Add Digits

Add Digits

What is this problem about?

The Add Digits interview question asks you to take a non-negative integer and repeatedly add all its digits until the result has only one digit. For example, if you start with $38$, you do $3 + 8 = 11$, then $1 + 1 = 2$. Since $2$ is a single digit, that is your final answer.

Why is this asked in interviews?

While simple to simulate, companies like Adobe and Bloomberg ask this to see if you can find a mathematical "shortcut." It’s a test of Number Theory knowledge—specifically, whether you understand how numbers relate to their base-10 representations.

Algorithmic pattern used

There are two ways to solve the Add Digits coding problem:

1. Simulation: Use a loop to sum the digits repeatedly.
2. Digital Root (Math Pattern): Use the mathematical formula for the digital root. In base 10, the result is simply num % 9. If the result is 0 and the number is not 0, the answer is 9.

Example explanation

Let's take $num = 942$.

• Simulation: $9 + 4 + 2 = 15 \rightarrow 1 + 5 = 6$.
• Math Shortcut: $942 \pmod 9$:
• $942 = 900 + 36 + 6$.
• All multiples of 9 disappear, leaving $6$. Both methods yield 6, but the math method is $O(1)$ time and space.

Common mistakes candidates make

• Ignoring the O(1) Constraint: Many candidates provide the $O(\log n)$ simulation loop without realizing a mathematical formula exists.
• Modulo 9 Pitfall: Forgetting that 9 % 9 is $0$, but the digital root of $9$ is $9$. A special check for num % 9 == 0 is required.

Interview preparation tip

In math-based coding problems, if the question asks you to do something "until a condition is met," check if there is a modular arithmetic property that can skip the repetition entirely.