Solution

Three Math Games.md

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+```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
+
+```