Python Practice Exercises – Part 2

In this week’s exercises, we focus on logical problem-solving with loops, conditionals, mathematical operations, and input validation.
Each task builds your understanding of how to combine basic programming concepts to solve real-world problems efficiently.

Try solving each problem first — then scroll down to see the solutions at the end.

LEVEL 1 – Logical & Mathematical Problems

1- Factorial – Largest Number Below 1,000,000,000

Write a script that determines the largest number n such that its factorial n! is still below 1,000,000,000.

Hint:
The factorial of 5 (short notation: 5!) is
1 * 2 * 3 * 4 * 5 = 120

2- Valid Date Check

The Meyer GmbH needs a module that checks whether a given date is valid.
If the date is correct, the variable datok should be set to 1, otherwise to 0.

Examples:

29.02.1999 → datok: 0  
29.02.2000 → datok: 1  
13.05.2000 → datok: 1  
32.05.2000 → datok: 0  
24.13.2000 → datok: 0  

For the year, the following must hold:
year > 1900 AND year < 2100

3- Powers of Two

Write a program that prints all powers of 2 whose result is less than 10,000.

Hint: use a loop and the ** operator.

Bonus: Format your output as follows:

2 ** 0 = 1  
2 ** 1 = 2  
2 ** 2 = 4  
2 ** 3 = 8  
2 ** 4 = 16  
...

4- Multiplication – Factor Pairs

Write a program that determines how many integer multiplier–multiplicand combinations exist for the product 8,420,000,
where both the multiplier and multiplicand are less than 10,000.

1000 * 8420 and 8420 * 1000 count only once.

5- Roman Numerals → Decimal Conversion

Write a Python program that converts a Roman numeral into its decimal (integer) equivalent.

The program should correctly handle subtractive notation such as:
IV = 4, IX = 9, XL = 40, XC = 90, CM = 900, etc.

Solutions

1- Factorial – Largest Number Below 1,000,000,000

limit = 1_000_000_000
result = 1
n = 1

while True:
    result *= n
    if result >= limit:
        n -= 1
        break
    n += 1

print(f"The largest n such that n! < {limit} is: {n}")

2- Valid Date Check

date_str = input("Enter a date in the format DD.MM.YYYY: ")

datok = 0  # 1 = valid, 0 = invalid

try:
    day_str, month_str, year_str = date_str.split(".")
    day = int(day_str)
    month = int(month_str)
    year = int(year_str)
except ValueError:
    print(f"{date_str} datok: 0 (invalid format)")
else:
    def is_valid_date(day, month, year):
        if not (1900 < year < 2100):
            return False
        if not (1 <= month <= 12):
            return False
        # Leap year check
        if (year % 400 == 0) or (year % 4 == 0 and year % 100 != 0):
            feb_days = 29
        else:
            feb_days = 28
        days = [0, 31, feb_days, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
        return 1 <= day <= days[month]

    if is_valid_date(day, month, year):
        datok = 1
    print(f"{date_str} datok: {datok}")

3- Powers of Two

limit = 10_000
exp = 0

while True:
    result = 2 ** exp
    if result >= limit:
        break
    print(f"2 ** {exp} = {result}")
    exp += 1

4- Multiplication – Factor Pairs

product = 8_420_000
max_value = 10_000
count = 0

for a in range(1, max_value):
    if product % a == 0:
        b = product // a
        if b < max_value and a <= b:
            count += 1
            print(f"a: {a}, b: {b}, check: {a*b}")

print("Number of valid (a, b) pairs:", count)

5- Roman Numerals → Decimal

roman_values = {
    "I": 1, "V": 5, "X": 10, "L": 50,
    "C": 100, "D": 500, "M": 1000
}

roman = input("Enter a Roman numeral: ").upper()
total = 0
length = len(roman)

for i in range(length):
    if roman[i] not in roman_values:
        raise ValueError(f"Invalid Roman numeral: {roman[i]}")

for i in range(length):
    value = roman_values[roman[i]]
    if i + 1 < length:
        next_value = roman_values[roman[i + 1]]
        if value < next_value:
            total -= value
        else:
            total += value
    else:
        total += value

print(f"The value of {roman} is {total}")