The Modular Operator

Write a program that prints the numbers from 1 to 100. For multiples of 3, print "Fizz" instead of the number. For multiples of 5, print "Buzz". For numbers which are multiples of both 3 and 5, print "FizzBuzz".

This problem tests your understanding of the modular operator ($\bmod$) and control flow. The key insight is that you need to handle the most specific condition (divisible by both 3 AND 5) correctly. Instead of checking divisibility by 15 first, you can build the output string incrementally — append "Fizz" if $n \bmod 3 = 0$, then append "Buzz" if $n \bmod 5 = 0$. This naturally produces "FizzBuzz" for multiples of both.

1. Loop through numbers 1 to 100.
2. For each number, initialize an empty string.
3. If $n \bmod 3 = 0$, append "Fizz" to the string.
4. If $n \bmod 5 = 0$, append "Buzz" to the string.
5. If the string is still empty (not divisible by 3 or 5), print the number itself.
6. Otherwise, print the constructed string.

• Checking divisibility by 3 before checking for both 3 and 5, which causes "FizzBuzz" cases to print only "Fizz"
• Using elif instead of separate if statements when building the string incrementally
• Forgetting that $0 \bmod 3 = 0$ is true, so starting from 0 instead of 1 gives an extra empty output

FizzBuzz is a classic interview warm-up that tests basic control flow and the modular operator. The string-building approach is more elegant than checking for 15 first, and it scales better if more conditions are added (e.g., "Jazz" for multiples of 7).