Find the Key of the Numbers

Find the Key of the Numbers

What is this problem about?

The Find the Key of the Numbers interview question is a numeric alignment problem. You are given three positive integers. First, you must pad each number with leading zeros so that they all have exactly four digits. Then, you generate a "key" by taking the minimum digit at each of the four positions (thousands, hundreds, tens, and ones) across all three numbers. The final result is the integer formed by these four "minimum" digits.

Why is this asked in interviews?

Google uses the Find the Key of the Numbers coding problem as an introductory task to evaluate a candidate's basic data processing skills. It tests your ability to handle number-to-string conversions, padding, and position-based comparisons. It’s a test of clean coding and attention to simple multi-step instructions within a Math interview pattern.

Algorithmic pattern used

This problem follows the Digit Extraction and Comparison pattern.

1. Padding: Convert each number to a 4-character string, adding leading '0's as needed.
2. Iterate Positions: Loop through each of the four positions (index 0 to 3).
3. Find Minimum: At each position, compare the characters (digits) from all three strings and pick the smallest one.
4. Construct Key: Concatenate these minimum digits into a new string and convert the result back to an integer.

Example explanation

Numbers: 1, 10, 1000

1. Pad to 4 digits: "0001", "0010", "1000".
2. Position 0 (thousands): min(0, 0, 1) = 0.
3. Position 1 (hundreds): min(0, 0, 0) = 0.
4. Position 2 (tens): min(0, 1, 0) = 0.
5. Position 3 (ones): min(1, 0, 0) = 0. Key string: "0000". Result: 0.

Common mistakes candidates make

• Missing Padding: Forgetting to treat numbers as 4-digit strings, which leads to incorrect positional alignment (comparing the "1" in 1 with the "1" in 1000).
• String vs Integer: Failing to convert the final string back to an integer, which removes unnecessary leading zeros (e.g., returning "0007" instead of 7).
• Looping errors: Over-complicating the digit extraction logic.

Interview preparation tip

Get comfortable with string formatting (like String.format("%04d", n) in Java or f-strings in Python). These built-in tools make "Padding" problems trivial and keep your code clean.