solution.py

# When you divide the successive powers of 10 by 13 you get the following remainders of the integer divisions:

# 1, 10, 9, 12, 3, 4.

# Then the whole pattern repeats.

# Hence the following method:
# Multiply the right most digit of the number with the left most number in the sequence shown above,
# the second right most digit to the second left most digit of the number in the sequence.
# The cycle goes on and you sum all these products.
# Repeat this process until the sequence of sums is stationary.

# ...........................................................................

# Example: What is the remainder when 1234567 is divided by 13?

# 7×1 + 6×10 + 5×9 + 4×12 + 3×3 + 2×4 + 1×1 = 178
# We repeat the process with 178:
# 8x1 + 7x10 + 1x9 = 87
# and again with 87:
# 7x1 + 8x10 = 87

# ...........................................................................

# From now on the sequence is stationary and the remainder of 1234567 by 13 is the same as the remainder of 87 by 13: 9

# Call thirt the function which processes this sequence of operations on an integer n (>=0).
# thirt will return the stationary number.

# thirt(1234567) calculates 178, then 87, then 87 and returns 87.

# thirt(321) calculates 48, 48 and returns 48


def thirt(n):
    reminders = [1, 10, 9, 12, 3, 4]
    r = []

    while True:
        s = 0
        for i, v in enumerate(str(n)[::-1]):
            s += int(v) * reminders[i % 6]

        n = s
        if s not in r:
            r.append(s)
        else:
            return r[-1]