human
Solve the following python programming problem given the following code:
# Define `fac(n)` function that returns the factorial of `n`.
# For values of n in 0..9. We precalculate the factorials
# since those are the only factorials we will need to solve
# this problem.
from scipy.special import factorial
def create_fac():
    factorials = [int(factorial(i)) for i in range(10)]
    def f(x):
        return factorials[x]
    return f
fac = create_fac()

# Define F(v) where v is a multiset in vector form.
def F(v):
    assert len(v) == 10
    s = 0
    for i in range(10):
        s += fac(i) * v[i]
    return s

# The following assertion should pass.
assert F([0,1,0,0,1,1,0,0,0,0]) == 145
assert F([1,0,0,0,1,2,0,0,1,0]) == 40585

# Vector equality works in python
assert [0,1,0,0,1,1,0,0,0,0] == [0,1,0,0,1,1,0,0,0,0]
assert [1,1,0,0,0,0,0,0,0,0] != [0,0,0,0,0,0,0,0,1,1]

# Define M(k) that converts a number k into a multiset vector.
def M(k):
    v = [0] * 10
    while k > 0:
        r = k % 10
        k = k // 10
        v[r] += 1
    return v

# The following assertions about M(k) should pass.
assert M(145) == [0,1,0,0,1,1,0,0,0,0]
assert M(541) == [0,1,0,0,1,1,0,0,0,0]
assert M(5141) == [0,2,0,0,1,1,0,0,0,0]
assert M(40585) == [1,0,0,0,1,2,0,0,1,0]

# Assertions to test relationships mentioned in the design.
assert F(M(145)) == 145
assert M(F([0,1,0,0,1,1,0,0,0,0])) == [0,1,0,0,1,1,0,0,0,0]
Given the above code, generate some markdown instructions for it.
assistant
#Here is Python code to calculate the factorials
.

I have no idea where take 2 is going.
Thinking in terms of multi sets
Observe that the sum of factorials for 145 is the same as the sum of factorials for any permutation of those digits. 541, 154, etc.
Let the notation {1145} denote a multi set of digits 1, 1, 4, and 5. For clarity, we will always list the smaller digits first. Also, since it is a multi set, repeated digits are allowed. For example, the repeated 1s in {1145}.
Let the function F(x) map a multi set x into a sum of factorials, as per the definition in problem 34.
Let the function M(y) map a number y into a multi set corresponding to its digits. For example M(123) == M(321).
Using this notation we can say the following about 145.
F(M(145)) == 145

Generalizing, we can rephrase problem 34 as finding all values y such that F(M(y)) == y. 
Observe that M(123) is the same as M(321). That is, a single multi set maps from multiple numbers. A many to one mapping. Another way to put this is to say that a multi set maps to one or more numbers. Given this, and that we are searching for factorial sums over multi sets, it makes more sense to search the space of multi sets than to search the space of numbers. 
Observe that given a multi set, there is exactly one factorial sum. Then we can evaluate if that sum is a curious number by computing its multi set. Therefore we can rephrase the problem in terms of multi sets as follows. This form is better suited for searching the space of multi sets. 
M(F(x)) == x

The next piece of the puzzle is how to navigate the space of multi sets in an efficient manner. Also, how would we know when to stop?
Vector representation for multi sets
Since the only set members in our multi sets are digits, we can represent our multi sets as vectors of digit counts. For example the multi set {1145} would be a vector [0,2,0,0,1,1,0,0,0,0].
Note: The count at the 0-th position of the vector is also important because 0! == 1.
Multi set equality using this notation is when two vectors have the same count at each digit position. In Python...