This python code
import random
# Generate random values of k and m between 1 and 5
k = random.randint(1, 5)
m = random.randint(1, 5)
# Calculate necessary variables
m_k = m - k
m_1 = m - 1
m_plus = m + 1
k_1 = k - 1
k_plus = k + 1
# Create with the correct answer marked
answers = [
f"\\checkmark \\; \\frac{{(n+{m}) !}}{{{k} ! (n+{m_k}) !}}", # Correct answer
f"\\frac{{(n+{m_1}) !}}{{{k_1} ! (n+{m_k}) !}}", # Wrong answer
f"\\frac{{(n+{m_plus}) !}}{{{k_plus} ! (n+{m_k}) !}}", # Wrong answer
f"\\frac{{(n+{m}) !}}{{{k_plus} ! (n+{m_k}) !}}" # Wrong answer
]
# Mix the answers
random.shuffle(answers)
# Generate text in LaTeX format
latex_output = f"""
After simplifying the expression
$$\\frac{{(n+{m_1}) !}}{{{k} ! (n+{m-k-1}) !}} + \\frac{{(n+{m_1}) !}}{{{k-1}! (n+{m-k})!}}$$
indicate which of the following results is correct:
\\[
\\square \\; {answers[0]} \\quad\\quad \\square \\; {answers[1]} \\quad\\quad \\square \\; {answers[2]} \\quad\\quad \\square \\; {answers[3]}
\\]
"""
print(latex_output)
The code generates a math quiz in LaTeX format with a question and four multiple-choice answers, one of which is correct. It randomly selects values for k and m between 1 and 5, calculates derived variables, creates the answers using factorial expressions, and shuffles them. Finally, it prints the LaTeX-formatted text to present the question and answers.
The fact is that sometimes I obtain results like this:
After simplifying the expression
$$\frac{(n+0) !}{1 ! (n+-1) !} + \frac{(n+0) !}{0! (n+0)!}$$
indicate which of the following results is correct:
\[
\square \; \frac{(n+2) !}{2 ! (n+0) !} \quad\quad \square \; \checkmark \; \frac{(n+1) !}{1 ! (n+0) !} \quad\quad \square \; \frac{(n+1) !}{2 ! (n+0) !} \quad\quad \square \; \frac{(n+0) !}{0 ! (n+0) !}
\]
The things I don't like are: expressions like (n+0)! where I would prefer just n!; and the +- signs that should denote a minus sign for the product of the signs but I can't manage to change. Do you have any suggestions regarding this?
You can try the following:
import random
# Generate random values of k and m between 1 and 5
k = random.randint(1, 5)
m = random.randint(1, 5)
def f(m):
if m > 0:
s = f"(n+{m})!"
elif m < 0:
s = f"(n{m})!"
else:
s = "n!"
return s
def g(m, k):
return rf"\frac{{{f(m)}}}{{{k}!{f(m-k)}}}"
# Create with the correct answer marked
answers = [
rf"\blacksquare \; {g(m, k)}", # Correct answer
rf"\square \; {g(m-1, k-1)}", # Wrong answer
rf"\square \; {g(m+1, k+1)}", # Wrong answer
rf"\square \; {g(m, k+1)}" # Wrong answer
]
# Mix the answers
random.shuffle(answers)
answers = "\\quad\\quad\n".join(answers)
# Generate text in LaTeX format
latex_output = f"""
After simplifying the expression
$$
{g(m-1, k)} + {g(m-1, k-1)}
$$
indicate which of the following results is correct:
$$
{answers}
$$
"""