MASTER YOUR LOGIC BUILDING:Phase 6 - Category 1: Number Logic

Number Logic

Why This Matters

Real problems rarely ask for just one thing. A form might check: Is this number positive? Even? Two digits? Does the digit sum divide evenly? Phase 6 is where you combine everything you've learned — loops, conditionals, digits, math — to solve multi-step number puzzles. Think of it like a checklist: each condition is one box to tick.

What You'll Learn

• How to break a complex number problem into smaller checks
• How to combine conditions with and, or, and not
• How to extract and use digits from a number
• A reliable step-by-step approach for any number logic problem

The Problem-Solving Recipe

When a problem feels overwhelming, follow these five steps:

1. Read carefully — underline every condition
2. List sub-tasks — what must be true?
3. Solve each piece separately — one variable per check
4. Combine — use and / or to join them
5. Test — try normal cases, edge cases, and "almost valid" cases

Example: A Number Must Pass Four Tests

"Is the number positive, even, two digits, AND does its digit sum come out even?"

Break it apart instead of writing one giant if:

num = int(input("Enter a number: "))

is_positive = num > 0
is_even = num % 2 == 0
is_two_digit = 10 <= num <= 99

digit_sum = 0
temp = abs(num)
while temp > 0:
    digit_sum += temp % 10
    temp //= 10
sum_is_even = digit_sum % 2 == 0

if is_positive and is_even and is_two_digit and sum_is_even:
    print("Passes all checks!")
else:
    print("Fails at least one check")

For num = 24: positive ✓, even ✓, two digits ✓, digit sum = 6 (even) ✓.

Useful Building Blocks

Check divisibility:

num % 3 == 0    # divisible by 3?
num % 5 == 0    # divisible by 5?

Count digits without converting to string:

count = 0
temp = abs(num)
while temp > 0:
    count += 1
    temp //= 10

Reverse digits:

reversed_num = 0
temp = abs(num)
while temp > 0:
    reversed_num = reversed_num * 10 + temp % 10
    temp //= 10

Common Mistakes & Tips

• Writing one unreadable mega-condition — split into named variables; your future self will thank you
• Forgetting negative numbers — use abs(num) when working with digits
• Off-by-one on ranges — "two-digit" means 10 <= num <= 99, not num < 100
• Not testing edge cases — try 0, negative numbers, single digits, and numbers that pass 3 of 4 checks
• Tip: Print each boolean (print(is_even)) while debugging — you'll instantly see which check fails

Practice Focus

• Check if a number is Armstrong (sum of cubes of digits equals the number)
• Find numbers in a range that are divisible by both 3 and 5
• Validate a number against 3+ custom rules you write yourself
• Given a number, print which conditions it passes and which it fails

Number logic is puzzle-solving with code. Take it one condition at a time — you've got this!