inline\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "from ipywidgets import interactive, fixed\n",
+    "from IPython import display\n",
+    "from random import randint\n",
+    "from time import sleep\n",
+    "from sympy import symbols, Eq\n",
+    "from sympy.solvers import solve\n",
+    "from sympy.parsing.sympy_parser import parse_expr"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "23fa0780-17a8-4801-ae5a-f4ee0172ae40",
+   "metadata": {},
+   "source": [
+    "# Projectile game"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0740f36c-6c52-422f-9db0-a6619a9a5ffb",
+   "metadata": {},
+   "source": [
+    "## Easy Mode"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 116,
+   "id": "f39607ff-7776-4d49-8de9-2f79bff89a92",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "6016d1e3623c4376bcf7aa7041f2beaf",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "interactive(children=(FloatSlider(value=0.0, description='a', max=25.0, min=-25.0), FloatSlider(value=0.0, des…"
+      ]
+     },
+     "execution_count": 116,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "xlo = -2\n",
+    "xhi = 20\n",
+    "ylo = -20\n",
+    "yhi = 120\n",
+    "\n",
+    "def graph(a, b, c, height, distance):\n",
+    "    plt.clf()\n",
+    "    fix = plt.subplot()\n",
+    "    plt.axis([xlo, xhi, ylo, yhi])\n",
+    "    plt.plot([0, 0], [ylo, yhi], \"black\")\n",
+    "    plt.plot([xlo, xhi], [0, 0], \"black\")\n",
+    "    wall_height = height\n",
+    "    wall_distance = distance\n",
+    "    plt.plot([wall_distance, wall_distance], [0, wall_height], \"brown\")\n",
+    "    plt.grid()\n",
+    "    plt.title(f\"{a:.1f}*x**2 + {b:.1f}*x + {c:.1f}\")\n",
+    "    \n",
+    "    x = np.linspace(0, xhi, xhi*1000)\n",
+    "    y = a*x**2 + b*x + c\n",
+    "    success = a*wall_distance**2 + b*wall_distance + c > wall_height\n",
+    "    x2 = []\n",
+    "    y2 = []\n",
+    "    for i in range(len(y)):\n",
+    "        if y[i] < 0:\n",
+    "            break\n",
+    "        if not success and x[i] > wall_distance:\n",
+    "            break\n",
+    "        x2.append(x[i])\n",
+    "        y2.append(y[i])\n",
+    "        \n",
+    "    y2[-1] = 0 # finally ball hits the ground (handling imprecisions and ball hitting walls)\n",
+    "    plt.plot([x2[-1]], [y2[-1]], 'ro')\n",
+    "    plt.plot(x2, y2, \"b\")\n",
+    "    plt.show()\n",
+    "\n",
+    "\n",
+    "slider_range = (-25, 25, 0.1)\n",
+    "wall_height = randint(2, yhi-20)\n",
+    "wall_distance = randint(2, xhi-2)\n",
+    "interactive_graph = interactive(graph, a=slider_range, b=slider_range, c=slider_range, height=fixed(wall_height), distance=fixed(wall_distance))\n",
+    "interactive_graph"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "810b43cb-8289-4952-8259-648add3bbb0e",
+   "metadata": {},
+   "source": [
+    "## Hard Mode\n",
+    "Now guess projectile paramaters without fiddloing with slider"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 127,
+   "id": "8b65fbea-7647-4e29-902e-ddd80170cdc8",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "xlo = -2\n",
+    "xhi = 20\n",
+    "ylo = -20\n",
+    "yhi = 120\n",
+    "\n",
+    "wall_height = randint(2, yhi-20)\n",
+    "wall_distance = randint(2, xhi-2)\n",
+    "\n",
+    "plt.clf()\n",
+    "fix = plt.subplot()\n",
+    "plt.axis([xlo, xhi, ylo, yhi])\n",
+    "plt.plot([0, 0], [ylo, yhi], \"black\")\n",
+    "plt.plot([xlo, xhi], [0, 0], \"black\")\n",
+    "plt.plot([wall_distance, wall_distance], [0, wall_height], \"brown\")\n",
+    "plt.grid()\n",
+    "display.display(plt.gcf())\n",
+    "\n",
+    "print(\"You're at origin, provide A, B and C values for projectile to get across wall.\")\n",
+    "a = float(input(\"A: \"))\n",
+    "b = float(input(\"B: \"))\n",
+    "c = float(input(\"C: \"))\n",
+    "\n",
+    "x = np.linspace(0, xhi, xhi*1000)\n",
+    "y = a*x**2 + b*x + c\n",
+    "success = a*wall_distance**2 + b*wall_distance + c > wall_height\n",
+    "x2 = []\n",
+    "y2 = []\n",
+    "for i in range(len(y)):\n",
+    "    if y[i] < 0:\n",
+    "        break\n",
+    "    if not success and x[i] > wall_distance:\n",
+    "        break\n",
+    "    x2.append(x[i])\n",
+    "    y2.append(y[i])\n",
+    "\n",
+    "if success:\n",
+    "    plt.title(f\"Awesome, {a:.1f}*x**2 + {b:.1f}*x + {c:.1f} worked!\")\n",
+    "else:\n",
+    "    plt.title(f\"Oops, {a:.1f}*x**2 + {b:.1f}*x + {c:.1f} did not work :(\")\n",
+    "    y2[-1] = 0 # ball hits the ground after hitting wall\n",
+    "\n",
+    "plt.plot([x2[-1]], [y2[-1]], 'ro')\n",
+    "plt.plot(x2, y2, \"b\")\n",
+    "display.clear_output(wait=True)\n",
+    "plt.show()\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5ef5840e-9c5a-41b0-8f79-2588f6915f78",
+   "metadata": {},
+   "source": [
+    "# Algebra practice game "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 144,
+   "id": "56df3e31-3cfe-47b8-bde5-2096cff8d941",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Solve for x in following equation:\n",
+      "34 - x / 18 = -49\n"
+     ]
+    },
+    {
+     "name": "stdin",
+     "output_type": "stream",
+     "text": [
+      "answer:  1494\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Pretty accurate!\n"
+     ]
+    }
+   ],
+   "source": [
+    "def rn(): # random integer\n",
+    "    return randint(-100, 100)\n",
+    "\n",
+    "def rop(): # random operation\n",
+    "    op = randint(1, 4)\n",
+    "    if op == 1:\n",
+    "        return '+'\n",
+    "    elif op == 2:\n",
+    "        return '-'\n",
+    "    elif op == 3:\n",
+    "        return '*'\n",
+    "    elif op == 4:\n",
+    "        return '/'\n",
+    "\n",
+    "def rpm(): # random plus minus\n",
+    "    if randint(0, 1):\n",
+    "        return '-'\n",
+    "    return ''\n",
+    "\n",
+    "x = symbols(\"x\")\n",
+    "\n",
+    "eq = \"\"\n",
+    "if randint(0, 1): # one step problem\n",
+    "    eq = f\"x {rop()} {rn()} = {rn()}\"\n",
+    "else:\n",
+    "    eq = f\"{rn()} {rop()} {rpm()}x {rop()} {rn()} = {rn()}\"\n",
+    "eq = eq.replace('- -', '+ ').replace('+ -', '- ').replace('- +=', '- ')\n",
+    "lhs, rhs = [parse_expr(part) for part in eq.split(' = ')]\n",
+    "sympy_eq = Eq(lhs, rhs)\n",
+    "\n",
+    "solution = round(solve(sympy_eq, x)[0], 2)\n",
+    "\n",
+    "print(\"Solve for x in following equation:\")\n",
+    "print(eq)\n",
+    "ans = [float(num) for num in input(\"answer: \").split('/')]\n",
+    "if len(ans) == 2:\n",
+    "    ans = ans[0]/ans[1]\n",
+    "else:\n",
+    "    ans = ans[0]\n",
+    "\n",
+    "if abs(ans-solution) < 0.01:\n",
+    "    print(\"Pretty accurate!\")\n",
+    "else:\n",
+    "    print(f\"Oops! correct answer was {solution} but your answer was {ans}\")\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4354b487-229b-40b3-92e9-74610bc74030",
+   "metadata": {},
+   "source": [
+    "# Scatter Plot Game "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 146,
+   "id": "4dac8ed5-b7dd-42d5-a4ed-e51af3324867",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdin",
+     "output_type": "stream",
+     "text": [
+      "Guess the location of point (x, y) on graph:  -28, 22\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Sorry, the correct answer was (-25, 24) but you provided (-28, 22)\n"
+     ]
+    }
+   ],
+   "source": [
+    "plt.clf()\n",
+    "xlo = -50\n",
+    "xhi = 50\n",
+    "ylo = -50\n",
+    "yhi = 50\n",
+    "\n",
+    "x = randint(xlo, xhi)\n",
+    "y = randint(ylo, yhi)\n",
+    "\n",
+    "fig = plt.subplot()\n",
+    "plt.axis([xlo, xhi, ylo, yhi])\n",
+    "plt.plot([x], [y], 'ro')\n",
+    "plt.show()\n",
+    "\n",
+    "gussed_x, gussed_y = [int(round(float(num.strip(' ')), 0)) for num in input(\"Guess the location of point (x, y) on graph: \").split(', ')]\n",
+    "\n",
+    "if gussed_x == x and gussed_y == y:\n",
+    "    print(\"You got it!\")\n",
+    "else:\n",
+    "    print(f\"Sorry, the correct answer was ({x}, {y}) but you provided ({gussed_x}, {gussed_y})\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8d9745ef-fe26-477f-a480-e146542b04c1",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.10"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/Three Math Games.md b/Three Math Games.md
new file mode 100644
index 0000000..079d6d5
--- /dev/null
+++ b/Three Math Games.md	
@@ -0,0 +1,231 @@
+```python
+%matplotlib inline
+import matplotlib.pyplot as plt
+import numpy as np
+from ipywidgets import interactive, fixed
+from IPython import display
+from random import randint
+from time import sleep
+from sympy import symbols, Eq
+from sympy.solvers import solve
+from sympy.parsing.sympy_parser import parse_expr
+```
+
+# Projectile game
+
+## Easy Mode
+
+
+```python
+xlo = -2
+xhi = 20
+ylo = -20
+yhi = 120
+
+def graph(a, b, c, height, distance):
+    plt.clf()
+    fix = plt.subplot()
+    plt.axis([xlo, xhi, ylo, yhi])
+    plt.plot([0, 0], [ylo, yhi], "black")
+    plt.plot([xlo, xhi], [0, 0], "black")
+    wall_height = height
+    wall_distance = distance
+    plt.plot([wall_distance, wall_distance], [0, wall_height], "brown")
+    plt.grid()
+    plt.title(f"{a:.1f}*x**2 + {b:.1f}*x + {c:.1f}")
+    
+    x = np.linspace(0, xhi, xhi*1000)
+    y = a*x**2 + b*x + c
+    success = a*wall_distance**2 + b*wall_distance + c > wall_height
+    x2 = []
+    y2 = []
+    for i in range(len(y)):
+        if y[i] < 0:
+            break
+        if not success and x[i] > wall_distance:
+            break
+        x2.append(x[i])
+        y2.append(y[i])
+        
+    y2[-1] = 0 # finally ball hits the ground (handling imprecisions and ball hitting walls)
+    plt.plot([x2[-1]], [y2[-1]], 'ro')
+    plt.plot(x2, y2, "b")
+    plt.show()
+
+
+slider_range = (-25, 25, 0.1)
+wall_height = randint(2, yhi-20)
+wall_distance = randint(2, xhi-2)
+interactive_graph = interactive(graph, a=slider_range, b=slider_range, c=slider_range, height=fixed(wall_height), distance=fixed(wall_distance))
+interactive_graph
+```
+
+
+
+
+    interactive(children=(FloatSlider(value=0.0, description='a', max=25.0, min=-25.0), FloatSlider(value=0.0, des…
+
+
+
+## Hard Mode
+Now guess projectile paramaters without fiddloing with slider
+
+
+```python
+xlo = -2
+xhi = 20
+ylo = -20
+yhi = 120
+
+wall_height = randint(2, yhi-20)
+wall_distance = randint(2, xhi-2)
+
+plt.clf()
+fix = plt.subplot()
+plt.axis([xlo, xhi, ylo, yhi])
+plt.plot([0, 0], [ylo, yhi], "black")
+plt.plot([xlo, xhi], [0, 0], "black")
+plt.plot([wall_distance, wall_distance], [0, wall_height], "brown")
+plt.grid()
+display.display(plt.gcf())
+
+print("You're at origin, provide A, B and C values for projectile to get across wall.")
+a = float(input("A: "))
+b = float(input("B: "))
+c = float(input("C: "))
+
+x = np.linspace(0, xhi, xhi*1000)
+y = a*x**2 + b*x + c
+success = a*wall_distance**2 + b*wall_distance + c > wall_height
+x2 = []
+y2 = []
+for i in range(len(y)):
+    if y[i] < 0:
+        break
+    if not success and x[i] > wall_distance:
+        break
+    x2.append(x[i])
+    y2.append(y[i])
+
+if success:
+    plt.title(f"Awesome, {a:.1f}*x**2 + {b:.1f}*x + {c:.1f} worked!")
+else:
+    plt.title(f"Oops, {a:.1f}*x**2 + {b:.1f}*x + {c:.1f} did not work :(")
+    y2[-1] = 0 # ball hits the ground after hitting wall
+
+plt.plot([x2[-1]], [y2[-1]], 'ro')
+plt.plot(x2, y2, "b")
+display.clear_output(wait=True)
+plt.show()
+
+```
+
+
+    
+![png](output_5_0.png)
+    
+
+
+# Algebra practice game 
+
+
+```python
+def rn(): # random integer
+    return randint(-100, 100)
+
+def rop(): # random operation
+    op = randint(1, 4)
+    if op == 1:
+        return '+'
+    elif op == 2:
+        return '-'
+    elif op == 3:
+        return '*'
+    elif op == 4:
+        return '/'
+
+def rpm(): # random plus minus
+    if randint(0, 1):
+        return '-'
+    return ''
+
+x = symbols("x")
+
+eq = ""
+if randint(0, 1): # one step problem
+    eq = f"x {rop()} {rn()} = {rn()}"
+else:
+    eq = f"{rn()} {rop()} {rpm()}x {rop()} {rn()} = {rn()}"
+eq = eq.replace('- -', '+ ').replace('+ -', '- ').replace('- +=', '- ')
+lhs, rhs = [parse_expr(part) for part in eq.split(' = ')]
+sympy_eq = Eq(lhs, rhs)
+
+solution = round(solve(sympy_eq, x)[0], 2)
+
+print("Solve for x in following equation:")
+print(eq)
+ans = [float(num) for num in input("answer: ").split('/')]
+if len(ans) == 2:
+    ans = ans[0]/ans[1]
+else:
+    ans = ans[0]
+
+if abs(ans-solution) < 0.01:
+    print("Pretty accurate!")
+else:
+    print(f"Oops! correct answer was {solution} but your answer was {ans}")
+
+```
+
+    Solve for x in following equation:
+    34 - x / 18 = -49
+
+
+    answer:  1494
+
+
+    Pretty accurate!
+
+
+# Scatter Plot Game 
+
+
+```python
+plt.clf()
+xlo = -50
+xhi = 50
+ylo = -50
+yhi = 50
+
+x = randint(xlo, xhi)
+y = randint(ylo, yhi)
+
+fig = plt.subplot()
+plt.axis([xlo, xhi, ylo, yhi])
+plt.plot([x], [y], 'ro')
+plt.show()
+
+gussed_x, gussed_y = [int(round(float(num.strip(' ')), 0)) for num in input("Guess the location of point (x, y) on graph: ").split(', ')]
+
+if gussed_x == x and gussed_y == y:
+    print("You got it!")
+else:
+    print(f"Sorry, the correct answer was ({x}, {y}) but you provided ({gussed_x}, {gussed_y})")
+```
+
+
+    
+![png](output_9_0.png)
+    
+
+
+    Guess the location of point (x, y) on graph:  -28, 22
+
+
+    Sorry, the correct answer was (-25, 24) but you provided (-28, 22)
+
+
+
+```python
+
+```
diff --git a/output_5_0.png b/output_5_0.png
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