Problem 3

Find two summands s1 and s2 for a given non-negative number n.

The following properties should hold: * s1 ≥ s2 * s1 + s2 == n * The digit 7 does not appear neither in s1 nor in s2.

Though the original problem did not state it, we enforce s1 > 0 and s2 > 0.

Functions:

number_to_digits(n)	Disassemble the integer n into individual digits.
digits_to_number(digits)	Assemble the integer from the given digits.
find_summands(n)	Find the two summands (s1, s2) which satisfy the conditions.

number_to_digits(n: int) → List[int]

Disassemble the integer n into individual digits.

Requires

• n > 0

Ensures

• digits_to_number(result) == n

• all(0 <= digit <= 9 for digit in result)

• result[0] != 0

• "".join(str(digit) for digit in result) == str(n)

digits_to_number(digits: Reversible[int]) → int

Assemble the integer from the given digits.

Requires

• all(0 <= digit <= 9 for digit in digits)

• len(digits) > 0

find_summands(n: int) → Tuple[int, int]

Find the two summands (s1, s2) which satisfy the conditions.

• s1 ≥ s2

• s1 + s2 == n

• The digit 7 does not appear neither in s1 nor in s2.

Requires

• n > 2

Ensures

• "7" not in str(result[1])

• "7" not in str(result[0])

• result[0] >= result[1]

• result[1] > 0

• result[0] > 0